Matthias Lopez

Jean-François Clément

Pascal Szriftgiser

Jean Claude Garreau

Dominique Delande

Experimental Test of Universality of the Anderson Transition

Keywords: numbers: 72.15.Rn, 03.75.-b, 05.45.Mt, 64.70.Tg

We experimentally test the universality of the Anderson three dimensional metal-insulator transition. Nine sets of parameters controlling the microscopic details of this second order phase transition have been tested. The corresponding critical exponents are independent (within 2σ) of these microscopic details, and the average value 1.63 ± 0.05 is in very good agreement with the numerically predicted value, ν = 1.58.

In the presence of a disordered potential, the classical diffusive transport of a particle can be inhibited by quantum interference among the various paths where the particle is multiply scattered by disorder, a puzzling phenomenon known as Anderson localization [1]. The dimensionality of the system plays a major role, which can be understood qualitatively from the scaling theory of localization [2]. In dimension d = 3 and above, there is a delocalized-localized (or metal-insulator in solid-state physics language) transition -known as the Anderson transition. An energy "mobility edge" E c , which is a decreasing function of disorder, separates localized motion at low energy from diffusive motion at high energy. On the localized side, the localization length ξ diverges algebraically ξ(E) ∝ (E c -E) -ν , with ν the critical exponent of the transition. On the diffusive side, the diffusion constant vanishes like D(E) ∝ (E -E c ) s with, according to the scaling theory, s = (d-2)ν [2,3]. A key prediction of the scaling theory is that the critical exponents are universal, that is, they do not depend on the microscopic details of the system, such as the correlation functions of the disorder, the dispersion relation of the particles, etc. Numerical experiments on simple models [4][5][6] such as the tight-binding Anderson model, have confirmed this universality, with a non-trivial value of the critical exponent around ν = 1.58 for spinless time-reversal invariant 3-dimensional (3D) systems [7]. However, there is a huge lack of experimental results. In this letter, we present accurate measurements of the critical exponent ν in 3D, and, by varying the various experimental parameters, test whether its value is universal.

Anderson localization is due to interference between long multiple scattering paths and is thus very sensitive to any mechanism destroying the phase coherence of the wavefunction, making its experimental observation and characterization very difficult [8]. In the context of electronic transport in disordered samples, electron-electron interaction is sufficiently important to partly invalidate the one-body Anderson scenario, leading to a critical exponent close to unity [9]. In a slightly different context, Anderson localization of acoustic [10] and electromag-netic [11][12][13] waves has been experimentally observed. There, absorption is a limitation, and the critical exponent ν ≈ 0.5 estimated in [13] does not agree with the numerical simulation result 1.58.

Cold atomic gases are conceptually simple systems which can be exposed to well controlled disorder. For sufficiently cold samples, the phase coherence time of the wavefunction describing the center of mass motion can be kept sufficiently long for atomic interferometry experiments to be routinely performed. Atom-atom interaction can be reduced to a minimum, either by using dilute cold gases, or by using a Feshbach resonance [14]. Direct observation of Anderson localization of atomic matter waves in a one-dimensional disordered [15] or quasi-periodic [16] potential has been reported, the disordered potential being created by the effective interaction with a detuned laser beam with a random spatial profile (speckle). Very recently, observations of the Anderson localization in a 3D atomic gases have been claimed [17]. However, the interpretation of both results involves heuristic assumptions, and a better understanding is needed before the observation of a mobility edge can be asserted.

This difficulty prompted the use of a slightly different system, where the disordered potential is replaced by classical chaotic dynamics. In the kicked rotor, a paradigmatic system of quantum chaos, quantum mechanical interference tend to suppress the classical chaotic diffusive dynamics, and to induce a phenomenon originally called dynamical localization, later discovered to be an analog of 1D Anderson localization in momentum space, by mapping the kicked rotor onto a quasirandom 1D Anderson model [18]. The experimental realization of the kicked rotor with laser-cooled atoms interacting with a pulsed standing wave allowed the first experimental observation of Anderson localization in 1D with atomic matter waves [19]. In order to observe the Anderson transition, however, an analog of the 3D Anderson model is needed [20]. Here, we focus on the so-called "quasi-periodic kicked rotor" in which three incommensurate frequencies are used to generate the 3D character [21], and shown in [22] to be strictly equivalent to an anisotropic 3D Anderson model, a fact further confirmed by a low-energy effective field theory [23]. Meticulous numerical experiments [6] have shown the universality of the critical exponent for this system, ν = 1.58 ± 0.02, in excellent agreement with values found in the literature for the Anderson model [4].

An experiment based on this system has characterized the Anderson metal-insulator transition [24], with the first experimental determination of the critical exponent ν = 1.4±0.3. The experimental setup, described in detail in [22] consists of laser-cooled cesium atoms interacting with a pulsed far-detuned standing wave (wavenumber k L = 7.4 × 10 6 m -1 and maximum one-way intensity 180 mW). The amplitude of the kicks is modulated with two frequencies ω 2 and ω 3 . The Hamiltonian reads:

H = p 2 2 + K cos x [1 + ε cos (ω 2 t) cos (ω 3 t)] N -1 n=0 δ(t -n) , (1)
where time is measured in units of the kicking period T 1 , space in units of (2k L ) -1 , momentum in units of 2 k L /k, with k = 4 k 2 L T 1 /M (M is the atom mass) playing the role of an effective Planck constant ([x, p] = ik) and K is the average kick amplitude. The kicks are short enough (duration τ = 0.8 µs) compared to the atom dynamics to be considered as Dirac delta functions. If ω 2 , ω 3 , π and k are incommensurate, this 1D quasiperiodic kicked rotor has a 3D Anderson metal-insulator transition, displaying localization in momentum space. Compared to [24] and [22], the signal to noise and the stability of the experiment have been greatly improved. Atomic momentum is measured by Raman stimulated transitions. The previous Raman frequency generation setup used direct current modulation of a master laser diode to drive the Raman slave lasers [25]. This system has been replaced by a fibered phase modulator driven at 9.2 GHz. Moreover, 3 (of 4) master diode lasers working with an external cavity setup have been replaced by distributed feedback lasers, extending the experiment stability from a few hours to several days. These improvements lead to much better experimental signals, making the determination of the critical exponent much more accurate and reliable, opening the possibility to test its universality.

A Sisyphus-boosted magneto-optical trap prepares an initial thermal state of FWHM 4 × 2 k L , much narrower than the final (localized or diffusive) momentum distribution, and -by time-reversal symmetryp(t) remains zero at all time t. We can directly monitor the dynamics rather than rely on "bulk" quantities such as the conductance, itself related to the diffusion constant. A good quantity characterizing the dynamics is p 2 (t) . For practical and historical reasons, the atomic momentum P is measured in units of two recoil momenta: In the diffusive regime, p 2 (t) increases linearly with time; in the localized regime, it saturates at long times to a value proportional to the square of the localization length. In [22], it was shown that, in order to characterize the Anderson transition, one should measure:

p = p k = P 2 k L . ( 2
)
k ω 2 2π ω 3 2π Path in (K, ε) Kc ν A 2.89 √ 5 √ 13
Λ(t) = p 2 (t) t -2/3 . (3)
Λ(t) scales like t -2/3 in the localized regime, like t 1/3 in the diffusive regime and is constant in the critical intermediate regime. By measuring Λ(t), one has thus a direct access to the state of the system. K is a control parameter playing the role of the energy in the Anderson model. The critical value K c is a mobility edge separating a localized regime at low K from a diffusive regime at large K.

The critical exponent ν can be determined from the algebraic divergence 1/(K c -K) ν of the localization length near the critical point. For fixed k, ω 2 , ω 3 , one can also chose a path in the (K, ε) plane which crosses the critical line "at right angle", i.e. faster, which improves the accuracy on the critical exponent. Rather than measuring the full momentum distribution to obtain p 2 (t) , we measure the atomic population in the zero-momentum class Π 0 (t).

As shown in [26], p 2 (t) is, by conservation of the number of atoms, proportional to Π -2 0 (t). The precise proportionality factor depends on the shape of the momentum distribution, which has been shown experimentally [26] to vary smoothly across the transition. The quantity measured experimentally, Λ exp (K, t) = Π -2 0 (K, t)t -2/3 , has the same critical point and the same critical exponent than Eq. (3). In the simplest experiment, parameters k, ω 2 , ω 3 , ε are fixed and Π 0 (K, t) recorded for several values of the control parameter K, from which Λ exp (K, t) is obtained.

