The research of microfluidic devices for the biology is at the conjunction of several disciplines since it involves electrical screening, optics, electronics, microfluidics and biology.

Since 80's the use of the electric field to treat or to monitor living cells leads to new promising ways of investigation in research laboratories and industry: cancer diagnosis, electrochemotherapy (insertion of a drug permeabilizing cell membranes), gene therapy (insertion of a therapeutic gene), immunotherapy (anti-tumor vaccines obtained by electrofusion of dendritic cells and cancer cells to reactivate the immune system).

Introduction

Microsystems dedicated to the characterization and manipulation of cells provides innovative tools for the research in molecular biology and leads the development of new treatments to better face illness such as leukemia or cancer.

In this PhD work we focus on the use of microfluidic devices for the sensing of electrical properties of single cell or cell tissue in order to understand qualitatively and quantitatively the effect of the pulsed electric field. In particular, one of our main objectives is to measure the electrical parameters of the main cellular compartments such as the cytoplasm and membrane to model the behavior of cells exposed to an electric solicitation. Moreover the study of the interaction between the electric field and single cells is a complementary approach to larger scale investigation that involves cellular tissues.

INTRODUCTION

Pag. [START_REF] Washizu | Electrostatic manipulation of DNA in microfabricated structures[END_REF] The application of electrical pulses to cells or tissue induces a change on their properties, especially on their membrane that becomes transiently permeable by temporarily allowing the passage of ions and macromolecules.

Phenomena induced by cell membrane permeabilization due to the electric field application were partially characterized by epi-fluorescence microscopy. However this approach is static, thus a real-time monitoring of the dynamics of the electroporation process is possible by electrical measurements. This work has as main objective to implement a real-time monitoring of electrical characteristics changes, within a wide frequency range, of a cellular tissue or a single cell, before, during and after the solicitation induced by a pulsed electric field.

A model of the biological system is proposed to better describe phenomena observed experimentally: the effect of electrical stress on cell viability, on the permeability of the outer membrane, induced effects on the intracellular compounds, dynamics of membrane fusion.

The degree of permeabilization of the biological sample (cell or cell tissue) is highly dependent on many parameters in non linear way, which makes difficult the precise interpretation of the phenomena.

The control in real time of the permeabilization represents a way to implement customized treatments where the electric solicitation is inhibited once the desired degree of permeabilization is achieved.

Eventually, this control system of the cell membrane permeabilization could be massively parallelized on a dedicated biochip for the electroporation of many cells, prior to cell fusion or integration of therapeutic vectors.

A multi-scale effects consideration provides a complete overview of the phenomenon, thus Pag. [START_REF] Aladame | WatsonBiologie moléculaire de la cellule1986Flammarion Médecine SciencesParis[END_REF] our study was carried on by approaching several models within the range of the tissue (millimeter scale) till the single cell (micromiter scale) by passing by the intermediate scales (cell spheroids characterization).

In the latter two cases (spheroid, single cell) the biological sample is isolated in a microfluidic biochip where a specific electrodes structure had been designed

(micrometer scale).

The first chapter introduces the AC electrokinetic techniques to manipulate, capture and separate bioparticles, indeed different electric field solicitations such as dielecrophoresis, travelling-wave dielectrophoresis and electrorotation are presented. In addition basics and mechanisms of electroporation are discussed. The chapter deals with the debate about the permeabilization theories (electropermeabilization vs electroporation) and finally accomplishes their combination.

It also shows the influence of each pulses electric parameters on the permeabilization and how those parameters can be set in order to introduce small molecules or macromolecules into the cell or in order to achieve cell membrane electrofusion. In all these applications, cell viability has to be preserved.

Being a very general method, the electroporation is applicable to different cell types and it can be used for various purposes. In medicine it is used for electrochemotherapy and gene-therapy. In biotechnology it is used for water and liquid food sterilization and for transfection of bacteria, yeast, plant protoplast, and intact plant tissue. A fully understanding of the phenomenon of electroporation, its mechanisms and its parameters optimization is a prerequisite for successful treatment.

The second chapter focuses on the permeabilization of the cell tissue, which is investigated through the impedance spectroscopy. The degree of permeabilization of the cell tissue is dependent on the characteristics of the PEF and governs the evolution of the electrophysiological properties of the cells composing the exposed tissue, in Pag. [START_REF] Goater | Electrorotation and dielectrophoresis[END_REF] particular its bioimpedance. To characterize the electrochemical properties of biological tissues we used the Cole-Cole model representing biological tissue as an equivalent electric circuit with a low frequency resistor R0, a high frequency resistance R∞ and a nonlinear fractional impedance CPE.

The influence of the pulse parameters (such as signal waveform, amplitude, pulse width, pulse number) on the permeabilization of the cell membrane and thus on its electrical properties is examined and discussed.

We finally proposed a combination of Cole-Cole model parameters to characterize the level of tissue permeabilization.

The third chapter approaches the electrical characterization of the single cell permeabilization. To do so, we designed a dedicated biochip where electrorotation experiments are monitored in real time. The electrorotation allows the identification of electro-physiological properties of cells by analyzing their rotational velocity when submitted to a rotating electric field.

In the proposed system, the cell is captured between the electrodes by a stationary wave (nDEP), a rotating electric field is then induced on the cell that consequently starts to rotate. Analysis of the rotational speed of the cell gives as results the estimation of the electrical properties of the bioparticles.

The application of this protocol before and after the application of electrical pulses provides information about the real-time permeabilization at the microscopic level.

Qualitative and quantitative information about the cell permeabilization are thus obtained.

Furthermore the chapter deals with the biochip conception, which was investigated to obtain the best performance in terms of homogeneity of the electric solicitations applied, and with the implementation of the estimation program, which has been chosen

for its robustness and its effectiveness.

Pag. 7

The fourth chapter deals with the permeabilization at the intermediate scale biological system: 3D cellular spheroids (human glioblastoma cell lines U87MG). Such cellular organization provides a good model of cancer development and presents several advantages for research laboratories compare to 2D cell culture and animal testing.

The chapter gives an overview of the electrical models through which the spheroids dielectric properties were investigated, a first approach is finally proposed.

In our work the spheroid's dielectric properties are determined by using the combined electrorotation and dielctrophoresis techniques. Changes of the dielectric properties due to the permeabilization process are discussed.

Pag. 9

Chapter 1

The interaction between electric field and biological species Since ancient times, before Newton enunciated the law of universal gravitation, scientists thought that interactions between bodies could take place only in the presence of their physical contact, or at least they put forward the hypothesis that there was a slight matter, ether, also present in the vacuum as propagation medium capable of transmitting the interaction from one point to another. From this erroneous, but interesting theory the concept of force field came, indeed a vector field: a field that associates to each point in space where it acts, a vector characterized by its own magnitude and direction.

After Newton's law draft, physicists attempted to solve the problem by assuming that between massive bodies (or between electric charges) existed some forces that could propagate instantaneously from one point in space to another, whatever the distance between the interacting bodies and without a contact or a connection material. Later the concept of instantaneous remote interaction was replaced with the concept of a field which showed to be one of the most fruitful ideas in physics.

To take an example, Faraday hypothesized that a charge (or mass) in a given region of space is able to perturb the surrounding space, thus if another charge (or another mass) is introduced in the same region as the first ones, it can warn the disturbance generated by it as a force acting on itself. This modification of space is known as a "field". Space Pag. [START_REF] Hamdi | Interaction champ électrique cellule :Conception de puces microfluidiques pour l'appariement cellulaire et la fusion par champ électrique pulse[END_REF] is not only the place where events take physical place but also it becomes a crucial element of the interaction as the location of the field.

The main aspect of this new theory is that the field generated by the first body in a point of the space exists independently from the fact that another body can be placed in that space; actually the force acting on the possible second body is due to the pre-existing field and it is not generated by the interaction force.

Suppose we have a piece of wood initially motionless in the water; by touching the water with a second piece of wood even at a point far from the first, we can remark an effect on the first one. The one, after a certain time, moves in response to the motion of the other, we could thus conclude that between the two pieces of wood there is an interaction and the water also perturbed the piece of wood. We could assert that the water corresponds to the field.

The electric force provides an example of this contactless force between two bodies. An electric charge acts on another electrical charge through an electrical field. This interaction was formalized and deduced experimentally by Coulomb is known as Coulomb's law. According to this law the force F exerted between two punctual charges q1 and q2 (called test charge), placed in a vacuum at a distance d from each other, is directly proportional to the product of the two charges and inversely proportional to the square of their distance:

F = q 1 q 2 4πε medium ε 0 . d d 3 (1.1)
where ε is the permittivity of the suspending medium and ε 0 the permittivity of free space.

Another example of contactless force is given by the gravitational field The Earth modifies the physical properties of the surrounding space so that each body placed in its Pag. 11 proximity feels its presence in the form of a force: the well-known gravitational force or weight force. This force has a radial direction toward the center of the Earth and it is given by:

F = g M * m r 2 " # $ % & ' (1.2)
where g is the gravitational constant (approximately 6.673×10 -11 N•(m/kg) 2 ), M is the mass of the Earth, m is the mass of the body interacting with the Earth and r is the distance between the centers of masses.

Furthermore the gravitational field does not vary over time and it can thus be defined as a stationary field.

If we consider a single charge, it induces a modification of the space that can be expressed as:

E = 1 4πε q r 2
= -grad(V ) (1.3) the latter, in the case of a uniform electric field due to a difference of potential ΔV between two electrodes placed at a distance d, becomes:

E = ΔV d (1.4)
Indeed, the electric field is a modification of the space produced by the charge regardless of the presence of the second.

Pag. [START_REF] Jones | Dielectrophoresis and magnetophoresis[END_REF] In 1820, during some experiments with electrical circuits, it was realized that a magnetic needle placed near a wire carrying current started to turn around itself, and returned to its original position only if the charge flow was interrupted. There was a close relationship between the electric and magnetic phenomena. Based on these experiences, the French physicists Jean-Baptiste Biot, Félix Savart and André-Marie Ampère found the exact relationships that bind the intensity of the current flowing through a circuit and the magnetic force produced by the passage of charges. Ampere studied the force acting between two circuits of length l carrying current, he discovered that this force depends on the product of the current intensity i 1 and i 2 (increases with increasing current) and is inversely proportional to the distance between the circuits d (decreases when they are driven apart); also, is repulsive if the two currents flowing in the same direction and attractive if the flow is in the opposite direction.

F = µ 0 2π i 1 i 2 l d (1.5)
where µ 0 is the magnetic constant.

In electrical fields as well as in gravitational fields, the field lines are closed. Actually in the first case, the positive and negative charges exist separately and in the gravitational case there is only one 'charge', the mass. On the other side, a magnet always has two poles and the lines of force are closed, the come out from one pole and enter to another.

When the electric field is due to particles in motion, a second component needs to be taken into account, the induced electric field. This induced electric field E is directly related to the magnetic field B created by these charges moving through the vector potential A:

Pag. 13

! E = - ∂ ! A ∂t
(1.6)

! B = ro " t ( ! A ) (1.7)
An electromagnetic field is thus a combination of an electric field and a magnetic field.

The resultant force of this field called Lorentz force which is subjected a particle of charge q moving at the speed v:

! F = q( ! E + ! v ∧ " B ) (1.8)
where E is the electric field and B is the magnetic field, they are furthermore expressed in Maxwell equations [START_REF] Maxwell | A treatise on electricity and magnetism[END_REF].

The electric field to handle biological particle

A particle suspended in a medium influenced by an electric field can give place to different effects according to its properties and to the field frequency.

Submitted to an electric field, a charged particle moves due to the Coulomb force; in particular it moves towards the cathode if it's positive charged, and it moves towards the anode in the opposite case; this movement is known as "electrophoresis". A neutral particle, in the same case, just shows a polarization (free charges move through the electrode with opposite charge), but it doesn't move along any direction.

Alignment is possible if a particle is suspended in a non-uniform electric field, the applied field induces a dipole inside the particle. The interaction between the nonuniform field and the induced dipole generates a force, which induces movement of the particle. If the particle is more polarizable than the dielectric medium, the dipole aligns Pag. [START_REF] Pethig | Enhancing traveling-wave dielectrophoresis with signal superposition[END_REF] with the field and moves in the direction of the field gradient. If the particle is less polarizable than the medium, then the induced dipole moves against the field gradient.

Indeed it is possible to induce a polarization and a movement of the particle by using a non-uniform electric field in two different ways: by using an electric field which is non-uniform in amplitude (case of "conventional" dielectrophoresis), by using an electric field which is non uniform in phase; the latter produces on particles a rotational or linear movement (respectively cases of electrorotation and travelling-wave dielectrophoresis) [START_REF] Pohl | Some effects of nonuniform fields on dielectrics[END_REF] In the field of biology, a widely used separation method based on the application of a DC electric field (DC Direct Current) on charged particles (DNA, proteins, etc.) in order to migrate them to the opposite electrode is known as electrophoresis [START_REF] Kumemura | Single DNA molecule isolation and trapping in a microfluidic device[END_REF][START_REF] Washizu | Electrostatic manipulation of DNA in microfabricated structures[END_REF]. Thus, it is possible to separate different substances of a charged mixture, depending on several parameters (such as size, shape, etc).

Biological species such as cells have surface chemical groups incline to loose or gain ions when submerged into a buffer at a given pH. This is the case for example of the carboxyl group (COOH), which has the tendency to loose the H +, leaving exposed the COO -which is negatively charged, another example is given by the amines that can combine with H + to become positively charge [START_REF] Aladame | WatsonBiologie moléculaire de la cellule1986Flammarion Médecine SciencesParis[END_REF]. Thus, the bilayer membrane confers to the cell a surface charge [START_REF] Goater | Electrorotation and dielectrophoresis[END_REF] that finally results in an electric double layer around the cell. Undergo the electric field application, this double layer is deformed [7], as shown in Figure1.1.

Pag. 15

Dielectrophoresis

DEP is a phenomenon in which a force is exerted on a dielectric particle when it is subjected to a non-uniform electric field. The advantage compare to the previous method is that the force does not require the particle to be charged. All particles exhibit dielectrophoretic activity in the presence of electric fields. Compared to the electrophoresis, which depends on the ratio charge/size of the particle, dielectrophoresis depends on the dielectric properties of the particle and the medium, thus enabling the ability to selectively manipulate uncharged bioparticles [START_REF] Cheng | Isolation of cultured cervical carcinoma cells mixed with peripheral blood cells on a bioelectronic chip[END_REF]. Furthermore, with new microtechnologies reduced dimensions can be easily achieved and various electrodes structures can be employed; it becomes quite easy to create strong non-uniform fields from low voltages (less than 10 or 20 V) [START_REF] Hamdi | Interaction champ électrique cellule :Conception de puces microfluidiques pour l'appariement cellulaire et la fusion par champ électrique pulse[END_REF].

Pag. [START_REF] Morgan | AC electrokinetics: colloids and nanoparticles[END_REF] In 1951 Pohl used for the first time the term "dielectrophoresis" referring to the induced movement of a polarizable particle due to the action of a non-uniform electric field [START_REF] Pohl | Some effects of nonuniform fields on dielectrics[END_REF].

The word etymology suggests a Greek source, indeed "phoresis" in ancient Greek meant movement while "dielectro" was chosen to evoke the origin of the phenomenon that is the polarization of dielectric media under the effect of the field.

A cell can be electrically described as composed of an insulating membrane separating the cytoplasm (modeled as a polarizable ionic solution) to the extracellular medium.

Each domain of this two-shell model (intra-cellular domain, membrane, extra-cellular domain) is characterized by its dielectric properties: the conductivity σ and the permittivity ε. This model is often simplified to the single shell model [START_REF] Çetin | Dielectrophoresis in microfluidics technology[END_REF], where the two inner concentric domains (the cytoplasm and the membrane) are simplified in one homogenous equivalent domain, defined by its averaged complex permittivity

The exposure of such a system to an electric field E leads to its polarization, the cell in such case behaves as an electrostatic dipole m and it is subjected to a force given by:

F !" = (m !" ∇ !" )E !" (1.9)
The cells used within this thesis can be treated as of spherical objects, thus the calculation of the dipole moment of such objects of radius r undergoing the action of an electric field E and immersed in a medium of permittivity ε m , is given by [START_REF] Jones | Dielectrophoresis and magnetophoresis[END_REF]:

m !" = 4πε m f CM (ω)r 3 E !" (1.10)
where fCM(ω) is the Clausius-Mossotti factor, strictly linked to the complex permittivity of both the cell and the suspending medium:

Pag. 17

f CM = ε p * -ε m * ε p * + 2ε m * (1.11) ε i * = ε 0 ε r,i -j σ i ω (1.12)
where ε i is the permittivity, σ i is the conductivity and ω is the angular frequency of the DEP signal [START_REF] Pohl | Some effects of nonuniform fields on dielectrics[END_REF].

Once defined the Force by the equation 1.9 and the dipolar moment as on the equation 1.10, a general expression for the time averaged dielectrophoresis force can be obtained [START_REF] Wang | A unified theory of dielectrophoresis and travelling wave dielectrophoresis[END_REF][START_REF] Pethig | Enhancing traveling-wave dielectrophoresis with signal superposition[END_REF] and it is valid for those cases when the nonuniformity of the electric field is due to a spatial variation in its amplitude or its phase.

F(t) = 2πε m r 3 (Re[ f CM (ω)]∇E rms 2 + Im[ f CM (ω)] E rms 2 x,y,z ∑ ∇ϕ) (1.13)
where E 2 RMS is the root mean square of the applied electric field and ϕ is its phase. The first term of equation 1.13 determines the case of the stationary field where a spatial variation of the amplitude confers the nonuniformity to the electric field, is known as conventional DEP (c-DEP) and it is proportional to the real part of the Clausius-Mossotti factor (Re [f CM ]) [START_REF] Pohl | Some effects of nonuniform fields on dielectrics[END_REF]. The second term of the equation 1.13 is given by the spatial nonuniformity of the applied electric field phase, it is known as Travelling wave dielectrophoresis (TW-DEP) and it depends on the imaginary part of the Clausius-Mossotti factor (Im [f CM ]) [START_REF] Cen | A combined dielectrophoresis, traveling wave dielectrophoresis and electrorotation microchip for the manipulation and characterization of human malignant cells[END_REF]. This c-DEP force drives the cell to the highest or lowest electric field regions, depending on the difference in polarizability of the particle and the suspending medium.

The direction of the DEP force depends on the frequency of the applied signal, the Pag. 18 volume of the cell, and the dielectric characteristics of both the cell and the external medium [START_REF] Pohl | Some effects of nonuniform fields on dielectrics[END_REF][START_REF] Pethig | Enhancing traveling-wave dielectrophoresis with signal superposition[END_REF][START_REF] Morgan | AC electrokinetics: colloids and nanoparticles[END_REF] (Figure 1.2). It has been demonstrated [START_REF] Khoshmanesh | Dielectrophoretic platforms for bio-microfluidic systems[END_REF][START_REF] Gascoyne | Dielectrophoresis-based sample handling in general-purpose programmable diagnostic instruments[END_REF] that at low frequencies (f <100 kHz), the membrane of the cell behaves as a dielectric having low losses and therefore a weak complex conductivity. The membrane represents a barrier limiting the polarization of the intracellular medium. On the other hand, the external medium shows a relatively low resistance. The electric field consequently remains confined into the extracellular medium and since the cell is less polarizable than the medium a negative dielectrophoretic (nDEP) behavior is induced (the cell will move towards the lowest electric field area) (Figure 1.2b).

When the frequency increases, the membrane gradually becomes more permeable to the electric field. Therefore, if the intracellular medium is more conductive than the extracellular medium, the cell is more polarizable than the medium and it will move towards the highest electric field value (a positive dielectrophoretic behavior is shown Pag. [START_REF] Castellarnau | Dielectrophoresis as a tool to characterize and differentiate isogenic mutants of Escherichia coli[END_REF] by the cell, pDEP). In particular, this situation occurs when low conductivity media are used for DEP experiments. On the contrary, if the cell is less polarizable than the medium, the electric field will essentially remain confined and the cell will move towards the lowest electric field area due to negative dielectrophoretic behavior. At high frequency (f > 10 MHz), the permittivity becomes predominant. The external medium has a permittivity (similar to water) much higher than that of the cell consisting of water, but also of proteins and other large molecules less polarizable. The medium becomes more polarizable than the cell, and once again negative dielectrophoresis behavior dominate.

For any arbitrary shaped particle, the frequency which characterizes the passage to nDEP to pDEP is given by [START_REF] Castellarnau | Dielectrophoresis as a tool to characterize and differentiate isogenic mutants of Escherichia coli[END_REF]:

f crossover = 1 2π (σ m -σ p )[σ m + A(σ p -σ m )] (ε p -ε m )[ε m + A(ε p -ε m )] (1.14)
where A represents the depolarization factor equal to 1/3 in the case of spherical shaped particle.

Nowadays, the dielectrophoresis method is widely used for several purposes:

1) Handling, capture and separation of biological entities (eukaryotic cells [START_REF] Frenea | Positioning living cells on a high-density electrode array by negative dielectrophoresis[END_REF][START_REF] Alshareef | Separation of tumor cells with dielectrophoresis-based microfluidic chip[END_REF],

bacteria [START_REF] Hölzel | Non-invasive determination of bacterial single cell properties by electrorotation[END_REF], yeasts [START_REF] Mernier | Label-free sorting and counting of yeast cells for viability studies[END_REF], algae [START_REF] Huang | Negative dielectrophoretic force assisted determination differences between autotrophic and heterotrophic algal cells using electrorotation chip[END_REF], DNA strand [START_REF] Kumemura | Single DNA molecule isolation and trapping in a microfluidic device[END_REF]) in microfluidic devices.

2) Efficient selection of different kind of cells [START_REF] Cheng | Isolation of cultured cervical carcinoma cells mixed with peripheral blood cells on a bioelectronic chip[END_REF] 3) Basic technique for cell electrofusion and cell electroporation [START_REF] Teissie | Fusion of mammalian cells in culture is obtained by creating the contact between cells after their electropermeabilization[END_REF][START_REF] Hamdi | Microarray of non-connected gold pads used as high density electric traps for parallelized pairing and fusion of cells[END_REF] 4) Assembly of carbon nanotubes or silicon nanowires [START_REF] Li | Fabrication of carbon nanotube field effect transistors by AC dielectrophoresis method[END_REF][START_REF] Englander | Electric-field assisted growth and self-assembly of intrinsic silicon nanowires[END_REF].

Pag. 20

Travelling-wave dielectrophoresis

As we already mentioned the TW-DEP is given by a nonuniformity in phase of the applied electric field. In this case electrodes are arranged in rows along which the electric wave is propagated by maintaining a 90° phase difference between adjacent electrodes (Figure 1.3).

Figure 1.3. Electrode arrangement to induce TWD where the special nonuniformity is given by the applied electric field phase [START_REF] Khoshmanesh | Dielectrophoretic platforms for bio-microfluidic systems[END_REF] By developing the equation 1.14 [START_REF] Cen | A combined dielectrophoresis, traveling wave dielectrophoresis and electrorotation microchip for the manipulation and characterization of human malignant cells[END_REF], a time average expression of the TW-DEP is defined as follow:

! F TWD = -4πr 3 ε m Im[ f CM (ω)]E 0(RMS ) 2 λ (1.15)
where λ is the repetitive distance between electrodes of the same phase.

Pag. 21

The direction of movement of the cell depends on the Clausius-Mossotti factor, and therefore on the frequency of the applied field. If Im[f CM (ω)]>0, the cell will move along the opposite direction respect to the applied electric field (the cell is directed on the direction of increasing φ). Conversely, for Im[f CM (ω)]<0, the cell follows the path of the electric wave (it moves in the direction corresponding to a decrease of φ).

