Víctor Acostasantamaría

Olivier Siret

Pierre Badel

Gaëtan Guerin

Vít Novacek

Frédéric Turquier

Stéphane Avril

Víctoracosta Santamaría
email: victor.acosta@emse.fr

Material model calibration from planar tension tests on porcine linea alba

Keywords: abdominal wall, linea alba, S-DIC, mechanical parameters identification, hyperelastic models

Introduction

Abdominal wall (AW) is a complex musculo-aponeurotic structure made of 2symmetrical parts that join in the sagittal plane along a mid-line named linea alba, as explained byPodwojewski et al., 2013 and[START_REF] López-Cano | Preventive midline laparotomy closure with a new bioabsorbable mesh: An experimental study[END_REF]. It is the most common site for laparotomy incision (World Health Organization, 2003) and it plays a key role in AW biomechanics during and after closure of incisions or hernia defects [START_REF] Van't Riet | Metaanalysis of techniques for closure of midline abdominal incisions[END_REF].From an anatomic point of view, linea alba is a midline raphe formed by interweaving of anterolateral abdominal muscle aponeuroses, as described by [START_REF] Gray | Anatomy of the human body[END_REF][START_REF] Dyce | Textbook of Veterinary Anatomy[END_REF] for respectively human and porcine anatomy.Porcine tissue have a similarly sized heart and body length to humans but it is unknown if they share histological similarities (Cooney et al., 2014). As commonly described, the width of linea albavaries significantlyfrom cranial to caudal. Typical porcine linea alba was observed to have an average width of 20 ± 5 mm (Cooney et al., 2014).

The mechanical properties oflinea albawerecharacterizedby different authors: [START_REF] Rath | The abdominal linea alba: an anatomo-radiologic and biomechanical study[END_REF], [START_REF] Grässel | Anisotropy of human linea alba: A biomechanical study[END_REF], [START_REF] Förstemann | Forces and deformations of the abdominal wall-a mechanical and geometrical approach to the linea alba[END_REF], [START_REF] Martins | Mechanical characterization and constitutive modelling of the damage process in rectus sheath[END_REF], [START_REF] Podwojewski | Mechanical response of animal abdominal walls in vitro: Evaluation of the influence of a hernia defect and a repair with a mesh implanted intraperitoneally[END_REF], (Tran et al., 2014) and (Cooney et al., 2014). These authorscharacterizedlinear elastic or hyperelastic properties to model the AW biomechanical behavior. Cooney et al., 2014 applied uniaxial and equibiaxial tension tests to identify the mechanical properties of the tissue.

The main goal of the present study is to characterize the mechanical behavior of the linea alba in the situation of a laparotomy closure. Atensile test, with 100% of the deformation in the transverse direction, is applied to obtain the mechanical properties. This test was chosen because it is globally similar to the loadingapplied to the linea alba during a laparotomy closure by suture.

Additionally, experimental studiesmay yield material properties that can be input in finite element models, as performed for instance by [START_REF] Hernández-Gascón | Understanding the passive mechanical behavior of the human abdominal wall[END_REF]Cooney et al., 2014.Finite-element model of midline laparotomy closure requiring knowledge of such material properties is currently under development (Nováček and Turquier, 2013). An accurate characterization of the biomechanical properties of linea alba is therefore an essential issue for the validity of the models.

In this work, we present anin vitro mechanical characterization oflinea alba using theplanar tension tests. The purpose is to compare the biomechanical properties at different locations of the abdominal wall (supraumbilical and infraumbilical zones). Samples of linea albawere harvested from five porcine abdominal walls.

Full-field deformation measurementswereperformed, for the first time ever,by stereo digital image correlation (S-DIC).Finally, an inverse approach was used to derive the parameters of different material modelsfrom the response of the tissue to each test.

Materials and methods

Preparation and dimensions of the specimens

Anterolateral AWs of five female pigs, aged 4-5 months and weighing about 45kg, were used for the current study. The AWs were removed from the animals less than 30 min after euthanasia at the VetAgro Sup -Veterinary Campus of Lyon (Marcy l'Etoile, France), and then kept frozen at -20 °C until testing. The AWs were cut along xiphoid process and costal margins and along pubic bones and iliac crests. Lateral incisions were done between iliac spines and the lower part of the rib cage. All the layers were preserved: muscles, aponeuroses, adipose tissue, skin and peritoneum. In a second phase, AWswere thawed at room temperature 16 h in order to cut outsamples.

After dissecting skin and adipose tissue on the ventral side and peritoneum on the dorsal side, 80 to 100 mm long rectangular samples were cut for the tensile tests. Thirty samples of linea alba were obtained from five different porcine abdominal walls. The linea alba tissue was divided in the supraumbilical and infraumbilical zones (above and below umbilicus, respectively). For each abdominal wall six samples were considered. Additionally, for each zone three different samples were obtained, see Figure 1a. With respect to the umbilicus, samples 1 and 6 are the most distant and samples 3 and 4 are the closest, see Figure 1a. Before the test, the samples dimensions were measured with a digital caliper.Considering the size of the samples and the relative flatnessof the surface, caliper seems to be an adequate technique of thickness measurement (O'Learyet al., 2013;Leeet al., 1996).

The sample height is denoted H 0 . For the supraumbilical and infraumbilical zones the reported H 0 was 24.5 ± 5.37 mm. Only the middle part of the sample is linea alba tissue, the remainder of the sample is composed of rectus abdominis muscle (RM) and rectus sheaths (RS), see Figure 1b. The width and the thickness of the linea alba are denoted W 0 and t 0 respectively, see Figure 1b.

Multiphoton imaging

Before the mechanical tests, collagen and elastin fibers were imaged using two photon excitation microscopy in a 500x500x150µm 3 volume (150µm being the depth) located inthe middle part of the samples (linea alba).The confocal microscope was Nikon A1R MP PLUS® (ivtv.ec-lyon.fr). The tissue was excited with an 800nm laser. The second harmonic generation (SHG) signal of the collagen fibers was collected through a 380-420 nm bandpass filter using a 20x objectives. The autofluorescence signal was also collected and subtracted to the SHG signal in order to image the elastin fibers.

Planar tension tests

During the experimental tensile test, only the middle tissue (i.e. linea alba), was subjected to tension. The RM and RS tissues were pressed by hydraulic clamps with 3 bars of pressure. Consequently, no sliding of the specimens was reported.In the geometrical definition of the samples, H 0 is larger than W 0 . The assumption of planar tension was satisfied in the experimental protocol (the height remained constant during the tensile test). In the tensile test the axial direction corresponded to the width (direction 2 in the global coordinate system, see Figure 1c). The transversal direction corresponded to the height of the specimen (direction 1). Finally, the out-of-plane dimension corresponded to the thickness (direction 3).Only the transverse direction was characterized with this experimental protocol.

The planar tension test was performed in an Instron machine (3343 -Series 3300 Load Frames). The testing machine was instrumented with a load cell (2519 Instron Series) to measure the axial force resulting of an imposed displacement, see Figure 1c. The vertical displacement was imposed to the movable clamp while the bottom clamp remained static, see Figure 1c. The test was performed at 0.2 mm/s cross-head velocity.The test lasted less than 10 minutes (7↔ 10 min). No significant dehydration effects were observed during the tests (Martins et al., 2011).

Measurement of strain maps by 3D-S-DIC

A non-contacting full-field measurement technique,called Stereo-Digital Image Correlation (S-DIC), was used tomeasure local displacements in the soft tissue [START_REF] Sutton | Image Correlation for Shape, Motion and Deformation Measurements: Basic Concepts, Theory and Applications[END_REF]. The S-DIC system (GOM, 5M LT) was composed of two 8-bit CCD cameras equipped with 50 mm lenses with a resolution of 1624 x 1236 pixels. Even for tensile tests a single camera is very sensitive to parasitic out of plane motions, even tiny, whereas a stereo system (with two cameras) is immune to this problem (Avril et al. 2008). A random speckle pattern was carefully deposited on the surface of each specimenusingspray paint as shown inFigure 1c. Previous studies have found the thin layer of spray paint has a negligible effect on the mechanical properties [START_REF] Zhang | Evaluating the mechanical behavior of arterial tissue using digital image correlation[END_REF].