As one cannot pursue the experiment for arbitrary long times, making the distinction between the true critical point where Λ exp (K c , t) is a constant and a neighboring point of small positive (localized) or small negative (diffusive) slope is difficult. To circumvent this, we use the finite-time scaling procedure explained in [22], which is a simple extension to the time domain of the finite-size scaling method used in solid-state physics [27]. We assume that there exists a scaling function F such that:

Λ exp (K, t) = F ξ(K)t -1/3 (4)
where ξ(K) is an unknown function to be determined. The idea, described in detail in [22,28] is that ξ(K) should be chosen so that F ξ(K)t -1/3 is an continuous function, safe for the divergence at the critical point, with two distinct localized and diffusive branches. In order to do so, we try to collapse the various experimental curves Λ exp (K, t), corresponding to each value of K, in a single curve, the various ξ(K) -associated to the localization length on the localized branch -being free fitting parameters. A typical scaling function is shown in Fig. 1 and the corresponding fit parameter function ξ in Fig. 2. Comparison with our previously published data, e.g. Fig. 3(c) in [24], shows a dramatic improvement in the quality of the measurements. Each point Λ exp (K, t) results from independent experiments, making the statistical errors rather easy to evaluate. We checked that the dispersion of points around the scaling function in Fig. 1 is of the order of ∆(ln Λ) ≈ 0.05, limited by the experimental uncertainties, the χ 2 per degree of freedom of the fit being typically slightly smaller than 1.

From finite-time measurements, it is impossible to extract a truly diverging ξ(K). Several spurious phenomena [22] are responsible for the observed cut-off: The dominant one is the finite duration of the experiment. Several sources of decoherence, such as spontaneous emission, collisions between atoms, residual effect of gravity because the laser beams are not perfectly horizontal, and the inhomogeneity related to the Gaussian inten- The "divergence" near Kc = 4.69 is a signature of a second order quantum phase transition. Several phenomena limit this divergence, see text for discussion. They are taken into account by a fit including a cut-off parameter, Eq. ( 5), shown as a solid curve, from which the critical exponent ν is extracted.

sity profile of the standing wave contribute to the cutoff. We have increased the phase coherence time up to 200-300 kick periods, in agreement with theoretical calculations [22]. In order to reduce uncontrolled systematic effects, we chose to use the same time interval -from 30 to 150 kicks -for the analysis of all experimental data. The finite duration is also responsible for systematic effects: It tends to slightly underestimate K c , but does not seem to shift significantly the critical exponent. Using a different interval, 30-120 kicks, produces ν values not differing by more than 0.05. A typical ξ(K) curve, Fig. 2, displays a clear "divergence" near the critical point (increase by more than one order of magnitude, much better than in [24]). It is itself fitted to extract the position of the critical point K c and the critical exponent ν, using the following formula:

1/ξ(K) = α|K -K c | ν + β ( 5
)
where β is a cut-off parameter taking into account the various limitations discussed above. As seen in Fig. 2 the fit is excellent. The fitting parameter ν depends on the range of K where the fit is performed. A too small range produces a large uncertainty in ν while the quality of the fit deteriorates for a too large range. To avoid any bias, we have fitted all data sets in the interval [0.8K c , 1.2K c ], for which the χ 2 per degree of freedom is of the order of 1. The uncertainties are calculated using a bootstrap method starting from the raw experimental data and their error bars, ending to the determination of ν through the construction of the scaling function. For data sets presented, no statistically significant anomaly has been detected. The statistical uncertainty on K c is very small, at most few 10 -2 , but the finite duration of the experiment is responsible for a systematic shift towards low K (see above).

In order to test the universality of the critical exponent, we have chosen a "reference" set of parameters, noted A in table I, which has the same parameters used in [24]. We have then modified the ω 2 and ω 3 frequencies for set B. We have also modified the path in the (K, ε) plane, either by changing K only (set C) or ε only (set D). In these two situations, the crossing of the critical regime is slower, making the accuracy on ν significantly worse. We have further modified the kicking period T 1 , which affects the effective Planck's constant k. Several smaller k values have been used in sets E, F and G. One larger value of k was used in sets H and I the difference between the two sets being the duration of the laser pulses. The fact that very close values of K c and the same critical exponent are obtained is a strong indication that our experimental system is well described by the model Hamiltonian, Eq. (1).

The final results are given in table I and plotted with their error bars (one standard deviation) in Fig. 3. They unambiguously demonstrate the universality of the localized-diffusive transition in the quasi-periodic kicked rotor. Moreover, all numerical values are compatible (within 2 standard deviations) with the best numerical determinations of ν = 1.58 ± 0.02, both for the kicked rotor and the Anderson model. They all markedly differ from the value 1 predicted by the self-consistent theory of localization [START_REF] Vollhardt | Electronic Phase Transitions[END_REF]. The later theory is an attempt to justify the scaling properties using a microscopic approach: It is qualitatively correct and gives simple physical pictures. For example, it has been used to successfully predict the momentum distribution at the critical point [26]. However, it lacks a key ingredient: At criticality, the wavefunctions display very large fluctuations which can be characterized by a multifractal spectrum [7,[START_REF] Martin | [END_REF]31]. Huge fluctuations are known to affect critical exponents of ther-modynamic phase transitions, it is thus no surprise that they also affect the Anderson transition. While quantum phase transitions are usually considered for the ground state of the system, it must be emphasized that the Anderson transition deals with excited states in the vicinity of the mobility edge, displaying much richer properties. Especially, ultra-cold atomic gases open the way to experimental studies of the interplay of disorder, interference and interactions.

Figure 1 :

 1 Figure 1: Typical scaling function constructed from the experimental data measured on the quasi-periodic kicked rotor (set E of Tab. I). The tip on the right side indicates the critical point of the Anderson transition, the diffusive (resp. localized) regime is the upper (resp. lower) branch. The dispersion of the points is an indication of the uncertainty on the measured data.

Figure 2 :

 2 Figure 2: (color on line) Red points with error bars: Characteristic length ξ(K) constructed from the experimental data (set E of Tab. I). At low K (localized regime), it is proportional to the localization length. At large K (diffusive regime), it is inversely proportional to the diffusion constant.The "divergence" near Kc = 4.69 is a signature of a second order quantum phase transition. Several phenomena limit this divergence, see text for discussion. They are taken into account by a fit including a cut-off parameter, Eq. (5), shown as a solid curve, from which the critical exponent ν is extracted.

Figure 3 :

 3 Figure 3: (color online) Experimental test of the universality of the metal-insulator transition. The critical exponent ν, measured for 9 different sets of parameters A-I, is universal, i.e. independent of the microscopic details. The error bars indicate one standard deviation, measured using the experimental uncertainties and a bootstrap technique. The horizontal dashed line is the commonly accepted value ν = 1.58, determined from extensive numerical calculations on various models. Parameter values: See Tab. I.

Table I :

 I The 9 sets of parameters used: k, ω2 and ω3 control the microscopic details of the disorder, K controls the amplitude and ǫ the anisotropy of the hopping amplitudes. The critical point Kc depends on the various parameters but the critical exponent is universal. The weighted mean of the critical exponent is ν = 1.63 ± 0.05. The duration of the kicks is τ = 0.8 µs for sets A-H, and τ = 0.96 µs for set I.

	B 2.89 C 2.89 D 2.89 E 2.00 F 2.31 G 2.47 H 3.46 I 3.46	√ √ √ √ √ √ √ √	7 5 5 5 5 5 5 5	√ √ √ √ √ √ √ √	4,0.1 4,0.1 13 3,0.435 17 13 7.5,0 13 3,0.1 13 4,0.1 13 4,0.1 13 4,0.1 13 4,0.1	8,0.8 8,0.8 10,0.435 7.5,0.73 εc=0.448 1.67±0.18 6.67 1.63±0.06 6.68 1.57±0.08 5.91 1.55±0.25 5.7,0.73 4.69 1.64±0.08 9,0.8 6.07 1.68±0.06 9,0.8 5.61 1.55±0.10 9,0.8 6.86 1.66±0.12 9,0.8 7.06 1.70±0.12

We thank G. Lemarié for useful discussions, and R. Holliger for help with the experiments.


Patrick Schiavone
email: patrick.schiavone@cea.fr

Emmanuel Promayon
email: emmanuel.promayon@imag.fr

Yohan Payan
email: yohan.payan@imag.fr

LASTIC: A Light Aspiration Device for in vivo Soft TIssue Characterization

This paper introduces a new Light Aspiration device for in vivo Soft TIssue Characterization (LASTIC). This device is designed to be used during surgery, and can undergo sterilization. It provides interactive-time estimation of the elastic parameters. LASTIC is a 3cm x 3cm metallic cylinder divided in two compartments. The lower compartment is a cylindrical chamber made airtight by a glass window in which a negative pressure can be applied. Put in contact with soft tissues, it can aspirate the tissues into the chamber through a circular aperture in its bottom side. The upper compartment is clinched onto the lower part. A miniature digital camera is fixed inside the upper chamber, focusing on the aspirated soft tissue. LASTIC is operated by applying a range of negative pressures in the lower compartment while measuring the resulting aspirated tissue deformations with the digital camera. These measurements are used to estimate the tissue elasticity parameters by inverting a Finite Element model of the suction experiment. In order to use LAS-TIC during surgical interventions, a library-based optimization process is used to provide an interactive time inversion.

Introduction

Physically based models are now widely used in the field of biomedical engineering, to represent human organs' geometrical and mechanical behavior. These models are mostly used to better understand and validate a given surgical treatment, to model physiological behaviour or to provide virtual simulators for clinicians. While virtual simulators were mostly limited to a single preset model, applications such as Computer Assisted Planning and Computer Aided Surgery sparked the need for patient-specific models. In order to precisely model and simulate a patient's organ or tissue, a specific geometry and a specific biomechanical model of the patient's organ or tissue has to be generated. This implies to build a conforming mesh of the patient's organ geometry, choose the appropriate constitutive law and extract the proper mechanical parameters from the patient tissue.