Electrorotation

In the case where the electric field is not uniform in phase (Travelling Waves and Electrorotation), the force exerted to the cell is sensitive to the imaginary part of the Clausius-Mossotti factor. The electrorotation technique was first presented in the 1980 by Arnold and Zimmermann [START_REF] Arnold | Electro-rotation: development of a technique for dielectric measurements on individual cells and particles[END_REF][START_REF] Arnold | Rotating-field-induced rotation and measurement of the membrane capacitance of single mesophyll cells of Avena sativa[END_REF], they proposed the use of electrode system shown in Figure 1.4, where the voltages applied to two adjacent electrodes are phase-shifted by 90°. The rotating field E applies a torque to the cell, inducing its rotation (electro-rotation phenomenon) [START_REF] Arnold | Electro-rotation: development of a technique for dielectric measurements on individual cells and particles[END_REF]:

Γ !" = m × E !" (1.16)
From equation 1.10 and equation 1.16 a time average expression of the torque can be defined [START_REF] Hughes | Nanoelectromechanics in engineering and biology[END_REF]:

Γ ROT (ω) = -4πε m r 3 Im[ f CM (ω)]E 2 (1.17)
Taking into account the rotational frictional force, the angular velocity of the cell becomes [START_REF] Morgan | AC electrokinetics: colloids and nanoparticles[END_REF]:

Ω ROT (ω) = - ε 0 ε m E 2 2η Im[ f CM (ω)] (1.18)
where η is the dynamic viscosity of the medium.

When Im [fCM(ω)]> 0, the phase shift between the dipole moment and the electric field is between 0 and 180 °, which induces an opposite direction of rotation of the cell respect to the electric field. Conversely, when Im [f CM (ω)<0, the phase shift is between -180 ° and 0 °, the direction of rotation of the cell is the same as the electric field.

To generate a rotating field a specific disposition, geometry, and powering of electrodes is used (Figure 1.5 a). In our study, four planar polynomial electrodes were employed, powered with four sinusoidal signals respectively 90° phase-shifted with the adjacent ones.

The cell rotates with a velocity that depends on its dielectric properties and on the frequency of the applied Electric Field (EF) across the imaginary part of the Clausius-Mossotti factor [START_REF] Arnold | Electro-rotation: development of a technique for dielectric measurements on individual cells and particles[END_REF][START_REF] Pethig | Electrokinetic measurements of membrane capacitance and conductance for pancreatic β-cells[END_REF][START_REF] Laforet | An Automated Platform for Cell Dielectric Spectroscopy[END_REF][START_REF] Han | An electrorotation technique for measuring the dielectric properties of cells with simultaneous use of negative quadrupolar dielectrophoresis and electrorotation[END_REF]. The electrorotation spectrum is defined as the rotational Pag. [START_REF] Mernier | Label-free sorting and counting of yeast cells for viability studies[END_REF] speed of the cell with respect to the frequency of the EF (Figure 1.5 b). Extraction of the electro-physiological properties of cells can be achieved from the rotation spectrum [START_REF] Pethig | Electrokinetic measurements of membrane capacitance and conductance for pancreatic β-cells[END_REF][START_REF] Yang | Dielectric properties of human leukocyte subpopulations determined by electrorotation as a cell separation criterion[END_REF][START_REF] Gimsa | Dielectrophoresis and electrorotation of neurospora slime and murine myeloma cells[END_REF]. As a possible application of such experience, this information might be used to distinguish malignant cells from healthy ones, based on their dielectric properties [START_REF] Han | An electrorotation technique for measuring the dielectric properties of cells with simultaneous use of negative quadrupolar dielectrophoresis and electrorotation[END_REF][START_REF] Becker | Separation of human breast cancer cells from blood by differential dielectric affinity[END_REF].

Electro-hydrodynamic effects

The application of an electric solicitation implies the action of other forces, which must be studied in order to take into account their effects. In the case of manipulation of living cells, since they have a size larger than 1 micrometer, the contributions of the Brownian motion and forces of Van der Waals forces is negligible. Nevertheless there are electro-osmotic effects and electro-thermic effects that need to be investigated.

Electro-osmotic effect

When we power electrodes with a given potential and a we immerge it into a buffer, the The tangent component induces a movement on the charged double layer as well as on the fluid present around the electrodes as described in Figure 1.7. This phenomenon is known as "electro-osmosis AC".

Its intensity depends on frequency, on the voltage applied and the conductivity of the medium.

Beyond a certain frequency (of the order of several tens of kHz), the double layer does not have time to form. Indeed, this electro-osmotic effect occurs at low frequency and they can considered negligible for our study (frequency range between tens of kHz and tens of MHz).

Pag. 25 Pethig was the first who remarked at low frequency the fromation of aggregates of particles between the electrodes powered with signal of opposite sign. At a first approach the phenomenon was explained as a manifestation of negative DEP, and the area on investigation was identified as local minima of the elecric field [START_REF] Pethig | Positive and negative dielectrophoretic collection of colloidal particles using interdigitated castellated microelectrodes[END_REF]. Later, the works of Green [START_REF] Green | Fluid flow induced by nonuniform ac electric fields in electrolytes on microelectrodes. III. Observation of streamlines and numerical simulation[END_REF], Ramos [START_REF] Ramos | The role of electrohydrodynamic forces in the dielectrophoretic manipulation and separation of particles[END_REF] and Gonzalez [START_REF] Green | Fluid flow induced by nonuniform ac electric fields in electrolytes on microelectrodes. I. Experimental measurements[END_REF] rejected this hypothesis by establishing a link between the behavior of particles and the electro-osmotic effects.

Electro-thermal effect

As we already mentioned the application of an electric field through the electrodes induce their polarization, which is responsible of some movemement into the buffer.

Additional movements can be also provoked by a heating effect. When the EF is applied within a medium of a given conductivity sm, the resulting Joule losses can be expressed as P=σ m E 2 [Wm -3 ] (where σ m is the conductivity of the buffer and E is the applied electric field ). When the applied EF is not homogeneous, the heating is consequently non homogeneus and a gradient of temperature ΔT appears. This gradient consequently generates gradients of conductivity and permittivity, respectively denoted α and β

Pag. 26

(equation 1. [START_REF] Castellarnau | Dielectrophoresis as a tool to characterize and differentiate isogenic mutants of Escherichia coli[END_REF]), inducing movement of mobile charges (ρ) in the liquid (equation 1.20) [START_REF] Morgan | AC electrokinetics: colloids and nanoparticles[END_REF].

α = 1 ε m ∇ε m ∇T β = 1 σ m ∇σ m ∇T (1.19) ρ = ∇(ε m E) = ∇ε m E +ε m ∇E (1.20)
The gradient of conductivity induces Coulomb forces while the gradient of permittivity induces dielectic forces. The whole time average electrothermic force acting on the liquid is thus given by:

F ETE ! " !!! = 0.5ε m ∇T E 2 ! " ! Π(ω) (1.21)
where P(ω) determines the intensity of this force and it depends on the parameters α and β as follow:

Π(ω) = α -β 1+ ωε m σ m # $ % & ' ( 2 - α 2 # $ % % % % % & ' ( ( ( ( ( (1.22)
The electrothermal effect is strongly dependent on the conductivity of the medium and can induce strong flow (v ~ 1 mm/s) in the whole freqeuncy range as shown in Figure 1.8.

Pag. 27

Electropermeabilization: basics and mechanisms.

The interaction between electric field and biological species has been observed for centuries; nevertheless the first studies describing the in vitro effect of pulsed electric field date from the late 1960s [START_REF] Sale | Effects of high electric fields on micro-organisms: III. Lysis of erythrocytes and protoplasts[END_REF][START_REF] Coster | A quantitative analysis of the voltage-current relationships of fixed charge membranes and the associated property of" punch-through[END_REF]. It was observed that the application of pulsed electric field induces a change in the cell membrane structure by creating preferential path for small particles to enter [START_REF] Zimmermann | Dielectric breakdown of cell membranes[END_REF][START_REF] Neumann | Permeability changes induced by electric impulses in vesicular membranes[END_REF][START_REF] Crowley | Electrical breakdown of bimolecular lipid membranes as an electromechanical instability[END_REF]. At the beginning of the study, only nonreversible permeabilization was induced (the cell membrane was damaged in a non reversible manner), however few years later, it was demonstrated that the change in cell membrane structure could be either not reversible or reversible, the latter phenomenon allows some molecules, in contrast to their nature, to cross the membrane [START_REF] Rols | In vivo electrically mediated protein and gene transfer in murine melanoma[END_REF][START_REF] Mir | Introduction of definite amounts of nonpermeant molecules into living cells after electropermeabilization: direct access to the cytosol[END_REF].

Eukaryotic biological cell is surrounded by its plasma membrane mainly composed of a thin lipid bilayer (about 5 nm) that acts as a boundary between the cell and its outside environment. The plasma membrane is a gateway that allows or blocks the entry or exit The cell membrane is composed of an assembly of lipids (phospholipids, glycolipids and cholesterol), carbohydrates and proteins self-organised in a thin bilayer (Figure 1.9 a). The exchange between the inner compartment and the external compartment of the cell are usually made through special channels, or by diffusion through the phospholipids in the case of lipophilic molecules.

The components of the cell membrane (phospholipids and cholesterol) present a polar part, rather compact, called "head" and a nonpolar part, more elongated respect to the head, know as "tail" (Figure 1.9 b). Thanks to this specific structure, in aqueous electrolyte solution, they aggregate by spontaneously forming a bilayer with the head oriented on the outer part and the tail on the inner part. Furthermore, unless phospholipids are kept together by weak interaction, the cell membrane appears as a very stable structure. ions can permeate and get inside the inner compartment in such high rate not be explained by simply talking about diffusion [START_REF] Deamer | Permeability of lipid bilayers to water and ionic solutes[END_REF].

From an electrical point of view, the plasma membrane can be considered as a thin insulating layer surrounded on both sides by aqueous electrolyte solutions.

Under certain conditions, such as pulsed electric field application, the integrity of the membrane is temporary disturbed and the rearrangement of its components leads to a formation of aqueous hydrophilic pores whose presence increases the transport of molecules through the normally impermeable membrane. The pulsed electric field applications also results in a change of membrane consistency that allow molecules to get in the inner compartment by being absorbed by the bilayer (Figure 1.10).

Membrane potential effects

The ion concentration gradient between the inside and outside of the cell ( The Nernst equation (equation 1.23) establishes the potential across the cell membrane based on the concentration gradient of each ion; it determines the membrane potential Eeq at which the specific ion species x is in equilibrium:

E eq,x = RT zF ln X [ ] o X [ ] i (1.23)
where R is the universal gas constant and it is equal to 8.314 JK -1 mol -1 , T is the temperature in Kelvin, z is the valence of the ion specie, F is the Faraday constant equal to 96,485 C mol -1 , [X] o is the concentration of the ion specie in the extracellular medium and [X] i is the intracellular concentration of the ion specie.

The resting potential varies from cell to cell and is thus an intrinsic characteristic of the sample, for instance for neurons its typical value is -70mV, for skeleton muscle cell it is -90mV and for epithelial cell cells its value is around -50mV. When applying pulsed electric field (width tens of microseconds up to several milliseconds) to a biological solution containing living cells, a difference of potential between the inner and the outer part of the membrane induces an accumulation of charges of opposite sign on the two Pag. 31 sides of the plasma membrane. This potential is called induced transmembrane potential (ΔΨi) [START_REF] Pauly | Über die Impedanz einer Suspension von kugelförmigen Teilchen mit einer Schale[END_REF]:

ΔΨ i = f ⋅ E ⋅ R ⋅ cos(θ ) ⋅[1-e - t τ m ] (1.24)
where f depends on dielectric and geometrical properties of the cell as shown in equation 1.25, R is the radius of the cell, θ is the angle between the point where the ΔΨ is calculated and the applied electric field (See figure 1.11) and τ m is the membrane charging time constant and it depends on the permittivity of the membrane (σ mem ), the cytoplasm (σ cyt ) and the external environment (σ m ) and on the permittivity (ε mem ) and the thickness (e) of the membrane (equation 1.26). When considering a spherical shaped cells having an insulating membrane, σ mem > σ m , σ cyt and the factor f can be simplified as equal to 3/2 [START_REF] Kotnik | Sensitivity of transmembrane voltage induced by applied electric fields-a theoretical analysis[END_REF]. This gives the Schwan equation [START_REF] Schwan | Electrical properties of tissues and cell suspensions: mechanisms and models[END_REF]:

f = 3⋅σ m [3⋅ d ⋅ R 2 ⋅σ cyt + (3⋅ d 2 ⋅ R -d 3 )(σ mem -σ cyt )] 2 ⋅ R 2 (σ mem + 2σ m )(σ mem + 1 2 σ cyt ) -2(R -d) 3 (σ m -σ mem )(σ cyt -σ mem ) (1.25)
τ m = R ⋅ ε mem d 2σ m σ cyt 2σ m +σ cyt + R d σ mem (1.26) Pag. 32
ΔΨ i = 3 2 ⋅ E ⋅ R ⋅ cos(θ ) (1.27)
The Schwan equation is widely used to determine the electric field needed to achieve the critical transmembrane potential for electroporation or electrofusion [START_REF] Lee | A micro cell lysis device[END_REF].

However, it has to be kept in mind that the Schwan's equation is valid only for spherical shaped cell submitted to an homogeneous external field, in the case of different shaped particles a shape factor has to be introduced [START_REF] Sukhorukov | The effect of electrical deformation forces on the electropermeabilization of erythrocyte membranes in low-and high-conductivity media[END_REF][START_REF] Gimsa | Analytical description of the transmembrane voltage induced on arbitrarily oriented ellipsoidal and cylindrical cells[END_REF].

A pulsed electric field reveals to be a way to increase the transmembrane potential in order to permeabilize the membrane [START_REF] Neumann | Biophysical considerations of membrane electroporation[END_REF].

Pag. 33

Being a really complex system composed by electrically charged species, a cell submitted to a pulsed electric field changes its membrane topology. The first effect of the pulses is the change of the spherical shape of the cell to an ellipsoidal one. The pulses application results in an alteration of the membrane proteins, this phenomenon affects mostly proteins that are not anchored to the cytoskeleton [START_REF] Teissie | Electropermeabilization of cell membranes[END_REF]. In the time immediately after the application of pulses (around 1 minute after) a significant increase of microvescicles is recorded, this eruption disappears if the cell recovers its original topology (in the case of reversible electroporation) after about 30 minute at room temperature.

Electropermeabilization is a threshold phenomenon and depending on the characteristics of pulses parameters can lead to reversible or irreversible electropermeabilization. In order to trigger the formation of transient aqueous pores in the cell membrane, the external solicitation should reach a critical value in the range [200mV-1V] [START_REF] Zimmermann | Electric field-mediated fusion and related electrical phenomena[END_REF][START_REF] Teissie | An experimental evaluation of the critical potential difference inducing cell membrane electropermeabilization[END_REF]. If the external electric field is kept below the critical threshold, the cell is able to recover its original membrane condition and thus we can talk about reversible electorporation [START_REF] Jordan | Electroporation and electrofusion in cell biology[END_REF]. If this is not the case and the electric field exceed the critical value, the cell membrane is irreversible damaged and the cell viability is compromised, the result is the irreversible electroporation [START_REF] Meaking | Electroporation-induced damage in mammalian cell DNA[END_REF][START_REF] Hamilton | Effects of high electric fields on microorganisms: II. Mechanism of action of the lethal effect[END_REF].

Depending on the desired outcome, reversible or irreversible electroporation are induced.

Joule heating

Since pulsed electric field is applied, an electrical current originated from electrodes is flowing through the medium. This current induces Joule heating resulting in an increase of the temperature in the sample , indeed it has to be taken into account. In the case of in vitro experiments, the heating can be controlled or limited by using a low conductive Pag. [START_REF] Yang | Dielectric properties of human leukocyte subpopulations determined by electrorotation as a cell separation criterion[END_REF] buffer and by delivering short pulses with low amplitude value. Furthermore, by considering that the heating is linearly related to the pulse width as shown by the equation 1.20, application of shorter pulses is a way to minimize deleterious heating effects [START_REF] Teissie | Electropermeabilization of cell membranes[END_REF]:

ΔT = σ m E 2 ρC p t (1.28)
where σ m represents the conductivity of the medium, ρ represents its volume density, Cp is its specific heat and t is the pulse width.

1.2.1

The electroporation and/or the electropermeabilization theor(y)ies.

It was previously mentioned that electric field pulses characteristics lead to a reversible or non-reversible permeabilization. Over the last decades reversible electroporation has been used as a promising technique for cancer treatments while irreversible electroporation was almost ignored at that time. However the latter was employed afterwards as a promising ablation technique. Irreversible electroporation requires pulsed electric field high in amplitude (~ 1kV/cm) and with long duration (~ 800 ms), such specific conditions can affect the transmembrane potential in an irreversible manner. The advantage of the irreversible electroporation is the high control of the affected area that can be also monitored with electrical impedance tomography [START_REF] Davalos | Tissue ablation with irreversible electroporation[END_REF].

In the case of more moderate pulses the potential difference across the membrane is also affected, but in a way that allow the bilayer to recover after a given time without putting in danger its viability. Reversible electroporation is mostly used in medicine and biotechnology to introduce no permeable species inside the cell, ranging from small Pag. 35 molecules (fluorescent dye, drugs, …) to big molecules (DNA, antibodies, etc..) [START_REF] Teissie | Electropermeabilization of cell membranes[END_REF][START_REF] Neumann | Fundamentals of electroporative delivery of drugs and genes[END_REF].

Nevertheless on this point the scientific community is divided. It is well known that the creation of membrane defects induce the access of large molecules inside the cell, but it is not clear, or it is not demonstrated, if phospholipids are just "destabilized" by allowing passage of molecules or if real channels (known as electropores) are created.

Indeed two theories exist (even a third one as the combination of the two). Thus the two terms electroporation and electropermeabilization are used depending on the theory used to explain the phenomenon.

1.2.2

The "pore formation" theory.

The structural integrity of the cell membrane can be perturbed by an applied pulsed electric field, indeed physicochemical mechanisms lead to a reorganization of the lipid bilayer [START_REF] Polak | On the electroporation thresholds of lipid bilayers: molecular dynamics simulation investigations[END_REF]. With conventional techniques it is not possible to observe nano-pores and to characterize in details the dynamics of the permeabilization phenomenon. Thus the needs to use computational methods; in particular Molecular Dynamics (MD)

simulations have been employed recently in order to investigate the pulsed electric field effects on the lipid bilayer [START_REF] Tarek | Membrane electroporation: a molecular dynamics simulation[END_REF][START_REF] Levine | Life cycle of an electropore: field-dependent and field-independent steps in pore creation and annihilation[END_REF].

In MD usually simulations are performed on a small number of molecules because of limits due to computer power or to the system speed execution, the simulations actually need a huge computer performance to be carried on. When performing MD simulations, information such as forces, positions and velocity or momentum are given at a specific time t, they are then used to predict momentum at a time t+Δt, where Δt is a femtosecond time step.

Once the pulsed electric field is applied a migration of water molecules and phospholipid head groups is remarked in the inner part of the bilayer, the first step of Pag. 36

the pore formation takes place as long as the external solicitation is applied. Once the pulsed electric field is removed, a decrease of the pore dimension is observed till the moment when water molecule and phospholipids head group migrate, this time in the opposite direction, out of the membrane interior. The life cycle of an electropore is characterized by two main steps: the pore creation and the pore annihilation (Figure 1.12).

Figure 1.12: The life cycle of an electropore [START_REF] Levine | Life cycle of an electropore: field-dependent and field-independent steps in pore creation and annihilation[END_REF].

Three minor steps can be analyzed within the pore creation. When the external pulsed electric field is applied, water molecules start to migrate between the bilayer by inducing the re-arranging of the membrane structure (initiation) [START_REF] Vernier | Water bridges in electropermeabilized phospholipid bilayers[END_REF]. The creation of the pore can proceed with the migration of the phospholipids head group in the inner part of the membrane where they reorganize themselves around the water defects and the finally merge (construction). The first step is finally completed with the pore Pag. 37 evolution (maturation). Pore annihilation begins when the pulsed electric field is removed, at this time the pore size pass through a quasi-stable step while it decreases its size (destabilization). The phospholipids head groups and the water molecules start to migrate to the out of the membrane (degradation), when the phospholipids are completely out of the membrane the deconstruction step is achieved; now only water molecules are inside the bilayer, but they move quickly to the two sides of the membrane in order to restore the original membrane structure (dissolution). Pore annihilation is a longer process compare to pore creation, MD also showed how some steps of the pore life-cycle are field-dependent while other are less affected by the electric field strength [START_REF] Tarek | Membrane electroporation: a molecular dynamics simulation[END_REF]. Pulsed electric field characteristics cannot be chosen by the customer because of the power limit of the computer, indeed in MD simulation we previously mentioned fs pulses are applied by assuming that it was enough to change the dynamic structure of the membrane and to induce the permeabilization.

The lipid bilayer "destabilization" theory

Electropermeabilization can not be reduced to simply formation of "holes" in the cell membrane since a large part of physiological control is hidden by the phenomenon [START_REF] Teissie | Mechanisms of cell membrane electropermeabilization: a minireview of our present (lack of?) knowledge[END_REF].

The transient cell membrane destabilization represents a stress for the cell, which can affect its functionality and, in the worst case, its viability. After the application of a pulsed electric field, cells need to be monitored, for minutes/hours, which is crucial in order to check the damage induced on them.

When applying to the cell a "long" pulse (which means ms duration pulses) through plate electrodes we can observe an induced electropermeabilization meaning that the organization of the membrane is changed and we have an exchange across the membrane. When the electric field is removed a "resealing" process is observed, Pag. 38 meaning that the permeabilization is slowly going to disappear (several seconds or minutes), but by the time the internal compounds are totally changed and some molecules could be extracted from the inner compartment. Indeed, the electropermeabilization phenomenon appears in two consecutives steps, one during the pulse application and another one after pulse application; the two processes have different kinetics. The first step is fast (µs to ms) and short, the pulse needs to be present but there is a limit linked to its width in order to avoid cell death. During this step electrophoretic effects can be observed. The second step, on the other hand, is a slow process, which lasts for long time after the pulse from a few seconds to several minutes.

When pulses are applied they induce an increase of the membrane difference potential (trigger); if a critical value is reached (200mV) the lipid bilayer is not able to withstand the forces on its membrane, thus the membrane can become leaky. The field strength influence mostly two aspects, it first triggers the permeabilization of the cell membrane and it is responsible of the surface geometry affected by the permeabilization. The leaky state induced on the membrane is followed by a reorganisation of the membrane (expansion) that takes place in a longer time scale (order of ms). Furthermore the density of the defects that appear on the membrane can be controlled by the pulse duration.

The increased conductance of the permeabilized part of the cell membrane quickly decrease as soon as the external field decrease below the critical value (stabilisation), nevertheless the cell membrane still remains permeable to some chemical compounds.

A slow annihilation of leaks (time scale of s) is observed and the membrane is thus able to recover its integrity (resealing). The resealing is strongly dependent on the temperature, so a really fast resealing takes place at 37°C while cell can be kept permeabilized for hours at low temperature (4°C). After the resealing, the viability is Pag. 39 not affected but the membrane properties are still modified and the cell needs hours in order to get back to the initial conditions.