During the mechanical tests, pictures were taken with both cameras of the S-DIC system at a frequency of 5 Hz. After the test was completed, the collected images were analyzed using the commercial correlation software ARAMIS (GOM, v. 6.2.0) to determine the three dimensional displacement of the tissue surface. For the image analysis, a facet size of 21 px and a facet step of 10 px were chosen based on the speckle pattern dot size, distribution, and contrast. A finite difference method was used to calculate the engineering strain locally in the specimen [START_REF] Avril | Comparison of two approaches for controlling the uncertainty in data differentiation: application to full-field measurements in solid mechanics[END_REF].

Material models

Hyperelastic models are commonly used to describe the mechanical behavior of rubber-like materials and soft tissues [START_REF] Ogden | Non-linear elastic deformations[END_REF]. These constitutive models are definedusinga strain energy density function 𝑊 𝑭 where 𝑭is the deformation gradient tensor.

In the present study, it was chosen to consider the three following strain energy density functions: Neo-Hookean, Ogden and Holzapfel-Gasser-Ogden [START_REF] Holzapfel | A new constitutive framework for arterial wall mechanics and a comparative study of material models[END_REF].

Moreover, it was assumed that the material remained incompressible, i.e. det 𝑭 = 1. Consequently, in terms of principal stretch𝜆 𝑖 , it may be written:

𝜆 3 = 𝜆 1 𝜆 2 -1 .
The Neo-Hookean strain energy density function is written such as:

𝑊 𝜆 1 , 𝜆 2 , 𝜆 3 = C 10 (𝜆 1 2 + 𝜆 2 2 + 𝜆 3 2 -3) (1)
where𝐶 10 is the unique parameter to be identified.

The strain energy density function of the Ogden model [START_REF] Ogden | Fitting hyperelastic models to experimental data[END_REF]is expressed in terms of the principal stretches such as:

𝑊 𝜆 1 , 𝜆 2 , 𝜆 3 = 2𝜇 𝛼 2 𝜆 1 𝛼 + 𝜆 2 𝛼 + 𝜆 3 𝛼 -3 (2)
where𝜇 and 𝛼 are two parameters to be identified.

A simplified form of theHolzapfel-Gasser-Ogden model [START_REF] Holzapfel | A new constitutive framework for arterial wall mechanics and a comparative study of material models[END_REF]was used here. The Neo-hookean term existing in the original model was neglected. Moreover, given the collagen fiber architecture described by [START_REF] Axer | Collagen fibers in linea alba and rectus sheaths: I. general scheme and morphological aspects[END_REF],it was assumedthat the stiffness is initially twice as large in the transverse direction of linea albaas in the axial direction, which leads to an initial fiber angle of 35.26°. Hence, the strain energy density function was expressed in terms of the principal stretches such as:

𝑊 𝜆 1 , 𝜆 2 , 𝜆 3 = 𝑘 1 2𝑘 2 exp 𝑘 2 /9 2𝜆 1 2 + 𝜆 2 2 2 -1 (3)
where 𝑘 1 and 𝑘 2 are two material parameters to be identified.

Material model calibration in planar tension tests

The strain data obtained in planar tension tests were averaged out across the area of linea alba. This confirmed that the shear strain could be neglected becausewe had𝜆 1 ≈ 1, where direction 1 was perpendicular to the tension direction (Figure 2). Then the main principal stretch value should be the direction of tension. It wasdenoted:𝜆 2 ∶= 𝜆.

The load value, denoted 𝐹, could be related to 𝜆 and to the models of Eq. 1, 2 or 3 such as:

𝐹 = 2𝑡 0 𝐻 0 𝜆 2 𝜕𝑊 𝜕𝜆 2 2 -𝜆 -2 𝜕𝑊 𝜕𝜆 3 2 𝜆 -1 (4)
In order to determine the parameters of Eq. 1, 2 or 3 predicting load values that maximize the agreement with the measured load values, thefollowing objective function was minimized:𝜃(𝛽) = 𝐹 𝑖 -𝐹 𝑖 (𝛽) 2 where 𝐹 𝑖 are the experimental load values and (𝐹 𝑖 (𝛽)

are the predictedload values for a set of model parameters 𝛽. Index 𝑖 represents the step number at which the measurement was performed. Given a random initialization point and convergence criteria, the optimal model parametersset𝛽 * were obtained.The coefficient of determination𝑅 2 = 1 -𝑅𝑆𝑆/𝑇𝑆𝑆was evaluated, where𝑅𝑆𝑆 = 𝐹 𝑖 -𝐹 𝑖 2 and 𝑇𝑆𝑆 = 𝐹 𝑖 -𝐹 2 where𝐹 is the mean value of the experimental loads measured throughout a given test. Optimization was performed using the function Lsqcurvefit in the Optimization Toolbox of MatLab® which solves nonlinear data-fitting problems in a least-squares sense.

Statistical analysis

Two inferences were considered for the statistical analysis in the comparison of the geometrical dimensions (W 0 and t 0 ). A normal distribution was tested by Anderson-Darling test for the parametric inference. In this case the test determines whether the data follow a normal distribution for a pre-determined level of significance of 95% (p-value ≥0.05). The results were presented as mean ± standard error. If the p-value was lower than the selected criterion, a non-parametric inference was applied to answer the null hypothesis test value with Wilcoxon test. The results were presented as median ± confidence intervals. A Kruskal-Wallis test was applied to define the statistical differences between populations. The statistical significance was set at p-value ≤0.05 with 95% confidence interval. The statistical methods applied were calculated using Minitab®.

Results

Dimensions of the specimens

From five different abdominal walls, thirty samples of linea alba were obtained. Two zones with respect to the umbilicus were defined for the abdominal wall (supraumbilical and infraumbilical). Additionally, for each abdominal wall six samples were considered, three samples for the supraumbilical zone and three for the infraumbilical zone.A statistic analysis was applied to evaluate the geometrical dimensions of the samples for both zones (supraumbilical and infraumbilical). The objective wasto determine the significant differences for the width (W 0 ) and thickness (t 0 ) of the experimental samples. For the first approach,we considered a descriptive statistics formulation assuming a parametric inference, normal distribution of the data and a non-random sampling.

For the supraumbilical and infraumbilical zones the reported data for W 0 and t 0 showed a non-normal distribution (p-value ˂ 0.05). With this result, it was not possible to demonstrate that the samples represent the same population. Therefore, it was necessary to consider a non-parametric inference. With this approach the populations were compared with the corresponding median and their respective confidence intervals, see Figure 2.

Regarding the supraumbilical zone, an increase in the distance with respect to the umbilicus corresponded to a decreasedof W 0 , see Figure 2a, whereas t 0 showed an opposite tendency, see Figure 2b. For W 0 and t 0 the statistical treatment determined significant differences between the samples 1 and 3 (p-value <0.05), defining them as non comparable samples (see Figure 2). Regarding the infraumbilical zone, an increase in the distance with respect to the umbilicus corresponded to a decrease inW 0 and t 0 , see Figure 2. However, the statistical treatment reported significant differences only for W 0 and between samples 4 and 6 (pvalue <0.05), see Figure 2a. Additionally, comparing the geometrical dimensions W 0 and t 0 for the supraumbilical and infraumbilical samples closer to the umbilicus (3 and 4, respectively), the non-parametric inference reported non comparable samples (p-value <0.05), see Figure 2. Therefore, the samples near the umbilicus could not be compared between them, nor with samples 1 and 6 of the supraumbilical and infraumbilical regions, respectively. Finally, the analysis determined statistical differences (p-value <0.05) between the supraumbilical and infraumbilical samples (1 -2) and (5 -6), respectively (see Figure 2).