Organ geometries are in general reconstructed from patient medical image data, such as computed tomography or magnetic resonance imaging. The mechanical behaviors depend on the deformable model parameters, e.g. the spring stiffness in discrete mass-spring models or the constitutive equation in Finite Element models. These parameters are often inferred from image-based deformation measurements (elastography) or experimental mechanical excitations on ex vivo or in vivo tissues. Mechanical experiments are generally performed on ex vivo tissue samples using mainly indentation/stretching devices that exert a stress onto a passive tissue and record its corresponding deformations [START_REF] Ottensmeyer | Minimally invasive instrument for in vivo measurement of solid organ mechanical impedance[END_REF]. With a precise control of the tissue sample size and of the external force directions and intensities, these experiments can provide reliable stress/strain curves, or even determine some tissue anisotropy.

The stress/strain laws provided by experiments on ex vivo tissues are very useful for virtual simulators as they mostly need average values for the elastic parameters. The same holds true for other applications such as computer aided planning since getting patient-specific in vivo measurements is extremely complex. However, it has clearly been shown ( [START_REF] Gefen | Are in vivo and in situ brain tissues mechanically similar?[END_REF], [START_REF] Kerdok | Effects of perfusion on the viscoelastic characteristics of liver[END_REF]) that the mechanical behavior of soft tissue can differ significantly between in vivo and ex vivo conditions for a number of reasons, including the vascularization of the tissue and the changes in the boundary conditions. Therefore, in vivo measurements seem almost mandatory to take into account patient specificities in Computer Assisted Planning and Surgery.

This paper aims at introducing the latest version of our in vivo suction device designed to be used in the context of Computer Assisted Surgery. This device takes into account the application constraints, i.e. full sterilization and interactive-time estimation of the tissues constitutive equations. By interactive time, we mean that the full process is not real time but is fast enough (less than a minute) to be used within the operation theater with no time penalty for the surgeon. The speed limiting factor is here the data acquisition, not the solution of the inverse problem of retrieving the mechanical parameters from the measured data. The next section provides a state of the art of the in vivo devices proposed in the literature while section 3 describes our suction device and explains how the constitutive equations are estimated in an interactive time. Section 4 provides some results for a clinical case. Section 5 ends the paper with a discussion and a conclusion.

In Vivo Devices: State of the Art

With the design of its Tissue Material Property Sampling Tool (TeMPeST), in parallel with Carter et al. [START_REF] Carter | Measurements and modelling of the compliance of human and porcine organs[END_REF], Mark Ottensmeyer [START_REF] Ottensmeyer | Minimally invasive instrument for in vivo measurement of solid organ mechanical impedance[END_REF] pioneered development of an indentation tool that could be used on in vivo tissues. The objective was to drastically reduce the size of the device in comparison with what is usually provided by commercial indentation machines. The TeMPeST is a 12 mm diameter minimally invasive instrument, designed to investigate viscoelastic properties of solid material under small deformations. A 5 mm right circular punch vibrates the material surface while recording applied load and relative displacement. Our lab bought a prototype of this device and tried to use it to characterize the elastic properties of tongue and cheek tissues. Despite the nice ergonomy and small size of the TeMPeST, we encountered important difficulties in estimating the elastic parameters of tongue and cheeks tissues. Indeed, it was almost impossible for the subjects to keep immobile while recording the force/displacements curves and of course impossible to stop the organ movements due to inner physiology such as blood flow and the corresponding beating movements. This leads to the loss of a fixed reference between the TeMPeST and the organs. The resulting measurements mixed the controlled TeMPeST punch as well as the organ natural displacements, which generated an error on the measured elasticity.

Other excitation methods including a robotic indenter [START_REF] Samur | A robotic indenter for minimally invasive measurement and characterization of soft tissue response[END_REF], a torsion device [6] or a ballistometer [START_REF] Jemec | Measurement of the mechanical properties of skin with ballistometer and suction cup[END_REF] exist. It is, however, unclear whether the problem of relative displacements between the excitation tool and the organ could be eliminated by these methods. On the other hand, suction techniques provide a full link between the device and the organ that guarantees that there is no uncontrolled relative motion. The principle of suction methods is the measurement of organ elevation caused by the application of a partial vacuum via a circular aperture in a measuring probe. For most human soft tissues, the relevant range for the negative pressure is between 10 mbar to 500 mbar. The deformation can be measured with an optical or ultrasound system. Starting from the pioneering work by Grahame and Holt [START_REF] Grahame | The influence of ageing on the in vivo elasticity of human skin[END_REF], several authors proposed suction cups ( [START_REF] Vuskovic | Device for in-vivo measurement of mechanical properties of internal human soft tissues[END_REF], [START_REF] Diridollou | In vivo model of the mechanical properties of the human skin under suction[END_REF], [START_REF] Mazza | Mechanical properties of the human uterine cervix: an in vivo study[END_REF]). Most devices were developed to be used on external tissues [START_REF] Wang | Portable gage for pressure ulcer detection[END_REF], some of them leading to commercial products designed specifically for dermatology market. Very few suction devices were developed and evaluated for tissues that are only reachable during surgery. To our knowledge, only the suction device of Vuskovic [START_REF] Vuskovic | Device for in-vivo measurement of mechanical properties of internal human soft tissues[END_REF] was tested on the uterine cervix during surgery and more recently on the liver [START_REF] Nava | In vivo mechanical characterization of human liver[END_REF]. This is probably due to the rather drastic sterilization process needed for each ancillary that has to be used in the sterile field of the operation theater. Sterilization is carried out using very rigorous processes such as (a) steam under pressure, (b) heat or (c) chemicals under a liquid, gaseous or plasma form. The fragile parts of a measurement device can be easily damaged under these conditions, especially electronic parts such as sensors, actuators or circuitry which are not very resistant to such severe environments and conditions. Moreover, not only are the parts in close contact with the operating field to be fully sterilized, but also every pieces of the instrument which could come into contact with any projection of liquid during surgery. Design can deal with this to a certain extent. For example, the electronic parts of the suction device of Nava et al. [START_REF] Nava | In vivo mechanical characterization of human liver[END_REF] are not sterilized but are integrated in the system and the authors mention that they are never in direct contact with the patient.

We recently developed a suction device that is able to meet the very rigorous sterilization and handling process imposed during surgery [START_REF] Schiavone | In vivo measurement of human brain elasticity using a light aspiration device[END_REF]. The device, which has no electronic component, is simple, light and can be considered as an ancillary instrument. The deformation of the aspirated tissue is imaged via a mirror using an external camera. The device was used to provided some measurements on a patient brain during a neurosurgery (Figure 1). This device was quantitatively evaluated on other organs such as tongue, cheeks and forearm skin. It appeared that the process needed to collect the photos from the camera, to measure the tissues elevation and to estimate the constitutive law was incompatible with an interactive-time use of the device. Such an interactive-time is needed in order to include soft-tissue modeling in Computer Assisted Surgery. In order to achieve interactive-time performance, improvements were sought in two area: a) the image capture and segmentation, and b) the elastic material parameter estimations. The following section describes these improvements and presents the latest version of our device.

3 Our New Suction Device

Device Description

The major drawback of the first version of the light suction device is that, since the camera is handheld, the camera optical axis is not always aligned with the mirror. Only the skill of the operator guarantees that the angular offset is close to zero therefore minimizing the parallax error in the aspired tissue height measurement. Another issue lies in the absence of synchronization between the image capture and the pressure measurement. Although the device is operated in static mode, several causes of short term (< 2 s) pressure variation can occur and cause the pressure reading to be shifted in time with respect to the image capture. This turned out to be one of the major cause of error in the measurements performed until then.

The new Light Aspiration device for in vivo Soft TIssue Characterization (LASTIC) is designed to overcome these issues while keeping the suction cup as light as possible and maintaining compatibility with the sterilization process required by an intra operative use. The basic design is not very far from the one of Vuskovic [START_REF] Vuskovic | Device for in-vivo measurement of mechanical properties of internal human soft tissues[END_REF] except for the compactness. This is a major advantage since it allows using the device even when the access to the tissue is limited in size. The light weight makes the device self positioned as soon as the negative pressure is applied. There is no need for a initial force exerted by the user to hold the suction cup in contact with the tissue. We use a 2 Mpixel mobile phone camera sensor VS6750 from STMicroelectronics. Its overall size is 1 cm. We had it fitted inside a very compact cylindrical case (33 mm in height ×34 mm in diameter) that encloses both the camera and the mirror. A scheme and a picture of the full device can be seen in Figure 2. It is made of two cylindrical parts that fit together. The lower part is fully passive, it encloses a 45 mirror and its mount. Its bottom side is drilled with a 10 mm circular hole. A lateral hole equipped with a Luer-Lock connector allows application of a negative pressure to the suction cup. An airtight transparent polycarbonate window closes the top end of this cylinder. This part is expected to withstand the full sterilization treatment.