Furthermore a faster resealing of lipid assemblies was remarked in lipid assemblies while it revealed to be slower in the case of cells. The difference highlights how the permeabilization is not just a matter or re-organisation of the lipid bilayer, but rather a cellular process that involves also the entire cell behaviour. Indeed during the resealing step a production of the reactive oxygen species in the permeabilized part of the cell surface was recorded. In last step of the phenomenon the cell totally recovered its original functions for a reversible electropermeabilization, in the case where induced alterations could not be repaired lead to cell death on the long term [START_REF]In vitro cell electropermeabilization[END_REF].

The combined theory

A well known parable from the Jain religion talks about six blind men were asked to determine what an elephant looked like by feeling different parts of the elephant's body.

"The blind man who feels a leg says the elephant is like a pillar; the one who feels the tail says the elephant is like a rope; the one who feels the trunk says the elephant is like a tree branch; the one who feels the ear says the elephant is like a hand fan; the one who feels the belly says the elephant is like a wall; and the one who feels the tusk says the elephant is like a solid pipe.

A king explains to them: All of you are right. The reason every one of you is telling it differently is because each one of you touched the different part of the elephant. So, actually the elephant has all the features you mentioned."

The parable illustrates a range of truths, it implies that one's subjective experience can be true, but such experience is limited and wrong unless all the others complete it.

In a similar way, we have seen two different theories employed and justified from different research groups, nevertheless as previously mentioned, the Pag. [START_REF] Green | Fluid flow induced by nonuniform ac electric fields in electrolytes on microelectrodes. I. Experimental measurements[END_REF] electropermeabilization phenomenon is such a complex phenomenon that it can be explained only if both theories are taken into account and combined.

The transient capability of the cell membrane of becoming permeable to molecules after pulsed electric field application is indeed due to a structure change of the lipid bilayer, which is destabilized with respect to the normal condition as well as to the creation and annihilation of electropores, which represents an easy path for ionic and molecular transport through the otherwise impermeable and selective membrane.

The influential parameters

Pulses parameters such as amplitude, width, repetitiona frequency, etc. are of primary importance within the permeabilization process since they determine the level of permeabilization achieved. Indeed their influence is hereafter investigated.

The pulses amplitude and duration

The permeabilization threshold value of transmembrane potential is substantially the same independent of the cell type. Furthermore the permeabilization threshold is lower for adherent cells (300 V/cm for adherent CHO cells) for cells in suspension (700 V/cm for CHO cells in suspension ) This property can be useful in the presence of complex tissues, which contains different type cell if we want to affect certain types of larger size cell [START_REF] Granneman | Seeing the trees in the forest: selective electroporation of adipocytes within adipose tissue[END_REF].

The EF amplitude is a parameter, which influences the permeabilized surface without affecting intracellular organelles [START_REF] Wolf | Control by pulse parameters of electric field-mediated gene transfer in mammalian cells[END_REF][START_REF] Rols | Electropermeabilization of mammalian cells. Quantitative analysis of the phenomenon[END_REF]. Indeed, transfection experiments performed on isolated mitochondria require an electric field 10 to 100 times higher than the fields generally used in vitro and in vivo to permeabilize the cells [START_REF] Collombet | Introduction of Plasmid DNA into Isolated Mitochondria by Electroporation A NOVEL APPROACH TOWARD GENE CORRECTION FOR MITOCHONDRIAL DISORDERS[END_REF].

As well as for the EF amplitude, also the duration has an effect on the permeabilization Pag. 41 phenomenon, it can be remarked from the literature that the threshold beyond which the permeabilization occurs is strongly dependent on the duration of the pulse [START_REF] Benz | Pulse-length dependence of the electrical breakdown in lipid bilayer membranes[END_REF].

It appears that the permeabilization threshold is strictly related to the pulse duration, indeed in one study [START_REF] Rols | Electropermeabilization of mammalian cells. Quantitative analysis of the phenomenon[END_REF] for adherent CHO cells with pulse durations from 2 µs to 20 µs it was found that there is a clear relationship between the EF threshold and the pulse duration (see equation 1.29).

E threshold (kV / cm) = 1.5 w(µs)

+ 0.3 (1.29)
Furthermore other studies showed how the pulse width can also have an effect on the pore size, thus small duration pulses induce the creation of a large number of small electropores while long duration pulses cause the creation of larger electropores since they have more time to enlarge [START_REF] Rols | Electropermeabilization of mammalian cells to macromolecules: control by pulse duration[END_REF].

The figure below summarizes some effects and some application related to both pulse amplitude and duration: According to the Figure 1.13, the same level of permeabilization can be achieved by combining the pulse duration and its amplitude. However below some critical values the permeabilization does not accur whichever the EF applied or the pulse width set.

The pulse count

Additionally, the number of pulses notably influences the permeabilization efficiency.

Besides the fact that the evolution of the level of permeabilization is not linear with the number of pulses, different levels of permeabilization are achieved when tuning the pulse count (Figure 1.14).

Figure 1.14: Influence of the specific energy Q on cell permeabilization of potato tissue [START_REF] Knorr | Impact of high-intensity electric field pulses on plant membrane permeabilization[END_REF].

The pulse shape

Another parameter that has been studied due to its effect on the permeabilization is the pulse's shape. In a presented study [START_REF] Kotnik | Role of pulse shape in cell membrane electropermeabilization[END_REF] the efficiency due to a different pulses shape has been compared, thus rectangular, triangular and sine pulses have been studied.

Pag. 43

Results reveal that electropermeabilization, cell death, and the peak of the uptake, all occur at the lowest EF value for rectangular pulses, and at the highest EF value for triangular pulses. Among the parameters that describe the pulse shape, the time during which the pulse amplitude exceeds a certain critical value has a major role in the efficiency of electropermeabilization. The theory of the electroporation actually attributes the increase of plasma membrane permeability to the formation of hydrophilic structures (''aqueous pores'') through the lipid bilayer [START_REF] Weaver | Theory of electroporation: a review[END_REF]. There is thus a threshold of transmembrane voltage above which formation of aqueous pores becomes energetically favourable. Indeed the probability of formation of individual pores increases with the duration of the above-threshold transmembrane voltage, and thus with the duration of electric pulses.

The pulse repetition frequency

The influence of the repetition frequency was recently investigated thanks to the evolution of new pulse generators, control systems and visualization techniques. Indeed Pucihar et al. [START_REF] Pucihar | The effect of pulse repetition frequency on the uptake into electropermeabilized cells in vitro with possible applications in electrochemotherapy[END_REF] show how by increasing the repetition frequency up to 8.3 kHz the uptake of Lucifer Yellow (LY) stays at similar levels. By applying 26 pulses of 30 ms width, the maximum uptake of LY was similar for the two repetitions frequency employed (1Hz and 8.3 Hz), but the voltage needed for this is different (respectively 219 V for 1Hz and 335V for 8.3V). By tuning the EF strength at high frequency the degree of permeabilization achieved is lower (Figure 1.15), the results is in agreement with the theory of the cell with an RC membrane (see section 2.2.1) [START_REF] Jordan | Electroporation and electrofusion in cell biology[END_REF].

Pag. 44 Further studies performed few years later showed the interest of increasing the frequency within electrochemotherapy to limit secondary troublesome effects, such as muscle contraction [START_REF] Miklavčič | The effect of high frequency electric pulses on muscle contractions and antitumor efficiency in vivo for a potential use in clinical electrochemotherapy[END_REF].

The cell membrane electropermeabilization: applications

As for all new techniques or methodologies, electroporation needs a given time to be developed, fully understood and implemented in clinical and industrial.

The first time the term electroporation appears in science was in 1958 when Stampfli remarked its influence on the node of Ranvier. The phenomenon has been split in two main branches: the reversible electroporation in which the sample totally recovers its original conditions and the irreversible electroporation which implies the death of the sample. In both cases the membrane electroporation induces a temporary non-selective increase of the permeability, thus any kind of molecules and chemical species can get inside and get out of the cell depending of the concentration gradient across the membrane.

Pag. [START_REF] Crowley | Electrical breakdown of bimolecular lipid membranes as an electromechanical instability[END_REF] Applications have been proposed, ranging from gene electrotransfer in biotechnology, biology, and medicine to cell killing in water sterilization, food preservation, and tissue ablation.

The applications in industry

Electroporation is an innovative method widely used in food processing to support the extraction of intracellular components such as sugar from beets [START_REF] Lopez | Enhancement of the solid-liquid extraction of sucrose from sugar beet (Beta vulgaris) by pulsed electric fields[END_REF][START_REF] Loginova | Pilot study of countercurrent cold and mild heat extraction of sugar from sugar beets, assisted by pulsed electric fields[END_REF] or juice from fruits [START_REF] Bazhal | Pulsed electric field treatment of apple tissue during compression for juice extraction[END_REF]. It is also a promising tool used for water sterilization and food preservation [START_REF] Vorobiev | Electrotechnologies for extraction from food plants and biomaterials[END_REF] or to extract lipid from algae for renewable energy production [START_REF] Hu | Microalgal triacylglycerols as feedstocks for biofuel production: perspectives and advances[END_REF].

Extraction of sugar from beets

One of the largest scale industrial applications of PEF is the extraction of sugar from beets. In order to do it sugar beets are cut into thin slices (called cossettes) and treated thermally with as little water as possible. Substances extraction takes place through diffusion and it is possible due to the destruction of cell membrane achieved by thermal denaturation at temperatures above 70˚C [START_REF] Sack | Research on industrial-scale electroporation devices fostering the extraction of substances from biological tissue[END_REF]. Since the diffusion coefficient is proportional to temperature, the extraction should take place at highest temperature as possible, however a too high temperature causes the denaturation of other cell wall substances that can thus become water-soluble and lead to impurities in the juice. A good compromise is represented by a temperature denaturation of 70-78°C and an extraction temperature of 68-73°C. The high temperature allows some bacteria surviving and thus causes a loss on the sugar production, thus the system needs some disinfectants for the purification procedure.

A combination of pressing and PEF-treatment could help to save energy consumption and to decrease the cost linked to purification products, nevertheless this procedure is Pag. [START_REF] Rols | In vivo electrically mediated protein and gene transfer in murine melanoma[END_REF] not nowadays easy to implement at large scale and as new technology requires a too high economic investment. Schultheiss et al. [START_REF] Schultheiss | Processing of sugar beets with pulsed-electric fields[END_REF] proposed a change in the employed chain of production with the aim to demonstrate the efficiency of the PEF application on the production process. They proposed a mobile test device KEA (Karlsruher Elektroporations Anlage -Karlsruhe electroporation device), which consists in a cylindrical chamber where stainless steel electrodes are axially and azimuthally distributed, the chamber has a section able to treat an entire sugar beet by delivering 8,8

kV/cm at 10 Hz. After treating a sugar beet in this chamber, it has been cold pressed or extracted in water at different temperature levels. Thus PEF can be applied in order to achieve a cell membrane permeabilization without changing important properties of the sample [START_REF] Bazhal | Pulsed electric field treatment of apple tissue during compression for juice extraction[END_REF]. It was actually proven that no changes were remarked on pH value, total sugars and total acidity. Furthermore the purity and the clarity of the juice extraction are enhanced and even the content of many nutritionally valuable compounds was retained or even enhanced [START_REF] Bobinaité | Application of pulsed electric field in the production of juice and extraction of bioactive compounds from blueberry fruits and their by-products[END_REF]. A strong point is also represented by the fact that the use of PEF is a technique that can be easily integrated in already existing industrial process and it does not require the development of a new extraction procedure (figure 1.17).

Pag. 48

Figure 1.17: Apple juice processing scheme. Comparison of conventional juice making process with electroplasmolysis treated apple mash and pomace [START_REF] Vorobiev | Electrotechnologies for extraction from food plants and biomaterials[END_REF] Indeed, PEF treatments can be used to avoid conventional disintegration techniques such as enzymatic treatment typically used in food industry for disruption of biological material prior to juice extraction or extracellular compounds recovery. The enzymatic treatment can actually be responsible of side effects in the juice making process since it may deteriorate textural properties of a product and cause loss of important residual components employable for further utilization.

Furthermore, when PEF are included into industrial process, after separation of the plant product from the plant processing residual material, it is possible from the latter to obtain antioxidant [START_REF] Balasa | Extraction of total phenolics from grapes in correlation with degree of membrane poration[END_REF]. In fact, since these food components have not been destroyed

with enzymatic or high-temperature treatments, a recovery of peptin and intracellular compound is enabled [START_REF] Schilling | Effects of pulsed electric field treatment of apple mash on juice yield and quality attributes of apple juices[END_REF].

Pag. 49

PEF treatments can thus enhance the quantity of juice yield obtained and result in higher pigment release in juice than from samples processed in a conventional way (higher ß-carotene content for istance [START_REF] Knorr | Food application of high electric field pulses[END_REF].

Producers have also to take into account that good flavour and colour characteristics of a product together with high nutritive value is of primary importance for a customers and PEF treatment was observed not to deterio-rate these properties maintaining fresh characteristics of the final product.

Water sterilization

The PEF treatment has found wide applications in food industry as mentioned previously in the disintegration or pasteurization of food products, but its use may also be useful in the treatment of wastewater, also considered as a product generated during processing. For example, the sludge as wastewater process result consists of large quantities of organic material mostly in the form of a variety of different organisms.

Koners et al [START_REF] Koners | Application of Pulsed Electric Field Treatment for sludge reduction on waste water treatment plants[END_REF] have shown a better separation of the sludge and a 45% reduction of total suspended solids in the excess sludge, by applying 15 kV/cm EF and an input energy of 100 kJ/l (figure 1.18). Compared to the traditional disintegration techniques (heat treatment, ultra sound treatments or mechanical rupture), PEF treatment induces a more efficient permeabilization of the cell membranes with the advantage of a short processing times.

Pag. 50

Lipid extraction from malgae

One of the big problems in our century is to find an alternative to fossil fuels and first generation biodiesel in order to meet the needs of world transportation. Thus in the late 1980s microalgae were conceived as the most promising renewable source of lipids able to solve this problem [START_REF] Davis | Techno-economic analysis of autotrophic microalgae for fuel production[END_REF]. The production of fuel by treating microalgae can be explained by four consecutive steps: the algae growth, its harvesting, the lipid extraction and the catalytic conversion of lipids to biofuels.

One way to enhance lipid extraction from algal biomass is to employ PEF technology.

The presence of the electric field aids in cell disruption resulting in significant increased lipid recovery. Furthermore, although PEF treatment does increase the total amount of lipids extracted, it does not change the lipid profile of the extract and it represents thus a non-invasive technique that impacts the quality of the extraction (Figure 1.19).

Pag. 51 Nowadays, the biggest barrier for the large-scale fuel production from algae is done by the final cost, estimated as $8.52/gal for open pond production and $18.10/gal for photobioreactors. This alternative feedstock actually needs to be economically competitive and thus an important technological breakthrough is required [START_REF] Zbinden | Pulsed electric field (PEF) as an intensification pretreatment for greener solvent lipid extraction from microalgae[END_REF].

Applications in medicine

In addition to the food industry, electroporation has found wide applications in clinical therapies. Indeed it is a promising tool for electrochemotherapy [START_REF] Mir | Effective treatment of cutaneous and subcutaneous malignant tumours by electrochemotherapy[END_REF][START_REF] Chang | Cell poration and cell fusion using an oscillating electric field[END_REF], gene electrotransfer for gene therapy [START_REF] Neumann | Fundamentals of electroporative delivery of drugs and genes[END_REF][START_REF] Chang | Cell poration and cell fusion using an oscillating electric field[END_REF], DNA vaccination [100] and tumor ablation [START_REF] Davalos | Tissue ablation with irreversible electroporation[END_REF].

Pag. 52

Electrochemiotherapy

Thanks to the capability of pulses electric field to increase the permeabilization of the cell membrane to hydrophilic molecules, electrochemiotherapy has become the most successful in vivo application for cancer treatment. This treatment consists in locally and reversibly electropermeabilize cancer cells after injecting a cytotoxic drug. Under conventional chemotherapy methods, the amount of drug entering into the cells is quite low due to the fact that the cell membrane is not permeable. Thus the necessity to increase drug dose in order to maximize the amount of active ingredient in the tumour cells. However, high doses cause significant side effects and toxicity in normal noncancerous cells.

The role of the permeabilization of tumour tissue just after injection of the drug will allow a massive entry of molecules of interest, and thus a reduction in dose required for the induction of an effect. During the first in vitro tests [START_REF] Mir | Introduction of definite amounts of nonpermeant molecules into living cells after electropermeabilization: direct access to the cytosol[END_REF]101] the effect of bleomycin

Gene therapy and DNA vaccination

Transfer of genes into cells or tissue using electrical pulses has also been implemented in medicine. Indeed, the use of electroporation avoids the use of any virus that may When electric field pulses are applied to the spheroid, the latter become permeabilized and it changes its structure; it is thus possible to monitor the delivery and quantify the effects of antitumor drugs in order to check the efficiency of the treatment [111].

As past literature has demonstrated [109], for classical electric conditions (train of 10 electric pulses, with amplitude of 500V/cm and width 5ms, delivered at 1Hz), it is possible to obtain almost 23% of correctly trasnfected cells and the percentace in the case of spheroid has revealed to be less than 1%.

These results show how the spheroid can be profitably used to mimic the in vivo situation, optimize the electrotranfer and prevent potential failures.

Tumor ablation

In the domain of irreversible eletcropermeabilization it is possible to permanently damage the tumour without intervening by surgery [START_REF] Davalos | Tissue ablation with irreversible electroporation[END_REF]. Indeed, the increase of the IRE could thus have a primary role in the clinical oncology; it could be implemented to successfully treat soft tissue malignancies and additionally large and complex tumours.

Pag. 56

Indeed, it reveals to be feasible, effective and extremely attractive due to its minimal invasiveness.

Conclusion

Since the past, the effects of the electric field on the particles have been investigated

from several researchers and research groups; thus several techniques based on the application of the electric field on the living have been employed, especially in the field of cell biology. In addition the use of PEF revealed to be a promising tool for other applications in the matter of food industry and food preservation as well as for biofuel production.

The efficiency of the elctropermeabilization is determined by the electric pulse parameters such as pulses amplitude, width and number. Their optimal values actually play an important role in the optimization of the permeabilization. Furthermore, when electric pulses parameters are not properly set cell viability is affected and irreversible electroporation takes place. We thus investigated the influence of pulses parameters in relation to the permeabilization level within a biological tissue through bioimpedance measurements.

Nowadays electropermeabilization is widely used in biology and food industry, nevertheless the knowledge of the dielectric characteristics (such as permittivity and conductivity of the membrane and the cytoplasm) of treated cells represents an important tile which needs to be investigated since it strictly influences the pulses electric field optimization. Starting from this consideration, we used the combination of three electric field solicitations (electrorotation, dielectrophoresis and pulses electric field) with the aim to establish the fingerprint of the cell and estimate its changes due to electropermeabilization.

Pag. 57

The literature offers a great quantity of studies regarding the basic mechanisms of electroporation at the single cell level, however when approaching a cell tissue model, the phenomenon become way more complex since the tissue is composed by cells in close contact and their proximity affects their communication. Thus the importance of a model that can mimic the in vivo cells organization changes when the permeabilization occurs: the 3D multicellular spheroid. The spheroid is actually composed of cell organized in a matrix where typical connections of the in vivo tissue are reproduced.

Pag. 59

Chapter 2

Bioimpedance measurement as a method to monitor biological tissue permeabilization

Bioimpedance measurement reveals to be a promising tool in biomedical engineering since it represents a method to monitor the physiological variations of a biological tissue. Furthermore the detection of dielectric properties changes due to pulsed electric field (PEF) application is a way to study the effect of the permeabilization phenomenon.

Nowadays, there is a growing interest in the application of PEF to the tissue since it Furthermore the monitoring of the bioimpedance of a cell tissue is a method that can be used to determine the efficiency of its electropermeabilization with respect to different PEF characteristics. Such analysis might be the key to determine the appropriate electrical conditions to achieve the desired degree of tissue permeabilization without causing unrecoverable alteration of the tissue.

The impedance spectroscopy.

In last years impedance spectroscopy revealed to play an important role in fundamental and applied electrochemistry and materials science. Indeed it was widely employed to characterize the electrical behavior of complex systems. Furthermore thanks to the current availability of commercial devices, able to cover from the millihertz to megahertz frequency range, it appears certain that impedance studies will become Pag. 61 increasingly used in the fields of electrochemistry, materials science and engineering, it is actually enhanced the knowledge of the theoretical basis for impedance spectroscopy and researches gain skill in the interpretation of impedance data.

Impedance spectroscopy is thus used to characterize electrical properties of materials and their interfaces with electronically conducting electrodes; via impedance spectroscopy it is actually possible to investigate the charge distribution and the interface of several kinds of solid/liquid materials such as ionic, semiconductors, mixed electronic-ionic, and even insulators (dielectrics).

Impedance measuring methods are conventionally distinguished according to the function employed to excite the sample, particularly respect to the independent variable (time or frequency). If the excitation and the response is recorder in the frequency domain, a small-amplitude sinusoidal excitation is sent to the sample. When the measurement is made in the time domain it is always possible to obtain the impedance as a frequency function by using the time-to-frequency conversion techniques such as Fourier or Laplace transformations.

If we defined X(jω) as the signal at the input of the system and Y(jω) the response of the system to the stimulus, the system a transfer function is determined as the output divided by the input:

G( jω) = Y ( jω) / X( jω) = Z( jω) (2.1)
In the case where the system receive as input a current I(jω) and gives as an output the corresponding voltage V(jω), the transfer function corresponds to the Impedance of the system itself Z(jω).

Being V(jω) and I(jω) complex numbers, representing respectively the voltage and current (magnitude and phase), the electrical impedance Z(jω) is a complex number.

Pag. 62

The impedance of the system can change in both amplitude and phase, that is why the Z(jω) represents as follow:

Z( j) = Z '+ jZ '' (2.2)
with Z' the real part of the impedance, Z'' the imaginary part and j is the imaginary number and represents the anticlockwise rotation by π/2 relative to the x axis.

The impedance Z can be plotted by using rectangular coordinates where Z' is in the direction of the real axis and Z'' is along the imaginary axis (Figure 2.1). The corresponding polar coordinates will give as result respectively the phase angle and the amplitude:

θ = arctan(Z ''/ Z ') (2.3) Z = [(Z ') 2 + (Z '') 2 ] (2.4) Pag. 63
In this chapter Z will be treated as frequency-dependent and the resulting evolution of Z respect to angular frequency w will give information about the full system: the impedance of the tissue and its interface with the electrodes.

The Bioimpedance

The term "bioimpedance" is employed when electrical properties of a biological tissue are measured by using a current flows through it. Indeed bioimpedance deals with the capability of the tissue to oppose ("impede") the passage of current circulation due to sample electrical properties. The bioimpedance measurement is frequency dependent and it varies with the different tissue type. The first impedance measurements on biological tissue refer to the late eighteenth century, with the experiments made by Galvani [118]. This field was investigated in order to know more about electrical properties of the sample under test.

It is common practice to depict equivalent circuit models of the tissue bioimpedance in order to attribute a physical meaning to the impedance parameters.

On a macroscopic scale, the living body is composed of a wide variety of biological tissues with very different properties. Within the biological tissues it is possible to distinguish between animal tissues and plant tissues. nerve tissue is specialized in receiving stimuli and transmit nerve signals (nervous system).

In the case of plant it is possible to distinguish between differentiated tissues derived from the undifferentiated cells of an embryonic tissues, which is therefore able to produce new tissues throughout all the plant life. Plant tissues are classified into tegumentary tissues (which constitute shell of the plant such as cork and bark); conductive tissues responsible of the plant support and fundamental tissues with the function of support, filling, and reserve.

Nevertheless, despite the differentiation and the specific functions, a biological tissue can be considered composed by an agglomerate of cell with similar form, structure and functions that, in the majority of cases, have common embryological origin.

