Lídice Vaillant

Elena Vigil

Fresnel Forcade

Thierry Thami

Hania Adnani

Christelle Yacou

André Ayral

Pierre Saint-Grégoire

On fundamental mechanisms in dye sensitized solar cells through the behaviour of different mesoporous titanium dioxide films

Understanding mechanisms in DSSCs is fundamental for their improvement; this includes the nanocrystalline semiconducting layer behaviour. Different mesoporous T iO2 layers are fabricated and analyzed for possible use in DSSC solar cells. The preparations included the addition of P123 triblock copolymer as structuring agent to the synthesized anatase sol. This preparation was also mixed with P25 T iO2 nanoparticles in one case and polystyrene latex in another. Mesoporous mixed T iO2 -SiO2 thin layers were also analyzed. The diverse morphology and features are studied by microscopic techniques and by means of spectral quantum efficiency of a photoelectrochemical cell (PEC) that uses as photoelectrode the unsensitized porous T iO2 layer. Contact angle measurements are also performed. We have found that a very high specific area due to very small nanocrystals and small pores can hinder electrolyte penetration in the pores formed by T iO2 nanograins, affecting photoelectrodes efficiency.

Introduction

Study and development of dye sensitized solar cells (DSSCs) is an up-to-date field of research. The main prospective of these devices is based on the possibility of achieving very inexpensive and efficient solar conversion. Fabrication of DSSCs is simpler than silicon or any thin film based solar cells, where technological steps require high temperatures, control of impurity concentration and high vacuum deposition process. Moreover, the conception of a threedimensional (3D) interface between active materials and the separation of roles of the absorber and the transporting materials are distinctive differences with traditional solar cells [1]. The fundamental structure of the cell remains essentially unchanged since its first appearance in scientific publications [START_REF] O'regan | Low cost and highly efficient solar cells based on the sensitization of colloidal titanium dioxide[END_REF]. The cell consists of three major important parts, the front electrode of nanostructured T iO 2 , the dye for light absorption and the electrolyte.

After absorption of sunlight, the dye injects electrons to the T iO 2 semiconductor, where they are transported by diffusion [START_REF] O'regan | Low cost and highly efficient solar cells based on the sensitization of colloidal titanium dioxide[END_REF]. The electrolyte regenerates the oxidized dye and transports holes to the counter-electrode. According to the role of nanostructured T iO 2 in DSSC, one important issue is obtaining T iO 2 films with adequate porosity and crystallinity at low temperature, preferably using simple technology. T iO 2 nanocrystalline and porous character determines a different working principle in DSSC when compared to traditional solar cells based on flat junctions. The nano-sized three-dimensional interface structure for the electron conducting medium (most frequently Send offprint requests to: porous nanocrystalline T iO 2 ) has different implications: first, light absorption by the sensitizer or dye is enormously enhanced since the real internal area of the porous T iO 2 with the attached sensitizer is orders of magnitude larger than the cell area. Second, it allows the electrolyte or other hole conducting medium to penetrate and surround the T iO 2 nanocrystals. Therefore, a three-dimensional (3D) heterostructure is formed. Third, it allows charge carriers to be transported in a medium different from that in which photon absorption creates them. Fourth, only diffusion currents are present because due to nanocrystal size there are no macroelectric fields that could generate drift currents. Fifth, it is a majority carrier device.

There are no excess minority carriers (holes) in the T iO 2 where electrons are transported. Electron-hole recombination does not play an important role in decreasing efficiency as in traditional solar cells. It is the main reason why no highly pure and perfect crystals are required. This causes that DSSCs are quite cheaper than traditional solar cells. Sixth, light suffers multiple scattering inside the 3-D heterostructure. All of these six phenomena determine the DSSC efficiency and all of them depend on the nanostructure of the employed T iO 2 , e.g., nanocrystal size, porosity, pore size, nanocrystal shape [3]. These, in turn, depend on the technology used in obtaining the mesoporous T iO 2 electron-conducting medium. Recently, several other techniques have been used for the T iO 2 film synthesis, including electrochemical anodization for obtaining arrays of nanorods [START_REF] Djam | R Proceedings GRASP: Graduate Research and Scholarly Projects[END_REF], and miscellaneous techniques for multiple layers [START_REF] Zhang | [END_REF]. However up to now, quantitative or semiquanti-tative analyses of the phenomena in the layers related to porosity, connectivity, and pore size, are rather scarce in literature. Because of the mentioned reasons, we analyze for possible use in DSSCs, some previously reported techniques for obtaining mesoporous T iO 2 for photocatalysis.

A simple sol-gel route for the synthesis at low temperature of mesoporous and nanocrystalline anatase thin films from titanium isopropoxide was reported by Bosc et al [START_REF] Bosc | A Simple Route for Low-Temperature Synthesis of Mesoporous and Nanocrystalline Anatase Thin Films[END_REF].