The upper part encloses the miniature camera and its mount as well as a Light Emitting Diode. The camera is precisely aligned with the mirror using a flexible adjustable mount. Proper focus setting is made by slightly screwing down or unscrewing the built-in camera lens mount. Due to the electronic components, this part cannot withstand elevated temperature. It can be sterilized either using a gas or liquid treatment thanks to a specifically designed air-tight cap that hermetically seals this part. When assembled, both parts constitute an airtight case that is put in contact with the tissues.

In addition to the hardware part of the device, we also significantly improved the data collection as well as the control of the negative pressure and its synchronization with the image capture. The negative pressure is applied using a syringe handled by a software-driven calibrated push-syringe. Since the pressure application is static, there is no pressure lag between the reading from the manometer and the suction cup. We also check for a steady reading from the manometer, which is an indication that no leak occurs. A software program controls the application of the negative pressure, the pressure measurement from an interfaced manometer as well as the synchronisation with the image acquisition. Each one of the three digitally interfacable instruments is connected to the data acquisition board of a laptop computer. A typical measurement takes less than ten seconds during which the pressure is decreased step by step and an image is taken at each step, synchronized with the pressure acquisition from the manometer.

The design of the new suction cup with a built-in miniature camera as well as a fully computer controlled user interface addresses the two major issues of the first version of our aspiration device. The alignment of the camera and the mirror is fixed and once aligned during the initial assembly of the cup, it does not need to be adjusted again. The synchronization of the pressure measurement with the image acquisition is guaranteed by the software controlled data acquisition.

Interactive-Time Estimation of the Constitutive Equation

The measurements provided by the LASTIC device are used to estimate the tissue elasticity parameters by inverting a Finite Element model of the suction experiment. The aim of this device is to be used in vivo in a context of Computer Assisted Surgery. This requires the solution of the inverse problem to be obtained in a very short time of the order of seconds. Since there is no rigorous mathematical solution of the inverse problem, our problem can boil down to a parametric non-linear optimization scheme. The unknown parameters are the coefficients of the mechanical constitutive law. Multiple schemes can be used to solve this optimization problem. The typical time of a Finite Element Model simulation of the suction experiment for one negative pressure value (which we will call the "direct problem") is approximately 25 seconds on a workstation (Intel Core 2 Quadri-processor Q6600). The exact conditions for the FEM simulation are detailed in [START_REF] Schiavone | In vivo measurement of human brain elasticity using a light aspiration device[END_REF]. Depending on the initial values, a standard optimization routine would need to run the direct problem several tens to several hundreds times with different parameter values before converging to the best set of parameters. The same order of magnitude holds if a global optimization routine such as a genetic algorithm or simulated annealing is used. Needless to say that the time needed to achieve a single optimization is far beyond the time allotted to this constitutive law determination during a computer assisted surgical intervention. That is the reason why we focussed our attention on a library-based method. The library method proves to be very successful whenever an optimization is required of a problem with a computer intensive direct problem. For example it is widely used to solve the inverse problem of electromagnetic diffraction in the so called scatterometry technique which is a nanometer scale dimensional metrology in the field of microelectronic technology [START_REF] Niu | Specular spectroscopic scatterometry[END_REF]. Other strategies exist that consist of making in advance a large number of time consuming direct problem computations, potentially coupled with a form of preprocessing then restricting the final search of the solution to a much simpler analytical or semianalytical problem. Surface response and neural network approaches are among those. Each one has its own pro and cons, we chose to use the simplest, yet brute force method of the library search.

The choice of the constitutive law as well as the detailed description of the Finite Element simulations have been presented in a previous paper [START_REF] Schiavone | In vivo measurement of human brain elasticity using a light aspiration device[END_REF], therefore we will not go in great detail here. Note that in order to avoid edge effects during the FEM resolution, the tissue depth should be more than 4 to 5 times the size of the aspiration hole, i.e. about 5 cm. Should the tissue be non homogeneous, this could be accounted for in the FEM model at the expense of a larger number of parameters and increased computation time. However, the type of inhomogeneity cannot be completely unknown, a priori knowledge has to be used in order for the FEM model to be described and parameterized. In light of the nonlinear stress-strain relationships given by our previous suction measurements on the brain, the medium was assumed to be an isotropic homogeneous and hyperelastic continuum. We selected a two-parameter Mooney-Rivlin strain-energy function, W , using only the first and third power of the first invariant of the right Cauchy-Green strain tensor. A best fit between the experimental data and the results from the calculation of the deformation vs negative pressure curve was used to determine the material constants a 10 and a 30 . In the library method, the calculations are performed in advance and at the time of the measurement, the results are looked up in a file where the computed results have been stored. It can take hours to generate the database, but it takes less than one second to find the best set of parameters in the library. This makes the use in an intraoperative environment fully viable. However, pressure variation is achieved step by step. The simple aspiration control set-up does not allow for dynamic pressure control and dynamic tissue response measurements. All measurements are therefore considered to be fully static.

4R e s u l t s

The LASTIC device has not been used yet for an intra-operative use. It was only evaluated in our lab with measurements on tongue and skin elasticities. Compared to the first version of our device described in [START_REF] Schiavone | In vivo measurement of human brain elasticity using a light aspiration device[END_REF], LASTIC proved much easier to use and install. In addition, the interactive-time estimation of the tissues constitutive equations is a major improvement.

A first quantitative evaluation of this inverse procedure was performed by comparing the results given by the optimization process conducted in Ansys software (Ansys 10 software, Ansys, Inc., Cannonsburg, PA) and by our library based optimization process. The brain measurements described in [START_REF] Schiavone | In vivo measurement of human brain elasticity using a light aspiration device[END_REF] were used. In Ansys, an advanced zero-order method, which only requires the dependent variable values, and not their derivatives (Subproblem approximation method), found the optimal values of a 10 = 240 and a 30 = 3420. Our library-based optimization process found a 10 = 210 and a 30 = 4900. The two constitutive laws are not significantly dissimilar in the pressure range considered (Figure 3, top). Furthermore, the cost-function space is rather smooth and free of local minima (Figure 3, bottom).

The computation times are hardly comparable as our optimization takes less than one second to find the best parameters.

Discussion/Conclusion

This paper introduced the latest version of our Light Aspiration device for in vivo Soft TIssue Characterization (LASTIC). Most of the constraints due to an intra-operative use have been taken into account, with a special focus on the sterilization process and on the interactive time estimation of the elastic parameters. The library search inverse method has been proposed to estimate the tissues constitutive laws and was quantitatively compared with a full optimization direct method based on Ansys Software. Starting from data collected on brain tissues, both methods lead to very similar constitutive laws that match the in vivo measurements. A full validation of the device and inversion method is ongoing that includes an estimation of the errors in the parameter determination as well as a comparison with other more conventional rheology instruments. This is first conducted on model materials such as elastomers or hydrogels.

Fig. 1 .

 1 Fig. 1. Light suction device used to measure brain elasticity: Schematic view (a), intraoperative use (b), photo of the aspirated tissue reflected in the mirror (c) -(from [14])

Fig. 2 .

 2 Fig. 2. LASTIC: scheme (left) and picture (center) of the new suction device. Example of an image captured by the camera during a depression of a PVC phantom (right).

Fig. 3 .

 3 Fig. 3. Comparison of the simulation results for the optimal constitutive laws given by Ansys and by our library-based optimization process, superimposed with measurements points (top). Value of the optimization cost function (least mean square) for the (a10,a30) considered range for the brain tissues characterization (bottom). The white circle corresponds to the local minima found by our method.

Acknowledgement

The authors wish to thank T. Boudou and J. Ohayon for their contribution to this work, especially the discussion about the aspiration experiment and model inversion.


Muhammad Tayyab

Athanasios Lontos
email: athanasios.lontos@imag.fr

Emmanuel Promayon
email: emmanuel.promayon@imag.fr

Jacques Demongeot
email: jacques.demongeot@imag.fr

Modelling and Image Processing of Constriction and Proliferation in the Gastrulation Process of Drosophila melanogaster

Keywords:

published or not. The documents may come   L'archive ouverte pluridisciplinaire

INTRODUCTION

During the morphogenesis of the gastrula, the second step of the embryogenesis after the blastula stage, we observe in the majority of the animal development dynamics, the following phenomena: i) the cell motion is partly guided by chemotaxis, in order to supply their substrate demand, and also to respect the epigenetic architecture ruled by morphogens, ii) the cell shape is due to a constriction controlled by cell differentiation and iii) the final gastric tube is obtained from cell proliferation relaxing the forces exerted on the cell plasmic membrane and optimizing the cellular "nutritive Area / inner Volume" (A/V) ratio. Concerning the differentiation process, some cells of the embryo start to take the shape of a bottle (bottle or flask cells), decreasing the surface at the interface with their nourishment fluid. At the end of the gastrulation, these bottle cells start to divide and grow, increasing their A/V ratio. In this paper, we are attempting firstly to follow by using image processing techniques the first phase of the gastrulation made of pure cell motion causing the invagination without any proliferation, and secondly to show that the cell constriction results in a streak starting on the two extremities of the embryo and propagating secondly to its central part. In order to simulate the initiation of this phenomenon, we use exclusively laws of physics and mechanics. For this purpose, we have created a threedimensional biomechanical model consisting of a group of cells, forming a structure with two areas: a cylindrical rigid area representing the main embryo body and two curved hemispheric areas constituting the embryo extremities. Each cell is modelled by a set of Newtonian contour particles defining the surface mesh and an inner particle, located at the geometric centre o f t h e c e l l , m i m i c k i n g t h e c e n t r o s o m e . Elastic forces are used to model the rigidifying effect of the tubulin and actin cytoskeleton, and contractile forces to model the action of the myosin fibers. In addition, we have modelled the role of the cadherins by connecting contour particles of adjacent cells. Finally, in order to ensure the symmetry from a partial mesh representing only a part of the embryo, we have applied boundary conditions to the particles located at the lateral e x t r e m i t y e d g e s o f t h e s i m u l a t e d structure. This biomechanical model shows that the inner folding starts at the curved area and then propagates to the rigid one, in accordance with the in vivo process. To compare these results with in vivo experiments, we have monitored the displacement o f t h e centrosome and the cell A/V ratio. Our numerical experiments made during the time lag observed through the microscopic imaging without proliferation suggest that our model adequately simulates thge in-vivo cell behaviour. In a first part, we present image processing techniques and results obtained by applying them on gastrulation microscopic recording of Drosophila melanogaster embryo from [2-6]. In a second part, we describe the biomechanical model of streak formation and the third Section will be devoted to the presentation of numerical simulations confronted to real images of the first invagination stage of the gastrulation.