The various functions are distributed among distinct populations of cells, tissues and organs, which can also be very far apart, thus a complex communication network is required. The signal between cells can be transmitted by two different ways related to the distance between them: between cells distant from each other, the signals must be exchanged in an indirect manner, through the secretion of substances such as hormones; is cells are close, communication takes place in a direct way, through structures which allow communication between adjacent cells (membrane proteins for instance) [119].

The electrical properties of a biological tissue is determined by its components, thus by the cells that compose the tissue itself.

As a first approximation, each of these cell can be considered as a membrane that encloses an intracellular compartment submerged on a extracellular medium. The cell constitution is actually far more complex, in fact the extracellular medium, which bathes the cells, contains protein and electrolyte (plasma, interstitial fluid) and the cell, enclosed by a plasma membrane lipid bilayer, contains organelles and the cell nucleus.

Moreover a tissue can be defined as an "aggregate of cells (and of substances produced by them) with similar structure and similar functions, and, for the most part, with common embryological origin [120]".

Pag. [START_REF] Polak | On the electroporation thresholds of lipid bilayers: molecular dynamics simulation investigations[END_REF] By taking into account the definition of biological tissue and by using the electrical modeling circuits theory, it is possible to derive a basic electrical model for the cell (Figure 2.2) where R e represents the extracellular medium, R i represents the intra cellular compartment and the cell membrane is modeled as a parallel of a resistance R m (that represents the ionic channels) and a capacitor C m (that represents lipid bilayer): Using a simple RC circuit, the permittivity is generally considered independent of frequency and the tissue has a frequency-dependent behavior that goes beyond the RC model. This is due to the various components (intracellular compartment, extracellular compartment and plasma membrane) that contribute differently to the total bioimpedance.

Thus when the Fricke model was first proposed, it was widely used since it represented a good approximation of the tissue behavior, nevertheless its limits became soon quite evident and they led to a more complex model formulation.

Cole-Cole model

Cole The total bioimpedance due only to the tissue is modeled as follow:

Pag. 69 The following figure 2.6 shows the typical impedance spectrum as module and phase evolution respect to the frequency. This structural orientation is also observed in muscle fibers and can be very complex, as is the case for cardiac tissue [132].This orientation leads to anisotropy of electrical properties of tissues. This anisotropy is a metrological problem of primary importance because the differences recorded following the directions of measurement are not negligible [132,133].

It has been found that skeletal muscle presents an anisotropy character which is the reason why the conductivity is higher along the fiber axis (longitudinal direction) rather than in the perpendicular direction [134]. Each of these two double layers consists in a part where there is a high concentration of charges and a side where there are almost no charges. Furthermore, in the case of conductors (conductive metal), electrons are concentrated in the immediate proximity of the interface and thus the corresponding double layer is very thin (on the order of 0.01 nm).

BIOIMPEDANCE MEASUREMENT AS

Pag. 72

Different is the case of the ionic conductors, the application of an electric field actually causes the formation of an empty area (without charges) adjacent to the interface, and a further diffused layer where the charge carriers are concentrated. In the absence of adsorption (attachment of ions on the electrode), the ions can not approach the electrode within a few 0.1nm (corresponding to the diameter of the solvent atoms surrounding the cations or adsorbed by the electrode). There is thus a zone corresponding to the dielectric of a capacitor. The thickness of the diffuse layer (also called layer of Gouy-Chapman) may be of the order of a few nanometers. The charges distribution in this area is subject to complex physical phenomena (diffusion, convection, electric force)

and it strongly depends on the frequency variation of the applied electric field. This particular distribution of loads at the interfaces results in very large impedance between the electrode and the biological environment for frequencies below a few kHz.

In general this effect of species release is mostly localized at the electrodes and it depends on their chemical nature (steel, stainless steel, aluminum, etc...), on the medium composition and on the electrical parameters. The redox species have deleterious effects on tissue and induce changes in the physical properties of the medium [136]. The spectroscopic study needs thus to take into account the contribution given by this interface impedance [137,138].

The latter was in our model represented by a Constant Phase Element (CPE) impedance (Z DL ) defined with the exponent β ( 0<β<1) as in (1):

Z DL = 1 ( jωC DL ) β (2.5)
The CPE Z DL , as a part of the impedance measurement, has to be evaluated when

The impedance measurements methods

When a sample is electrically stimulated, a multitude of fundamental microscopic processes occur and they give an overall electrical response. The effect of voltage application might induce the release of metal ions that can alter the sample around the electrodes; indeed when the solution facing the electrodes contains electro-active species, a redox current appears above the Nernst voltage, which leads to the release of metal ions.

The flow rate of the current thought the tissue can be influenced by several parameters such as the ohmic resistivity of both the electrodes and the electrolyte, the reaction rates at the electrode-electrolyte interfaces and the structure of the sample (such as anomalies or presence of second phase regions).

Pag. [START_REF] Collombet | Introduction of Plasmid DNA into Isolated Mitochondria by Electroporation A NOVEL APPROACH TOWARD GENE CORRECTION FOR MITOCHONDRIAL DISORDERS[END_REF] Even if the interface between the electrodes and the electrolyte is actually jagged, full of structural defects, electrical short and open circuits, for simplicity we can assume that it is smooth with a simple crystallographic orientation.

In order to perform a measurement of the impedance, the most standard approach consist on sending a voltage or current to the interface and measuring the impedance phase shift and amplitude. Available commercial instruments are able to measure the impedance as a function of frequency automatically in a wide frequency ranges [mHz to MHz] and are easily interfaced to computer programs. To perform the impedance measurements two main electrodes configuration are employed: 4-points probes method and the 2-points probes method.

Whatever is the method chosen, the reached results generally fall into two categories:

the characterization of the sample itself, meant as an entity with given conductivity, dielectric constant and equilibrium concentrations of the charged species or the characterization of the electrode-sample interface phenomenon such as adsorptionreaction rate constants, diffusion coefficient of species in the electrodes and release of chemical species from electrodes.

The 4-points probes method

In the 4-points probes method, a constant current is injected into the tissue through one As the voltmeter absorbs substantially no current, the measured impedance Z is independent of the interface impedances. The impedance resulting by the measurements electrodes pair is linked to the conductivity and permittivity of the sample.

The 2-points probes method.

The 2-points probes method is the easiest one, in such a configuration ( At low frequencies (above a few tens of kHz), the contribution of the impedances due to electrodes is negligible in the sample impedance. For lower frequencies, the impedances of interfaces are not negligible and may even be very large compared to the sample impedance, thus its quantification is a relevant point. There are two ways to determine the sample impedance from 2-points probes impedance measurements:

-it is possible to determine the interface impedance from a measurement on a sample of known electrical properties having the same interface as the impedance sample to be tested (it is know as "substitution" method). The interface impedance can then be subtracted from the total impedance to determine the sample impedance. This method is not very accurate because it is very difficult to make a reference sample of the same chemical composition as the sample studied;

-the parameters of the interface impedance model can be determined from the total impedance measured considering that the sample impedance can be neglected for the lowest frequencies

For our measurements, we employed the 2-probes point method, we used two conductive needle electrodes of 0.63 mm diameter, 1mm distance between needle and Pag. [START_REF] Yarmush | Electroporation-based technologies for medicine: principles, applications, and challenges[END_REF] 11.6 mm length. These needles are used for both applying the pulse electric fields and bioimpedance measurement (Figure 2.12). Once the electrical model and the measurement protocol are defined, it is possible to estimate the dielectric properties of the tissue by fitting the bioimpedance cspectrum.

The goal of parameter estimation is to obtain the numerical values of the parameters of a model that describes the system of interest. Let's call p the vector of parameters, the mathematical model that describes a generic system is represented by a function G(p).

This model provides a prediction of the values of the output G(p'). If experimental measurements z of the output are available, we can write the equation:

z = G(p') +ε s (2.10)
where ε s is the error linked to the estimation.

Pag. [START_REF] Kotnik | Role of pulse shape in cell membrane electropermeabilization[END_REF] impedance spectrum z and the impedance estimated with these electrical elements. The cost function to be minimized is defined as in equation 2.10:

C = argmin p z -G(ω, p) 2 j=1 N ∑ (2.16)
where G(ω,p) is the estimated impedance, z is the measured impedance, both depending on the electrical pulsation ω. p represents the parameters (elements of the electrical model) to be estimated. N represents the number of measurement points used for the minimization.

The algorithm was implemented thanks to the function 'lsqcurvefit', in MATLABTM environment. This function, to perform the minimization of C, uses the Levenberg-Marquardt algorithm known for its robustness which is one of Gauss-Newton methods.

Bioimpedance changes due to electroporation

Recently it has been proposed that bioimpedance measurements can provide real time feedback on the outcome of the electroporation treatments [141].

Pulsed Electric Field (PEF) applied to cells or cell tissues induces a biological change on the cell's properties, in particular to its membrane that becomes permeabilized (electropermeabilization phenomenon) [START_REF] Neumann | Fundamentals of electroporative delivery of drugs and genes[END_REF][START_REF] Weaver | Theory of electroporation: a review[END_REF]112,142,143]. This phenomenon temporarily increases the capability of the cell membrane to be crossed by ions and macromolecules.

The permeabilization of a tissue reveals to be complicated to analyze since a tissue is composed of cells that are close to each other, furthermore neighboring cells, even if In our work biological tests were performed on vegetal tissue (Solanum tuberosum potatoes). Bio-impedance evolution with respect of time before and after application of PEF was investigated.

The measured bioimpedance (Figure 2.13) was analyzed by using the following methodology: (i) From the bioimpedance measurements (Ztot) obtained before and after the pulses, both the contribution of the tips/tissue interface (electrochemical effect: ZDL) and the contribution of the tissue (biological effect: Zbio) (Figure 2.13) were separated, (ii) then from the fitting algorithm the tissue components were extracted (iii) and the degree of permeabilization P due to the application of the pulses was finally calculated.

Pag. 81 The level of permeabilization P of the tissue is defined for this study as shown in [START_REF] Goater | Electrorotation and dielectrophoresis[END_REF], where (ΔRf) and (ΔRi) represent respectively the bio-impedance excursions before and after the PEF application (see Figure 2.14). (ΔRf) and (ΔRi) are directly dependent on the extracellular and intracellular resistances, and are largely affected by the permeabilizing pulses (( 7), ( 8)). P is a normalized parameter in relation with (ΔRi).

P = ΔR i -ΔR f ΔR i *100 (2.6
)

ΔR i = R0 bp -R∞ bp (2.7) ΔR f = R0 ap -R∞ ap (2.8)
The bioimpedance spectrum represented in Figure 2.14 is also used to estimate the bioimpedance components of the tissue (R0, R∞, τ and α), and their variations with the permeabilizing pulses. For the needs of this study, a normalized component evolution before and after pulses application was also defined as follows:

χ( f ) = χ ap / χ bp (2.9)
All impedance components discussed in the thesis are averaged from at least 7 successive measurements on the same vegetal sample. Indeed the variability of tissue characteristics in different vegetal samples is considerable. However, even in the case where the same sample is used, the variability of cell sizes and shapes, as well as the variability of the quality of the contact between the tissue and the electrodes cannot be avoided, which might affect the sensitivity of the determination of the degree of permeabilization [151].

Instrumentation and experimental setup

The pulsed electric field was applied with a function generator Agilent 33250A.

Respective effects of the amplitude, pulse width and pulses number of the waveform was investigated. Desired pulses amplitude was achieved by using an amplifier NF corporation HSA4101.

Pag. [START_REF] Lopez | Enhancement of the solid-liquid extraction of sucrose from sugar beet (Beta vulgaris) by pulsed electric fields[END_REF] The measurements were performed by using impedance analyzer (HP 4194A). As previously explained, we used two conductive needle electrodes both used to apply the pulse electric fields and measure the bioimpedance. The electric field considered in each experiment is taken as the ratio between the voltage applied and the distance d (d=1mm)

between the two needles.

The impedance analyzer was controlled with MATLABTM through GPIB (General Purpose Interface Bus) interface.

Influence of pulses parameters on the tissue permeabilization.

The efficiency of the permeabilization of biological tissue depends on several parameters, such as the molecular composition of the tissue, the chemical interaction with electrodes, but above all on the electric field pulses parameters applied to permeabilize the membrane. As already mentioned in the Section 1, the study of those characteristic has been investigated by several groups [START_REF] Kotnik | Role of pulse shape in cell membrane electropermeabilization[END_REF]136,152]. In our study we also performed some measurements in order to clarify the role of the pulse's width, its amplitude, its count and its rising/falling time is the electropermeabilization process.

Influence of the pulse duration

Using a train of respectively 50-100-200-500 µs squared unipolar pulses delivered with a frequency of 1 Hz, corresponding to the field amplitude E=500 V/cm, it was confirmed that the degree of permeabilization P is in relation with the pulse duration and its repetition (Figure 2.16). Cell membranes are indeed more affected by the pulse when its duration increases and when several pulses are applied (Figure 2.16).

Pag. 85

Influence of the pulse amplitude and of the number of pulses

The permeabilization efficiency is notably influenced by the PEF amplitude, as increasing the amplitudes induces an higher degree of permeabilization (Figure 2.16), Indeed with a train of 100 µs squared unipolar pulses delivered with a frequency of 1 Hz, corresponding to the field amplitude E=350 V/cm, the permeabilization of the tissue remains low whereas with a train of 100 µs squared unipolar pulses delivered with a frequency of 1 Hz, E=500 V/cm the tissue is permeabilized even with a low number of pulses (Figure 2.16). Besides, Figure 16 shows that the evolution of the level of permeabilization is neither linear with the electric pulse amplitude, nor with the number of pulses. Different levels of permeabilization are achieved when tuning PEF strength as well as pulses number.

A way to better control the level of permeabilization is to reduce the PEF intensity while increasing their cumulative effect with higher number of pulses. Nevertheless the treatment time might be drastically increased in that case, due to the nonlinear dependence between the number of pulses and the permeabilization level (Fig. 2.16, case of E=350 V/cm).

Influence of the pulse rise time

Keeping the amplitude and duration constant for applied PEF, the rising time and falling time of pulses had been tuned in order to estimate their influence on permeabilization.

The experimental results highlight that these PEF characteristics, with rising time and falling time evolution between 5 ns up to 1 µs, do not have a significant effect on the level of permeabilization, at least in these experimental conditions. The same result was also shown by another group [START_REF] Kotnik | Role of pulse shape in cell membrane electropermeabilization[END_REF], that performed electropermeabilization measurements on a cuvette with pulses of different rise-and fall-time.

Pag. 87

Influence of thermal effects

The temperature dependence of EF effects on tissue permeabilization is another aspect that needs to be taken into account. It was actually proven that higher degrees of permeabilization are achieved when the exposed tissue is also submitted to heat solicitation [115,153].

In the present situation, the temperature elevation induced within the vegetal tissue by the application of PEF was evaluated in order to distinguish the permeabilization phenomena from the heating effects on the tissue:

ΔT = σE 2 ρC p t (2.17)
where σ represents the tissue conductivity (approximated to 0.1 S/m), ρ represents its volume density (700 kg m -3 ) and Cp its specific heat (Cp=3.8 kJ (kg K) -1 ). ΔT corresponds to the temperature elevation proportional to the duration of the electric field pulse.

For the highest electric field applied during experiments (700 V/cm), and the longest pulse width (500 µs), the temperature elevation estimation was: ΔT=0.09 K, which can be neglected.

Influence of the specific energy per pulse

The relation between the degree of permeabilization P and the specific energy per pulse Q (defined as follows [START_REF] Knorr | Impact of high-intensity electric field pulses on plant membrane permeabilization[END_REF] was investigated (Figure 2.16):

Pag. 88 Q = σE 2 ρ t (2.18)
where σ represents the tissue permittivity (σ=0.1 S/m), ρ the tissue volume density (r=700 kg m-3), E the field amplitude (E=500 V/cm), t the pulse's width.

With permeabilizing pulses corresponding to a field amplitude E=500 V/cm, the permeabilization level is represented with respect to Q, for three different numbers of applied PEF (Figure 2.16). Considering the presented specific experimental conditions, the level of permeabilization increases with the specific energy per pulse as well as with the number of pulses. Indeed tuning both Q and the number of pulses permits the control to the electropermeabilization level, as mentioned in [START_REF] Knorr | Impact of high-intensity electric field pulses on plant membrane permeabilization[END_REF].

Effect of electropermeabilization with respect to Cole-Cole equation

As discussed, a method to monitor the level of electropermeabilization of a tissue is the estimation of its bioimpedance components. Different methods can be used for that purpose: the analysis of the transient time response The resistive impedance of the extra cellular medium R0 is widely affected by the application of PEF as the cell membrane becomes permeabilized allowing the passage of ionic currents. In contrast, R∞ does not change significantly after PEF application (Figure 2.17). Indeed, R∞ represents the combination of the extra cellular medium and intra cellular medium, which are barely affected by the pulses application. Using R0 to monitor the degree of permeabilization of the tissue remains thus quite natural and simple.

For the component α, linked to heterogeneity of cell characteristics in the cell-tissue

[155], one can notice that its value slightly decreases with the degree of permeabilization. This is mainly due to applied experimental conditions, as the cells of the tissue are not all exposed to same electric field value, depending on their position with respect to the electrodes composed of two needles. Indeed the permeabilization degree is inhomogeneous in the tissue, but the a component remains nearly unchanged

Pag. [START_REF] Schultheiss | Processing of sugar beets with pulsed-electric fields[END_REF] because it is dominated by the characteristics of the heterogeneity of the not permeabilized tissue.

The variation of τ is directly linked to the variation of the membranes capacitance Cm as described in the first part of the paper. For the lower level of permeabilization (P<10 %), where t increases softly, water molecules penetrating the membranes contribute to the rise of Cm, as already mentioned by other studies [START_REF] Levine | Life cycle of an electropore: field-dependent and field-independent steps in pore creation and annihilation[END_REF]156], due to the larger relative permittivity of the water compared to the one of the phospholipids. In addition, the thinning of the cell membrane due to the increasing of electrostatic pressure induced by the application of PEF might contribute to the elevation of Cm.

Nevertheless, for higher degrees of permeabilization, the spatial heterogeneity of the applied electrical field due to applied experimental conditions leads to a large increase of the ionic conductivity in the permeabilized zone of the tissue where the cell membranes are destructured. The validity of a global Cole-Cole model for the whole tissue should be examined carefully in that case. Until a large degree of permeabilization is reached (P<40 %), the estimated time-constant t barely changes, as it is dominated by the characteristic time-constant of the non-permeabilized part of the sample. This leads to a large over-estimation of Cm, due to the averaging effect of the employed model that does not take into account the spatial heterogeneity of the permeabilization. Cm does not represent anymore the membrane capacitances for high levels of permeabilization.

Finally the use of the Cm component as a permeabilization level indicator is sensitive and well adapted for the low levels of permeabilization (P<10 %). The use of this component, estimated from a global Cole-Cole bioimpedance model for the whole tissue, is more limited when high permeabilization levels are considered (P>40 %).

Indeed such a global model does not reflect spatial heterogeneity of the permeabilization in the applied experimental conditions.

Pag. 91

1.10 From bioimpedance to electrorotation -the importance of the miniaturization.

In order to have a complete overview of the permeabilization phenomenon a microscopic study (single cell level) is performed.

In this case the system is composed by miniaturized devices, thus a deep check of the new generated physical balances needs to be investigated. Nevertheless, the miniaturization approach reveals to be useful when micro-species are under investigation.

In microdevices where electrical solicitations are applied, the miniaturization has the advantage of reducing the temperature rise resulting from the heat generation by Joule effect, the heat exchanges are actually favored by a better ration surface to volume, However a disadvantage of microelectrodes is that their impedance is much higher compared to macro-electrodes due to the interface phenomenon. The result of this phenomenon is a so-called "interface capacitance", or "double layer capacitance" resulting from interaction between ions and molecules in the boundary between the surface of the electrolyte and the measuring electrodes. This capacitance is inversely The investigation of the permeabilization phenomenon at the single cell level, which will be the core of the next chapter, will be thus not performed with bioimpedence measurements, but with a technique where different electrical solicitations (DEP, ROT and PEF) are combined.

3.

MONITORING THE PERMEABILIZATION OF A SINGLE CELL IN A MICROFLUIDIC DEVICE WITH A COMBINED DIELECTROPHORESIS AND ELECTROROTATION TECHNIQUE

Pag. 93

Chapter 3

Monitoring the permeabilization of a single cell in a microfluidic device with a combined dielectrophoresis and electrorotation technique

The interest for single cell characterization is explained both by the need to diagnose illness (cancer, for instance) and the importance of understanding how external electric solicitations can impact the cell and its development (electromagnetic exposure, for example).

The study of the electric field effects on the body requires a preliminary knowledge of the phenomena which occur at the level of the cell, the basic unit of life. Thanks to improvements in biochemistry, genetics and laboratory techniques, the mechanisms regulating the inner behavior of the cell are being better understood.

A single cell represents a complex biological/physical structure and its study involves vast areas of investigation. In the presented work, we mostly investigate the electrical properties of the cell in order to understand qualitatively and quantitatively the effect of the electric field. In particular, one of our main objectives is to measure the electrical parameters of the main cellular compartments, such as the cytoplasm and membrane, in order to propose a tool to analyze the behavior of the cell subjected to an electric field source. The study of the interaction of the field with cells is considered as a step to be Pag. [START_REF] Knorr | Food application of high electric field pulses[END_REF] associated to the study of the tissue behavior (presented in the previous chapter) in order to acquire a complete overview of the electropermeabilization phenomenon at different size-scale.

Over the past decades, AC electrokinetic phenomena such as dielectrophoresis, travelling wave dielectrophoresis and electrorotation have been increasingly investigated in lab-on-chip and microfluidic devices [START_REF] Hughes | Nanoelectromechanics in engineering and biology[END_REF]162,163].

Electric field pulses can actually increase the permeability of the cell membrane by changing its structure [START_REF] Rols | Electropermeabilization of mammalian cells. Quantitative analysis of the phenomenon[END_REF]; a reversible or non-reversible electropermeabilization can thus be achieved.

Several studies have been proposed regarding the investigation of cell permeabilization and its efficiency, with certain presenting the fluorescence miscroscopy as a method of investigation [START_REF] Kotnik | Role of pulse shape in cell membrane electropermeabilization[END_REF]136,152]. The electropermeabilization is thus quantified by analyzing the penetration of non-permeant dyes (such as trypan blue), the penetration of fluorescent dyes (such as propidium iodide or calcein) or by measuring the release of the intracellular compound (such as ATP) [START_REF] Teissie | Electropermeabilization of cell membranes[END_REF]. When employing this method, cells are usually submerged in a buffer containing the dye, PEF are induced and after an incubation time of few minutes (5 minutes in the case of trypan blue) observed under a microscope [START_REF] Rols | Electropermeabilization of mammalian cells. Quantitative analysis of the phenomenon[END_REF].

In other studies, researchers employ the classic cell biology approach, they work on a large number of cells by performing experiments in cuvette, and the access to particular relevant parameters from a global measurement is possible by averaging over the cell population. Sometimes this approach does not reflect the cellular diversity and may be not sufficient. It then becomes necessary to perform measurements on single cells, which is the only way to obtain proper assess to the characteristic inhomogeneity of the sample.

We thus propose a combination of three electrical solicitations (conventional dielectrophoresis, electrorotation, PEF) within a microfluidic device in order to monitor DIELECTROPHORESIS AND ELECTROROTATION TECHNIQUE Pag. [START_REF] Koners | Application of Pulsed Electric Field Treatment for sludge reduction on waste water treatment plants[END_REF] in-situ the dielectric properties of a single cell, and its changes during electropermeabilization. Furthermore, we propose to characterize the efficiency of the electropermeabilization protocols for drug delivery by using such approaches.