The optimization of the synthesis parameters enabled the room temperature preparation of clear sols consisting of dispersed anatase nanocrystallites [START_REF] Bosc | A Simple Route for Low-Temperature Synthesis of Mesoporous and Nanocrystalline Anatase Thin Films[END_REF]. By the addition of a templating agent to the starting sols, the porosity and specific surface area were controlled, and layers exhibiting ordered mesoporosity were prepared [START_REF] Bosc | A Simple Route for Low-Temperature Synthesis of Mesoporous and Nanocrystalline Anatase Thin Films[END_REF]. Also a method was developed for the preparation at low temperature of mesoporous mixed T iO 2 -SiO 2 thin layers [7]. The effect of addition of silica on the crystalline structure, on the mesostructure, on the porosity and on the photocatalytic activity was investigated. Nanocomposite solids consisting of amorphous silica and anatase nanocrystals were produced [7]. For 80% molar titania content, no significant decrease of photocatalytic activity was found compared to pure anatase [7]. Ayral and coworkers [START_REF] Bosc | TiO2 anatasebased membranes with hierarchical porosity and photocatalytic properties[END_REF] also prepared stable complex organic-inorganic hybrid suspensions by mixing a polystyrene latex aqueous suspension with the titania hydrosol containing the nonionic triblock copolymer. These suspensions were deposited as thin films. Solvent evaporation induces the formation of spherical micelles by self-assembly of the amphiphilic molecules during the drying of the films. Two types of isolated spheri-cal macropores (few ten nanometers) and mesopores (4-5 nm) were reported to be generated inside the layers by the thermal removal of the polystyrene particles and of the micelles, respectively [START_REF] Bosc | TiO2 anatasebased membranes with hierarchical porosity and photocatalytic properties[END_REF]. The remaining inorganic network exhibits an additional interconnected microporosity with a mean pore size of 1.5 nm, resulting from the aggregation of the anatase nanoparticles [START_REF] Bosc | TiO2 anatasebased membranes with hierarchical porosity and photocatalytic properties[END_REF]. In the literature, DSSCs are studied as a complete device, i.e., sealed and with sensitization. Generally, analysis of the T iO 2 used for making the DSSC is not performed independently -as We have used methods reported by Bosc et al in [START_REF] Bosc | A Simple Route for Low-Temperature Synthesis of Mesoporous and Nanocrystalline Anatase Thin Films[END_REF], [7] and [START_REF] Bosc | TiO2 anatasebased membranes with hierarchical porosity and photocatalytic properties[END_REF] to obtain mesoporous T iO 2 in order to study possible application in DSSC. A fourth suspension type was also used for deposition of thin films, the sol-gel reported in [START_REF] Bosc | A Simple Route for Low-Temperature Synthesis of Mesoporous and Nanocrystalline Anatase Thin Films[END_REF] mixed with nanocrystalline T iO 2 P-25 powder supplied by Evonik.

Samples labeled D

This preparation intended, by adding P-25, to change some characteristics of the T iO 2 film, like porosity and to introduce scattering centers to increase the light path in the active layer. An aqueous suspension of P-25 was prepared following the procedure described in [START_REF] Bosc | A Simple Route for Low-Temperature Synthesis of Mesoporous and Nanocrystalline Anatase Thin Films[END_REF]. After obtaining the sol-gel described for samples A (titania hydrosol with the triblock copolymer), it was mixed with the T iO 2 P-25 suspension. Mixed volumes were calculated to obtain in the films 20% of T iO 2 nanocrystals coming from the titania nanopowder P-25. Films were deposited on conducting 15 Ω/square FTO glass TCO22-15 of Solaronix by doctor-blading.

Samples labeled S

For the preparation at low temperature of mesoporous mixed T iO 2 -SiO 2 thin layers [7], tetraethoxysilane (TEOS) diluted in ethanol was used as silica precursor. The procedure described in II.1.1 was followed to obtain the acidic anatase hydrosol. After stirring for 3.5 h, the obtained anatase hydrosol was mixed with the TEOS ethanolic solution under vigorous stirring. This favors a fast hydrolysis of the silicon alkoxide. Concentrations were calculated in order to obtain 80% molar T iO 2 content and 20% SiO 2 molar content. The structuring agent P123 is finally added as previously explained. Films were deposited on conducting 15 Ω/square FTO glass TCO22-15 of Solaronix by doctor-blading.

Samples labeled L

The last preparation sought the presence of macropores (∼ 100 nm) and mesopores (∼ 4-5 nm) in the porous T iO 2 films. After obtaining the sol-gel described for samples A (titania hydrosol with the triblock copolymer), it was mixed with a polystyrene latex aqueous suspension (20% molar concentration). Polystyrene particles had a diameter < φ > ∼ 90 nm and they create macropores when thermally removed. After mixing, stirring proceeded for 30 min at 30 o C. Films were deposited by dip-coating (withdrawal rate = 5 inches/min) on conducting 15 Ω/square FTO glass TCO22-15 of Solaronix. All film types were dried at room temperature and under controlled humidity (relative humidity RH = 70%) for over 24 hours. After this, they were pre-treated thermally in an air atmosphere: temperature was increased at 0. In Fig. 1d) one can observe that each scale has a black elliptical center surrounded by colored rings identified as Newton rings. It seems that each scale is firmly attached in the center and Newton rings reveal that they tend to separate towards the periphery. Straight boundaries and alignment of scales are observed probably due to instability of the T iO 2 film-substrate interface that causes this ordered microscopic cracking. Cracking can be explained by a reduced plasticity of the thin films under drying stresses, due to the presence of a polymeric silica network linking together the anatase nanoparticles.

Scanning electron microscopy

SEM was also used in order to study materials morphology. Figure 2 shows a sequence of pictures for the four studied samples, taken at the same magnification. Again samples A and D differ little when observed using SEM.

Comparison of Fig. 2a) and Fig. 2b) shows that sample D is rougher than sample A. This can be explained by the incorporation of nanocrystals from P25 (having a mean diameter of 25 nm) in sample A preparation which is known to give rise to nanocrystals of less than 10 nm diameter [START_REF] Bosc | Mesostructure of Anatase Thin Films Prepared by Mesophase Templating[END_REF]. What is even more interesting is the very particular structure observed in Fig 2c ) for samples in which latex was added. It seems that when the T iO 2 surrounds the latex in the preparation before thermal treatment, selforganization of latex balls occurs in a rather regular way.