II. IMAGE PROCESSING

2.1. Image processing techniques: cell countouring and counting Many cell-based research studies require the counting of cells prior to beginning an experiment. Estimation of cell density in various regions of embryo is thus an integral part of such studies. Profile counts or stereological techniques could be used to have an estimate of the cell density in a particular region. The regions where cell density increases enormously 3.2 The model Each cell evolves following the mechanical laws: 1) the sum of the orthogonal forces exerted on the cell walls is equal to its mass (proportional to its inner area) times its orthogonal (to the wall) acceleration. The external forces are the resultant of the extracellular (Pext) and intracellular (Pint) pressure, the contact forces being exerted by the neighbouring cells (sharing a part or the whole of the wall) exerted by other cells and the internal force is due to the cell pressure exerted via the cyto-skeleton and the plasmic membrane [START_REF] Leptin | Gastrulation in Drosophila: the logic and the cellular mechanisms[END_REF]. Each force is equal to a coefficient (e.g. the physical pressure) times the length of the wall on which it is exerted 2) If we suppose that the initial cell configuration is in an equilibrium state, we calculate an admissible set of parameters values respecting this equilibrium 3) Then, we leave the cell system evolve depending on the energetic balance r u l i n g

The revolution symmetry breaking consists in making two cylinders inside the embryo cylinder, one coming from the ventral furrow and giving the digestive tube (this phase is called gastrulation) a n d t h e o t h e r c o m i n g f r o m t h e d o r s a l furrow and giving the neural tube ( t h i s p h a s e i s c a l l e d neurulation)

. The first gastrulation step consist in an apical concentration overfluctuation of one of the cytoskeleton components (myosin, actin, tubulin,...) or one of the enzymes (ADenylate Kinase -A D K -o r N u c l eoside Diphosphate Kinase -NDK) or one of the energy molecules (ATP, GTP) involved [START_REF] Glade | Numerical Simulations of microtubule self-organisation by reaction and diffusion[END_REF][START_REF] Tabony | Biological selforganisation by way of microtubule reaction-diffusion processes[END_REF][START_REF] Tabony | Microtubule selforganisation as an example of the development of order in living systems[END_REF][START_REF] Glade | ! t u b u l e s e l f -organisation by reaction-diffusion processes causes collective transport and organisation of cellular particles[END_REF][START_REF] Glade | Numerical Simulations of microtubule self-organisation by reaction and diffusion[END_REF][START_REF] Tabony | Biological selforganisation by way of microtubule reaction-diffusion processes[END_REF]. This apical overconcentration diffuses and reaches the extremities [START_REF] Oda | Real-time imaging of cell-cell adherens junctions reveals that Drosophila mesoderm invagination begins with two phases of apical constriction of cells[END_REF][START_REF] Dawes-Hoang | Folded gastrulation, cell shape change and the control of myosin localization[END_REF] of the cylindric portion of the embryo at which gap junctions are less important with the cells of the "hemispheric" terminations. Then two first bottle cells can appear at the two extremities of the diffusion line, then this first contraction can propagate until the center of the cylindric part as noticed in [START_REF] Oda | Real-time imaging of cell-cell adherens junctions reveals that Drosophila mesoderm invagination begins with two phases of apical constriction of cells[END_REF][START_REF] Dawes-Hoang | Folded gastrulation, cell shape change and the control of myosin localization[END_REF] during the 6 first hours of the gastrulation in Drosophila melanogaster. After this first phase of the ventral furrow formation, for regularizing the tensegrity forces, based on a synergy between balanced tension and compression components of cells, first divisions occur from extremities to center by applying the first Thom's cell law. We can simulate such a process on a transversal slice of the embryo and reproduce the invagination of the gastrulation from both the contraction and consecutively the proliferation phases.

The end of the cell and tissue growth stops correspond to the end of the morphogenesis process: this can be observed when the second Thom's tissue law is applicable (the surface to volume ratio of an organ becoming adverse) or when the organ is completely covered by an anatomic boundary like an aponeurosis made of fibrous cells or an autoassemblage of extracellular ingredients.

In both these cases, a couple of morphogens acting often simultaneously i n opposit e (e. g. a coupl e of acti vat or and inhibitor like BMP-7 and BMP-2 in feather morphogenesis in the chicken [START_REF] Abbas | Synchrony in Reaction-diffusion models of morphogenesis: applications to curvature-dependent proliferation and zero-diffusion front waves[END_REF][START_REF] Michon | BMP-2 and BMP-7 play antagonistic roles in feather induction[END_REF][START_REF] Forest | What is the biological basis of pattern formation of skin lesions? Viewpoint 4. Skin Patterns belong to three main types, determined at three steps of development[END_REF][START_REF] Demongeot | Biological boundaries and biological age[END_REF] can induce the chemotactic motion of fibroblats or the biosynthesis of the elements constituting the auto-assemblage (like proteins and phospholipids). The fact that for a certain value of their viscosity ratio, the morphogens can coexist for a relatively long time in a precise location can greatly favor the birth of anatomic organ boundaries.

II. NUMERICAL SIMULATIONS

The myosin is supposed to diffuse in all directions from a cell in which an excess of myosin is synthesized caused by random fluctuations over-expressing its gene, notably along a directrix

V. CONCLUSION

We given in this paper some examples (centred around the gastrulation process) concerning d i f f e r e n t s t e p s o f morphogenesis modelling f r o m e x p e r i me n t a l a c q u i s i t i o n o f pertinent data until the interpretation in a mathematical framework of the dynamic or the g e o m e t r i c f e a t u r e s o f observed forms and functions.

We will in the future increase the spatial and temporal resolution of the data by sampling in 3D with a good precision in space (e.g. by using confocal or biphotonic microscopic information), in time (e.g. by using the cine-microscopy) and in function (e.g. by using the Raman vibrational, infrared,..., spectro-microscopy), in order to detect precisely the frontiers between the successive phases of the morphogenetic process of revolution symmetry breaking in the embryo, i.e., i) the morphogen diffusion, ii) the cell migration, iii) the bottle cell differentiation, iv) the streak contraction and v) cell the proliferation ensuring vi) the tube closure.

  t h e c y t o s k e l e t o n a p i c a l polymerization [ 4-6] c o n t r o l l e d b y a s p e c i f i c g e n e t i c regulatory n e t w o r k c o m p r i z i n g e s s e n t i a l l y c o n c e r t i n a ( c t a ), actin, myosin, Rho and RhoGEF genes [7-10], by choosing a small time step, by updating sequentially each cell and by calculating their displacements respecting the no-overlapping rule. At each step we update the cell common walls by supposing that cell contacts are close, ensured between cells by cadherins and gap junctions [11,12], and with the extracellular matrix by integrins and adhesins. Cell motion involves a change in its inner area: we suppose that growth occurs where internal forces Fint are larger than external ones Fext (cell has to be stretched), as for constrained growth in continuous media mechanics. When the external forces dominate, the cell is s u p p o s e d c o m p r e s s i b l e a n d c a n b e constricted. The cells divide longitudinally or laterally when their ratio perimeter over area is too small [13-17].

Figure 3 :

 3 Figure 3: Left: cell contraction due to myosin (experiments [36]). Centre: progressive invagination and streak formation. Right: myosin diffusion along a directrix of the cylindric part of the embryo (green arrow) provoking the invagination before the tube closure (red star). The zero-diffusion domain for myosin is indicated in yellow.


Dr Heleen H Arts
email: h.arts@antrg.umcn.nl

Ernie M H F Bongers

Dorus A Mans

Sylvia E Van Beersum

Machteld M Oud

Emine Bolat

Liesbeth Spruijt

Elisabeth A M Cornelissen

Janneke H M Schuurs-Hoeijmakers

Nicole De Leeuw

Valérie Cormier-Daire

Han G Brunner

Nine V A M Knoers

Ronald Roepman

C14ORF179 encoding IFT43 is mutated in Sensenbrenner syndrome

Background

Sensenbrenner syndrome is a ciliopathy that is characterized by skeletal and ectodermal anomalies, accompanied by chronic renal failure, heart defects, liver fibrosis and other features.