The cell and its dielectric properties

The cell represents the elementary living unit. From an electrical point of view the cell can be modeled by taking into account the existence or absence of nucleus and organelles within it as well as by considering the presence of a single cell membrane or a cell wall, thus a cell can be classified as:

-prokaryotic cell (no nucleus and with a cell membrane and a wall), generally associated with the multi-shell model for dielectric characterization;

-eukaryotic cell (with the presence of the nucleus and a cell membrane such as for mammalian cells), generally associated to the single-shell model for dielectric characterization. Notwithstanding that cells can be responsible for extremely different functions inside the body, their structure remains universal: a bilayer membrane (surrounded in some cases by a wall), the inner compartment (the cytoplasm with all organelles) and the outer compartment (the external medium).

The cellular membrane is mainly composed of a lipid bilayer where the hydrophilic head is facing the medium due to their hydrophilic properties. The phospholipid molecules confers a very fluid structure to the plasma membrane : in fact, the two layers of phospholipid tails can easily slide onto each other.

DIELECTROPHORESIS AND ELECTROROTATION TECHNIQUE

Pag. [START_REF] Davis | Techno-economic analysis of autotrophic microalgae for fuel production[END_REF] This structure also enables the cellular membrane to carry on an important selective function. Since the two layers of phospholipid tails are hydrophobic, the only substances that can cross the membrane are other hydrophobic substances (such as lipids, steroid hormones and fatty acids) or very small molecules, such as molecules of water. Instead, the hydrophilic substances (ions and polar molecules) cannot pass trhough the phospholipid bilayer of the membrane and are therefore unable to enter into the cell without the intervention of some mechanisms which involve membrane channels. The phospholipids bilayer also contains cholesterol molecules (which affect the membrane rigidity), membrane proteins and glycoproteins. Membrane proteins are divided into two categories: the integral proteins and peripherial proteins.

While the integral proteins are linked to the lipid bilayer and passes sevrsl transmembrane domains.

The peripherial proteins are based on one of the two sides of the membrane and have no connection with the hydrophobic interior of the bilayer.

The cytoplasm is composed of a viscose substance, the cytosol, consisting of water (which represents 75-85% of the total weight of the cell), inorganic substances dissociated into ionic form (especially K + ions, Na + , Ca ++ and Mg ++ ) and different organic molecules (including proteins with enzymatic or structural functions). It contains specific organels such as the nucleus, mitochondria, chloroplasts, the endoplasmic reticulum, the Golgi apparatus, and lysosomes. The nucleus is protected by a porous nuclear membrane. Within the nucleus, the DNA codes all the information necessary for the regulation of cellular activities and for the determination of the characteristics of each single cell.

Indeed, from a biological point of view, the cell is an extremely complex reality regulated by a complicated system where each components perform a specific vital function.

DIELECTROPHORESIS AND ELECTROROTATION TECHNIQUE

Pag. 97

From a first approximation, a biological cell can be electrically modeled as a conductive sphere (representing the averaged content of the cell) surrounded by an insulating membrane. This representation is known as the single shell model (Figure 3.1). Each part of this designed structure behaves as a dielectric material characterized by real conductivity σ and a relative permittivity ε: respectively σ mem and ε mem for the membrane and σ cyt and ε cyt for the cell content and cytoplasm. Typical dielectric values of such a cell modeled with the single-shell model are summarized on the table 3.1, they are referred to a cell with a membrane thickness d=5 nm and a cell radius r= 5µm (strictly depending on the cell line studied):

3.

MONITORING THE PERMEABILIZATION OF A SINGLE CELL IN A MICROFLUIDIC DEVICE WITH A COMBINED DIELECTROPHORESIS AND ELECTROROTATION TECHNIQUE

Pag. 98 Cell cytoplasm 40 -80 0,1 -1

By taking into account the general expression for the complex permittivity of a particle, the complex permittivity of both the membrane and the cytoplasm is defined as follows:

ε mem * = ε 0 ε r,mem -j σ mem ω (3.1)
ε cyt * = ε 0 ε r,cyt -j σ cyt ω (3.2)
where ε 0 represents the permittivity of the vacuum equal to 8,85*10 -12 F/m, ε r is the relative permittivity of the cytoplasm and of the membrane and σ represents their electrical conductivity.

The single-shell model combines all this dielectric properties with geometrical factors in order to define a complex permittivity for the multilayer sphere. Furthermore, in the case of spherical particles the equivalent permittivity ε c * can be expressed as follow

[165]: where R is the radius of the cell and e represents the thickness of the cell membrane (about 5 nm).

ε c * = ε mem * R p R p -e " # $ $ % & ' ' 3 + 2 ε cyt * -ε mem * ε cyt * + 2ε mem * " # $ $ % & ' ' R p R p -e " # $ $ % & ' ' 3 - ε cyt * -ε mem * ε cyt * + 2ε mem * " # $ $ % & ' ' (3.
When an external electric solicitation is applied to the cell, the response of the latter is due to the interaction between the cell itself (and thus its complex permittivity ε c ) and the extracellular medium (characterized by a conductivity σ m and a permittivity ε m ). The Clausius-Mossotti factor f CM summurizes this dielectric interaction.

f CM is a complex number the value of which depends on value depends on the dielectric properties of the external medium, on the polarisable particle and on the shape of the particle; it evolves in respect of the angular frequency of the applied AC electric solicitation.

The Clausius-Mossotti factor is expressed as follow:

f CM = ε p * -ε m * ε p * + 2ε m * (3.4)
where ε * p and ε * m are respectively the complex permittivities of the polarizable particle (the cell) and the medium.

The cell polarization due to electric field application

The exposure of a cell (considered as a dielectric particle) to an electric field leads to its polarization. Under the effect of a non-uniform electric field, an internal reorganization of charges polarizes the cell and confers to it the properties of a dipole. The charge organization depends on the electric field frequency, thus at each range of frequencies the behavior and the effects are different:

3. The resulting medium polarization due to the applied electric field can have several origins and the mechanisms occur at a characteristic time response. Some of them are instantaneous while others need some time after the polarization is achieved to take place. Indeed there are different mechanisms of polarization: the electronic polarization (polarization arising from the displacement of electrons with respect to the nuclei with which they are associated, upon application of an external electric field.), the ionic polarization (referred to the ionic movement due to the applied electric field), the orientation polarization (also known as dipole polarization, arising from the orientation of molecules which have permanent dipole moments arising from an asymmetric charge distribution) and the interfacial polarization (linked to the charges that move within the interface between two material having different dielectric properties).

MONITORING THE PERMEABILIZATION OF A SINGLE CELL IN A MICROFLUIDIC DEVICE WITH

Impedance studies showed that the cell presents three frequency-dependent dispersion or relaxations when the AC solicitation is applied [168]. This dispersion is associated with absorption of energy from the AC by the dielectric body and they are known as dispersion α, β and γ (Figure 3.2).

DIELECTROPHORESIS AND ELECTROROTATION TECHNIQUE

Pag. 101 As it can be remarked from the spectrum, at low frequency the membrane make the cell a perfect insulator and the conductivity is given mostly by the extracellular medium.

When the frequency increases, the conductivity increases as well and simultaneously the permittivity value decrease. The permittivity decrease is associated with the three main dispersion α, β and γ. The highest is the associated frequency, the smaller is the structure responsible for the relaxation.

The α dispersion appears at low frequency (up to 10 4 Hz), it was shown for the first time by Schwann [START_REF] Schwan | Electrical properties of tissues and cell suspensions: mechanisms and models[END_REF]and is due to the insulating behavior of the cell membrane, the dispersion β (occurring between 10 4 and 10 7 Hz) also called Maxwell-Wagner dispersion introduced by Cole [169], is the result of the charging membrane bilayer; the dispersion γ occurs beyond 10 7 Hz and reflects the orientation of all dipoles in the system [START_REF] Jordan | Electroporation and electrofusion in cell biology[END_REF], it is linked to the relaxation of water molecules composing the sample and the media.

The polarization is fundamental to study the behavior of particles subjected to electric fields. An electrically neutral particle, polarized under the effect of a uniform electric field, does not experience a movement, the same occurs when a uniform electric field is

Dielectrophoresis and f CM

Dielectrophoresis is based on the polarizability properties of the cell and external medium and it consists of applying an electric field non-uniform in amplitude.

As it was shown in the section 1.1.1, the dielectrophoretic force is spatially dependent on the electric field gradient and frequentially on the Clausius-Mossotti factor. This factor reflects the difference between the polarizability of the cell and its suspending 3.

MONITORING THE PERMEABILIZATION OF A SINGLE CELL IN A MICROFLUIDIC DEVICE WITH A COMBINED DIELECTROPHORESIS AND ELECTROROTATION TECHNIQUE

Pag. 103 medium at the frequency of the non-uniform electric field applied. Knowledge of the Clausius-Mossotti factor values (positive or negative) is used to determine the direction and magnitude of the dielectrophoretic force acting on a cell:

-If Re(f CM ) >0, the particle is more polarizable than the suspending medium.

Charges are distributed in such a manner that the sum of the Coulomb forces produces a force directed towards the highest electric field. This is the case of positive dielectrophoresis (pDEP).

-If Re(f CM ) <0, the particle dipole moment is directed to the highest electric field region. This is the case of negative dielecrophoresis (nDEP).

The analysis of the Clausius-Mossotti factor sign and thus of the dielectric properties of the cell can predict the effects of the electric solicitation (Figure 3.3).

Electrical and geometrical parameters of the cell directly influence the

Clausius_Mossotti factor as shown in the following spectra (Figure 3.4). Table 3.2

summarizes the values used for the calculations, for each DEP curve the parameter under investigation was changed as shown in legend and the other parameters were kept fixed. At low frequency the interaction between the cell and the applied electric solicitation is mostly characterized by the cell membrane, thus at the simulated conditions, the first 3.

MONITORING THE PERMEABILIZATION OF A SINGLE CELL IN A MICROFLUIDIC DEVICE WITH

Traveling Wave Dielectrophoresis and f CM

The traveling wave dielectrophoresis is proportional to the Im(f CM ) as well as to the non uniform phase of the applied electric field. This force carries the cell in the direction of the wave propagation (or in the opposite direction) depending on the sign of the imaginary part of the Clausius-Mossotti. For example, when the latter is positive, the particles are attracted to the lower phase (they thus move from electrodes with phase DIELECTROPHORESIS AND ELECTROROTATION TECHNIQUE Pag. 106 90° to the electrodes with phase 0°, direction called "co-field TW") and if the sign is negative, the movement is towards the highest phase ("anti-field TW") [171].

1.12.3 Electrorotation and f CM When the electrodes disposition is along a line and thus the travelling wave is linear, the field induces a translational movement of the particle (TWD discussed in the previous paragraph). In the case where the electric field is rotating, the particle experiences a rotational movement as the induced dipole m tries to align with the rotational applied electric field E (Section 1.1.3).

The electrorotation, as well as the TWD, is proportional to the imaginary part of the Clausius-Mossotti factor and the rotational direction of the cell depends on its sign.

When Im(f CM )>0 the cell rotates in the opposite direction of the field, otherwise the rotation of both the field and the cell follow the same direction.

The electrorotation spectrum is sensitive to the dielectric properties of the cell and it changes depending on the value of the permittivity and the conductivity of the cytoplasm and of the membrane and in respect with the radius and the extracellular medium as shown in Figure 3.5. For each ROT curve the parameter under investigation was changed as shown in legend and the other parameters were kept fixed (see Table 3.2).

Pag. 107 3.

MONITORING THE PERMEABILIZATION OF A SINGLE CELL IN A MICROFLUIDIC DEVICE WITH A COMBINED DIELECTROPHORESIS AND ELECTROROTATION TECHNIQUE

Pag. 108

As past literature has demonstrated [START_REF] Goater | Electrorotation and dielectrophoresis[END_REF][START_REF] Arnold | Electro-rotation: development of a technique for dielectric measurements on individual cells and particles[END_REF], the first pic of the curve is related to the membrane properties while the positive pic is mainly due to the characteristic of the cytoplasm. This dependency is quite remarkable from the As a consequence of the pore creation, the DEP crossover frequency shifts towards high frequencies, that means that the frequency at which the cell expresses pDEP is higher compared to normal conditions [148]. This is explained as a change in the membrane permittivity that slightly decreases after PEF delivery. Furthermore, this result is in consistent with the simulation previously shown in Figure 3.4 regarding the influence of the ε mem on the DEP curve.

3.

MONITORING THE PERMEABILIZATION OF A SINGLE CELL IN A MICROFLUIDIC DEVICE WITH A COMBINED DIELECTROPHORESIS AND ELECTROROTATION TECHNIQUE

Pag. 110

Material and method : Combination of electric solicitations for cell manipulation.

As previously reported, the electrorotation and conventional dielectrophoresis are linked to the imaginary part and the real part of Clausius Mossotti factor respectively and they can be experienced by the cell simultaneously.

We investigated the combination of three types of electrical solicitation (DEP, electrorotation, PEF) within a microfluidic device, in order to monitor and analyze the electro-physiological properties of two different cell lines (human leukemic T cell lymphoblast and murine melanoma cell B16F10) submitted to a pulsed electric field.

The cell is trapped and isolated thanks to a negative DEP force (nDEP), and electrically characterized by electrorotation experiments before and after treatment by PEF.

1.13.1 The design of the electrodes structure.

The proposed biodevice should firstly achieve the cell trapping by DEP, then induce the rotational movement by superimposing ROT and finally apply the PEF to permeabilize the cell membrane. Several possible designs for the electrodes were investigated in order to fulfill the desired functions with optimal performances.

Finite element simulations COMSOL TM Multiphysics 3.5(COMSOL Inc., Newton, MA)

were used to evaluate the electric field mapping within the biodevice, in the area delimited by the four-electrodes set (see figure 3.6c-d).

Pag. 111 Various electrodes' shapes (including squared and parabolic electrodes), with various characteristic dimensions (gap, curvature) were compared (Figure 3.6c).

To compare the performances of the electrode shape in term of homogeneity (Figure 3.6d), we determined the spatial zone where the variation of the EF intensity, compared 3.

MONITORING THE PERMEABILIZATION OF A SINGLE CELL IN A MICROFLUIDIC DEVICE WITH A COMBINED DIELECTROPHORESIS AND ELECTROROTATION TECHNIQUE

Pag. 112

to the EF at the center of the structure is less than 10%. The operation was repeated for all field angles (Figure 3.6d). The field homogeneity is of prime importance when applying electrorotation, as an homogeneous torque is required in the trapping zone in order to estimate the cell electrical parameters from electrorotation experiments. The polynomial electrode showed the best performance in terms of homogeneity for the rotating field amplitude.

In addition, the polynomial electrodes have the advantage of being capable of generating a radial DEP force in the plane (it only depends on the distance from the center of the four-electrode set [START_REF] Kotnik | Sensitivity of transmembrane voltage induced by applied electric fields-a theoretical analysis[END_REF]).

The parabolic electrodes were defined with polynomials derived from Laplace's equations, their edges lying on a circle centered in zero with a radius of A (equation of the equipotentials:

x 2 -y 2 = ± A).
By imposing a potential V 1 and V 2 on adjacent polynomial electrodes, at any point (x, y) of the central area between the four electrodes structure the potential obtained ϕ can be expressed as [START_REF] Frenea | Positioning living cells on a high-density electrode array by negative dielectrophoresis[END_REF]:

φ(x, y) = V i A (x 2 -y 2 ) i = 1, 2 (3.5)
From the latter, and expression of the EF along the x and y axis and the expression of the EF norm can be deduced as follow:

E x = ∂ϕ ∂x = - V 2 -V 1 A x (3.6) E y = ∂ϕ ∂y = - V 2 -V 1 A y ( 3.7)
DIELECTROPHORESIS AND ELECTROROTATION TECHNIQUE Pag. 113

E = V 2 -V 1 A x 2 + y 2 (3.8)
which indicates that the EF norm is proportional to the distance from the center and at that point its value is zero.

The set of electrodes with polynomial shape was thus chosen for our experiments.

On the proposed device architecture, electrodes are located on the same plane (z=0). In such a configuration, when increasing the amplitude of EF, the cell levitates above the plane of the electrodes until a given position where this force is compensated by the buoyancy force. This phenomenon can be modeled with four punctual charges in place of the electrodes and a spherical harmonic development. The conventional theory of the DEP force, based on the induced dipole, neglects the presence of induced higher-order moments and thus does not predict the levitation of the cell when high electric field strength is applied. In order to take the levitation into account, the system is modeled as composing of four charges placed on the four electrodes acting on the cell modeled as a quadripolar component [174]. The force along the z axis induced on the cell is thus

given by [175]:

F z = -3 f CM Q 2 r 5 πε m d 7 z d 1+ z d " # $ % & ' 2 " # $ $ % & ' ' 6 (3.9)
where f CM is the Clausius-Mossotti factor previously detailed on the section 1.1.1, 2d is the distance between two face to face electrodes, r is the radius of the cell and Q is the equivalent charge on the electrodes.

3.

MONITORING THE PERMEABILIZATION OF A SINGLE CELL IN A MICROFLUIDIC DEVICE WITH A COMBINED DIELECTROPHORESIS AND ELECTROROTATION TECHNIQUE

Pag. 114

Thanks to this levitation, the friction force between the cell and the substrate is advantageously avoided.

1.13.2 The biochip fabrication.

We designed and fabricated an electrorotation microfluidic device composed of 4 parabolic planar electrodes, deposited on a glass substrate, with 75 µm and 150 µm distance between face-to-face electrodes (Figure 3.7). A 20 nm chromium adhesion layer, covered by 150 nm thick gold layer, was sputtered on a quartz substrate. A first photolithography was employed to pattern both layers, the process included the deposition of S1805 Shipley photoresist by spin coating at v=1000 rpm for 30 s, a prebake at 115 °C for 1 min was performed followed by the UV illumination (intensity=16 mW/cm 2 , t=8 s). A developing step was then performed (by using the developer 351 for 1 min), followed by the Au etching with KI (4g KI, 1g I 2 , 40ml H 2 O, t=7 s) and the Cr etching (ChromeEtch18 micro resist technology, t=45 s). The resist was finally removed with acetone (see figure 3.7). The microfluidic level was patterned thanks to a second photolithography: a 30 µm high microfluidic chamber was defined by SU8 thick resist, which deposition was made by SU8 2025 spincoating in 2 steps the first one for 5 at a velocity v 1 =500 rpm and a second for 30 s at a velocity v 2 =3000 rpm.

A soft-baking preceded the UV illumination (intensity=16 mW/cm 2 , t=18 s). The procedure ended with a post-bake exposure, a developing (MicroChem SU8 developer, t=6 min) and hard-baking (T=175 °C, t=2 h). The fluidic chamber was covered by a microscope slide (d=170 µm) for the optical observation and recording of the cell electrorotation.

DIELECTROPHORESIS AND ELECTROROTATION TECHNIQUE

Pag. 115 A single cell was firstly trapped in the center of the four electrodes using negative dielectrophoresis force (nDEP) [START_REF] Gimsa | Analytical description of the transmembrane voltage induced on arbitrarily oriented ellipsoidal and cylindrical cells[END_REF], and then submitted to an electrorotation torque (ROT) induced by a propagative rotating electrical field [START_REF] Neumann | Biophysical considerations of membrane electroporation[END_REF]. Pulsed Electric Field (PEF) was superposed to induce the electropermeabilization effect (Figure 3.8a). These three field solicitations were applied simultaneously thanks to homemade external electronics (composed by summing amplifiers, Figure 3.8.b label 4) Movement of cells, observed under a microscope, were acquired with an ultra-fast camera and finally digitalized (Figure 3.8a label 5). From the analysis of images sequence, the rotational velocity versus frequency was calculated. Two electrorotation spectra related to cell characteristic both before pulse application (BP) and after pulses application (AP) were acquired and analyzed. The changing of the electrical parameters, induced by the PEF application, was monitored thanks to the use of the fitting algorithm between the experimental and theoretical spectra.

DIELECTROPHORESIS AND ELECTROROTATION TECHNIQUE

Pag. 118

Nevertheless, the rotational velocity of the cell driven by the electrorotation torque is non-linearly dependent on the dielectric properties of the cell. As a matter of consequence, the function to be minimized, that characterizes the distance between experimental and theoretical spectra, is highly non-linear and may present several local minima.

Gauss-Newton algorithms, and in particular trust-region-reflective algorithm provide a solution for solving such non-linear criteria to be minimized. In our case, the least nonlinear squares algorithm included in Matlab software © (Mathworks, Natick, MA)

was used and adapted to our problem. Trust region algorithms were chosen because they are reliable and robust, as they can be applied to ill-conditioned problems [176].

The trust region approach is based on the approximation of the studied function f by a model q, in a neighborhood N (the trust region). The approximate model q is minimized within N, playing with the parameters. Whether these parameters minimize or do not minimize f, the trust-region is widened or shrunk.

The non linear cost function to be minimized in our problem is

∑ = Ω - = n i p p z p f 1 2 ) , ( min arg ) , ( ω ω (3.14)
where Ω(ω,p) is the estimated angular velocity as expressed in the equation 1.18 (section 1.1.3), z is the measured rotational velocity of the cell, p represents the parameters to be estimated (real conductivity and real permittivity of the cytoplasm and of the membrane). n represents the number of iterations used for the convergence.

The algorithm was initialized using initial values taken from literature [164]. Details about the estimation program is available in the ANNEX A.

DIELECTROPHORESIS AND ELECTROROTATION TECHNIQUE

Pag. 119

The Thermal effect

As mentioned in section 1.1.4, thermal effects are a consequence of the EF application thus they need to be taken into account in order to know the temperature increase during the experimental session.

The system employed for the single cell study is composed by a biochip (detail of the fabrication process are given in section 3.3.3) where the SU8 channel is confined on the upper part by a glass slide (see Figure 3.9). When the voltage is applied to the electrodes, Joule heating effects occur in the conductive media and a consequently heat transfer takes place; this heat is evacuated from the device through conduction and convection. The volume of conductive media submitted to the electric field (in our case red area in Figure 3.10a) is considered as the 3. In this volume of investigation we calculate Joule losses P j :

MONITORING THE PERMEABILIZATION OF A SINGLE CELL IN A MICROFLUIDIC DEVICE WITH

P J = σ m E eff 2 V (3.10)
where σ m is the conductivity of the sample (here 0.1 S/m), E is the value of the applied electric field and V is the volume of medium submitted to the electrical field. The total value of the EF is calculated by taking into account the contribution of the electrorotation and the dielectrophoresis, the latter is directly proportional to the Pag. 121 distance from the center (where it's value is hypothetically zero) as explained in the section 3.3.2.

A thermal resistance R cond,top given by the conduction between the volume of interest and the cover glass interface and a thermal resistance R conv,top given by the convection phenomenon that take place in the exchange between the cover glass interface and the external environment. Symmetrically R conv,bottom and R cond,bottom can be defined to model the heating exchange along the glass substrate.

The whole system is thus modeled as in Figure 3.11 where the heating is dispersed by a total thermal resistance R therm,tot , which is the result of the four contributions R cond,top , R conv,top , R cond,bottom and R conv,bottom . The thermal resistances due to conduction transfer and to the convection exchange are calculated as follow:

3.

MONITORING THE PERMEABILIZATION OF A SINGLE CELL IN A MICROFLUIDIC DEVICE WITH A COMBINED DIELECTROPHORESIS AND ELECTROROTATION TECHNIQUE

Pag. 122

R cond = 1 λ l S cond (3.11) R conv = 1 h ⋅ S conv (3.12)
where λ is defined as the thermal conductivity (equal to 1 [W/m K] for glass), S cond is the surface of exchange between the heating source and the cover glass, h is the heat transfer coefficient equal to 10 [W/m 3 K] and S conv is the surface of exchange between the cover glass and the external environment.