Considering the above comparative results for the infraumbilical and supraumbilical zones, the samples closer to the umbilicus reported differences with the remaining samples. In conclusion, considering the geometrical factors (W 0 and t 0 ), samples 3 and 4 could not be taken into account to identify the parameters of the mechanical behavior of the linea alba. The final geometrical dimensions are reported in Table 1.With respect to the umbilicus distance, W 0 was reduced by 36% between samples 2 and 1 in the supraumbilical zone and t 0 was increased by 25.45%. Moreover, for the infraumbilical region, t 0 was almost constant and W 0 was reduced by 16.39 % between samples 5 and 6, with respect to the umbilicus distance.

Microscopic observations

As linea alba is prolongation of rectus sheaths and, more generally, fascias of lateral muscles, its structure is known to follow fiber orientation of lateral abdominal muscles. Observations using the second harmonic generation confocal microscope revealed differences between collagen fiber orientations on the outer (ventral) side of the samples and on the inner (dorsal) side of the samples. Transverse fiber orientations were predominant on the dorsal side for both supraumbilical and infraumbilical samples whereas oblique fiber orientations were predominant on the ventral side in supraumbilical samples only, see Figure 3. Our findings are in good agreement with [START_REF] Axer | Collagen fibers in linea alba and rectus sheaths: I. general scheme and morphological aspects[END_REF] except for ventral side in infraumbilical samples which may be explained by different anatomy of pigs compared to humans as pointed out by (Cooney et al, 2014) especially when considering differences in muscle insertions.

Planar tension tests

All the tissue samples displayed a similar mechanical response under planar tension, see Figure 4. Three stages are distinguishable in a typical stress-strain curve: an initial stage from which the hyperelastic parameters can be identified (shown with a solid line in Figure 4), then a tearing stage with an inversion of the curvature. The laststage represents the rupture where the stress returns to zero. The tearing and rupture always occurred in the muscular bits of the samples that were pressed with the clamps. The strain levels reported for the linea alba were relatively low (less than 10%), sufficiently below the damage threshold for this tissue. In general, the highest stress levels were reported for the infraumbilical samples, whereas the supraumbilical samples showed the highest strain levels, see Figure 4.

The first stage of these curves was used to deduce the hyperelastic parameters. In order to validate the planar tension hypothesis, the variation of the width of the specimen was determined thanks to the displacements provided by the S-DIC technique. The average transverse strain remained less than 0.1%, which validates the assumption of planar tension tests (λ 1 ≈ 1).

Ten specimens were rejected after the statistical analysis that was applied to evaluate the geometrical dimensions of the samples. These specimens correspond to the samples closer to the umbilicus (samples 3 and 4), see Figure 1. To define the hyperelastic parameters weconsidered twenty samples of linea alba from five different abdominal walls. For each abdominal wall four specimens were considered, two samples for the supraumbilical zone (1 and 2) and two for the infraumbilical zone (5 and 6), see Figure 1. For each region, the identified parameters reported a normal distribution (p-value > 0.05), assuming a descriptive statistics formulation. However, one and two samples for the infraumbilical and supraumbilical zones respectively, reported mechanical parameters that were considered like outliers.The identified hyperelastic parameters are reported in Table 2, for the three evaluated models: Neo-Hookean, 2 and 3,respectively). The data were reported with the corresponding mean ± standard deviation.

Comparing the mechanical parameters between the supraumbilical and infraumbilical zones thestatistical treatment determined significant differences.Regarding the Neo Hookean model and the parameter C 10 , for both zones significant differences was determined (p-value <0.05), defining them as non comparable parameters. Moreover, the C 10 parameters reported for each zone differ in85%.Concerning the Ogden model, the statistical treatment reported significant differences only for µ parameter (p-value <0.05). The µ parameters reported for the infraumbilical and supraumbilical zones differ in 92%. For the alpha parameters and between the regions,the difference is 7.95%.Finally, for the Holzapfel-Gasser-Ogden model the significant differences was reported only for k 1 parameter (p-value <0.05). For the supraumbilical and infraumbilical zones the k 1 and k 2 parameters differsin 91 and 18%, respectively.

The Ogden and Holzapfel-Gasser-Ogden models provided excellent fits with determination coefficients of 0.99 and 1.0 for the supraumbilical and infraumbilical samples, respectively, see Table 2. The Neo-Hookean model seemed less appropriate with determination coefficients of 0.73 and 0.89, respectively. This may be explained by the almost systematic Jshaped stress-strain curves. In this sense, the parameters of Ogden and Holzapfel-Gasser-Ogden models were appropriate to reproduce the J-shape.

Using the identified parameters with the Holzapfel-Gasser-Ogden model, the stress-stretch curves in planar tension for the supraumbilical and infraumbilical samples were plotted on the same graph, see Figure 5. Twenty samples of linea alba were collected for the study, ten for each zone (supraumbilical and infraumbilical). The results are presented as mean ± standard deviation for different stress and strains levels.

For the supraumbilical zone, an increase in the stretch increases the dispersion with respect to the stress mean values that are reported. Moreover, the infraumbilical region shows a similar tendency with a higher average deviation compared with the results of the supraumbilical zone, see Figure 5. Finally, an increase in the stress levels for the supraumbilical and infraumbilical samples, increases the dispersion with respect to the stretch mean values and with similar trends, see Figure 5.

Considering the previous results of the geometrical dimensions comparison, the analyses determined statistical differences between the supraumbilical and infraumbilical zones. Additionally, the planar tension results reported differences in the stress and strain levels for both zones. This explains the differences for the mechanical behavior and parameters found for the linea alba.

Discussion

The purpose of this study was to determine the biomechanical properties of linea alba subjected to planar tension (representing physiological healthy conditions).This is the first study ever reporting simultaneously the biomechanical response of linea alba to planar tension both at infraumbilical and supraumbilical location. Indeed, results reported in the literature focused on infraumbilical samples from which tensile specimens could be more easily cut. As the supraumbilical linea alba is narrower and thicker, this does not permit to cut classical tensile samples. In our study this drawback was overcome. The linea alba and the surrounding muscles were tested in a single tensile test. The non-contact S-DIC technique was used to measure the strain fields in the linea alba region.

Even if the current study was performed on porcine tissues, the distribution patterns were similar to human ones, as was observed by [START_REF] Axer | Collagen fibers in linea alba and rectus sheaths: I. general scheme and morphological aspects[END_REF]. We found significant differences between supraumbilical and infraumbilical samples, the latter being significantly stiffer. Such a difference was not reported by [START_REF] Grässel | Anisotropy of human linea alba: A biomechanical study[END_REF] for the reason explained above (impossible to carry out a traditional tensile test protocol on supraumbilical linea alba). However, structural and microstructural observations confirmed the differences between supraumbilical and infraumbilical samples. Indeed, supraumbilical linea alba is thicker and narrower than infraumbilical linea alba because it contains a layer of collagen fibers diagonally oriented. This structural difference between supraumbilical samples and infraumbilical linea alba was reported by [START_REF] Axer | Collagen fibers in linea alba and rectus sheaths: I. general scheme and morphological aspects[END_REF]. The presence of diagonal fibers in supraumbilical linea alba, extending from aponeuroses of oblique muscles, accounts for a more compliant response to transverse planar tension than in infraumbilical linea alba where most of the fibers are oriented in the transverse direction.