Methods

SNP array analysis and standard sequencing techniques were applied to identify the causative gene. The effect of the identified mutation on protein translation was determined by western blot analysis. Antibodies against intraflagellar transport (IFT) proteins were used in ciliated fibroblast cell lines to investigate the molecular consequences of the mutation on ciliary transport.

Results

We performed homozygosity mapping and positional candidate gene sequence analysis in two siblings with Sensenbrenner syndrome of a consanguineous Moroccan family. In both siblings, we identified a homozygous mutation in the initiation codon of C14ORF179. C14ORF179 encodes IFT43, a subunit of the intraflagellar transport complex A (IFT-A) machinery of primary cilia. Western blots revealed that the mutation disturbs translation of IFT43, inducing the initiation of translation of a shorter protein product from a downstream ATG. The IFT-A protein complex is implicated in retrograde ciliary transport along axonemal microtubules. We show that in fibroblasts of one of the by Sensenbrenner affected siblings, disruption of IFT43 disturbs this transport from the ciliary tip to its base. As anterograde transport in the opposite direction apparently remains functional, the intraflagellar transport complex B proteins accumulate in the ciliary tip. Interestingly, we obtained similar results using fibroblasts from a Sensenbrenner syndrome patient with mutations in WDR35/IFT121, encoding another IFT-A subunit.

Conclusions

Our results indicate that Sensenbrenner syndrome results from disrupted IFT-A mediated retrograde ciliary transport.

INTRODUCTION

Sensenbrenner syndrome or cranioectodermal dysplasia (CED; MIM 218330) is a rare autosomal-recessive heterogeneous ciliopathy that is primarily characterized by skeletal abnormalities (e.g. craniosynostosis, narrow rib cage, short limbs, brachydactyly) and ectodermal defects. [START_REF] Sensenbrenner | New syndrome of skeletal, dental and hair anomalies[END_REF][START_REF] Levin | A heritable syndrome of craniosynostosis, short thin hair, dental abnormalities, and short limbs: cranioectodermal dysplasia[END_REF] Nephronophthisis leading to progressive renal failure, hepatic fibrosis, heart defects, and retinitis pigmentosa have also been described. [START_REF] Amar | Expanded phenotype of cranioectodermal dysplasia (Sensenbrenner syndrome)[END_REF][START_REF] Fry | Connective tissue involvement in two patients with features of cranioectodermal dysplasia[END_REF][START_REF] Konstantinidou | Cranioectodermal dysplasia: a probable ciliopathy[END_REF][START_REF] Zaffanello | Sensenbrenner syndrome: a new member of the hepatorenal fibrocystic family[END_REF] Recently, mutations in two genes have been found to cause Sensenbrenner syndrome, IFT122 (encoding intraflagellar transport protein 122; MIM 606045) and WDR35 (encoding WD repeat-containing protein 35; MIM 613602). [START_REF] Walczak-Sztulpa | Cranioectodermal Dysplasia, Sensenbrenner syndrome, is a ciliopathy caused by mutations in the IFT122 gene[END_REF][START_REF] Gilissen | Exome sequencing identifies WDR35 variants involved in Sensenbrenner syndrome[END_REF] Both genes encode proteins that are part of the intraflagellar transport (IFT) complex A (IFT-A). This multisubunit complex, consisting of at least six proteins, forms the core of a particle that is mobilized by the cytoplasmic dynein/dynactin motor. The IFT-A particles use the microtubule bundles of the ciliary axoneme to carry membrane vesicles and other "cargo" proteins from the tip of a cilium to its base (retrograde IFT). [START_REF] Piperno | Distinct mutants of retrograde intraflagellar transport (IFT) share similar morphological and molecular defects[END_REF][START_REF] Cole | The intraflagellar transport machinery of Chlamydomonas reinhardtii[END_REF] Both retrograde and anterograde IFT (transport towards the ciliary tip), are required for ciliary assembly, disassembly and homeostasis. [START_REF] Piperno | Distinct mutants of retrograde intraflagellar transport (IFT) share similar morphological and molecular defects[END_REF][START_REF] Cole | The intraflagellar transport machinery of Chlamydomonas reinhardtii[END_REF][START_REF] Kozminski | The Chlamydomonas kinesin-like protein FLA10 is involved in motility associated with the flagellar membrane[END_REF]

METHODS

SNP array analysis

Genomic DNA was isolated from peripheral blood samples of two siblings with Sensenbrenner syndrome and their parents. Each DNA sample was genotyped with an Affymetrix 250K NspI array (Affymetrix, Santa Clara, CA, USA), which contains 262,000 SNPs. Array experiments were conducted according to protocols from the manufacturer. The 250K SNP genotypes were analyzed with Genotyping Console software (Affymetrix). PLINK [START_REF] Purcell | PLINK: a tool set for whole-genome association and population-based linkage analyses[END_REF] (available online) was used for calculation of regions of homozygosity.

Mutation analysis

Candidate genes were sequenced using patient genomic DNA. Primers for C14ORF179 and TTC8 were designed with the Primer 3 program (freely available online); primer sequences are listed in Supplemental Table 3. All coding exons of C14ORF179 and TTC8 were amplified by PCR and analyzed forward and reverse with a dye-termination chemistry (BigDye Terminator, version 3 on a 3730 DNA analyzer; Applied Biosystems). PCR conditions are available upon request.

DNA constructs

A full length cDNA clone (IRAUp969A1256 from ImaGenes) was used as a template to amplify full length C14ORF179 (NM_052873, isoform 1) with Gateway compatible primers. A consensus kozak sequence "gccgccacc" or a C14ORF179 5'UTR fragment "gtttccaggaagtgacgtcaggcggccgcggag" was included in the forward primers, just prior to the "atg". PCR products were used to create Gateway-adapted constructs by using the Gateway cloning system (Invitrogen). C14ORF179 was then cloned into two vectors, the Gateway-adapted SF-TAP vector (with a C-terminal Strep II-FLAG-tag) [START_REF] Gloeckner | A novel tandem affinity purification strategy for the efficient isolation and characterisation of native protein complexes[END_REF] and p504 (with a C-terminal eYFP tag). [START_REF] Arts | Mutations in the gene encoding the basal body protein RPGRIP1L, a nephrocystin-4 interactor, cause Joubert syndrome[END_REF] Wild type constructs and vectors containing the translation initiation codon mutation were made.

Transfection and western blot analysis

HEK293T cells (human embryonic kidney) were transfected with plasmid DNA using effectene (Qiagen) in Dulbecco's modified Eagle's medium (DMEM) with 10% Fetal Calf Serum (FCS) according the manufacturer's instructions. 24 hours after transfection, cells were lysed in ice cold lysis buffer (1x TBS, 0,5% NP-40 with complete protease inhibitor cocktail, Roche). Lysates containing IFT43-eYFP and IFT-Strep II-FLAG were cleared by centrifugation at 4 °C for 10 minutes at 14,000 g.

After adding NuPAGE sample buffer with reducing agent (Invitrogen) to the samples, lysates were heated for 10 minutes at 70 °C. Samples were subsequently analyzed by SDS-PAGE (by using a NuPAGE Novex 4%-12% Bis-Tris SDS-PAGE gel) followed by western blotting using α-FLAG (Flag M2 mouse monoclonal, Sigma, 1:1000) and α-GFP (GFP mouse monoclonal, Roche, 1:1000) antibodies. IRDye800 (Rockland) goat anti-mouse IgG was used as a secondary antibody (1:10,000). Blots were washed with PBS with 0.1% Tween-20. Fluorescense was detected on a Li-Cor Odyssey 2.1 infrared scanner.

Immunocytochemistry

Fibroblast cells from Sensenbrenner patients (CL10-00031 and CL10-00021) and a control individual (CL10-00010) were stained with antibodies to the following proteins: IFT88 and IFT57 (rabbit polyclonal; both kindly provided by G. Pazour; 1:300 and 1:250, respectively); GT335 (mouse monoclonal; kindly provided by C. Janke; 1:1500); RPGRIP1L (guinea pig polyclonal; SNC040, 1:500), [START_REF] Arts | Mutations in the gene encoding the basal body protein RPGRIP1L, a nephrocystin-4 interactor, cause Joubert syndrome[END_REF] and acetylated alpha-tubulin (mouse monoclonal, Zymed laboratories, 1:1000). The secondary antibodies (all from Molecular Probes) that were used are as following: anti-guinea pig IgG Alexa Fluor 568 and 488 (1:300), anti-rabbit IgG Alexa Fluor 568 and 488 (1:300) and anti-mouse IgG Alexa Fluor 405 (1:300). Fibroblast cells were seeded (~1:3) on sterile cover glasses and incubated for 24 hours at standard cell culture conditions in Dulbecco's modified Eagle's medium (DMEM) with 20% Fetal Calf Serum (FCS). Cells were subsequently serum-starved for 48 hours with DMEM with 0,2% FCS to stimulate cilia formation. Cells were then briefly washed in PBS and fixed in 2% paraformaldehyde in PBS for 20 minutes. Cover glasses were subsequently blocked with freshly made 2% BSA in PBS, followed by a 1 hour incubation with the primary antibody at room temperature. Cells were washed with PBS and then incubated with secondary antibodies for 30 minutes. Cover glasses with the stained cells were placed upside-down on a drop of Vectashield (Vector Laboratories) on a microscopic glass slide. Microscopic analysis was performed on a Zeiss Axio Imager Z1 fluorescene microscope (Zeiss) with an ApoTome slider.