The heat dissipation is not homogeneous along the cover glass and along the glass substrate since it follows a radial direction. From the total angle θ (see Figure 3.12), the cover glass was discretized into small portions with a constant angle aperture θ/7; in the same way the glass substrate was also discretized. For each portion we calculate the contribution to the whole defined thermal resistances R cond,top , R conv,top , R cond,bottom and R conv,bottom .

Figure 3.12: Discretization of the cover glass for the thermal resistance calculation.

Pag. 123

Starting from all these considerations, the temperature elevation can be evaluated as:

ΔT = R therm,tot ⋅ P J (3.13)
By taking into account the ability of the system to dissipate the heat through the biochip materials, an increase of temperature of 1.2 K was obtained, which can be acceptable for the study performed.

The temperature profile along the surface of the cover glass highlights the presence of a dissipation gradient; nevertheless a preferential dissipation direction is identified in the portion of cover glass above the volume of interest and a secondary path for heating exchanges appears along the material when distances from the center of the cover glass.

The result obtained from our approximation (Figure 3 3.

MONITORING THE PERMEABILIZATION OF A SINGLE CELL IN A MICROFLUIDIC DEVICE WITH A COMBINED DIELECTROPHORESIS AND ELECTROROTATION TECHNIQUE

Pag. 124

The evaluation of the thermal effect needs to be validated by more precise methods, indeed a temperature topography could be mapped by using a staining fluorescent dye as shown in the literature [177].

The permeabilization analysis with the combined DEP and ROT techniques.

The presented microfluidic device, combining DEP and ROT to monitor the permeabilization induced by PEF application, was used to carry on experiments with two different cell lines: Jurkat E 6.1 and B16F10.

Jurkat cells (human leukemic T cell lymphoblast) were cultured in RPMI 1640

Medium, supplemented with 10% fetal bovine serum and 1 % penicillin/streptomycin while B16F10 cell line (murine melanoma cell) were cultured in DMEM Medium, supplemented with 10% fetal bovine serum and 1 % penicillin/streptomycin. The experimental protocol adopted to prepare the sample was the same for both cell lines. As previously mentioned the single cell was trapped in the center by nDEP, while electrorotation was induced in order to extract the electrophysiological properties from the spectrum acquired before and after the PEF application. Using our fitting methodology (previously discussed in section 3.3.4) between the experimental and theoretical spectra, the values of conductivity and permittivity of the membrane and cytoplasmic compartment were estimated before and then after PEF application. Results obtained for B16F10 and Jurkat cells are shown in table 3.3. This data highlights the changes induced by electropermeabilization on these cell parameters.

The precision of the estimation was qualified using the root mean square error, which showed to converge to a value lower than 0.02 rps.

The trend of the evolution of the membrane and cytoplasm conductivities and permittivity is related to the biophysical phenomena induced by the PEF application. In particular, the cell membrane becomes permeable to small ions, thus inducing the conductivity of the cytoplasm (σ cyt ) to decrease, while inducing the medium conductivity (σ m ) to increase (ions are released from the cells towards the buffer). In addition, as mentioned in previous studies [START_REF] Teissie | Electropermeabilization of cell membranes[END_REF], the electropermeabilization induces an increase of the membrane conductivity σ mem , which is also detected in our experiment, as can be seen in table 3.3. In consequence to the PEF delivered to the cell, a global decrease of the rotational velocity was noticed, all over the electrorotation spectrum (Figure 3.14a-b).

Electropermeabilization induce changes in cell electrical parameters such as complex permittivity of both the membrane and the intra-cellular compartment. As mentioned in the literature [START_REF] Zimmermann | Electric field-mediated fusion and related electrical phenomena[END_REF], water defects are introduced within the membrane during the electropore formation, followed by a reorganization of the phospholipids head. Such water molecules' introduction and bilayer reorganization lead to the increase of the membrane conductivity (σ mem ) [178], and permittivity [173]. The lipid bilayer conductivity is linked to the increasing of both number and size of electropores [172].

The evolution of the imaginary part of f CM (ω), which is dependent on the parameters' evolution after PEF application, is in good accordance with the experimental observations of the rotational velocity of the cell. Indeed, the evolution of the parameters (decrease of σ cyt , increase of σ m , σ mem and ε mem ) induces a decrease of the imaginary part of f CM (ω), that lead to a diminution of the rotational velocity.

PEF application also influences the DEP properties of the cell, as we already mentioned in a previous study [179]. The real part of the Clausius-Mossotti factor is deduced from the estimated electrical parameters: Figure 3.14c-d highlights the fact that when permeabilized, the cells lose progressively their capability to respond to positive dielectrophoretic force (pDEP). For the higher degrees of permeabilization, cells become less polarizable than the surrounding medium, regardless of the frequency of the applied field. Thus, the capability to respond to pDEP (bandwidth corresponding to pDEP in the spectrum) might be an indicator of the degree of permeabilization.

Such a microfluidic platform is very convenient to monitor a single cell: indeed it highlights the increase of its membrane conductivity, and simultaneous decrease of its cytoplasm conductivity after PEF application. The evolution of the permittivity of both membrane and cytoplasm was also monitored, thanks to our parameter estimation method.

This technique combining conventional dielectrophoresis and electrorotation to analyze the evolution of cell dielectric properties might be a relevant method when monitoring the level of electropermeabilization.

DIELECTROPHORESIS AND ELECTROROTATION TECHNIQUE

Pag. 128

Electrorotation experiment to detect cancer progression.

Identification, selection and separation of biological particles from complex sample interrogation are of fundamental importance in the generation of new era cancer diagnostic and treatment.

Cancer includes a large number of tumor diseases, which affect various types of cells and tissues and have different characteristics depending on the affected organ and of the degree of malignancy.

Nevertheless, despite a wide spectrum of tumor disease, its various forms share some characteristics, among which include the proliferative capacity of the cells composing the tumor and their aggressiveness towards the other tissues of the host.

The previously presented method, the rotating electric field through a sample medium can be used to elucidate the phenotypic differences of sequentially staged cancer cells.

These differences can be detected as electro-physiological traits intrinsic to a cell which are both dependent upon structures both on/within the cell.

We describe in this section how the combined ROT and DEP techniques have been used

in the framework of a collaboration to detect minute changes in cancer cells at different stage of the disease.

These experiments were done within the partnership between our group (BIOMIS, ENS Cachan within the IDA, CNRS SATIE) and prof. Rafael V. Nevertheless, since the fitting is made mainly on the experimental points located at low frequency only hypotheses concerning the cytoplasm dielectric evolution can be advanced. Further measurements need to be performed in order to validate our hypothesis.

1.17 Electrorotation as a versatile tool to estimate dielectric properties of multi-scale biological samples.

The study of the rotational velocity as a function of the frequency and the employment of the fitting algorithm, results in the dielectric properties of the biosample.

The microfluidic system described in this chapter provides an efficient tool to analyze and monitor in-situ the dielectric properties of a single cell, and its changes during electropermeabilization.

The dielectric properties of the trapped cell were extracted from the electrorotation spectrum with our dedicated fitting algorithm, which allowed us to characterize the level of permeabilization, in the case of two cell lines (Jurkat cell line and B16F10 cell line), prior and then after the application of pulsed electric field solicitation.

We observed an increase of the membrane conductivity and permittivity after the PEF application due to water molecules introduction into the lipid bilayer as well as to the pore formation. The permeabilization of the cell membrane and consequently its capability to let pass to small ions, also resulted is a decrease of the cytoplasm conductivity.

It has also been shown along the chapter that the electrorotation can be employed to detect minute changes not only between different biological species, but also within the same sample to identify the stage of cancer for instance.

Pag. 132

The work performed during the scientific collaboration at VirginiaTech highlights important changes in the dielectric properties of both cytoplasm and membrane induced by the cancer disease. Although the proximity in health conditions between MOSE-preIV and MOSE-FFL cell lines, the electrorotation is revealed to be extremely sensitive. Indeed when the stage of cancer evolves the membrane become more permeable since its membrane conductivity increases and the internal re-structuration leads to a decrease of cytoplam conductivity.

The next chapter will demonstrate the versatility of the method by showing its efficiency for a different scale sample; electrorotation will be actually employed to monitor the permeabilization of larger size sample such as spheroids. Spheroids represent a promising model for the in vitro cancer investigation since they can combine the accuracy of the in vivo tests with the advantages of the in vitro study, a throrough description of this tumor model will be treated hereafter.

Pag. 133

Chapter 4

The spheroid, a promising "in vitro" model for tumor

analysis: towards the permeabilization study

The study presented in the previous chapter about the single cell permeabilization analysis through the electrorotation technique provides an insight as to how a single cell reacts to PEF application. In this chapter, we extend the application of this method to multicellular organization.

In and so the process that normally takes place in "natural" conditions is altered. Indeed, a relationship exists between cancer and its host given its internal development. This relationship is not present in a simulated injection into a patient who has a fully Adopting them as a model in the study of the effects of antitumor drugs [190,191] shows their pertinence and their relevance for assessing the efficiency of molecules [192].

Some groups culture spheroids taken directly from the patient biopsies [193,194] ,

which is a very promising alternative to treatments, as the model can in fact be used in clinical practice to select customized medication and treatments for each patient.

In this context, the multicellular spheroid is revealed to be an advantageous tool in the study of the complex reaction of the biological tissue when PEF are applied [195]. More than a mere aggregate of cells, spheroids are a complex cell matrix where each Pag. 135 component (the cells) has a specific function for the whole structure growth, and where cells communicate amongst themselves through a specific vascularized biological tissue. Due to their heterogenic structure, they can represent a potential bridge to cover the gap between human studies and animal testing [196,197].

The multicellular spheroid.

The multicellular spheroids appeared in science in 1970, initially described by Sutherland et al. [198]. They were presented as a system of cells placed in a 3D space The presence of extracellular matrix and the complex composition of the spheroid (different levels with cells at different states) creates a microenvironment, the response of which is different from that obtained with cells cultured in a conventional manner (2D) [201]. Indeed, most cell types, when cultured in 3D, secrete components that lead to the formation of an extracellular matrix, advantageous to the biological investigation [202][203][204].

Several known cancer cells can be treated in order to obtain spheroids [204][205][206].

Furthermore, it is also possible to cultivate different cell lines and create a heterogeneous cellular microenvironment, which better reflects reality [207,208]. One of the limits presented by the spheroid is that they are not always able to reproduce the tumor microenvironment, which implies the presence of non-tumor cells and stroma [209].

Even if the 3D multicellular culture is more physiologically relevant than the 2D cellbased models it presents some limits and can fail when reproducing real tissue responses:

-The experimental medium represents a disadvantage of the cell culture system (its conductivity is usually low to avoid Joule heating) and it can in fact modify the effects of certain drugs and fail to mimic the system under investigation.

-Even when the 3D cell culture is developed starting from a patient's biopsy, the latter may not be representative of the whole tumor and thus cannot fully predict its response.

-The experimental microenvironment never replaces the original physiologic conditions and thus some aspects can be missed (the immune response contribution for instance).

-It is impossible to perfectly reproduce the drug dose and duration of exposure since the sample size is much smaller than the real tumor's volume.

-In consequence, the evaluation of the clinical utility of the test can be difficult

Spheroid: a model for electropermeabilization

Nowadays, despite some difficulties linked to the limit of the 3D cell culture, the spheroids represent a promising model for in vivo tumors. For instance, multicellular spheroids can be used during the permeabilization process in order to study the effect of electrochemiotherapy treatment; the efficiency of the permeabilization was tested from Gibot et al.

[111] by using the PI penetration.

As complex structure compare to the single cell, the spheroid requires specific PEF conditions in order to be permeabilized. Hereafter we reported some results derived from the literature regarding the effects of PEF on the level of permeabilization of the spheroid and on its morphology [111].

The permeability of the spheroid after the application of PEF was visualized after labeling the cells with propidium iodide (PI). Images were studied 30 minutes after the application of PEF a duration which normally allows the plasma membrane to recover its integrity [START_REF] Teissie | Mechanisms of cell membrane electropermeabilization: a minireview of our present (lack of?) knowledge[END_REF] and which depends on the electrical parameters used and the set temperature. By extending the results obtained from isolated cells to spheroids; one can suggest that the cells in which the PI is detected after this time are permeabilized irreversibly, thereafter dying from electroporation.

In order to have a complete overview of the phenomenon, the electropermeabilization of The study performed on the multicellular spheroid cohesion from L. Gibot et al. [111] also highlights the changes in the morphology due to PEF application.

The study highlights that the outer cell layer of the spheroid does not appear homogeneously positive to the PI, unlabeled areas are noticeable and many positive cells are present in the medium around the spheroid. This is due to the fact that dead cells are detached from the spheroid during the manipulations following the effect of PEF.

Furthermore, it has to be noticed that, in the case of mixed spheroids i. The effect of PEF on spheroid does not apparently change the macroscopic structure of the sample nor does it preserve its margins. The case of PEF combined with the insertion of antitumor drugs highlights a different response; in this case the edge of the spheroid actually appears damaged and small aggregates of cells start to dissociate from the periphery of the spheroid depending on the drug employed (bleomycin, cisplatin or doxorubicin).

This study demonstrates that the injection of tumor drugs has a drastic effect on the spheroid structure, and thus eventually on the tumor structure, when PEF are applied. The permeabilization of a single cell occurs above the threshold of [300-400] V/cm when almost 30% of cells in suspension are successfully permeabilized. The amount of PI penetrating inside the cells increases significantly beyond 500 V/cm until a permeabilization effectiveness of 80%.

Pag. 142

Spheroids are revealed to have a permeabilization threshold lower than the single cell;

indeed, already at 200 V/cm a remarkable permeabilization percentage is recorded. The highest percentage of permeabilizion in spheroid is obtained for field amplitude between 300 V/cm and 400 V/cm. This percentage actually decreases and reaches a plateau above 500 V/cm. This upper limit in the permeabilization percentage is a clear sign of the difficulty in permeabilizing the inner shell of the spheroid, whichever EF is applied. One reason can be found in the spheroid structure : cell-cell contact strongly affects the shape of the cells composing the spheroid, therefore the EF inside the spheroid can be modified by such complex structures if its permeabilization effectiveness is compromised [146].

Notable differences are also observed on the viability, indeed single cell survival is slightly affected at 400 V/cm and it drastically collapses above 500 V/cm, while spheroids show a better recovery capability even when a high electric field is applied.

When the cell viability is strongly compromised (500 V/cm), the spheroids only show a stop growth for the first 2 days and then they return to grow normally. Furthermore, when field strength of 800 V/cm is induced, spheroids show a loss of cells from the outer layer by a consequent decrease in size, but after 6 days they return to their normal growth rate.

Material and method : Study of spheroid's permeabilization through the combined DEP and ROT technique

The multicellular spheroid can be used to optimize the in vivo technique. It has been shown that PEF applied to the spheroid induce a change in the outer layer and, if the EF strength is high enough, cause the permeabilization of the whole sample.

In the case of the single cell, as with multicellular spheroids, electrical parameters changing thanks to electrical solicitations provide a method of obtaining the fingerprint Pag. 143

of the spheroid state. The knowledge of dielectric parameters' evolution with respect to PEF application is necessary to optimize cancer treatment and obtain customized therapies.

The estimation of the dielctric properties of the spheroid has been performed by using the same method presented in the section 3.3 for the dielectric characterization of single cells. The estimation of the electric properties has been obtained by implementing the fitting algorithm shown in section 3.4. Indeed, as the spheroid is assimilated to a spheric shaped object, it can be studied through the Clausius-Mossotti factor f CM . The thorny aspect is represented by the heterogeneity of the 3D spheroid structure and consequently by the definition of the complex permittivity of the whole object ε * object .

The spheroid modeling

The electric model of the spheroid is difficult to establish as such cell assembly is three Different electric model have been tested in order to find the one that properly reflects the behavior of the sample undergoing electric solicitations.

-Homogeneous particle model Our first approach is to investigate how efficient the simple model, where the spheroid is considered as an homogenous particle characterized by a complex permittivity ε p * and surrounded by the buffer with a permittivity ε m and conductivity σ m . If we take into account the contribution of the spheroid's outer shell, this model could represent an approximation at low frequency.

Pag. 144

Such a particle is modeled as follow:

ε p * = ε 0 ε shell -j σ ω shell " # $ % & ' R e (4.1)
where ε shell is the permittivity of such homogeneous particle, σ shell is its conductivity, R is the radius (60 µm) and e is the shell thickness (9 nm). main limits: it does not take into account the heterogeneity gradient of the spheroid which is a peculiar structural characteristic of the sample, and for high frequency, it does not demonstrate the presence of the inner compartment that subsequently cannot be electrically characterized.

-Single shell model A model more complex than the one just described is represented by the single shell model (previously showed on the Section 3.1 and 3.4.1) where the sample is considered as composed of two main compartments: the outer shell of a given thickness (characterized by permittivity ε r,out and conductivity σ r,out ), an inner compartment also characterized by a given complex permittivity ε in * , everything submerged into a buffer which has its proper permittivity ε m and conductivity σ m .

The particle is modeled as follow:

ε p * = ε out * R p R p -e " # $ $ % & ' ' 3 + 2 ε in * -ε out * ε in * + 2ε out * " # $ % & ' R p R p -e " # $ $ % & ' ' 3 - ε in * -ε out * ε in * + 2ε out * " # $ % & ' (4.2)
where

ε out * = ε 0 ε r,out -j σ out ω (4.3) ε in * = ε 0 ε r,in -j σ in ω (4.4)
R p represents the radius of the spheroid (R p =60 µm) and e is the thickness of the outer layer (e=9 nm).

Pag. 146

As can be remarked from the Figure 4.5, the single-shell model looks more appropriate than the previous model since it is able to make an estimation for both low and high frequencies. The complex permittivity of the inner and outer compartment thus becomes:

Pag. 148

ε in * = ε 0 ε r,in -j σ in (ω) α (4.5) ε out * = ε 0 ε r,out -j σ out (ω) β (4.6)
where ε 0 represents the permittivity of the vacuum equal to 8,85*10 -12 F/m, ε r,in and , ε r,out are respectively the relative permittivities of the inner compartment and of the outer shell and σ in and σ out represents their electrical conductivities.

The factors α and β can vary across the range [0,1] indicating respectively the lowest and higher degree of homogeneity.

The Clausius-Mossotti factor f CM defines the interaction between the spheroid itself (characterized by a complex permittivity ε p * ) and the extracellular medium (characterized by a complex permittivity ε m * ) due to an external electric solicitation:

f CM = ε p * -ε m * ε p * + 2ε m * (4.7)

The multicellular spheroid preparation

The spheroid preparation was made by Dr. Emilie Bayart from the department of The cells were collected by centrifugation and resuspended in an isotonic medium (σ m =0.1 S/m) prepared for the electrorotation experiments.

4.4.1_The spheroid dielectric proeprties estimation

When a spheroid is submitted to an electric field, it polarizes and experiences a force which leads to its rotation [START_REF] Khoshmanesh | Dielectrophoretic platforms for bio-microfluidic systems[END_REF].

The spheroid was first captured in the center of the biochip structure by using the DEP force and then a rotational movement was induced thanks to the ROT solicitation. The analysis of the first results obtained with the spheroid shows the predominant insulating behaviour of the outer cell layer of the cell assembly (negative peak of the velocity at low frequencies). A fitting within this low frequency region between the negative velocity peak and the modified single shell model leads to the permitivitty and conductivity of the outer shell and inner shell respectively, as provided in the table 4.1:

1.22

The spheroid for permeabilization study.

To study how the electropermeabilization affected the dielectric prameters of the spheroid, the latter was subjected to a train of 10 PEF with 3kV/cm amplitude and 100 µs, delivered with a frequency of 1Hz. Once the permeabilization was achieved, the ROT was applied in order to record the changes in dielectric properties. The cells located on the external layer are subjected to a higher degree of permeabilization and show changes in conductivity of the outer shell comparable to those observed during the single cell permeabilization experiments. As was noticed during the single cell study, after permeabilization the conductivity and the permittivity of the outer layer increases due to water molecules that are introduced within the cell matrix. Due to PEF application, the interspace between cells composing the spheroid is damaged and the emergence of gaps between the cells occurs. Some cells separate from the structure as previously reported [111] and the interspace that is created is filled by the medium that normally surrounds the spheroid. We advance the hypothesis that the insertion of this medium into the matrix can be considered as a possible contribution to the consequent inner conductivity enhancement.

The homogeneity of the inner compartment is barely influenced by the PEF application, and as such, we hypothesize that in our experimental conditions, the inner compartment is barely affected and its structure does not show remarkable changes. Different is the case of the outer compartment, which is strongly affected by the PEF application, as important damages occur at the external layer. A slight increase of the homogeneity factor β is estimated. Nevertheless, the spheroid preserves it heterogenic character.

Pag. 153

Further investigation of a more realistic model, possibly corresponding with the observations of this experiment, yet taking into account the complexity and heterogeneity of the spheroid, is desirable.

Conclusion

In this chapter we applied the electrorotation to determine the fingerprint of the 3D cellular model.

The 3D multicellular spheroid can be assimilated to a spherical shaped object and thus can be studied through the Clausiu-Mossotti factor f CM . We have shown that the combined DEP and ROT technique can be applied to characterize, from a dielectric point of view, the multicellular spheroid. Furthermore, the evolution of dielectric properties after PEF application can be investigated in the same manner. The detection of small changes in the complex permittivity of both the inner and the outer compartments shows the relevance of the method and its sensitivity. When the permeabilization occurs, the permittivity and the conductivities of both the inner and outer compartments evolve. In the destruction of the outer shell structure, "electropaths" are constructed through the outer compartment, as a consequence small molecules getting inside the inner compartment by passing through the outer shell gaps.

The conductivity and the permittivity of the outer layer increase. No remarkable effects are noticed on the parameters modeling the homogeneity of the inner compartment, which is most likely due to the fact that the level of permeabilization achieved is not enough to compromise the inner structure.

Conclusion and perspectives

Electric field is commonly used to interact with living cells, therefore AC electrokinetic phenomena such as dielectrophoresis, travelling wave dielectrophoresis and electrorotation are quickly becoming popular manipulation tools for lab-on-chip and microfluidic devices.

In addition, pulsed electric fields (PEF) are applied to provoke cell membrane permeabilization, which is a technique that temporarily increases the capability of a First, the monitoring of the bioimpedance of a cell tissue is presented as a method to determine the efficiency of its electropermeabilization with respect to different PEF characteristics. Such analysis might be the key to dynamically determine the appropriate electrical conditions to achieve the desired degree of tissue permeabilization without causing unrecoverable alteration of the tissue.

We demonstrated how pulse characteristics, such as rising time and falling time, -The viability of the cells, once submitted to all these field sollicitations (DEP, ROT, PEFs) should be confirmed more systematically, in order to characterize the side-effects of those treatments. To do so, the biosample recovering should be included in the design (in flow electroporation).

-The so called "co-culture" of spheroid from different cell lines should be used in order to mimic the tumor microenvironment or presence of the immune system.