This gives rise after calcination to a network of denselypacked pores with diameters of 50-100 nm. Sample S (Fig. 2d) clearly shows a different organization, where two types of porous matrix can be observed. One is formed by big pores of 400 -500 nm in diameter, attributed to holes left after departure of the spherical micelles. The surrounding matter is composed of small grains, of typical size around 8 nm giving rise in the space left between them, to very small pores. The introduction of 20% of SiO 2 in the T iO 2 leads to a more regular mesoscopic organization, which recalls very regular organization observed in pure SiO 2 [14]. Film thickness was determined using cross section SEM images. Thickness values are 1.7, 1.0, 0.3 and 2.5 µm for samples A, D, L and S, respectively. The thick- ness difference will be taken into account when making comparisons among samples light-response.

Spectral response and external quantum efficiency (IPCE)

Spectral response of all four types of samples obtained from the short-circuit spectral photocurrent is shown in 4). This confirms a response time significantly longer than 0.04 s. For other samples it was possible to compare the modulated and non-modulated maximum spectral response values.

After determining peak wavelength for modulated spectral response, continuous light intensity measurement was performed at this wavelength. Samples maximum spectral response value for constant illumination is shown in Table 1. External quantum efficiency or IPCE can be obtained from the spectral response values and it is also shown in Table 1. In order to compare films performance, differences in sample thickness and morphology must be taken into account when considering the problem of charge transport. The mechanism for electron transport within the

I ∼ ω S real R (1)
where ω will be called effective interface coefficient and is meant to be the fraction of the real area that is effective in extracting holes from the T iO 2 to the electrolyte.

That is, the T iO 2 -electrolyte three dimensional interface (S interf ace ) is not equal to the real surface (S real ) because pores might be too small to allow penetration or movement of electrolyte ions. S real designates the T iO 2 surface within the layer, and R is an effective electrical resistance of the T iO 2 layer that depends on diffusion length and recombination time. We assume that light scattering and electron transfer from the T iO 2 to the FTO are second order effects. To estimate the samples real surface, the geometrical organization of the nanoparticles in the samples is schematically depicted in Fig The surface S real of a sample of mass m can be written as :

S real = S BET m (2)
where S BET is the specific surface; the mass m is in turn given by:

m = (1 -p)ρ m (T iO 2 )S 0 d (3)
Here, p is the porosity, ρ m (T iO 2 ) is the mass density of pure (3.84 g/cm 3 [ref]), S 0 is the visible area which is given by the light spot area (the same for all measurements) and d is the thickness of the sample. This estimation of S real does not take into account the contact zones between nanoparticles due to necking which are expected to reduce S real . This underestimation would nevertheless introduce an error of less than 10% in S real which would not modify the conclusion based on estimations. I. It is assumed that IPCE depends linearly with sample thickness. This is true when samples are thinner than optimum thickness value which is the case for our thin samples. As can be observed, samples A have the pores) [START_REF] Bosc | A Simple Route for Low-Temperature Synthesis of Mesoporous and Nanocrystalline Anatase Thin Films[END_REF][START_REF] Bosc | TiO2 anatasebased membranes with hierarchical porosity and photocatalytic properties[END_REF]. This pore size could be too small for the elec- Considering expressions (1), ( 4) and ( 5),one can write that the current (I) is proportional to:

< S s >= (1 -p)S 0 (5)
I = (1 -p)ωS real /ρ el τ (6)
Therefore

ω ∼ I S real d ρ el τ 1 -p (7)
assuming that ρ el τ has approximately the same value for all samples since all of them involve at a microscopic level, T iO 2 nanograins in contact with each other, we get:

ω ∼ I S real d/(1 -p) = ω * (8)
We present in Table 2 values of ω * for samples A, D, L:

We see that ω * has the smallest value for sample A (525 x 10 -5 ), which means that the electrolyte would poorly interact with the T iO 2 surface, while it is approximately twice larger for sample L, and more than ten times larger for sample D. Samples D would hence have the T iO 2 mesoporous layer in which the effective interface area is the largest. In the above considerations, we did not take into account the effect of diffusion length nor of the recombination time, nor of light scattering but we think that the resistive mechanism approach leads to an estimation that should be relevant in first approximation. To check our qualitative explanation for the different IPCE, we have looked for information on the wetting properties and capillarity of the structures by performing the contact angle measurements described below.

Contact angle measurements

Contact angle and capillarity are related phenomena. In porous materials, where liquid deposited on the surface can percolate inside the pores, the volume of the deposited drop will diminish as a function of time as a result of two mechanisms, namely liquid evaporation, and liquid penetration within the layer. Since external liquid evaporation is expected to occur with the same time constants in all cases, the differences of rate of drop volume change among samples, if any, can be attributed to the penetration mechanism. However, it is rather difficult experimentally, to estimate the volumes with accuracy by use of image processing, whereas the measurement of contact angle is easier and more accurate. Contact angle should depend on the given porosity and it must also decrease as a function of time, as a consequence of the volume variation. We could then expect a behavior similar to the one depicted in Fig. 6. [START_REF] Hilden | Numerical analysis of capillarity in packed spheres: Planar hexagonal-packed spheres[END_REF]. Fig. 7 shows contact angle measurements for the different types of samples studied. After the initial measurement at 5 s, the contact angles diminish at a faster rate than evaporation would induce, which is attributed to the penetration of the liquid into the layer.

In these conditions, a pronounced angle decreasing versus time expresses the facility for the liquid to penetrate into the layer. According to this, it is in sample D that the liquid penetrates more easily into the layer, followed by A and L which have similar results, which is in agreement with the previous presented analysis.