Above the umbilicus, transverse deformation of abdominal wall is limited by thoracic cage. Abdominal wall in this region experiences more deformation resulting from trunk movement then intra-abdominal pressure. Oblique fibers in linea alba transmit tensions especially in trunk rotation. The abdominal wall, under the umbilicus, has to respond more to a loadinginduced by intra-abdominal pressure. The tensions, in linea alba, are transmitted mostly by transverse fibers. Our findings confirm such hypothesis: linea alba function correlates well with microstructure which determines macroscopic mechanical behavior. However, this study was done on porcine tissues and validity of this hypothesis would need to be confirmedwith respect to human anatomy.

The stress/stretch curve of linea alba below the umbilicus was very close to that reported by (Cooney et al., 2014) for linea alba tested in the transverse direction, see Figure 6. Generally,the stress experienced by linea alba was of the same order of magnitude as reported by (Abdelounis et al., 2013) for anterior rectus sheath, see Figure 6.

The stress applied in our tests remained below the strength values reported by (Hollinsky & Sandberg 2007) for linea alba (respectively 10.0±3.4 MPa above and 8.4±3.1 MPa below the umbilicus).The global behavior of infraumbilical linea alba to planar tension is in very good agreement with the results obtained on human samples by [START_REF] Grässel | Anisotropy of human linea alba: A biomechanical study[END_REF], even though these authorsdid not observe significant differences in position (supraumbilical vs. infraumbilical). (Rath, et al., 1997) also reported for human rectus sheath a coefficient of elasticity greater for the infraumbilical than for the supraumbilical tissue, which is the same tendency as our results.

Material models and corresponding parameters are fundamental in development of robust computational models simulating healthy physiological conditions, and also midline laparotomy closure and/or abdominal wall repair in case of hernia. Such models would be helpful in assessment of performance of medical devices and surgical techniques in order to improve the clinical outcome.Finite element models of AW were already published by our group [START_REF] Guérin | Impact of the defect size, the mesh overlap and the fixation depth on ventral hernia repairs: a combined experimental and numerical approach[END_REF] or others [START_REF] Hernández-Gascón | Understanding the passive mechanical behavior of the human abdominal wall[END_REF]Cooney et al., 2014). They need to be fed with material parameters. Most of the finite-element models of soft tissues require hyperelastic models [START_REF] Holzapfel | A new constitutive framework for arterial wall mechanics and a comparative study of material models[END_REF]. Previous data published by [START_REF] Grässel | Anisotropy of human linea alba: A biomechanical study[END_REF]Cooney et al., 2014) provided elastic and hyperelastic parameters of linea alba, respectively. However, our study is the first one to report the significant differences for the material properties of the linea alba between the supraumbilical and infraumbilical zones.

The use of full-field strain measurements becomes more and more commonplace in soft tissue biomechanics [START_REF] Romo | In vitro analysis of localized aneurism rupture[END_REF][START_REF] Brunon | Mechanical characterization of liver capsule through uniaxial quasi-static tensile tests until failure[END_REF]. In the current study, it permitted a contactless measurement of strains in planar tension. Usually, in experimental tests carried out on soft tissues, strains are measured by dividing the displacement of the tensile machine by the initial length of the specimen. Here this approach was not possible because the tensile machine induced deformation not only of linea alba but also of the muscular parts surrounding it. Therefore, the total displacement of the tensile machine was the sum of the deformation of all the different tissues constituting the samples. Thanks to full-field strain measurements with the S-DIC technique, it was possible to assess the average strain of linea alba only and eventually to derive the intrinsic material properties of linea alba only.

This study presents a number of limitations that could be addressed in future studies:

1. The axial stretch applied in planar tension tests remained relatively small (stretch limited to 1.1 max). This was due to the fact that tearing always occurred in the muscular tissue squeezed in the grips before exceeding 10% strain in thelinea alba. In a human cadaveric study, [START_REF] Nováček | A New Methodology for Abdominal Wall Biomechanical Strain Analysis[END_REF] observed average anterior abdominal wall strain of 5% at intra-abdominal pressure of 4 kPa. In comparison, [START_REF] Grässel | Anisotropy of human linea alba: A biomechanical study[END_REF] applied strains varying from 5% to more than 30% by testing linea alba alone. The main asset of our protocol is that the samples of linea alba were not damaged during the planar tension tests, and the same samples can be used for other experimental protocols like the suture pull-out test. No macroscopic damage was observed. The applied strain was lower or of the same order of magnitude as the in vivo strain experienced by abdominal wall (Śmietaoski et al., 2014;Szymczak et al., 2014).

2. Our studies focused on porcine linea alba. This represents some advantage as pigs are very often used as animal models for investigating laparotomy closure by suture and for surgeon practice. However, the possible differences between porcine models and humans may exist. We noticed a significant difference between supra-umbilical and infra-umbilical responses in planar tension. Such difference was not reported in humans even if the protocol for testing human linea alba was less sophisticated and generated a lot of scatter in the results [START_REF] Grässel | Anisotropy of human linea alba: A biomechanical study[END_REF].

3. The effect of freezing and thawing on the biomechanical properties of the samples was not characterized. Moreover, all the tests were carried out at room temperature.

Repeating the tests in conditions closer to the physiological ones should be the object of another study.

Conclusions

Samples of linea albafrom five different porcine abdominal wallswere tested in planar tension. It was shown that the Ogden model and the Holzapfel-Gasser-Ogden models are appropriate to reproduce their mechanical response. The linea alba located above the umbilicus was significantly more compliant than below the umbilicus. This difference which is firstly reported here is consistent with the tissue microstructure. These results have important consequences as they indicate that regional variations of material properties should be considered to set-up finite-element models of AW in healthy physiological conditions and of AW during laparotomy closure by suture.

6.

TABLES

Figure 1 .

 1 Figure 1. (a) Schematic of the porcine abdominal wall and location of the 30 samples obtained. (b) Picture of two dissected samples and definition of the dimensions H0, W0 and t0. (c) Schematic of the tensile test machine and S-DIC system used to measure local displacements and strains.

Figure 2 .

 2 Figure 2. Geometrical dimensions comparison of linea alba samples.

Figure 3 .

 3 Figure 3. Confocal microscopy of the collagen fibers in linea alba. (a) infraumbilical sample, outer side. (b) supraumbilical sample, inner side. The black dotted lines represent the fiber directions."

Figure 5 .

 5 Figure 5. Stretch-(fitted) stress curves and standard deviation for supraumbilical and infraumbilical zones.

Figure 6 .

 6 Figure 6. Comparison of the stretch/stress curves for linea alba.

Table 1 .

 1 Geometrical dimensions of linea alba samples (width and thickness).

		Geometrical Dimensions -Estimated Median [Confidence Interval]
	Zone	Samples	Width W 0 (mm)	Thickness t 0 (mm)
		1	3.2 [-1.25; +2.15]	3.45 [-0.7; +1.05]
	Supraumbilical
		2	5.0 [-1.55; +5.80]	2.75 [-0.95; +0.9]
		5	15.0 [-1.85; +3.35]	1.5 [-0.4; +0.2]
	Infraumbilical
		6	12.5 [-3.25; +3.50]	1.5 [-0.3; +0.15]

Table 2 .