The production of bigger size spheroids (order of centimeter) could represent a way to better simulate the tumor behavior and to optimized the system to deliver PEF. A additional study of the biochip design needs to be faced in order to keep favorable electric topography distribution, as well as the use a higher level models, taking into account the successive concentric layers. Bio-impedance could be a way to dynamically monitor dielectric properties of large spheroids, and an increase of the frequency range (up to GHz) should give access of its internal organization. En particulier nous essayons d'obtenir une signature électrique, sur une large bande de fréquence, de l'évolution en temps réel des propriétés de systèmes biologiques (tissus/cellules/systèmes membranaires), en réponse à des stimuli électriques. Ce travail de thèse a débouché sur l'établissement de modèles analytiques électriques macroscopiques; cependant une approche microscopique a été également abordée. Les expériences effectuées sur des biopuces microfluidiques appareillées de réseaux d'électrodes ont permis de confronter les modèles à la réalité physique et biologique, les microsystèmes employés offrent les avantages de la miniaturisation et permettent de travailler au niveau de la cellule unique, appliquant des champs électriques de forte amplitude, de forte fréquence, localisés spatialement.

Title : Study of cell membrane permeabilization induced by pulsed electric field -electrical modelling and characterization on biochip.

Keywords : cell membrane permeabilization, pulsed electric field, cell modelling, microfluidics biochip

Abstract : The use of the electric field to interact with cells provides promising tools for new cancer treatments: electrochemotherapy, gene therapy, immunotherapy. The application of electrical pulses to cells or cell tissues induces a change on their properties, in particular on their membrane, which becomes permeabilized. This phenomenon temporarily increases the capability of cell membranes to be passed from ions and macromolecules. These phenomena are not fully understood by the scientific community, so the purpose of my thesis is to contribute to model and characterize the biophysical phenomena occurring during the application of electric pulses.

In particular we investigate, on a wide frequency band, dielectric properties changes induced on biological systems (tissue/cell/membrane) in response to electrical solicitations. We investigate the dynamics of electropermeabilization at the macroscopic level (cell tissues) through electrical analytical models; however, a microscopic approach is also discussed. Experiments on microfluidic biochip are used to explain, the physical and biological phenomena occurring during permeabilization. The use of miniaturized devices (microsystems) for single cell investigation offers the advantages of applying electric fields with high amplitude, high frequency, spatially localized.

Figure 1 . 1 :

 11 Figure 1.1: (a) A particle with a charged surface submerged into a buffer is surrounded by a layer composed by ions (b) the particle surrounded by a charge cloud just described (c-d) Under the effect of the electric field, the charges of the external layer are redistributed and the cloud is conseuqently deformed [8].

Figure 1 . 2 .

 12 Figure 1.2. (a) A spatial variation of the amplitude confers the nonuniformity to the eleectric field, case of c-DEP [17]. (b) Plot of the Re[f CM (ω)] with respect to frequency of the applied electric field and crossover frequencies.

Figure 1 . 4 :

 14 Figure 1.4: Electrodes geometry and signals phase shifted in order to apply electrorotation solicitation.

Figure 1 . 5 .

 15 Figure 1.5. (a) Electrode arrangement for rotating field induction. (b) Theoretical electrorotation spectrum.

  elecrodes acquire a charge corresponding to the sign of the applied voltage and thus the Pag. 24 ions present in the solution form a charged double layer at the interface electrodeselectrolyte. The electric field generated by the electrodes presents two component, a normal components E n and a tangent component E t parallel to the electrodes (Figure 1.6).

Figure 1 . 6 :

 16 Figure 1.6: Induced movement of the charged double layer due to the tangent components of the electric field applied [37].

Figure 1 . 7 :

 17 Figure 1.7: Fluid path due to electro-osmotic effect [38].

Figure 1 . 8 :

 18 Figure 1.8: Map of the electro-osmotic effect and electro-thermal effect as function of the conductivity ofthe medium and the frequency of the applied electric field[START_REF] Morgan | AC electrokinetics: colloids and nanoparticles[END_REF]

Pag. 28 of

 28 molecules and chemical species; it regulates what can enter into the cell and what should exit from it.

Figure 1 . 9 :

 19 Figure 1.9: (a) Cell membrane composition. (b) Single phospholipid representation [https://www.blendspace.com/lessons/F5UuH0JQSWpvLA/membrane-biol-e-trasporti].

Figure 1 . 10 :

 110 Figure 1.10: Changes in cell membrane phospholipid bilayer structure and organization before and after pulsed electric field application.

Figure 1 . 11 :

 111 Figure 1.11: Eelectric field applied on a particle of a radius r. red arrows represent the resting potential (ΔΨ 0 ) and black arrows the induced transmembrane potential (ΔΨ i ) [50].

Figure 1 . 13 :

 113 Figure 1.13: Different effects obtained when applying PEF to a cell. Reversible electropermeabilization, irreversible electropermeabilization and thermal damage as a function of electric field strength and exposure duration [77].

Figure 1 . 15 :

 115 Figure 1.15: Influence of delivering frequency of pulses on the degree of permeabilization P. Biological tissue was exposed to a train of monophasic pulses applied to (a) a space-champed membrane, total duration of train 20 ms and (b) a spherical cell, total duration of train 10 µs [82].

Figure 1 .

 1 16 shows the sugar beet treated and untreated with the KEA process and the respective extraction obtained by cold pressing at 32 bar for 15 min. The droplets that are clearly visible at the surface of the treated beet show how the PEF application is able to break the membrane by allowing the leakage of substances.

Figure 1 . 16 :

 116 Figure 1.16: Cut through sugar beets before and after treatment in the reaction chamber together with the corresponding yield of juice obtained by cold pressing with 32 bar pressure for 15 minutes.

Figure1. 18 :

 18 Figure1.18: Cumulative total soluble solids (TTS) and energy input during a 2 month trial. PEF processing od 200 l of sludge at 5l/hour, 15kV/cm and 35°. Retention time of 14 days (adapted from Toepfl 2006)[START_REF] Koners | Application of Pulsed Electric Field Treatment for sludge reduction on waste water treatment plants[END_REF]

Figure 1 .

 1 Figure 1.19: (a) Lipid extraction efficiency for control sample, sample after heating treatment and sample after PEF treatment. (b) Lipid profile for control sample, sample after heating treatment and sample afterPEF treatment[START_REF] Zbinden | Pulsed electric field (PEF) as an intensification pretreatment for greener solvent lipid extraction from microalgae[END_REF]

(

  anti-cancer agent by induction of DNA breaks) was combined with electrical pulses. The combination of the ant-cancer agent and electroporation was sucessfully applied to an animal [102] and clinical tests were performed [103]. In 2006, the protocols were standardized and dedicated generators were commercialized on the market (CliniporateurTM)[104]. Nowadays, over 100 clinical centres efficiently perform electrochemotherapy treatments.

  cause a risk to the patient [105, 106]. Furthermore is reported the first successful clinical test in Phase I gene electrotransfer on cancer patients [107]. The first experience Pag. 53 of DNA electrotransfer was reported in 1982 when electric pulses in the intensity range of 5-10 kV/cm with a duration of 5-10 µs were applied in order to increase the uptake of DNA into cells [100]. Despite its use in medicine, the mechanism of gene transfer is not fully understood, the process is actually more complex that simple diffusion of DNA through the electropores formed by electric field pulses, a representation of the most important steps are shown in figure 1.20.

Figure 1 . 20 :

 120 Figure 1.20: Steps involved in gene electrotransfer. The mechanism underlying transfer of DNA across the permeabilized membrane is still unclear. Dy referring to Figure 1.20: A.(Before PEF application) the DNA is labeled with a fluorescent marker. No natural adsorption of DNA on plasma membrane is observed. B. (During PEF application) (1) plasma membrane is electropermeabilized. (2) DNA undergo electrophoretic migration. (3) DNA aggregates are formed. C. (After PEF application) (4) 30 min after PEF application, DNA translocation into the cytoplasm occurs. (5) DNA molecules migrate into cytoplasm. (6) DNA molecules are presented at the nucleus level 2h after PEF application. (7) 24h after electrotransfection, eGFP expression is detected through fluorescente microscopy [108].

  pulse duration or of the pulses number may lead to extensive or permanent permeabilization of the cell membrane, which eventually provokes the cell death due to ions leakage. The irreversible electropermeabilization associated to minimal thermal Pag. 55 damage is the key of a molecularly selective tissue ablation method known as nonthermal irreversible electroporation (NTIRE) [112]. Irreversible electroporation (IRE) is a promising technique that makes possible treatment of sarcomas by placing minimally invasive electrodes within the region to be treated; furthermore it preserves the extracellular matrix, the vasculature of the tissue and other sensitive structures. Robert E. Nell II et al. [113] showed of the IRE treatment combined with chemiotheraphy, both employed for a canine histiocytic sarcoma resulted in a complete remission 6 months after diagnosis (Figure 1.21). Furthermore it resulted in the improvement of the quality of life of the patient and owner since two weeks after the treatment, the patient was able to perform daily activities such as controlled leash walks and swimming [113].

Figure1. 21 :

 21 Figure1.21: Efficiency of IRE treatment for canine histiocytic sarcoma, complete tumour regression achieved 6 months after initial treatment [113].

  represents a non-thermal technology for clinical and industrial application[START_REF] Mir | Effective treatment of cutaneous and subcutaneous malignant tumours by electrochemotherapy[END_REF][START_REF] Chang | Cell poration and cell fusion using an oscillating electric field[END_REF] 114, 115]. For example it has been shown how the PEF application enhances the effectiveness of the chemotherapeutic drugs since it allow non-permeant molecules to enter into the cell[START_REF] Mir | Effective treatment of cutaneous and subcutaneous malignant tumours by electrochemotherapy[END_REF]. Preclinical trials with mice have shown the great advantage of the local delivery achieved by applying the PEF after the administration of the drug[103, 116]. As just mentioned, the tissue permeabilization represents also a field of interest for industrial application such as food preservation and processing[117].The capability of monitoring in real time physiological changes of the tissue is a way to customize treatments and optimized experimental conditions. Thus several groups investigated tissue permeabilization by using either optical or electrical methods (fluorescence microscopy and bioimpedance spectroscopy respectively). In the case of fluorescence spectroscopy, the idea is to insert into the tissue a dye which emits an optical signal when the permeabilization is successfully Pag. 60 achieved; the tissue is previously treated by PEF and successively stimulated at a characteristic excitation wavelength in order to check if there is an emission signal, in some cases the detection is performed after few days depending on the fluorescence molecule employed. This technique reveals to be efficient and precise, nevertheless a proper experimental platform needs to be set in order to perform the study and, consequently, associated costs are really high. Compare to fluorescence methods, bioimpedance technique is easily implemented (only a set of 2 or 4 electrodes are needed and a low-cost instrumentation) and it has the advantage of monitoring physiological changes in real time. We thus propose to use bioimpedance spectroscopy as an innovative approach to monitor, quantify and analyze changes induced by various characteristics of PEF applied by a simple pair of metal needles inserted in the tissue. The dependence of the tissue model (here the Cole-Cole model) with the level of permeabilization is deeply examined and discussed.

Figure 2 . 1 :

 21 Figure 2.1: Representation in rectangular coordinates of the complex impedance Z.

  Animal tissues mostly get formed during embryonic development from the three germ layers (ectoderm, mesoderm, endoderm). Animal tissues consist of specialized cells organized in an environment were a specific fluid fills the intercellular spaces (extracellular matrix). They are grouped into four main categories: epithelial, connective, nervous, and muscular. The epithelial tissue has a protective function (epithelium); the connective tissue plays a function of connection and support for the other tissues; muscle tissue is constituted by cells called muscle fibers (muscle); the Pag. 64

Figure 2 .

 2 Figure 2.2 (a) Equivalent electric circuit of a cell (b) semplified cell model derived from (a) (c) Electric circuit of a cell where Rm is neglected and Cm* represents Cm/2 [121].

Figure 2 . 3 : 67 1. 7 Electrical model for tissue 2 . 2 . 1

 23677221 Figure 2.3: Current path in a cell suspension at different frequency range (a) At low frequencies the cell is totally isolated by the membrane and the current is not able to penetrate into the cell. (b) The insulating effect of the cell membrane decreases as the frequency increases, and a part of the current is able to flow through the cell. (c) At high frequency the cell membrane is a short-circuit and current pass trough the membrane by reaching the cytoplasm [122]

Figure 2 .

 2 Figure 2.4 shows the electrical circuit scheme used by Fricke and Morse [123] as a tissue model.

Figure 2 . 4 :

 24 Figure 2.4: Fricke model to study the tissue behavior where the extracellular compartment is modeled by a resistance Re, the intracellular compartment is modeled by a resistance Ri and Cm is the capacity of the plasma membrane.

  [128] in his first work in 1928 developed a new electrical circuit to model the tissue; he first defined the impedance of a single cell, and then expanded the work to a suspension of homogeneous bioparticles, which represent the global tissues. The innovation introduced by Cole's is the incorporation in the circuit diagram of an element of constant impedance phase (constant phase element: CPE). The Cole-Cole article in 1941 [129] has provided a fundamental point in the history of research on the electrical properties of tissues and membranes. The Cole-Cole model represents the biological tissue as an equivalent electrical circuit (figure 2.5) with a resistance at low frequency R0, a resistance at high frequency R∞ and a non linear capacitor (CPE: Constant Phase Element) ZCPE= (1/jω) α Cm with 0<α<1 [130, 131]. R0 represents the extra cellular medium, it models the outer compartment at it assumes an important value at low frequency, R∞ is a composition of both intra and extra cellular medium, τ is the characteristic time constant of the tissue τ=[(R0-R∞)*Cm] 1/α ,α is related to the heterogeneity of cell size and on the morphology of the living tissue and it can vary between 0 and 1.

Figure 2 . 5 :

 25 Figure 2.5: Cole-Cole model for the tissue. R0 represents the extra cellular medium, R∞ is a composition of both intra and extra cellular medium, τ is the characteristic time constant of the tissue and α is related to the heterogeneity of cell size and on the morphology of the living tissue.

Figure 2 . 6 :

 26 Figure 2.6: (a) Impedance module and phase through a bode diagram.

Figure 2 . 7 :

 27 Figure 2.7: Nyquist representation of the bioimpedance.

71 1. 8 1 . 8 . 1

 718181 A METHOD TO MONITOR BIOLOGICAL TISSUE PERMEABILIZATION Pag. Material and method : Impedance measurement technique The electrode-tissue interface Bioimpedance measurements require physical contact between the system and the tissue of interest. This contact is an interface between a conductor (electrode of the measurement device) and an ionic conductive medium (biological tissue to investigate). The presence of an electric field at this interface results in the formation of a "double layer" in each medium (Figure 2.8) [135].

Figure 2 . 8 :

 28 Figure 2.8: Interaction between the electrodes and the electrolyte.

  electrophysiological components are estimated. The global electrical model takes into account the presence of the capacitance C DL with two impedances put in serial with the tissue impedance Zbio (Figure 2.9) Pag. 73

Figure 2 . 9 :

 29 Figure 2.9: Cell tissue structure and its electrical model.

75 Figure 2 . 10 :

 75210 Figure 2.10: Electric scheme of the 4-points probes method [140].

Figure 2 .

 2 [START_REF] Çetin | Dielectrophoresis in microfluidics technology[END_REF]) a current generator is connected to the sample and a multimeter detects the fall of voltage across the sample directly from the power cables of the generator. In this case the wires used to power the sample are the same used to detect the voltage drop, thus the voltage value measured in this way is the sum of the voltage drop across the sample and that in the wires.Pag.[START_REF] Rols | Electropermeabilization of mammalian cells to macromolecules: control by pulse duration[END_REF]

Figure 2 . 11 :

 211 Figure 2.11: Electric scheme of the 2-points probes method [140].

Figure 2 . 1 . 8 . 5

 2185 Figure 2.12: (a) The biological sample. (b) the 2-probes point employed for the impedance measurement.

80 1. 9 . 1

 8091 they are not in direct contact, affect each other due to mutual electrical shading [144-146]. Pag. Degree of tissue permeabilization As previously affirmed, the bioimpedance of tissues is often used to characterize the changes induced by the electrical field on tissues [141]. An equivalent electric circuit can model impedance changes in normal conditions and after PEF application. According to the current models (Cole-Cole model [121, 130]) the components are linked to the physical elements of the cell or cell tissue (resistances for the ionic conductions, capacitances for the polarization effects and the charging at the cell membrane, constant phase element to characterize the size dispersion of cells in a circuit [121, 130, 131]). The Cole-Cole model characterizes electrically a biological tissue and highlights some phenomena that induce cellular structure changes. Thus, extraction of Cole-Cole bioimpedance components is a common practice to evaluate physiological and pathological status of a biological tissue [147].

Figure 2 . 13 :

 213 Figure 2.13: Combination of biological and electrochemical effects on impedance spectrum. (a) Module of the bioimpedance. (b) Nyquist diagram of the bioimpedance.

  The application of PEF affects the values of the components of the Cole-Cole bioimpedance model. In that case, the Nyquist diagrams of bioimpedance spectrum (Zbio) before and after PEF application highlight the fact that the electropermeabilization phenomenon affects two main aspects: i) the conductivity of the tissue at very low frequency (the right edge of Nyquist diagram shifts to the left on the real axis, Figure2.13), due to the passage of ions through the cells whose membrane becomes partly permeable[START_REF] Knorr | Impact of high-intensity electric field pulses on plant membrane permeabilization[END_REF][148][149][150] ii) the degree of homogeneity decreases at high frequencies, Fig.2.13b (the curve tilt of the Nyquist diagram).

Figure 2 . 14 :

 214 Figure 2.14: Example of impedance module before and after application of PEF inducing permeabilization

Figure 2 .

 2 Figure 2.16: (a) Example of impedance module before and after application of PEF inducing permeabilization (b) Influence of pulses width on the degree of permeabilization P. Biological tissue was exposed to a train of respectively 50-100-200-500 µs squared unipolar pulses delivered with a frequency of 1 Hz, with an amplitude of 500 V/cm. (c) Influence of amplitude of pulses on the degree of permeabilization P. Biological tissue was exposed to a train of 100 µs squared unipolar pulses delivered with a frequency of 1 Hz, with an amplitude of 350 V/cm, 500 V/cm and 700 V/cm. (d) Influence of the specific energy Q on the degree of permeabilization P , cases of 10-15-20 pulses.

  [154] or the analysis of the frequency response, as developed hereafter. The components of the Cole-Cole model (R0, R∞, τ, α) are estimated thanks to the fitting algorithm. On the basis of those four components, Cm is then deduced from the expression of t. An example of the estimation of Cole-Cole components, from both experimental and model spectra is represented in Figure2.13: the star line corresponds to the measured spectrum of bioimpedance whereas the continuous line represents the estimated spectrum of the bioimpedance (fitting error lower than 1 %); The fitting method permits to isolate the contribution of electrodes polarization.

Figure 2 .

 2 Figure 2.17 shows how the Cole-Cole components (R0, R∞, τ, α) as well as the capacitance Cm evolve with an increasing degree of permeabilization.

Figure 2 . 17 :

 217 Figure 2.17: Estimation of bioimpedance components evolution with respect to degree of permeabilization. Tissue was submitted to a train of [5-10-15] 100 µs squared unipolar pulses delivered at a frequency of 1 Hz, with an amplitude of 500 V/cm. Results are normalized respect to their initial value (before pulses application).

  which limits the temperature rise to only a few degrees[157]. This is strictly true if the heat is easily dissipated. It is therefore advantageous to have devices which are good thermal conductors: such as silicon substrate instead of glass or polymer. Furthermore the scale effect enables to obtain high electric fields value with a power supply voltage of a few volts, indeed for a distance between the two electrodes d = 1cm or d = 100 µm we can reduce the voltage of one thousand and get the same dielectrophoretic force[158].

  proportional to the electrode surface[159]. Therefore, this double layer capacitance creates an additional phenomenon in the measurement by increasing the measurement error[160, 161]. The detection of a single cell bioimpedance spectrum is thus Pag. 92 complicated and it requires a proper biochip structure to avoid contribution due to the interface between electrodes and the sample.

Furthermore the species composed

  by eukaryotic cells are divided into two main categories: unicellular organisms and multicellular organisms where cells are grouped into tissues to form the different organs. The typical diameter size of eukaryotic cells is in the range of ten micrometers.

Figure 3 . 1 :

 31 Figure 3.1: Single shell model for a spherical shape cell.

  frequency the structure of the cell membrane is predominant, the latter actually behaves as a insulator -at high frequency a current starts to flow in the intracellular medium, from an electrical point of view the membrane is considered as a short-circuit. The conductivity increases and becomes representative of both the extra and the intracellular compartment [166]. Internal ions move toward the electrode of opposite polarity; nevertheless they are stopped by the plasma membrane [167]. The same process occurs within the extracellular compartment leading to charge accumulation at the cell / medium interface.

Figure 3 . 2 :

 32 Figure 3.2: Dielectric spectrum of a biological tissue with relaxation mechanisms associated[168]

  applied to a dipole, Coulomb forces acting on the dipole are actually compensated and DIELECTROPHORESIS AND ELECTROROTATION TECHNIQUE Pag. 102 the polarization does not produce net electric force capable of moving the cell (Figure 2). The conditions of polarizability of the particle and non-uniformity of the field are thus both necessary to observe the movement of the cell [170]. Charged particles, subjected to a uniform electric field move towards the electrode of the opposite polarity (Figure 3.3).

Figure 3 . 3 :

 33 Figure 3.3: Effects of a uniform electric field on charged particles and neutral body. Specific case of the electrically neutral bar which aligns with the field.

Figure 3 . 4 :

 34 Figure 3.4: Re[f CM ] dependence on the cell parameters (radius, permittivity and conductivity of both the cytoplasm and the cell membrane) and extracellular medium conductivity.

4 - 10 9 ]

 4109 A COMBINED DIELECTROPHORESIS AND ELECTROROTATION TECHNIQUE Pag. 105DEP crossover frequency is determined by the ε mem acting on the frequency range [10 Hz. When the membrane permittivity increases, the first crossover frequency shifts towards the left; thus a cell with a high ε mem will show pDEP earlier in the frequency range than a cell with a high membrane permittivity. The membrane conductivity σ mem also acts at low frequency ([10 2 -10 6 ]Hz) by slightly influencing the intensity of the nDEP force felt by the cell. As well as the σ mem which determines the DEP force intensity at low frequency, the ε cyt is responsible of the DEP strength at high frequency (beyond 10 9 Hz). According to simulations, the cytoplasm conductivity σ cyt , as well as the medium conductivity σ m , are influencing the DEP curve within all the frequency range, they represent the key parameters for the determination of nDEP or pDEP. Indeed, depending on their value it is possible for the particle to be trapped by the area of EF maxima or EF minima (case of pDEP and nDEP respectively) or to show only nDEP properties. Finally the geometrical parameter r (radius of the cell) responsible of changes in the frequency range [10 4 -10 9 ]Hz, can barely determine the passage between the frequency range where the cell shows nDEP properties and the frequency range where the cell starts to move towards the high EF value (pDEP phenomenon).

Figure 3 . 5 :

 35 Figure 3.5: influence of cell parameters (radius, permittivity and conductivity of both the cytoplasm and the cell membrane) and extracellular medium conductivity on the electrorotation spectrum.