Conclusions

Mesoscopic T iO 2 layers with different characteristics as specific area, porosity and pore dimension have been compared. T iO 2 photoelectrodes on conducting glass substrates are fabricated with these layers and they are used in a twoelectrode photoelectrochemical cell to measure the corresponding spectral response and IPCE. To increase efficiency of the photoelectrochemical cell, the area of the

  we do and consider relevant to do [9]. In order to characterize the T iO 2 porous samples obtained by different synthesis routes we propose to use spectral photocurrent response and spectral quantum efficiency of a photoelectrochemical cell (PEC) that uses as photoelectrode the unsensitized porous T iO 2 layer. Advantages of these techniques to characterize the porous T iO 2 film for DSSC are discussed. The mentioned techniques are complemented with contact angle measurements. Optical microscopy and scanning electron microscopy (SEM) are also used to better understand the relation between texture at different scales and physical properties.

1

 1 Technology used for each of the different samples studied

2. 1 . 1

 11 Samples labeled A Ti(IV) isopropoxide was used as T iO 2 precursor. The titanium isopropoxide was hydrolyzed under vigorous stirring by the addition of an aqueous solution of hydrochloric acid. Solutions were prepared in the following conditions: the titanium concentration in the sol, [T i] = 0, 023 molL -1 ; the HCl/T i ratio, a = 1; the H 2 O/T i hydrolysis ratio, h = 20. Stirring at constant temperature T = 30 o C occurred during t = 3 h 30 min to obtain the acidic anatase hydrosol. After this time, to generate ordered mesoporosity by the templating effect, the structuring agent (the triblock copolymer poly(ethylene oxide)-poly(propylene oxide)poly-(ethylene oxide), EO20PO70EO20, labeled P123) was added under stirring at T = 30 o C; which was continued during 30 min. The added amount of this large amphiphilic molecule was defined by the volume fraction of the copolymer in the dried layer, assuming that the inorganic phase is pure anatase. The added amount of P123 corresponds to a volume fraction of 70%. Films were deposited on conducting 15 Ω/square FTO glass TCO22-15 of Solaronix by doctor-blading.

  photoelectrochemical cells (PEC). The PEC arrangement used for photoelectrode characterization has been previously described[11]. PEC spectral photocurrent was measured in a system with a 150 W halogen-xenon lamp coupled to a monochromator LOMO MDR-12. A calibrated silicon photodiode was used for measuring incident monochromatic light intensity, which is necessary to determine both spectral response and external quantum efficiency (IPCE). This photodiode has an enhanced spectral response in the blue, violet and near UV. At constant illumination (nonmodulated light intensity) the photocurrent was measured around spectra peak values using an Agilent 34410A multimeter. Only signals with higher photocurrent values could be measured for constant illumination due to the presence of noise. To measure low photocurrent values, i.e. to obtain the whole spectrum, a lock-in amplifier SR510 modulated at 14 Hz was used instead of the multimeter. However, the response time of PECs was found to be larger than 0.05 s; therefore measurements performed at 14 Hz differ from those at constant illumination. Because of this, external quantum efficiency values are reported for spectra

Fig. 1 .

 1 Fig. 1. Optical microscope images of the four studied samples corresponding, from left to right to preparations A, D, L and S.

Fig. 2 .

 2 Fig. 2. SEM pictures of the T iO2 samples obtained. From left to right, pictures correspond to samples A, D, L and S.

Fig 3 .

 3 Fig 3. The spectral range in which the samples respond is quite similar. Due to the low current values, this spectral response is measured modulating incident light intensity at 14 Hz in order to eliminate noise by using a lock-in amplifier. This means that in each cycle the sample is illuminated during ca. 0.036s. As can be observed in Fig. 3, the highest spectral response values correspond to sample D that was obtained by adding P-25 to the sol-gel with the templating agent. A and L show similar spectral response,

Fig. 3 .

 3 Fig. 3. Spectral response of all samples for light modulated at 14 Hz. Graphs correspond to: D -solid squares; A -open circles; L open triangles, S asterisks.

Fig. 4 .

 4 Fig. 4. Spectral response and IPCE of sample D. Filled squares refer to spectral response obtained under continuous light illumination, from which IPCE triangles were obtained. Open squares is the spectral response at 14 Hz modulated light.

T iO 2

 2 layer is a difficult problem that still gives rise to debates, an important question being what is the mechanism leading to an electron mobility smaller by several orders of magnitude in mesoporous titanum dioxide, than in T iO 2 single crystals. Besides, other particular questions are what is the exact role of sub band gap states (with a multiple-trapping charge transport involving them) and the nature of traps (located at grain boundaries or at grain surface) that limit the electron transport. The microscopic mechanisms are out of the scope of the present paper, and we attempt here a simple phenomenological model, giving estimates of the behaviour, in order to better understand the results. It can be considered that the measured photocurrent coming from the sample is in first approximation proportional to:

Fig. 5 .

 5 Fig. 5. Schematic representation of the diverse morphologies obtained in the studied preparations

  For samples A we can consider p ∼ 40% and S BET = 197 m 2 /g [7], which gives a real surface S real [A] = 758 cm 2 . In the case of sample D (Fig 5b), the mass is divided in very small nanocrystals with the properties of sample A (occupying 80% of the total volumen) and bigger T iO 2 nanocrystals dispersed in the volume of the sample and occupying 20% of it. Because of this, we can consider contributions from both nanoparticles dimensions. To estimate the nanoparticles contribution we assume that nanocrystals in P-25 T iO 2 are nearly spherical with the diameter φ = 25 nm and that they are dispersed within the D preparation without forming aggregates, which appears to be the case as observed by SEM. For spheric nanocrystals, the surface to volume ratio is equal to 6/φ. Considering the sum of all nanocrystals surfaces and previous assumptions, the estimated value is S real [D] = 419 cm 2 . Sample L has 80% of small particle with the properties of sample A, so S real [L] = 113 cm 2 . In order to compare samples, values of IPCE that would correspond to 1 µm thick samples are shown, in Table

  photocarriers current, and τ depends on the tortuosity of electrons path and it may be defined as the ratio of the average real length of electron path within T iO 2 divided by d. For analyzing the problem of electron transport, since the motion takes place on the average in the direction perpendicular to the layer, we propose to consider the sample as formed by a series of nanograins rows following this direction. Then, one can deduce:

Fig. 6 .