 2 Material parameter identification of 3 hyperelastic models for supraumibical and infraumbilical zones.

			Mechanical Parameters -Estimated Mean ± Standard Deviation
		Neo Hookean Model		Ogden Model		Holzapfel-Gasser-Ogden Model
	Zone
		C 10 (MPa)	R²	µ (MPa)	Alpha (-)	R²	k1 (MPa)	k2 (-)	R²
	Supraumbilical	0.61 ± 0.34 0.73± 0.13	0.39 ± 0.37 38.57 ± 15.55 0.99± 0.01	0.46 ± 0.36 63.03 ± 38.42 0.99± 0.01
	Infraumbilical	4.08 ± 1.94 0.89± 0.06	4.61 ± 2.54 35.73 ± 14.79	1.00	5.04 ± 2.67 77.04 ± 63.91	1.00


A Aryan

B Guillet

J M Routoure

C Fur

P Langlois

L Méchin

Measurement of thermal conductance of La 0.7 Sr 0.3 MnO 3 thin films deposited on SrTiO 3 and MgO substrates

We present measurements of the thermal conductance of thin-film-on-substrate structures that could serve as thin film uncooled bolometers. Studied samples were 75 nm thick epitaxial La 0.7 Sr 0.3 MnO 3 thin films deposited on SrTiO 3 (001) and MgO (001) substrates patterned in square geometries of areas ranging from 50 µm × 50 µm to 200 µm × 200 µm. The model allows estimating thermal boundary conductance values at the interface between film and substrate of 0.28±0.08 × 10 6 W•K -1 •m -2 for LSMO / STO (001) and 5.80±2.98 × 10 6 W•K -1 •m - 2 for LSMO / MgO (001) from measurements performed in the static regime. Analytical expressions of thermal conductance and thermal capacitance versus modulation frequency are compared to measurements of the elevation temperature due to absorbed incoming optical power. The overall good agreement found between measurements and model finally provides the possibility to calculate the bolometric response of thin film bolometers, thus predicting their frequency response for various geometries.

I. INTRODUCTION

A bolometer is a thermal radiation sensor. [START_REF] Budzier | Thermal Infrared Sensors[END_REF][START_REF] Kruse | Elements of Infrared Technology[END_REF][START_REF] Rogalski | Infrared detectors[END_REF][START_REF] Richards | [END_REF] It is composed of an absorbing element that converts the incident electromagnetic radiation to heat and an electrical resistance thermometer that measures the elevation of temperature ∆T induced by the absorbed radiation.

The absorbing element with thermal capacitance C is connected to a thermal bath at fixed temperature T 0 (thermostat or cold head) through a thermal conductance G, which includes the thermal boundary conductance at the interface between film and substrate. This thermal boundary conductance is a quantity used to describe the heat conduction between two materials in contact. It is of high importance to evaluate its value, in case of thin-film-on-substrate systems and in particular of thin film bolometers.

The optical responsivity ℜ V (expressed in V•W -1 ) of a bolometer of electrical resistance R is defined as the output voltage ∆V(f) per incoming radiation power ∆P(f), where f is the modulation frequency of the incoming radiation power. It is directly related to the elevation of temperature in the bolometer ∆T(f) and in the case of a constant current biased bolometer, it can be written as:

          τ π + η ×       × = ∆ ∆ × ∆ ∆ = ∆ ∆ = ℜ 2 V ) f 2 ( 1 G I dT dR ) f ( P ) f ( T ) f ( T ) f ( V ) f ( P ) f ( V ) f ( (1)
where η is the absorption coefficient (dimensionless), I is the bias current (expressed in A), G is the thermal conductance of the device (expressed in W•K -1 ), τ = C / G is the thermal time constant (expressed in s), C is the thermal capacitance (expressed in J•K -1 ). The basic approach described by equation (1), which considers that G and C are constant in all the investigated modulation frequency and temperature range, leads to the conclusion that the bolometer is a first order system with a cut-off frequency equals to f 0 = (2πτ) -1 . However, G and C are not strictly frequency independent in the case of film-on-substrate devices, and this is the purpose of this paper to study their frequency dependence, as well as to evaluate the thermal boundary conductance between the LSMO film and the substrate.

In section II, we will describe the thermal model that we have used for thin-film-onsubstrate bolometers, which is adapted from Ref. 5 and 6. Section III gives the experimental details, i.e. the sample description and the measurement conditions. La 0.7 Sr 0.3 MnO 3 (LSMO) thin films deposited on SrTiO 3 (001) (STO) and MgO (001) substrates patterned in the form of meander-shaped strips that cover square areas of 50 µm × 50 µm, 100 µm × 100 µm, and 200 µm × 200 µm were studied. LSMO is a promising material for room temperature bolometers since it presents a large variation of its electrical resistance versus temperature at the temperature of its metal-to-insulator transition, i.e. above room temperature. 7,8,9,10 The Temperature Coefficient of the Resistance TCR=(1/R)×(dR/dT) of LSMO is around 2% K -1 in the 300-340 K temperature range indeed. 7,8 In addition, LSMO thin films show low electrical noise, which let expect competitive noise equivalent power at room temperature. [9][10][11][12] The thermal properties of the tested substrate material are given in section IV. Using measurements of the thermal conductance performed in the static regime and the simplified model, thermal boundary conductance values at the interface between film and substrate were evaluated for each substrate material. The temperature elevation versus the modulation frequency of the incoming radiation power from a laser diode, named ∆T(f)/∆P(f) were finally made and compared to the proposed model. A conclusion is given in section V.

II. THERMAL MODEL

A. Electro-thermal analogy

The thermal model is based on heat conduction from film to substrate, neglecting radiative and convective leakage, since samples are placed in vacuum, as well as thermal leakage due to wires. To describe it, we used the conventional analogy between thermal and electrical parameters. [START_REF] Lienhard | A heat transfer text book[END_REF] The heat transfer analysis can then be made much simpler by creating an equivalent electrical circuit of the problem as shown in figure 1, similarly to the one proposed by Bozbey in Ref. 14.

In the model described in figure 1, we defined η•∆P(f) as the absorbed power at the surface of the sample (in W), G F and C F the thermal conductance and the thermal capacitance of the patterned thin film, G S and C S the thermal conductance and the thermal capacitance of the substrate. Thermal conductances are expressed in W•K -1 and thermal capacitances in J•K -1 .

Two thermal interfaces have to be considered in this description, the film/substrate interface and the substrate/sample holder interface. A•g FS is the thermal boundary conductance at the film/substrate interface and A'•g ST is the thermal boundary conductance at the substrate/thermostat interface, where A is the bolometer area and A' is the substrate to thermostat contact area. g FS and g ST are named the thermal boundary conductances (in W•K - 1 •m -2 ) between film and substrate, and between substrate and thermostat, respectively. The total heat flow from film surface to sample holder is governed by the thermal conductance G, which can be written as follows in the steady state:

ST S FS F g ' A 1 G 1 g A 1 G 1 G 1 ⋅ + + ⋅ + = (2)

B. Thermal boundary conductance

The thermal boundary conductance depends on the surface of the contact area as well as on the interface quality [START_REF] Kreith | Principles of Heat Transfer[END_REF][START_REF] Bergman | [END_REF] . To our knowledge, no value of thermal boundary conductance between LSMO thin films and STO or MgO substrates has been reported in literature so far.

Nahum et al. [START_REF] Nahum | [END_REF] [18][19][20][21][22] , on STO substrates (1×10 7 -2×10 7 W•K -1 •m -2 measured using optical-transient grating method and thermoelectric method) 22,23 , and semiconductor YBCO on MgO substrates 24 . For manganese oxides, some values have been reported for La 0.7 (Pb 0.7 Sr 0.3 ) 0.3 MnO 3 thin films on STO and LaAlO 3 substrates (10 7 W•K -1 •m -2 measured using pulsed microwave method) 25 , and La 0.65 Ca 0.35 MnO 3 on STO substrate (≥ 10 6 W•K -1 •m -2 measured using pulsed microwave method) 26 .