Images were processed with AxioVision (Zeiss) and Photoshop CS4 (Adobe Systems).

Accession numbers and web resources

Accession numbers of the C14ORF179 gene and a list of the web resources that were used in this study can be found in Supplementary Materials and Methods.

RESULTS

Clinical studies and genotyping

To identify additional genetic defects underlying Sensenbrenner syndrome, we conducted genome-wide homozygosity mapping by using Affymetrix 250K arrays in a consanguineous family from Moroccan descent with two siblings with Sensenbrenner syndrome (family P05-1040, Figure 1 and Supplemental Table 1). Homozygosity analysis by using PLINK [START_REF] Purcell | PLINK: a tool set for whole-genome association and population-based linkage analyses[END_REF] revealed that the largest-and secondlargest homozygous regions of the affected siblings from family P05-1040 (individuals II:1 and II:2, Table 1) are overlapping; this region was 25.2 Mb on chromosome 14 (containing 158 annotated RefSeq genes), with SNP_A-2107558 and SNP_A-2312334 as bordering SNPs (Figure 1, Table 1 and Supplementary Table 2).

Other homozygous regions shared less overlap, indicating that the genetic defect was most likely to be found in the region on chromosome 14 that contains the genes C14ORF179 and TTC8.

Given that IFT122 and WDR35, which are both associated with Sensenbrenner syndrome, are part of the IFT-A protein complex, we selected C14ORF179 as our primary candidate, as this gene encodes the human orthologue of another member of the IFT-A complex, IFT43. [START_REF] Piperno | Distinct mutants of retrograde intraflagellar transport (IFT) share similar morphological and molecular defects[END_REF][START_REF] Cole | The intraflagellar transport machinery of Chlamydomonas reinhardtii[END_REF] In addition, we selected TTC8 (tetratricopepteide repeat domain 8; MIM 608132) as a candidate gene. This gene encodes an IFT regulator and is disrupted in Bardet-Biedl syndrome (BBS; MIM 209900). [START_REF] Ansley | Basal body dysfunction is a likely cause of pleiotropic Bardet-Biedl syndrome[END_REF][START_REF] Ou | Functional coordination of intraflagellar transport motors[END_REF]

Mutation detection

Sequence analysis of candidate genes TTC8 and C14ORF179 in the affected siblings excluded genetic defects in TTC8 as a cause of Sensenbrenner syndrome in these patients, but did reveal a homozygous variation in the translation initiation codon in exon 1 of C14ORF179 (c.1A>G) (Figure 2A). This variation cosegregates with the disorder in the family, as both (related) parents are heterozygous for this variation (Figure 2A). The c.1A>G variant was neither present in dbSNP, nor in 192 Dutchand 122 Moroccan control alleles, respectively, which provides further evidence for the pathogenicity of the identified mutation.

In an attempt to identify more mutations in C14ORF179, we screened this gene for mutations in four unrelated Sensenbrenner patients who did not carry WDR35 mutations. We did not identify mutations in these patients. Since homozygosity mapping in patients from two consanguineous Sensenbrenner families did not reveal major stretches of homozygosity in the regions containing WDR35, IFT122 or C14ORF179, it is likely that the heterogeneity in Sensenbrenner syndrome extends beyond these three genes.

C14ORF179 mutation causes aberrant translation of the encoded IFT43 protein

C14ORF179 contains 10 exons that encode two major protein isoforms derived from alternative splicing that only vary in a central segment of both isoforms (Figure 2B-C). Although ATG>GTG mutations have been reported to be pathogenic (e.g. in hereditary osteodystrophy, [START_REF] Patten | Mutation in the gene encoding the stimulatory G protein of adenylate cyclase in Albright's hereditary osteodystrophy[END_REF] Norrie disease, [START_REF] Isashiki | Novel mutation at the initiation codon in the Norrie disease gene in two Japanese families[END_REF] and beta-thalassemia [START_REF] Hattori | A new beta-thalassemia mutation (initiation codon ATG----GTG) found in the Japanese population[END_REF]), it has also been described that the GTG codon can be used as an initiation codon, albeit rare and inefficient. [START_REF] Touriol | Generation of protein isoform diversity by alternative initiation of translation at non-AUG codons[END_REF][START_REF] Chen | Translational efficiency of redundant ACG initiator codons is enhanced by a favorable sequence context and remedial initiation[END_REF][START_REF] Hwang | Demonstration of GTG as an alternative initiation codon for the serpin endopin 2B-2[END_REF] We therefore investigated the effect of the c.1A>G mutation in C14ORF179 on its encoded protein. To test if this mutation diminishes translation or if it leads to translation initiation from a downstream ATG (most likely from the first downstream ATG in exon 2), we cloned the full length C14ORF179 cDNA with and without the c.1A>G mutation into expression vectors encoding eYFP-and Strep II-FLAG fusion tags. Western blot analysis of the recombinant tagged IFT43 proteins reveals that the translation initation codon mutation indeed disturbs translation; introduction of the mutation yields IFT43 proteins with a lower molecular weight of ~3 kDa compared to wild type proteins (Figures 2D and2E). This is in agreement with translation initiation at the second ATG of the coding sequence (in exon 2), at position c.A64, that becomes the first available initiation codon due to the mutation. This results in an N-terminal deletion of 21 amino acids (p.Met1_Val21del) in the same open reading frame.

Mutation in C14ORF179/IFT43 disrupts ciliary transport

The structure of IFT43, the protein product of C14ORF179, remains largely elusive as the protein contains no significant homology with any structural or functional motifs (as determined by using SMART [START_REF] Schultz | SMART, a simple modular architecture research tool: identification of signaling domains[END_REF]) (Figure 2C). The protein was initially studied in Chlamydomonas reinhardtii. [START_REF] Piperno | Distinct mutants of retrograde intraflagellar transport (IFT) share similar morphological and molecular defects[END_REF] The Chlamydomonas orthologue is part of the intraflagellar transport complex A that is involved in retrograde transport in the cilium. [START_REF] Piperno | Distinct mutants of retrograde intraflagellar transport (IFT) share similar morphological and molecular defects[END_REF][START_REF] Cole | The intraflagellar transport machinery of Chlamydomonas reinhardtii[END_REF] The IFT-A protein complex consists of IFT43, IFT121/WDR35, IFT122, IFT139, IFT140 and IFT144 [START_REF] Cole | The intraflagellar transport machinery of Chlamydomonas reinhardtii[END_REF], and is associated to THM1 and TULP3. [START_REF] Mukhopadhyay | TULP3 bridges the IFT-A complex and membrane phosphoinositides to promote trafficking of G protein-coupled receptors into primary cilia[END_REF] Recently, it was shown that IFT43 directly binds to IFT121/WDR35, which supports a tight relationship between these two proteins. [START_REF] Cole | SnapShot: Intraflagellar transport[END_REF] This is remarkable, since IFT121/WDR35 is the protein product of WDR35, a previously identified Sensenbrenner gene. [START_REF] Gilissen | Exome sequencing identifies WDR35 variants involved in Sensenbrenner syndrome[END_REF] Studies in multiple species, including Chlamydomonas reinhardtii, Caenorhabditis elegans, Drosophila melanogaster and Trypanosoma brucei, have shown that disruption of retrograde transport leads to formation of bulged cilia that contain an accumulation of IFT-B complex proteins in their tips. [START_REF] Mukhopadhyay | TULP3 bridges the IFT-A complex and membrane phosphoinositides to promote trafficking of G protein-coupled receptors into primary cilia[END_REF][START_REF] Iomini | Protein particles in Chlamydomonas flagella undergo a transport cycle consisting of four phases[END_REF][START_REF] Iomini | Retrograde intraflagellar transport mutants identify complex A proteins with multiple genetic interactions in Chlamydomonas reinhardtii[END_REF][START_REF] Blacque | The WD repeat-containing protein IFTA-1 is required for retrograde intraflagellar transport[END_REF][START_REF] Absalon | Intraflagellar transport and functional analysis of genes required for flagellum formation in trypanosomes[END_REF][START_REF] Tran | THM1 negatively modulates mouse sonic hedgehog signal transduction and affects retrograde intraflagellar transport in cilia[END_REF] In order to validate the disruptive effect of the identified mutation in C14ORF179 in family P05-1040 (Figures 1 and2), we stained fibroblasts from one of the affected siblings (II:2) using antibodies against the IFT-B complex protein members IFT88 and IFT57. Indeed, we identified a similar accumulation of IFT-B complex proteins in the distal part of the ciliary axoneme and in the ciliary tip (Figure 3 and Supplementary Figures 1 and2), while in cilia of control fibroblasts, these proteins were less abundant and primarily localized at the basal body and transition zone. Subsequently, we compared these ciliary defects with the phenotype of cilia in fibroblasts from a Sensenbrenner patient with WDR35 mutations (a patient that we described previously [START_REF] Gilissen | Exome sequencing identifies WDR35 variants involved in Sensenbrenner syndrome[END_REF]), and found nearly identical defects (Fig 3

and Supplementary

Figures 1 and2). Moreover, similar to what was reported for Sensenbrenner patients with IFT122 mutations, [START_REF] Walczak-Sztulpa | Cranioectodermal Dysplasia, Sensenbrenner syndrome, is a ciliopathy caused by mutations in the IFT122 gene[END_REF] we found that cilia from patient fibroblasts (II:2, Figure )   are somewhat shorter than those of healthy controls (Supplementary Figure 3).