 6 Fig. 6. Schematic evolution in time of the behavior of a drop in contact with a porous substrate showing the decrease of drop volume and contact angle.

Fig. 7 .

 7 Fig. 7. Contact angle evolution with time for A, D, L and S samples.

Table 1 .

 1 Samples characteristics and IPCE values Sample d(µm) S real (cm 2 ) IPCE(%) IPCE/d

	(d = 1µm)

Table 2 .

 2 Effective interface coefficient ω * according to expres-

	sion (8)
	Sample d(µm) IPCE/Sinterx(10 5 ) 1-p(%) ω * x(10 5 )
	A	1.7	188.7	60	525
	D	1.0	4125.6	68	6188
	L	0.3	1668	48	1084

Acknowledments

We are grateful to the French Embassy in Havana for financing mobility of cuban researchers in France ("FSP Cuba", project Enermat) and to the Conseil Régional Languedoc Roussillon for the financement of invited professor positions in the University of Nîmes.


Thi Nguyet

Que Nguyen

Pierre Jeannesson

Audrey Groh

Dominique Guenot

Cyril Gobinet

Fourier-transform infrared imaging and clustering: toward an automated histology of normal colon

à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Fourier-transform infrared imaging and clustering: toward an automated histology of normal colon

Thi Nguyet Que NGUYEN [START_REF] Trevisan | Extracting biological information with computational analysis of Fourier-transform infrared (FTIR) biospectroscopy datasets: current practices to future perspectives[END_REF][START_REF] Arbelaitz | An extensive comparative study of cluster validity indices[END_REF] , Pierre JEANNESSON 1,2 , Audrey GROH 3 , Dominique GUENOT 3 , Cyril GOBINET Abstract -Fourier-transform infrared (FTIR) imaging is currently used as a non-destructive and label free method for analyzing biological specimens. Combined with unsupervised clustering method, this biophotonic approach allows to perform a spectral histopathology of human tissues. However, this method requires the subjective choice of the number of clusters. To overcome this problem, we developed a hierarchical double application of 9 cluster validity indices (CVIs) using K-Means clustering. Applying this approach to FTIR images of normal human colon tissue samples, PBM and SI reveal to be the most efficient indices in retreving the main structures of colon histology. These results suggest that the hierarchical double CVI application is thus a promising method for an automated spectral histology.

Index Terms -Optical Imaging, Image Processing, Signal Processing.

I. INTRODUCTION

In biophotonic, Fourier-transform infrared (FTIR) imaging is a non destructive and label-free technique for analyzing samples. This approach spatially records vibrational information which is directly linked to the chemical composition of samples. Recent studies [1] have shown that the combination of this biophotonic approach with unsupervised clustering method, such as K-Means (KM), allows to perform a spectral histology of human tissues. However, this method requires the subjective choice of the number of clusters k. To automatically estimate the optimal k, cluster validity indices (CVIs) have been developed for clustering methods.

In this study, to automate the spectral histology, we developed a hierarchical double CVI application for FTIR imaging. The performance of this approach was then evaluated on 9 different CVIs, using KM partitions estimated on FTIR images acquired on healthy human colon tissue sections.

II. MATERIALS AND METHODS

II.1. FTIR imaging datasets

Five formalin-fixed paraffin-embedded tissue blocks of normal colon zones were obtained from colon cancer surgery of four patients. For each block, two adjacent 6µm thick slices were prepared. The first slice was mounted on a CaF 2 window for FTIR imaging (Perkin Elmer). The second slice was stained with Hematoxylin-Eosin (HE) for conventional histology, and used as a reference for comparison with FTIR imaging. Each FTIR image was recorded with 6.25µm spatial resolution, on the mid-IR range of 900 to 1800 cm -1 with 4 cm -1 spectral resolution. In order to avoid chemical deparaffinization, an in-house Matlab code was applied for neutralizing the spectral interferences from paraffin.

II.2. Hierarchical double CVI application

A CVI is a mathematical function that measures the quality of a partition. By performing a KM clustering for different values of k, 2 ≤ k ≤ k max , this function calculates the ratio between the compactness and separation of clusters for each KM partition. The optimal number of clusters is defined as the number of clusters giving the optimal CVI value. To realize an objective and automated spectral histology, a hierarchical double application of CVIs to KM results with 2 ≤ k ≤ 20 is proposed. For each spectral image, this method is applied using the following steps: i) The CVI is first applied on the KM results of the spectral image.

The optimal number of clusters estimated by the CVI is the number of main clusters k main composing the dataset. ii) Then, on each main cluster, KM is applied for 2 ≤ k ≤ 20, and a second application of the CVI on these KM results estimates the optimal number of sub-clusters. iii) The final optimal number of clusters k opt is thus the sum of estimated optimal numbers of sub-clusters. The corresponding optimal double CVI partition is obtained by assembling all the k main estimated optimal sub-partitions together.