(5×10 6 W•K -1 •m -2 )

C. Heat diffusion into substrate

Thermal models describing the optical responsivity of high critical temperature superconducting film-on-substrate bolometers at different modulation frequency ranges can be found in literature 5,6,23,[27][28][29][30][31] . Fardmanesh et al. 27,28 proposed a one-dimensional (1D) thermal model for HTS thin film bolometers on thick substrates. They modeled the substrate as a cylinder and used the heat diffusion equation. This model was validated for large superconducting patterned areas compared with the substrate thickness at low and midrange modulation frequencies (1 Hz -10 kHz). Fardmanesh et al. 29 presented a 2D analytical model that better describes the results especially at high frequencies compared to the previous 1Dmodel. Gaugue et al. 30 have also developed a 2D analytic model and a 3D numerical model, with and without consideration of the thermal boundary conductance between film and substrate. They showed that the 2D model can be used to predict the optical responsivity of an illuminated pixel, and the 3D model to evaluate inter-pixel crosstalk taking into account the thermal interface. More recently, and based on the last work, Jagtap et al. 24 implemented a 3D thermal model taking into account the film/substrate interface and film thickness. Grossmann et al. 31 have proposed a 2D analysis for microbolometer arrays, which allows the analysis of thermal crosstalk and estimates the effects of finite substrate thickness. Most of the above cited models concern detection areas larger than substrate thickness. They do not strictly apply to our case where active detection areas are ranging from 50 µm × 50 µm to 200 µm × 200 µm on substrate thickness of 1 mm.

We have modeled the contact between the film and the substrate as an hemisphere of radius a, as shown in figure 2 and previously proposed in Ref. 5 and Ref. 6. In this model the heat flux is radial into the substrate. The contact area is represented by a hemisphere of surface 2πa 2 , which is set equal to the surface of the thin film bolometer A = L 2 , in case of a square of side L. The heat transfer equations in solids can be found in [START_REF] Carlslaw | Conduction of Heat in Solids[END_REF] . From the integration of the temperature gradient over the contact area between film and substrate (A = L² = 2πa²), the thermal conductance of the substrate G S can be written as 5,6 :

        +         + × π × κ × = L 2 L S S f 2 f f 2 f 1 2 L ) f ( G (3)
where f is the incident power modulation frequency (in Hz), κ S is the substrate thermal conductivity (in W⋅m -1 ⋅K -1 ), f L = D / L 2 is the frequency at which the thermal diffusion length

) f /( D L D π =
(in m) becomes equal to 2 a ×

. L D gives the characteristic penetration depth of temperature variation into the substrate 5,6,[27][28][29][30][31][START_REF] Carlslaw | Conduction of Heat in Solids[END_REF] . D is called the thermal diffusivity of the material, and has units of m 2 ⋅s -1 . It measures the ability of a material to conduct thermal energy relative to its ability to store thermal energy and is defined as D=κ/(c p ×ρ v ), where c p is the specific heat capacity at constant pressure expressed in J⋅kg -1 ⋅K -1 , ρ v is the mass density expressed in kg⋅m -3 , and κ is the thermal conductivity expressed in W⋅m -1 ⋅K -1 .

Depending on the modulation frequency f compared to f L , two asymptotic behaviors can be distinguished as reported in table I. At low frequency, so called hereafter static regime, (where L D >> 2 a ×

, which means that the heat flows deep into the substrate), the thermal conductance of the substrate writes:

π × κ × = = << 2 L ) 0 ( G ) f f ( G S S L S (4)
In the static regime, G S is therefore independent of the modulation frequency, varies linearly with sample size L and the thermal conductivity of the substrate material κ S . At high frequency, so called dynamic regime, (where L D << 2 a ×

, which means that the heat does not flow deep into the substrate and that the thermal boundary conductance may play an important role in the total thermal conductance as will be seen later), the thermal conductance of the substrate writes:

L S L S f f 2 L ) f f ( G × π × κ × = >> (5)
In the dynamic regime, G S therefore depends on frequency as f 1/2 .

In order to fully characterize the electro-thermal properties of the thin-film-on-substrate bolometer, one also has to evaluate its thermal capacitance. For a thin film bolometer element with area A=L 2 and thickness t F , the film thermal capacitance can be neglected because of the very small volume involved and the total thermal capacitance can be estimated by the substrate thermal capacitance C S . The latter depends on the heated volume, which depends on the modulation frequency and is therefore hard to define analytically. Rewriting equations ( 4) and

(5) as a / L ) 0 ( G ) f f ( G 2 S S L S × κ = = << and ) 2 / L /( L ) f f ( G D 2 S L S × κ = >>
, respectively, actually corresponds to the thermal conductance of a heated volume of square area L² and thickness a in the static regime (f<<f L ) and of square area L² and thickness 2 / L D in the dynamic regime (f>>f L ). Two asymptotic expressions of C S depending on the modulation frequency compared to f L can then be written as reported in table I.

III. EXPERIMENTAL DETAILS

A. Sample description

The 75 nm thick LSMO films were deposited by Pulsed Laser Deposition (PLD) at 720 °C in a O 2 pressure of 0.35 mbar (i.e. 34.7 Pa) on 1 mm thick STO (001) and on MgO (001) substrates. All LSMO films were (001) oriented as revealed by X-ray diffraction (figure 3). Inset of figure 3 shows the electrical resistivity versus temperature characteristics of the unpatterned LSMO films. In order to make low electrical resistive connections a 200 nm thick gold layer was deposited by ion-beam on the LSMO films. The latter were patterned by UV photolithography and argon ion etching to form meander-shaped strips that covers square areas of 50 µm × 50 µm, 100 µm × 100 µm and 200 µm × 200 µm (see inset of figure 4).

They can be composed of 5 or 7 lines, or only one, thus forming a square. Each meander includes two gold pads for supplying the bias current, and two gold pads carrying out the voltage measurements. The connections between the external circuitry and the patterned film with gold contact pads were finally made using aluminium wires by ultrasonic bonding.

B. Measurement conditions

The LSMO samples were glued using silver paste onto a copper plate equipped with a heating element (allowing to heat in the 300-380 K range) and placed in a vacuum chamber equipped with an optical window. The chamber was evacuated by a secondary pump, and no cooling system was used. A temperature controller was used to maintain a temperature stability of ±15 mK during measurements at a fixed temperature. The LSMO meanders were current biased in a four probe configuration using a quasi-ideal dc current source, which exhibits quasi infinite output impedance and negligible noise contribution. [START_REF] Routoure | AIP Conference Proceedings[END_REF] A low-noise voltage amplifier with gain of 220 was used to measure the voltage of the LSMO samples.

Many methods to measure the thermal conductance of thin films, which can significantly deviate from its bulk form [START_REF] Brotzen | [END_REF] , have been reported in literature. Among them, we can cite the 3ω method 35,36 , the non-contact photothermal method 37 , and the electrothermal method 38 . The thermal conductance can be experimentally seen as the inverse of the ratio of the temperature elevation ∆T(f) of the bolometer that receives the power ∆P(f). In our experiments, we used two types of incoming power. In the static regime, we used Joule heating to induce a temperature increase in the meander-shaped strips (electrothermal method). In the dynamic regime (1 Hz -100 kHz range), we used a modulated laser diode (635 nm, 5 mW) to heat the meanders, and we recorded the optical responsivity ℜ V (f) versus modulation frequency (photothermal method). Measured and modelled (using calculated G(f)) optical responsivity ℜ V (f) versus modulation frequency will be compared.

The electrothermal technique was found to be more accurate to determine the value of G(0) and will be described below. Voltage versus current V(I) and electrical resistance versus temperature R(T) characteristics were used. The V(I) was measured, using the precision parameter analyzer HP4156B, by applying a sweep varying bias current (I) in the devices (using the two current pads: I+, I-) and by measuring the voltage (V) across it (using the two voltage pads: V+, V-). The R(I) characteristics can be easily calculated from V(I) by dividing V by I. The R(T) characteristics have to be measured independently. By fitting the R(T) data in the vicinity of the temperature of the experiment T 0 using a linear expression, we can deduce the temperature of the bolometer T(R) as function of its electrical resistance R. The temperature of the bolometer T can finally be expressed as function of the dissipated electrical power P J =V×I in the bolometer electrical resistance due to Joule effect to obtain T(P J ) characteristics from the R(I) characteristics, by substituting R to T, and I to P J , respectively.