DISCUSSION

We report on a family with two children with Sensenbrenner syndrome who carry a mutation in the translation initiation codon of C14ORF179. This is the third gene associated with Sensenbrenner syndrome and in line with the other two genes (WDR35 and IFT122), C14ORF179 also encodes a member of the IFT-A particle (IFT43). Mutations in WDR35 can cause both Sensenbrenner syndrome and the more severe (and embryonically lethal) Short Rib-Polydactyly (personal communication, P.J. Lockheart). We therefore suggest that both syndromes are part of a phenotypic spectrum of IFT-A complex disruption, similar to what has been proposed for Joubert syndrome and allied ciliopathies like Meckel-Grüber syndrome and Bardet-Biedl syndrome. The remaining protein activity then determines the severity of the disease phenotype. Indeed, in all genes associated with Sensenbrenner syndrome identified thus far, only mutations with a relatively mild disruptive character (mainly missense mutations, sometimes in combination with a truncating mutation) were identified, including the mutation described in this report which results in a small, N-terminal truncation of IFT43. In this respect, it is interesting to note that although we show that such mild mutations in cilia of Sensenbrenner patients' fibroblasts disrupt retrograde transport, they do not abrogate ciliogenesis.

Sensenbrenner syndrome clinically overlaps with Jeune syndrome (also known as Asphyxiating Thoracic Dystrophy; ATD; MIM 208500). Skeletal anomalies such as brachydactyly, short limbs and a narrow thorax have been reported in both disorders.

A skeletal characteristic that is unique for Sensenbrenner syndrome is craniosynostosis, however, only the youngest sibling in family P05-1040 displayed this typical characteristic (Supplementary Table 1, patient II:2). This complicated the initial clinical diagnosis in this family as it was unclear whether this family suffered from Sensenbrenner syndrome or a mild form of Jeune syndrome. Like in Sensenbrenner syndrome, genes associated with Jeune syndrome encode proteins involved in ciliary transport. Mutations have been identified in IFT80 (intraflagellar transport 80; MIM 611177) that encodes an IFT-B complex protein, as well as in DYNC2H1 (dynein, cytoplasmic 2, heavy chain 1; MIM 603297) which is a retrograde motor transporting the IFT-A particle. [START_REF] Beales | IFT80, which encodes a conserved intraflagellar transport protein, is mutated in Jeune asphyxiating thoracic dystrophy[END_REF][START_REF] Dagoneau | DYNC2H1 mutations cause asphyxiating thoracic dystrophy and short rib-polydactyly syndrome, type III[END_REF] Because of the clinicaland functional overlap between Sensenbrenner and Jeune syndrome, we also performed mutation analysis in 17 Jeune patients. Although we did not detect any C14ORF179 mutations in these patients, which indicates that this is not a frequent cause of Jeune syndrome, it remains a functional candidate gene.

In conclusion, we identified a homozygous mutation in the translation initiation codon in C14ORF179 that causes Sensenbrenner syndrome in a consanguineous family of Moroccan descent. The identified genetic defect interferes with translation, resulting in a shortened protein. Consistent with the disruption of a member of the IFT-A protein complex, fibroblasts from one of the affected siblings (II:2) show a typical IFT-A defect (i.e. accumulation of IFT-B complex proteins in the ciliary tip). Our results demonstrate that Sensenbrenner syndrome results from defects in retrograde intraflagellar transport. Variations of the initiation codon and upstream sequence of C14ORF179 are indicated. The initiation codon mutation interferes with translation, resulting in a shortened protein (lane 3). The difference between the mutated and the wild type protein is approximately ~3 kDa in both α-FLAG and α-GFP immunoblots (compare lanes 2 and 3). A wildtype construct with a kozak sequence (instead of the '5 UTR fragment of C14ORF179) was used as a control for protein expression.

Figure 3. IFT88 and IFT57 accumulate in distal ends of cilia in fibroblasts from

Sensenbrenner patients with C14ORF179 and WDR35 mutations. A) Fibroblasts were stained against the IFT-B complex protein IFT88, GT335 (a marker of the proximal cilium) and RPGRIP1L (a transition zone marker). IFT88 (green); GT335 (purple); and RPGRIP1L (red). Comparison of the IFT88 staining in control fibroblasts with cells from Sensenbrenner patients reveals that IFT88 accumulates in the ciliary tips of the patient's fibroblasts. Note, that there is a certain extent of variability between IFTdefects in cilia from the patients; i.e. in some cilia the IFT88 staining is more intense (and more distal) than in others. B) Fibroblasts from Sensenbrenner patients with C14ORF179 and WDR35 mutations were stained for IFT57 (an IFT-B complex protein), and two markers that stain the base of the cilium, GT335 and RPGRIP1L. IFT57 (green); GT335 (purple); and RPGRIP1L (red). Like IFT88, IFT57 accumulates in the distal ends of cilia in fibroblasts from the patients.

Figure 1 .

 1 Figure 1. Family P05-1040 is affected by Sensenbrenner syndrome. (A) P05-1040 is

Figure 2 .

 2 Figure 2. Mutations in C14ORF179 cause Sensenbrenner syndrome. (A) In family

Table 1 . Homozygosity mapping in Sensenbrenner family P05-1040

 1

	Patient Chromosome Bordering SNP	Bordering SNP	Size of	# SNPs in	Homozygous
			(5')	(3')	region	homozygous	region (i.e.1 =
					(Mb)	region	largest, 2 =
						second largest)
	II:1	14	SNP_A-2107558 SNP_A-1781135 25.3	2425	1
	II:2	14	SNP_A-2107558 SNP_A-2312334 25.2	2398	2
				overlap 25.2
	II:1	2	SNP_A-2123667 SNP_A-1865387 2.7	407	11
	II:2	2	SNP_A-1959026 SNP_A-2248948 18.8	2130	5
				overlap 2.6
	II:1	11	SNP_A-1895498 SNP_A-4197277 6.0	271	6
	II:2	11	SNP_A-2268220 SNP_A-4197277 6.0	276	11
				overlap 6.0
	II:1	11	SNP_A-4204835 SNP_A-2142191 4.1	408	9
	II:2	11	SNP_A-4204835 SNP_A-4205202 4.1	407	14
				overlap 4.1
	II:1	3	SNP_A-1923781 SNP_A-2252922 1.4	95	18
	II:2	3	SNP_A-1820067 SNP_A-1974247 5.1	394	13
				overlap 1.4
	II:1	3	SNP_A-1972308 SNP_A-1829330 1.1	108	24
	II:2	3	SNP_A-1972309 SNP_A-1972369 2.0	209	17
				overlap 1.0
	II:1	17	SNP_A-2206444 SNP_A-1872313 1.1	71	23
	II:2	17	SNP_A-2302032 SNP_A-2156489 1.1	73	23
				overlap 1.1
	II:1	5	SNP_A-4210912 SNP_A-4202173 1.0	54	28
	II:2	5	SNP_A-2084301 SNP_A-2293403 1.1	64	22
				overlap 1.0

Acknowledgements

We thank the Sensenbrenner and Jeune families for their participation. We also thank P.L. Beales, A.F.M. Hoogeboom, B.C.J. Hamel, I. Stolte-Dijkstra, D. Doherty and other clinicians for supplying additional Sensenbrenner and ciliopathy patients. We thank R. Boulouiz and A. Bertoliavella for providing Moroccan control DNA samples, G. Pazour for sharing the anti-IFT88 and anti-IFT57 antibodies, and C. Janke for the GT335 antibody. We thank T. Merkx and S. van der Velde-Visser for technical assistance, and F.M.P. Cremers, A.I. den Hollander, J. Fransen, J. te Riet and M. Wijers-Rouw for helpful discussions. This research was supported by grants from the Dutch Kidney Foundation (KJPB 09.009 to H.H.A), the European Community's Seventh Framework Programme FP7/2009 under grant agreement no: 241955, SYSCILIA (to R.R.), and a grant from the Netherlands Organization for Scientific Research (NWO Vidi-91786396; to R.R.).

Funding

Dutch Kidney Foundation; Netherlands Organization for Scientific Research (NWO); European Community's Seventh Framework Programme FP7/2009.

Ethics Approval

This study was approved by the Medical Ethics Committee of the Radboud University Nijmegen Medical Centre.

Informed Consent

Obtained. This includes written informed consent from the parents of the patients (II:1 and II:2) for publication of the images.

Competing interests

None.

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