III. RESULTS

The k opt estimated by this approach applied on the 5 spectral images are listed in Table 1. Data show that PBM and SI are the most effective indices since their k opt varied between 8 and 20 while exactly matching the main colon tissue structures (Figure 1(a) and (b)) for the 5 samples. Concerning Dunn, OS and SV, they often exhibited dramatically high k opt (k opt ≥ 40) , thus complicating the assignment of clusters to the corresponding histological structures (Figure 1(c)). By contrast, DB, COP, SWC and XB estimated low k opt inducing optimal partitions which partially correspond to the histological structures. For example, the optimal SWC partition (Figure 1(d)), assigned the cyan cluster to both the muscularis mucosae and the lamina propria.

IV. DISCUSSION-CONCLUSION

In this study, the traditional single application of CVIs has been tested on the FTIR images (data not shown) and mainly leads to an under-estimation of the number of clusters, thus preventing retrieval of the main structures of human normal colon tissue. Theoretically, CVI works correctly for dataset composed of compact and separated clusters, which is not a property fulfilled by FTIR spectral datasets acquired on normal human colon. For this, the proposed hierarchical double application of CVI succeeds in retrieving the structures of colon tissue, permitting to realize an automatic spectral histology. However, the number of layers of the hierarchical application of CVI is obviously dependent on the considered dataset. An objective criterion needs thus to be defined.

In conclusion, spectral histology is a new concept associating FTIR imaging and clustering. To overcome the subjective choice of the number of clusters, a hierarchical double CVI application for KM partition was proposed. This procedure achieves an automated spectral histology, since the main human normal colon tissue structures are detected for all the analyzed FTIR images.

Figure 1 :

 1 Figure 1: Comparison between conventional histology and pseudo color-coded images reconstructed by double CVI applications for patient sample 1. (a) HE stained image of tissue with 4 histological structures of colon. Optimal partition estimated by (b) PBM (k opt = 10), (c) Dunn (k opt = 316) and (d) SWC (k opt = 4). Scale bars indicate 100µm.

  1,2 * 1 Université de Reims Champagne-Ardenne, Equipe Biophotonique et Technologies pour la Santé, UFR de Pharmacie, Reims, France. 2 CNRS UMR 7369, Matrice Extracellulaire et Dynamique Cellulaire (MEDyC), Reims, France. 3 Université de Strasbourg (UdS), EA 3430 Progression tumorale et microenvironnement. Approches translationnelles et Epidémiologie. Fédération de Médecine Translationnelle de Strasbourg (FMTS), Strasbourg, France.

*

Corresponding author (email: cyril.gobinet@univ-reims.fr).

Table 1 :

 1

	Patient sample	1	2	3	4	5
	CVI	PBM SI Dunn OS SV DB COP SWC	10 13 326 316 180 257 278 9 8 9 10 9 9 20 10 40 392 394 333 374 228 378 22 58 21 7 7 8 4 4 5 4 4 4 7 4 5 4 4 4
		XB	5	6	8	4	4

k opt estimated by hierarchical double CVI application on the FTIR images. Bold values represent the optimal partitions that retrieved at least the main histological structures of normal human colon.

ACKNOWLEDGMENTS

Authors thank Cancéropôle Grand-Est, Ligue contre le Cancer, the URCA technological platform of cellular and tissular imaging PICT-IBiSA, Région Champagne-Ardenne, Région Alsace and Ministère de l'Enseignement Supérieur et de la Recherche for financial support.


Agnès Drochon
email: agnes.drochon@utc.fr

Laurine Redelsperger

Florian Devin

Analytical solution for the pulse wave propagation in a deformable artery in the presence of an external magnetic field

Keywords: Biomechanics, Medical physics, Modeling

I. INTRODUCTION

Several biomedical applications require a good knowledge of the physics of blood flow and pressure pulse propagation in a deformable vessel, in the presence of an external static magnetic field: -In the case of Magnetic Resonance Imaging (MRI) of the heart, the charged particles of the blood get deflected by the Lorentz force, thus inducing electrical currents and voltages across the vessel wall and in the surrounding tissues. These voltages disturb the electrocardiogram (ECG) detected at the surface of the thorax, making the ECG-based image synchronization inaccurate. Several approaches have been proposed to correct the ECG signals for these magnetohydrodynamic (MHD) induced artifacts [START_REF] Abi-Abdallah | Cardiac and respiratory MRI gating using combined wavelet sub-band decomposition and adaptive filtering[END_REF]. On the contrary, other groups [START_REF] Kyriakou | Patientspecific simulations and measurements of the magneto-hemodynamic effect in human primary vessels[END_REF], decided to try to use the MHD effect measured with ECG as a biomarker of cardiac output, since it is sensitive to magnetic flux density, flow orientation with respect to the magnetic field lines, and velocity of the blood. Frauenrath et al. [START_REF] Frauenrath | Detailing the use of MHD effects for synchronization of MRI with the cardiac cycle: a feasibility study[END_REF] even propose to use the MHD induced voltage itself as a tool for cardiac synchronization.

-Pulse wave velocity (PWV) is known to be an indicator of arterial stiffness, and, as a matter of fact, a predictor of cardiovascular risk. MRI has been proposed by several groups as a noninvasive tool to assess PWV [START_REF] Ibrahim | Measuring aortic pulse wave velocity using high-field cardiovascular magnetic resonance: comparison of techniques[END_REF].