The slope at the origin (at T 0 ) of the P J (T) characteristics directly gives G(0), the total thermal conductance of the LSMO film-on-substrate bolometers in the static regime (i.e. f<<f L ).

IV. MEASUREMENTS AND ANALYSIS

A. Thermal properties of the substrate

B. Simplified model

Considering our actual experimental conditions, equation (2) describing the total thermal conductance of the thin-film-on-substrate bolometers can be simplified. The substrate thickness is 1 mm, which is always higher than a (a=L×(2π) -1/2 ). It means that the heat flow from the film surface does not exceed the substrate thickness, thus (A'•g ST ) -1 being negligible.

Finally, considering the LSMO film thickness t F = 75 nm, we have a>>t F for all the investigated bolometer areas. Consequently, the total thermal conductance of our LSMO thinfilm-on-substrate bolometers of surface A is given by :

) f ( G 1 g A 1 ) f ( G 1 S FS + × = (6)
where G S (f) is given by equation ( 3). It is recalled here that in this model the lateral heat flow is assumed to be negligible in comparison to the perpendicular one.

The overall expression of G(f) can finally be written, using equations ( 3) and ( 6) as:

        +         + × π × κ +         +         + × π × κ × = L 2 L FS S L 2 L S 2 f 2 f f 2 f 1 2 g L f 2 f f 2 f 1 2 L ) f ( G (7)
Equation ( 7) and equation (1) show that the optical responsivity of thin-film-onsubstrate bolometers will be mainly influenced by the thermal properties of the substrate material (κ S and c pS ×ρ VS through f L ), and by the thermal boundary conductance at the film/substrate interface (g FS ).

C. Measurement of the thermal boundary conductance at the film/substrate interface

Both calculated values of G S (0), i.e. the thermal conductance of the substrate in the static regime using equation ( 4), and measured G(0) values will be used to estimate g FS . G(0) values were measured as described in section III.

2 L g 1 L ) 0 ( G κ × π + = (8)
and κ S values of table II gives thermal boundary conductance at the film/substrate interface g FS of 0.28±0.08 × 10 6 W•K -1 •m -2 for LSMO / STO (001) and 5.80±2.98 × 10 6 W•K -1 •m -2 for LSMO / MgO (001). Values of g FS for LSMO / MgO (001) are more than one order of magnitude higher than for on STO (001), and showed higher dispersion. When L is reduced, G(0) is more dependent on the thermal boundary conductance of the film/substrate interface, whereas at large L values, the substrate thermal conductivity is more influent. At these large sizes, the penetration length becomes higher and the role of the substrate material dominates the total thermal conductance.

D. Frequency behaviour

The good agreement between calculated and measured static total thermal conductance was demonstrated in section D. We will now consider the dynamic behaviour of the thermal conductance and of the thermal capacitance in order to express the frequency response of the bolometer responsivity using equations ( 3) and ( 7), asymptotic expressions of C S given in table I, numerical values of the material thermal properties given in table II, and measured values of the thermal conductance g FS . The frontier between the two asymptotic regions is obtained at f=f L for the thermal conductance and for the thermal capacitance.

The normalized modulus of the measured optical responsivity versus modulation frequency of the laser diode has been compared to the normalized calculated elevation of temperature ∆T(f) produced by the absorption of a power ∆P(f), which writes as :

                        π + = ∆ ∆ 2 S Hz 1 at Normalized ) f ( G ) f ( C f 2 1 ) f ( G ) 0 ( G ) f ( P ) f ( T (9)
using equation ( 1), G(f) given in equation ( 7) and C S (f) given in table I. Measurements and calculations using equation ( 9) are compared in figures 6-a) and 6-b) for all sample sizes and both substrate materials. The frequency response of the measured optical responsivity and of the calculated elevation of temperature both show a low-pass behavior. Measurements show a plateau region at low frequencies, a f -1 dependence at high frequencies (> 10 kHz), and a f -1/2 dependence at the intermediate frequencies. The proposed calculations does not reproduce the f -1 dependence observed at high frequencies. We can also observe that the discrepancy between calculations and measurements is higher for the smaller sample areas for both LSMO/STO and LSMO/MgO samples, which very probably originates from the 1D nature of the model. Indeed the lateral diffusion of heat in the LSMO film and in the substrate is not taken into account. It can explain why the measured cut-off frequencies at -3dB reported in Table IV are always smaller (with a higher difference again for the smaller areas) than the calculated ones, in which the heated volume is underestimated. However as reported in table IV, the calculations reproduce satisfactorily the measured cut-off frequencies, taking into account the fact that calculations were made using equation ( 9) without any fitting using thermal parameter values of substrate materials found in literature. Simple calculations based on the basic first order model also show that the cut-off frequencies f 0 =G(0)/(2πC S (0)) are about 2-3 times lower than f L values. Therefore only the model taking into account the dependence of both G and C with frequency can be used to calculate the cut-off frequency of the studied LSMO thin film on STO or MgO substrates. Compared to suspended structures where the thermal conductance can be lowered by 3 orders of magnitude [49], the LSMO thin-film-on-substrate bolometers offer the possibility of realizing relatively fast bolometers while keeping high enough sensitivity, which is currently under evaluation.

V. CONCLUSION

A one dimensional thermal modeling of the thermal conductance of LSMO thin film on substrate bolometers has been presented. Calculations in both the static and the dynamic regimes were compared to measurements. In the static regime, the thermal conductance was measured using electrical heating whereas in the dynamic regime, the frequency response of the thermal conductance was measured using optical heating from a laser diode. The model allows estimating thermal boundary conductance values at the interface between film and substrate of 0.28±0.08 × 10 6 W•K -1 •m -2 for LSMO / STO (001) and 5.80±2.98 × 10 6 W•K -1 •m - 2 for LSMO / MgO (001). Some discrepancy between calculations and measurements in the dynamic mode was observed, which was higher for the smaller sample areas, and probably originates from the 1D nature of the model. Finally, the overall good agreement between measurements and model both in the static and dynamic modes allows predicting the frequency response of the responsivity of LSMO thin film bolometers on different substrate materials, knowing their thermal properties. The model can be used to define optimized dimensions for bolometer presenting either higher responsivity or higher cut-off frequency depending on the targeted application.

Table captions:

Table I: Expressions of the thermal conductance G S (f) and of the thermal capacitance C S (f) of the substrate as a function of the modulation frequency f for a thin-film-on-substrate bolometer of surface A = L 2 . κ S , c pS and ρ vS are the thermal conductivity, the specific heat capacity at constant pressure and the mass density of the substrate material, respectively.

Table II: Thermal properties of the different materials used at 300 K; κ is thermal conductivity, c p is the specific heat capacity, ρ v is the mass density and D is the thermal diffusivity.

Table III: Measured G(0) values for all the studied LSMO patterned geometries on both STO (001) and MgO (001) substrates at 330 K. G(0) values are shown together with their standard deviations (95.4% confidence interval).

Table IV: Calculated f 0 =G(0)/(2πC S (0)), f L , calculated and measured cut-off frequency f C at -3dB for all sample sizes and both substrate materials. showing the hemisphere of surface 2πa 2 , which is set equal to the surface of the film A = L 2 ;

(b) a two dimensional cross section, where t F is the film thickness and t S is the substrate thickness. Table I: Expressions of the thermal conductance G S (f) and of the thermal capacitance C S (f) of the substrate as a function of the modulation frequency f for a thin-film-on-substrate bolometer of surface A = L 2 . κ S , c pS and ρ vS are the thermal conductivity, the specific heat capacity at constant pressure and the mass density of the substrate material, respectively.

f << f L f >> f L Heated volume L 2 × a L 2 × L D / 2 Substrate thermal conductance G S (f) π × κ × 2 L S L S f f 2 L × π × κ × Substrate thermal capacitance C S (f) π ρ × × 2 c L vS pS 3 f f 2 c L L vS pS 3 π ρ × ×
Table II: Thermal properties of the different materials used at 300 K; κ is thermal conductivity, c p is the specific heat capacity, ρ v is the mass density and D is the thermal diffusivity. showing the hemisphere of surface 2πa 2 , which is set equal to the surface of the film A = L 2 ;

(b) a two dimensional cross section, where t F is the film thickness and t S is the substrate thickness.