Figure 3 . 5 ,

 35 the changes in the membrane conductivity and permittivity actually modify the curve at low frequency while the changes in the cytoplasm conductivity and permittivity mostly influence the second pic of the curve.The cytoplasm permittivity ε cyt is responsible of the rotational velocity of the cell at high frequency, at that frequency the membrane does not represent a barrier anymore and thus the inner compartment of the cell determines the effects of the applied electric field. The ε cyt appears in a large frequency range of the electrorotation spectrum by modifying the spectrum in terms of highest rotational velocity achieved by the cell. The membrane dielectric properties are fully present at the first pic of the curve, the membrane conductivity σ cmem influences the shape and the negative pic while the membrane permittivity ε cmem causes a shift of the negative pic to the lowest frequency and a consequent shift of the crossover frequency at which the rotational direction is inverted. The cell radius affects the crossover frequency, it induces a shift of the spectrum towards low frequencies. Different is the case of the medium conductivity whose change could totally modify the shape of the curve till a point where no positive pic is detected anymore.A set of measurements placed at relatively low frequency (till 10 7 Hz) can lead to a study of the membrane properties, while a more accurate estimation of the cytoplasm properties can be obtained with measurements covering the high frequency range (beyond 10 8 Hz).The electrorotation is revealed to be more sensitive in respect of parameter changes compare to the dielectrophoresis, small changes of membrane conductivity for instance are more easily detectable from the ROT curve since they provoke a bigger modification of the curve with respect to the Re[f CM (ω)] curve. According to our Pag. 109 simulations, cytoplasm permittivity appears earlier in the ROT curve (slightly before 10 8 Hz) compare the DEP (after 10 9 Hz) and this represents an advantage when taking into account the work frequency limit of commercial waveform generators. Furthermore it turns out to be easier the detection and the consequently calculation of a rotational velocity of the cell (generated by rotating field) than a translation movement of the cell (induced by DEP force). 1.12.4 Pulsed electric field During the application of PEF, an increased permeability of the cell membrane is induced as result of the structural changes of the lipid bilayer. The cell membrane, which is usually considered as a barrier for water-soluble molecules, modifies its organization enabling the entrance of different chemical species into the inner compartment. All these changes in the lipid bilayer structure lead to an evolution of the dielectric parameters and consequently of the Im[f CM ] that thus represents a way to monitor the cell permeabilization [148].Indeed, as a result of the electropores creation, the cell membrane conductivity increases[172]. This change suggests that membrane conductivity is a parameter that can be used, complementary to the others, to monitor the cell permeabilization. As well as σ mem , the conductivity of the cytoplasm σ cyt changes, by decreasesing after PEF application[173].

Figure 3 . 6 :

 36 Figure 3.6: (a) Electrodes arrangement to induce rotating electric field. (b) Theoretical electrorotation spectrum for Jurkat cell line (eukaryotic cell) (c) 2D EF distribution for polynomial electrodes' shape with different field angles (ϕ=0, ϕ=-π/2, ϕ=π/4) and for squared electrodes' shape (d) spatial zone corresponding to 10 % homogeneity of the EF amplitude , compared to the EF at the center of the 4electrodes set. Numerical calculation made for all EF angles

Figure 3 . 7 :

 37 Figure 3.7: Microfabrication process of the biodevice: (a) 20 nm chromium adhesion layer deposited on a quartz substrate, covered by 150 nm thick sputtered gold layer; (b) both layers patterned thanks to conventional photolithography; spin coating with S1805 Shipley photoresist, prebake and UV light exposure; (c) Au etching with KI followed by Cr etching and finally resist removing in acetone; (d) the microfluidic chamber was defined by SU8 thick photoresist; (e) top view of the fabricated microdevice.

Figure 3 . 9 :

 39 Figure 3.9: Heating transfer within the biochip and respective thermal resistances associated.

  A COMBINED DIELECTROPHORESIS AND ELECTROROTATION TECHNIQUE Pag. 120 heating source. A topography of the difference of Temperature ΔT of the heating source is obtained through Comsol® simulation as shown in Figure 3.10b, the temperature map highlights a greater enhance of the temperature in the areas where electrodes are closer, in that areas the electric field strength actually reaches higher values compare to other parts.

Figure 3 .

 3 Figure 3.10: (a) Area of interest used to calculate the heating volume. (b)Temperature topography in the chamber at the electrodes level when applying DEP force.

Figure 3 . 11 :

 311 Figure 3.11: Representation of thermal resistances involved into the heat exchange of the system.

  .13a) is in agreement with the thermal simulation obtained through Comsol® environment (Figure 3.13b), which shows the decrease of Temperature while distancing from the center.

Figure 3 .

 3 Figure 3.13: (a) T profile obtained from calculated approximation. (b) Temperature profile obtained through Comsol simulations.

  Cells were collected by centrifugation, washed three times with a low conductivity buffer (σ m =0.1 S/m) and re-suspended in an isotonic medium (σ m =0.1 S/m) prepared for the electrorotation experiments. The experimental buffer is prepared by mixing into deionized water 0.25mM of sucrose, 10mM of TRIS (Tris-hydroxymethylaminomethane) and 1mM of MgCl 2 . The resulting pH value is 7 and the osmolarity of 300mOsm.

3 .

 3 MONITORING THE PERMEABILIZATION OF A SINGLE CELL IN A MICROFLUIDIC DEVICE WITHA COMBINED DIELECTROPHORESIS AND ELECTROROTATION TECHNIQUE Pag. 125 1.15.1 The dielectric properties estimation.

Figure 3 .

 3 Figure 3.14. (a -b) Electrorotation spectra of B16F10 and Jurkat cell lines before and after pulses application. (c -d) Estimated Dielectrophoresis spectra of B16F10 and Jurkat cell lines before and after pulses application

  MOSE-FFL: late stage cells that were selected as the most malignant phenotypes from MOSE-preIV cells.The Figure3.15 shows the experimental results of experiments performed on the three stages within a ROT spectrum and the consequent estimation of the rotational velocity:

Figure 3 . 15 .

 315 Figure 3.15. Experimental electrorotation points of MOSE-E, MOSE-preIV and MOSE-FFL cells fitted for dielectric properties estimation.

  the case of 2-D cell culture, cells create an extracellular matrix that is different than the matrix of cells within the tissue environment. The extracellular matrix is less dense than in the biological tissue and it cannot properly model the barrier for tissue permeabilization and drug delivery. Some groups avoid this problem by using animal testing. Although this provides us with good examples of in vivo tumors, it raises complications in terms of experimental protocol and ethical permission [180]. Furthermore the experiments performed on animals are based on the induced tumor that grows in a healthy environment. In reality, the tumor grows little by little and changes the environment around itself by compromising important tissue structure and functions. The injection of a tumor into a patient (the animal in this case) who is in good health does not properly demonstrate the reality of the disease progress. When tumor cells are injected into the animal in order to induce cancer, the injected tumor cells are already able to develop the disease Pag. 134

  functioning immune system [181]. Nevertheless, the animal model represents the only way, at present, to study the development of cancer's development in a body where the immune system response can be investigated. In this context, the study of a new, more human-reliable model is imperative for basic research purposes. The combination of in vivo cancer's behavior, provided through animal-testing, alongside the advantages of in vitro experiments could represent a challenge for this area of investigation. Indeed, a 3D multicellular model reproduces the tissue-like structure and it can mimic many aspects of the human response [182]. Thus, 3D spheroids are a physiologically relevant model which can reproduce biological functions and responses of real tissue better than the traditional 2D cell monolayers culture . Nowadays, the use of the spheroid model can enhance our understanding of tumor behaviour [183, 184]. Indeed, spheroids are used for the screening of therapeutic molecules [185, 186], in order to test the efficiency of cancer treatments [187] and the capability of a carrier to penetrate the cell membrane [188, 189].

  characterized by a synergy and the complexity typical of biological tissue, showing a structure particularly close to cancer's biological tissue[110]. A spheroid is composed of three main macroscopic layers (Figure4.1b): an external proliferative compartment where the cells remaing highly active and carry on their regular activities, an intermediate compartment where cells are in a quiescent state and eventually a necrotic core (its presence depends on the size of the spheroid). It is thus possible to recognize a gradient in the state of the cells' health when moving from the external side to the inner compartment of the spheroid structure. When approaching the core of the spheroid, a lack of oxygen provokes a hypoxic condition and thus the inner compartment becomes necrotic, corresponding with a typical, unvascularized tumor tissue[199].The thickness of each layer composing the spheroid depends on the whole size of the sample and varies depending on the cell line employed. Figure 4.1a shows the proportional size of these compartments, and refers to various gradients of depicted metabolites [200]. The figure 4.1b highlights the similarity between cancer and the spheroid, which thus represents a simplified cancer prototype. Pag. 136

Figure 4 . 1 :

 41 Figure 4.1: (a) Combination of spheroid median sections with respect to various gradients of depicted metabolites [200] (b)The spheroid as a model to study in vitro tumor response. Similarity within the two structures: the in vitro spheroid and the tin vivo tumor.

Pag. 138

 138 Despite such limitations, important positive correlations were obtained from specific neoplasms such as gastric [210], ovarian [211] and colorectal [212].

  the spheroid was studied by Chpinet et al. [109] using both confocal microscopy and flow cytometry. The confocal microscopy is useful to have a qualitative response and the flow cytometry is important to quantify the response of the single cell after its dissociation from the spheroids. The Figure 4.2b presents images obtained with confocal microscope, the spheroid was subjected to electric field of increasing intensity; Pag. 139 the confocal images show the spatial distribution of permeabilized cells in the spheroids. As visible from the Figure 4.2b the number of permeabilized cells homogeneously increases with the electric field intensity at the spheroid surface. Permeabilization is detected from an electric field value of 200 V/cm to an electric field value of 800 V/cm. It is remarked that at 500 V/cm, all the cells on the spheroid surface are fluorescent. The Figure 4.2c shows the spheroids along the z axis, spheroid images show the fluorescence signal in the spheroid core decreases.

Figure 4 . 2 :

 42 Figure 4.2: (a) train of ten pulses lasting 5 ms at a frequency of 1 Hz were delivered at different electric field intensity at room temperature (b) Permeabilized spheroid with respectively confocal acquisitions and phase contrast images. The red fluorescence is given by the propidium iodide uptake. (c) Optical slices obtained with the confocal microscope for 800 V/cm. For all images scale bar represents 100 µm [109].

Pag. 141 1 . 19 . 1

 1191 Comparison between cell in suspension and spheroidCell responses in suspension and spheroid when a pulsed electric field is applied differ significantly. As can be deduced from the literature on this subject [109] the permeabilization level, as well as the survival curves, are different for a single cell and for spheroids. The Figure4.3a shows the percentage of permeabilized cell with respect to EF strength calculated through the PI uptake; electropermeabilization of spheroid is analyzed by quantifying the response at the single cell level after dissociation of the cells from the spheroids (Figure4.3b).

Figure 4 . 3 :

 43 Figure 4.3: (a) Permeabilization of cell with respect to increasing EF strenght. (b) Permeabilization of spheroid with respect to increasing EF strenght [109].

  dimensional and includes three different cellular stages: proliferative cells in the outer layers, quiescent cells in the center of the spheroid, and possible dead cells in the heart [214].

Figure 4 .

 4 Figure 4.4 shows the result of the experimental rotational velocity of the spheroid fitted by employing this model:

Figure 4 . 4 :

 44 Figure 4.4 : Experimental rotational velocity fitted with the homogeneous particle model.

Figure 4 . 5 :

 45 Figure 4.5 : Experimental rotational velocity fitted with the single-shell model.

Figure 4 . 6 :

 46 Figure 4.6 : Spheroid equivalent model obtained from the modified single-shell model.

Figure 4 .

 4 Figure 4.7 shows the ROT curve obtained for the estimation of the dielectric properties of the spheroid:

Figure 4 . 7 :

 47 Figure 4.7 : ROT spectrum and referred estimated dielectric properties of a spheroid Human U87MG glioblastoma.

Figure 4 .

 4 Figure 4.8 shows how the ROT spectrum changes due to the PEF application:

Figure 4 . 8 :

 48 Figure 4.8: ROT spectra of Human U87MG glioblastoma spheroid before and after PEF application. The sample was permeabilized by a train of 10 rectangular pulses with 3kV/cm amplitude and 100 µs, delivered with a frequency of 1Hz.

  The use of a modified single-shell model represents a first approach to investigate the changes in dielectric properties during the permeabilization process. The introduction of the two-dispersion factors α and β demonstrates the concept of heterogeneity that is Pag. 154 missing from the single-shell model. Nevertheless a new electrical model must be developed in order to better mimic the spheroid response to PEF application. The 3D cell-based model can improve the predictability of the cell-based assay. Furthermore if cells are collected from the primary tumor cells of the patient, the solutions achieved are far beyond what can be done in animal studies; the personal response of each tumor to the PEF application can be investigated quickly and safely and provides a real, personally adapted solution for each patient. Pag. 155

  cell's membrane to allow the passage of various macromolecules. The electropermeabilization achieved can be reversible or not reversible depending on pulses characteristics. This work presents an electrical engineering approach to quantify and analyze dielectric changes induced by various characteristics of PEF applied at different scale level: macro-scale level (tissue characterization), micro-scale level (single cell characterization), as well as intermediate level (spheroid study).

  figure out how the level of permeabilization and its homogeneity can be monitored by using the combination of two components of the Cole-Cole bioimpedance model: the capacitance C m, which is the most sensitive indicator for the low levels of permeabilization (P<10-20 %) and the resistance R0, which characterizes fairly well the higher level of permeabilization.Concerning the study of single cells and spheroids we used the electrorotation technique to monitor the level of permeabilization. This is an alternative method to impedance measurements.Mechanical velocity measurements on the biological objects submitted to several types of electrical solicitations (Dielectrophoresis, Electrorotation and Pulsed electric field) was performed and discussed. In the proposed system, the dielectrophoresis is first applied to trap the sample where a rotating electric field induces a rotational movement of the sample. The rotational velocity analysis is then used for dielectric properties estimation, thanks to a fitting algorithm that we developped. The system was successfully tested with two different cell lines (Jurkat cell line and B16F10 cell line) and with spheroids (human glioblastoma cell lines U87MG) on the frequency range of 10 kHz up to 20 MHz. Electric field pulses were finally applied in order to permeabilize the cell membrane in condition of reversibility.After the application of electric field pulses the structure of the cell membrane experiences a structure change and thus electropores may be formed. The formation of the latter allows small molecules to enter inside the sample by reaching the intracellular

  function of % the frequency w % p1 = epsc, p2 = sigmc % p3 = epsme, p4 = sigmme Pag. 175 malignant glioma in a canine patient. Technology in cancer research & treatment, 2011. 10(1): p. 73-83. 115. Lebovka, N.I., I. Praporscic, and E.

Titre:

  Etude de la perméabilisation d'une membrane cellulaire par un champ électrique pulsé: développement d'une modélisation électrique -caractérisation sur biopuces à cellules Mots clés : perméabilisation cellulaire, champ électrique pulsé, modélisation électrique, biopuces microfuidiques Résumé : L'utilisation du champ électrique pour agir sur le vivant permet d'envisager la recherche de nouveaux traitements contre le cancer : l'ElectroChimioThérapie, la thérapie génique, l'immunothérapie. L'application d'impulsions électriques sur des cellules ou des tissus induit un changement sur leurs membranes qui deviennent perméables. Ce phénomène permet d'augmenter temporairement la capacité des membranes cellulaires à laisser passer les ions et les macromolécules. Ces phénomènes ne sont pas totalement maitrisés ni compris par la communauté scientifique. Ainsi le but de mon travail de thèse est de contribuer à modéliser et caractériser les phénomènes biophysiques intervenant lors de l'application de sollicitations électrique.

Table 1

 1

	.1) is

Table 1 .

 1

1:Typical intracellular and extracellular ions concentraton for a mammalian cell.

Table 2 .

 2 1. Extimated value for biotissue before permeabilization and after a percentage of

	permeabilization of 36%
	R0 (kΩ)	R∞ (Ω)	t(s)	α	C m
						(F)
	Before	2.1	66.7	9.38e-5	0.83	2.4e-7
	pulses
	After	1.3	59	9.18e-5	0.73	9.5e-7
	pulses

Table 3 .

 3 1. General values of dielectric properties for a mammalian eukaryotic cell [164].

	Single-shell	ε rel	σ [S/m]
	compartment
	External medium	80	10 -1
	Cell membrane	2 -10	[0,1 -10]x10 -7

Table 3 .

 3 2: Values adopted for each parameter within the DEP simulation.

	Parameter Radius	σ medium	σ membrane	ε membrane, rel σ cytoplasm	ε cytoplasm, rel
	Value	5 µm	0,1 S/m	1e -6 S/m	6	0.4 S/m

Table 3 .

 3

	3. Estimated electrophysiological parameters of cell before and after permeabilization of the
	membrane throughout a series of fifteen 100 µs unipolar PEF delivered with a frequency of 1 Hz, with an
	amplitude of 952 V/cm.
	Cell line		σ mem [S/m] ε mem,rel	σ cyt [S/m]	ε cyt,rel
	Jurkat E 6.1 Before	0,40e-4	6,30	0,19	40,00
		pulses
		After pulses 0,84e-4	6,90	0,13	47,60
	B16F10	Before	9e-7	5,6	0,14	43,3
		pulses
		After pulses 4,9e-6	8	0,10	47,4

  e. spheroids where both cancer and healthy cells are presented into the structure, only normal cells remain viable after ECT while tumor cells are totally destroyed. The same results had been observed on patients by clinicians [213], and we can thus deduce that the mixed spheroids are a proper predictable in vitro model for therapeutic response.

Laure

Gibot et al. [111]

demonstrated that the structure of a multicellular spheroid changes when specific antitumor drugs (bleomycin, cisplatin or doxorubicin) are injected and PEF are simultaneously applied. They showed changes when the spheroids were treated with only anti-tumor drugs and with anti-tumor drugs + the ECT method.

Table 4 .

 4 1. Estimated electrophysiological parameters of spheroid Human U87MG glioblastoma.

	Spheroid	σ out [S/m]	ε r,out	σ in [S/m]	ε r,in	α	β
	Human
	U87MG	1,5e-7	6	0,6	57	0,9	0,46
	glioblastoma

Table 4

 4

	.2 summarize

Table 4 .

 4 2. Estimated electrophysiological parameters of spheroid before and after permeabilization of the membrane throughout a series of ten 100 µs unipolar PEF delivered with a frequency of 1 Hz, with an amplitude of 3 kV/cm.

	Spheroid		σ out	ε out,rel	σ in	ε in,rel	α	β
			[S/m]		[S/m]
	Human U87MG	Before pulses	1,5e-7	4,9	0,45	16,7	0,95	0,48
	glioblastoma	After pulses	1e-6	6,98	0,79	52,5	0,9	0,54

  Vorobiev, Combined treatment of apples by pulsed electric fields and by heating at moderate temperature. Journal of Food Engineering, 2004. 65(2): p. 211-217. 116. Belehradek, J., et al., Electrochemotherapy of spontaneous mammary tumours in mice. European Journal of Cancer and Clinical Oncology, 1991. 27(1): p. 73-76. 117. Taiwo, K., A. Angersbach, and D. Knorr, Influence of high intensity electric field pulses and osmotic dehydration on the rehydration characteristics of apple slices at different temperatures. Journal of Food Engineering, 2002. 52(2): p. 185-192. 118. Foster, K.R. and H.P. Schwan, Dielectric properties of tissues. Handbook of biological effects of electromagnetic fields, 1995. 2: p. 25-102. 119. http://www.sapere.it/sapere/medicina-e-salute/il-medico-risponde/guida-alla-Biologia-cellulare/le-comunicazioni-all%E2%80%99interno-dell%E2%80%99organismo/comunicazioni-tra-cellule.html. 120. Treccani. http://www.treccani.it/. 121. Fricke, H., A mathematical treatment of the electric conductivity and capacity of disperse systems I. The electric conductivity of a suspension of homogeneous spheroids. Physical Review, 1924. 24(5): p. 575. 122. IBRAHIM, M., Mesure de bioimpedance électrique par capteur interdigités. 2012. 123. Fricke, H. and S. Morse, The electric capacity of tumors of the breast. The Journal of Cancer Research, 1926. 10(3): p. 340-376. 124. Ohmine, Y., et al., Noninvasive measurement of the electrical bioimpedance of breast tumors. Anticancer research, 1999. 20(3B): p. 1941-1946. 125. Morimoto, T., et al., Measurement of the electrical bio-impedance of breast tumors. European surgical research, 1990. 22(2): p. 86-92. 126. Morimoto, T., et al., A study of the electrical bio-impedance of tumors. Investigative Surgery, 1993. 6(1): p. 25-32. 127. Chauveau, N., et al., Ex vivo discrimination between normal and pathological tissues in human breast surgical biopsies using bioimpedance spectroscopy. Annals of the New York Academy of Sciences, 1999. 873(1): p. 42-50. 128. Cole, K.S., Electric impedance of suspensions of spheres. The Journal of general physiology, 1928. 12(1): p. 29-36. 129. Cole, K.S. and R.H. Cole, Dispersion and absorption in dielectrics I. Alternating current characteristics. The Journal of Chemical Physics, 1941. 9(4): p. 341-351. 130. Elwakil, A.S. and B. Maundy, Extracting the Cole-Cole impedance model parameters without direct impedance measurement. Electronics letters, 2010.

	46(20): p. 1367-1368.

Université Paris-Saclay

Espace Technologique / Immeuble Discovery Route de l'Orme aux Merisiers RD 128 / 91190 Saint-Aubin, France

THE ELECTRIC FIELD TO HANDLE BIOLOGICAL SAMPLE

THE ELECTRIC FIELD TO HANDLE BIOLOGICAL SAMPLE Pag. 58

BIOIMPEDANCE MEASUREMENT AS A METHOD TO MONITOR BIOLOGICAL TISSUE PERMEABILIZATION

Pag. 166

References Pag. 167

Pag. [START_REF] Knorr | Impact of high-intensity electric field pulses on plant membrane permeabilization[END_REF] When it is not possible to represent the dependence of the model from parameters with simple sums or products, but there is a quadratic or exponential dependence, we have to face a non-linear model.

For these models there is no closed form solution to the estimation problem, in the cost function G(p) parameters do not appear linearly, and this means that there is no single point of minimum of the function, but several local minimum points, as shown in Figure 1. [START_REF] Cen | A combined dielectrophoresis, traveling wave dielectrophoresis and electrorotation microchip for the manipulation and characterization of human malignant cells[END_REF]. There are various methods to achieve a solution for an iteration process, the most used is the method di Gauss-Newton. Once the cell electrorotation spectrum is determined, the extraction of the dielectric properties becomes a matter of parameter estimation (conductivity and permittivity of both cytoplasm (σ cyt , ε cyt ) and membrane (σ mem , ε mem )).

DIELECTROPHORESIS AND ELECTROROTATION TECHNIQUE

Pag. 130 electrorotation spectra. However FFL cell lines and pre-IV cell lines can be discriminated through their ROT spectrum, as they show different dielectric properties.

It is revealed that the rotation velocity decreases with the degree of the cancer and consequently the electrophysiological properties of the three cell lines evolve by following the direction of aggressiveness.

The resulting dielectric properties are summarized in table 3.4. Estimation of the electrical parameters highlights an increase in the membrane conductivity and a decrease in the membrane permittivity as the cancer progresses.

Previous studies showed haw tumor cells are easier to permeabilize than healthy cells;

such behavior can result in a higher capability of the tumor cell to let molecules or ions pass through the membrane.

When the tumor evolves towards a more malignant status, a decrease in the cytoplasm conductivity is measured.

Changes in the cytoplasm might be connected to the fact that the dimension of the nucleus of the cell changes with the cancer progression, the nucleus actually grows with the cancer evolution. Ongoing studies on the evolution of the ratio radius_cyt/radius_nucleus show that the phenotypic characteristics of the cells are strictly linked to the healthy status of the cell and can consequently influence the conductivity or the permittivity of the internal compartment.

Pag. 161 emi = @(w)epsmi-i*sigmmi./w; %only function of w ec = @(w,p1,p2)p1-i*p2./w; %function of w,p1,p2 eme = @(w,p3,p4)p3-i*p4./w; %function of w,p3,p4

omega_s [START_REF] Maxwell | A treatise on electricity and magnetism[END_REF][START_REF] Washizu | Electrostatic manipulation of DNA in microfabricated structures[END_REF]