-Quite recently, a new direction of research has emerged, aiming at harvesting intracorporeal energy to provide continuous power to implanted medical devices. The advantage would be to avoid costly and tedious replacement or recharging of these medical implants. Pfenniger et al. [START_REF] Pfenniger | Design and realization of an energy harvester using pulsating arterial pressure[END_REF] propose a prototype that converts the expansion and contraction of an artery (due to pulsatile blood pressure changes) into electrical energy by electromagnetic induction. For a Newtonian incompressible fluid, the MHD equations are defined by a coupling of Maxwell's electromagnetic equations and Ohm's law, on the one hand, and the Navier-Stokes equations including the Lorentz force on the other hand. An optimal modelisation of the magnetohydrodynamic flow of blood should include the pulsatility of flow, the deformability and conductivity of the vessel wall, together with the induced electrostatic and electromagnetic fields. This leads to a complex mathematical problem and analytical solutions may be found only under restrictive hypotheses. To our knowledge, the solutions that may be found in the literature assume that the vessel is rigid. The present work provides a solution including the vessel wall deformability by a coupling of fluid equations and equations for the motion of the wall, in the case of simple sinusoidal flow, non-conducting wall and neglected inductions.

II. THEORY

The calculations are conducted following the method proposed by Womersley [START_REF] Womersley | Oscillatory motion of a viscous liquid in a thin-walled elastic tube. I-The linear approximation for long waves[END_REF] and by Atabek and Lew [START_REF] Atabek | Wave propagation through a viscous incompressible fluid contained in an initially stressed elastic tube[END_REF].

The main velocity component of the blood is longitudinal (along z). The radial component (which is related to the wall deformability) is small, when compared with the longitudinal component. The vessel wall is assumed to be thin, elastic and isotropic. The analysis is restricted to waves whose wavelengths are very large compared with the radius of the tube, and it is further assumed that the amplitude of the pressure disturbance is sufficiently small so that non-linear terms of the inertia of the fluid are negligible compared with linear ones. The B 0 field is transverse to the vessel. The Lorentz force acting on the fluid is expressed as j^B 0 , where j is the electric current density, given by σ(u^B 0 ) (σ is the electric conductivity of the blood, and u is the fluid velocity field). The equations describing the motion of the wall, and the boundary conditions between the fluid and the deformable wall are the same as in [START_REF] Atabek | Wave propagation through a viscous incompressible fluid contained in an initially stressed elastic tube[END_REF]. The solutions of this system of equations are searched for the case of the propagation of forced pressure waves which are harmonic in t (time) and in z. All the variables (pressure, radial and longitudinal fluid velocities and wall displacements) take the form X(r,t,z)=X*(r)exp[iω(t-(z/c))], with i the complex number such that i 2 = -1, ω the circular frequency of the forced oscillations, and c, the velocity (complex) of propagation of the oscillations. A frequency equation, which is quadratic in the square of the propagation velocity, is obtained. Two out of four roots of this equation give the velocity of propagation of two distinct outgoing waves. The remaining two roots represent incoming waves corresponding to the first two waves. One of the waves propagates more slowly ("Young mode") than the other ("Lamb mode"). This last type of waves is essentially longitudinal waves through the tube wall, modified with the existence of the fluid.

III. RESULTS

The influence of the magnetic field intensity and of the amplitude of the pressure perturbation on the two fluid velocity components, on the two wall displacement components and on the wave celerity is demonstrated (see for example Figure1). The magnetic field induces some flow reduction and some flattening of the fluid velocity profiles. It also induces a reduction of the wave celerity of the Young mode. These effects heighten when B 0 increases. However, in the range of the values of B 0 used in routine MRI (B 0 <10 Tesla), they remain quite negligible.

The influence of the wall deformability can also be established through the comparison of the present solution with the solution of Sud et al. [START_REF] Sud | Effect of magnetic field on oscillating blood flow in arteries[END_REF], obtained with the same hypotheses except that the tube is rigid.

IV. DISCUSSION -

In spite of the numerous simplifying hypotheses, it seems that this solution allows to capture some important features of the physical problem. It is also hoped that such analytical solutions may be used to validate the 3D computational fluid dynamics codes that may be developed by other groups.

Figure 1 :

 1 Figure 1: Propagation and damping of the radial displacement of the wall, for the « Young mode » wave celerities, obtained for a 10 mmHg pressure perturbation in the vessel. The displacements (full scale = 80 microns) are plotted against (ωt) (in radians), for different longitudinal positions ( z = 0; z = λ/4; z = λ/2; z =3λ/4; z = λ). The influence of the magnetic field, B 0 , is included in the non-dimensional Hartmann number, M, defined as: M = RB 0 ((σ/η) 1/2 ) , where R is the "mean" radius of the vessel (1 cm), σ the blood electric conductivity (0.5 S/m), and η its dynamic viscosity (4 mPa.s). M= 1.2 thus corresponds to B 0 = 10.7 Teslas, M = 10 corresponds to B 0 = 89.4 T,,... The other data used here were: blood density = 1050 kg/m 3 , wall density = 1100 kg/m 3 , frequency = 75 b.p.m., Young modulus of the vessel wall = 10 6 Pa, wall thickness = 2 mm, Poisson coefficient = 0.5.


Ihsen Farah

Thi Nguyet Que Nguyen

Audrey Groh

Dominique Guenot

Pierre Jeannesson

Cyril Gobinet
email: cyril.gobinet@univ-reims.fr

Optimal Spectral Histology of Human Normal Colon by Genetic Algorithm

Keywords: Image Processing, Signal Processing, Optical imaging

Fourier transform infrared (FTIR) imaging combined with unsupervised clustering method, such as k-means, achieves a real histology of human tissues. This technique has been successfully applied to diagnose different cancers. However, the clustering methods used in spectral histology are local search algorithms, i.e. these methods converge to a local optimum. Metaheuristics are effective methods to overcome this problem and to reach the optimal solution. In this work, we propose a genetic algorithm for the optimal clustering of FTIR images of normal human colon tissues. The obtained results show the efficiency of the proposed genetic algorithm to retrieve more precisely than k-means the structures of normal colon.

I. INTRODUCTION

Fourier transform infrared (FTIR) imaging is a technique used to measure the absorption of light by a sample. This technique acquires the IR spectra of the bioactive molecules, giving an overall molecular information of the sample, in a non-destructive and non-invasive manner without staining or marking. By FTIR spectroscopy, the structural and metabolic changes in cells and tissues can be detected. This technique has been successfully applied to diagnose different cancers, such as esophageal, stomach and colorectal cancers [START_REF] Old | Vibrational spectroscopy for cancer diagnostics[END_REF]. FTIR imaging is a recent extention of FTIR spectroscopy for the mapping of samples. This technology provides a data cube, composed of two spatial and one spectral dimensions. Each pixel of a FTIR image is a IR spectrum containing information characterizing the molecular composition of the tissue in that point. Applied to human tissue sections and associated with unsupervised clustering methods such as k-means, IR spectral imaging carries out an authentic spectral histology since different tissue structures can be determined according to their biomolecular composition. This approach has recently been applied for different types of tissues, such as colon, skin and cervix [START_REF] Walsh | Label-Free biomedical imaging with Mid-IR spectroscopy[END_REF]. However, unsupervised clustering methods are local search methods that converge to a local optimum and depend on initialization. In this work, we propose a genetic algorithm to estimate a global optimum for the spectral histology of human normal colon.

II. MATERIALS AND METHODS

II.1. FTIR imaging and processing

Five formalin-fixed paraffin-embedded tissue blocks of normal zones were prepared from a colon part surgically removed from five patients with a colon cancer. For each tissue block, two consecutive 6µm thick slices were cut with a microtome. The first slice was mounted onto a calcium fluoride (CaF 2 ) window. The second slice was mounted on a glass window and stained by Hematoxylin and Eosin (HE) for conventional histological analysis. For data preprocessing, three steps are applied. First, atmospheric correction was performed on each FTIR image by Spectrum Image software to remove water vapor and CO 2 contributions. Second, the spectral range was limited to the 900 -1800 cm -1 fingerprint. Third, the spectra were numerically corrected from paraffin signal and baseline, and normalized using Extended Multiplicative Signal Correction (EMSC) method.

II.2. Genetic algorithm for the clustering of FTIR images

For most of combinatorial optimization problems, which are NP-hard, it is very difficult to find the optimal solution especially for large-scale problems. Indeed, the exact methods require a lot of memory and take a lot of run time. It is thus necessary for practitioners to use methods providing a (sub) optimal solution within a reasonable time, such as metaheuristics. In this work, we propose a genetic algorithm (GA), whose fitness is the objective function of k-means, to achieve the IR spectral histology of human normal colon. The initial phase of our algorithm is to randomly construct P chromosomes. Each chromosome is represented by a vector of integers (genes) which represent the class to which belongs each spectrum. Next, three phases are applied iteratively. During the first phase, each chromosome is represented on a wheel by a portion proportional to the value obtained after applying an exponential scaling to its fitness. P/2 homogeneous random draws are made on the wheel leading to the selection of P/2 chromosomes (the parents). In the second step, P/2 multiple crossovers are made. In fact, two parents, selected randomly, swap a part of their genes between two points selected randomly. At the end of the second stage, P/2 children are produced. During the third step, each chromosome has a probability p of mutation. When a chromosome is chosen, two genes (from two different classes) are selected and exchanged. At the end of these phases, a new population, constitued by P/2 chromosomes selected in the first step and P/2 chromosomes obtained after application of crossover and mutation, is obtained. The three steps are repeated M times.

III. RESULTS

After tests, we set the parameters of our algorithm as follows : P = 100, M = 50, p = 0.1. Our results show on 5 different sections that our GA provides a better clustering than k-means, compared to the reference image. Figure 1 shows an example. The crypts are more precisely defined in Figure 1 (c) (red cluster) than Figure 1 (b) (green cluster). Also, the solution given by the GA is able to reveal the heterogeneity of the lamina propria by representing two classes in Figure 1 (c) (cyan and orange clusters) instead of one in Figure 1 (b) (red cluster). The comparison of fitness between k-means (307.3424) and GA (299.3287) confirms the better quality of the solution provided by GA.

IV. DISCUSSION-CONCLUSION

Applied on FTIR images of human normal colon, the proposed GA estimates more precise results than a classic clustering method such as k-means. The different structures of the human normal colon and the heterogeneity of the lamina propria are detected by GA. However, the computational time is greater for the GA. One way of overcoming this problem is to hybridize GA with a local search method to accelerate the convergence to a global optimum.

In conclusion, the spectral histology is an innovative technique that proposes an alternative for conventional histology. For optimal classification, a genetic algorithm was proposed. The results show that genetic algorithm is effective to optimally detect all structures of human normal colon tissue and their heterogeneity unlike k-means method.

Figure 1 :

 1 Figure 1: (a) HE stained image of tissue where the muscularis mucosae, the crypts, the lamina propria, and the submucosa are respectively annotated by numbers (1), (2), (3) and (4). (b) k-means partition with k = 7 (fitness = 307.3424). (c) GA partition with k = 7 (fitness = 299.3287). (d) Fitness variation of GA between the best solution in first population (fitness = 306.9284) and the last population (fitness = 299.3287).

ACKNOWLEDGMENTS

Authors thank Cancéropôle Grand-Est, Ligue contre le Cancer, the URCA technological platform of cellular and tissular imaging PICT-IBiSA, Région Champagne-Ardenne, Région Alsace and Ministère de l'Enseignement Supérieur et de la Recherche for financial support.