Figure captions:Figure 1 :

 1 Figure captions:

Figure 2 :

 2 Figure 2 : (a) Schematic representation of the film/substrate contact area in three dimensions

Figure 3 :

 3 Figure 3: X-ray diffraction patterns in the θ-2θ configuration of the LSMO films on STO (001) and MgO (001) substrates. Inset shows the electrical resistivity versus temperature characteristics of the unpatterned LSMO films.

Figure 4 :

 4 Figure 4: Measured electrical power versus temperature characteristics for all the studied LSMO patterned geometries on STO (001) substrates at 330 K.

Figure 5 :

 5 Figure 5: Measured and calculated using equation (9) total static thermal conductance G(0) of the LSMO film-on-substrate bolometers.

Figure 6 :

 6 Figure 6: Measured and calculated (using Eq. 9) responsivity normalized at 1 Hz at 330 K for LSMO film on (a) STO, (b) MgO, and (c) dependence of the measured and calculated cut-off frequencies (from graphs a and b) versus sample size L.

Figure 1 :

 1 Figure 1: Equivalent electrical circuit using electro-thermal analogy used to describe our thinfilm-on-substrate bolometers.

Figure 2 :

 2 Figure 2 : (a) Schematic representation of the film/substrate contact area in three dimensions

Figure 3 :

 3 Figure 3: X-ray diffraction patterns in the θ-2θ configuration of the LSMO films on STO (001) and MgO (001) substrates. Inset shows the electrical resistivity versus temperature characteristics of the unpatterned LSMO films.

Figure 4 :

 4 Figure 4: Measured electrical power versus temperature characteristics for all the studied LSMO patterned geometries on STO (001) substrates at 330 K.

Figure 5 :

 5 Figure 5: Measured and calculated using equation (9) total static thermal conductance G(0) of the LSMO film-on-substrate bolometers.

Figure 6 :

 6 Figure 6: Measured and calculated (using Eq. 9) responsivity normalized at 1 Hz at 330 K for LSMO film on (a) STO, (b) MgO, and (c) dependence of the measured and calculated cut-off frequencies (from graphs a and b) versus sample size L.

  Table II summarizes the thermal properties of the different substrate materials used in our experiments, together with those of the LSMO film and the copper used as sample holder. The thermal conductivity of STO is five times smaller than that of MgO, but they have close volumetric thermal capacity c p ×ρ v . The values for D mentioned in table II have been calculated using the reported κ, c p and ρ v values.

Table III :

 III Measured G(0) values for all the studied LSMO patterned geometries on both STO

	100	1.86 ± 0.05	10.09 ± 0.84
	200	3.21 ± 0.18	20.77 ± 1.60
		12 39	544 40 Erreur !	5170 41	4.3
			Source du
			renvoi
			introuvable.
	MgO	51 42	923 43	3600 44	15.4
	Cu	398 45	381 43	8960 44	117
	LSMO	2.46 46	568 46,47	6600 48	0.7
	(001) and MgO (001) substrates at 330 K. G(0) values are shown together with their standard
	deviations (95.4% confidence interval).
	Sample size		G (0) (×10 -3 W•K -1 )
	L (µm)	LSMO		LSMO
			/ STO (001)	/ MgO (001)
	50		0.85 ± 0.02	5.91 ± 0.76
			18

Table IV :

 IV Calculated f 0 =G(0)/(2πC S (0)), f L , calculated and measured cut-off frequency f C at -3dB for all sample sizes and both substrate materials.

			STO			MgO
	Sample size	f 0 (Hz)	f L (Hz)	f C (Hz)	f C (Hz)	f 0 (Hz)	f L (Hz)	f C (Hz)	f C (Hz)
	(µm)	(calc.)	(calc.)	(calc.)	(meas.)	(calc.)	(calc.)	(calc.)	(meas.)
	50	542	1720	487	254	4262	6160	2405	1029
	100	206	430	161	94	1258	1540	554	415
	200	69	108	49	48	345	385	135	139

ACKNOWLEDGMENTS :

The authors wish to acknowledge S. Lebargy and J. Gasnier for their technical support.


R Cataudella
email: s.cataudella@uniurb.it

N Puillandre

GENETIC ANALYSIS FOR CONSERVATION OF AUSTROPOTAMOBIUS ITALICUS POPULATIONS IN MARCHES REGION (CENTRAL ITALY)

Keywords: Austropotamobius italicus, subspecies, taxonomy, conservation Austropotamobius italicus, sous-espèces, taxonomie, conservation

The genetic characteristics of white-clawed crayfish populations in Marches Region (Central Italy) was investigated to plan conservation strategies. In order to clarify their taxonomic status, 50 specimens from ten populations were collected in six different hydrographic drainages of the Umbro-Marchigiano Appennine. The genetic relationships of the Austropotamobius italicus specimens were assessed using DNA sequences of the mitochondrial DNA 16S rRNA gene.The 3 distinct haplotypes M1, M2, M3 detected have been compared to those available in GenBank corresponding to four subspecies described for A. italicus. Our results confirmed the presence of both subspecies A. i. carsicus (M1 & M2) and A. i. meridionalis (M3) in Marches region. Two mixed populations with both subspecies have been characterized. These new data of the genetic structure of population will be used to plan management and recovery programs.

INTRODUCTION

The white-clawed crayfish, Austropotamobius pallipes complex, is widespread throughout Europe and its range has been drastically restricted [START_REF] Holdich | Distribution of crayfish in Europe and some adjoining countries[END_REF] due to a combination of several factors affecting the habitat quality or the health of populations [START_REF] Füreder | The freshwater crayfish Austropotamobius pallipes in South Tyrol, Heritage species and bioindicator[END_REF]. To protect the existing populations, numerous conservation plans thoughout Europe have emerged during the last 10 years, often including genetic analysis of populations to help management decisions. These studies have revealed a high genetic structure among European populations and more particularly among Italian ones [START_REF] Santucci | Allozyme diversity of European freshwater crayfish of the genus Austropotamobius[END_REF][START_REF] Lörtscher | Genetic population structure of Austropotamobius pallipes (Lereboullet 1858) (Decapoda, Astacidae) in Switzerland, based on allozyme data[END_REF]GRANDJEAN et al., 2000;[START_REF] Largiader | Assessment of natural and artificial propagation of the white-clawed crayfish (Austropotamobius pallipes species complex) in the Alpine region with nuclear and mithocondrial markers[END_REF][START_REF] Fratini | Phylogeography of the threatened crayfish (genus Austropotamobius) in Italy, implications for its taxonomy and conservation[END_REF][START_REF] Trontelj | Phylogenetic and phylogeographic relationships in the crayfish genus Austropotamobius inferred from mitochondrial COI gene sequences[END_REF][START_REF] Zaccara | Taxonomic implications in conservation management of white-clawed crayfish (Austropotamobius pallipes) (Astacidae, Decapoda) in Northern Italy[END_REF]2005). These authors reported the presence of two well differentiated groups in Europe corresponding to pallipes and italicus specimens. Although discussions on the status of these two groups are still in progress, separate species status for pallipes and italicus was originally proposed by GRANDJEAN et al. (2002) and accumulating evidence favours that interpretation. Within italicus species, these studies showed a strong genetic structure with the presence of four differentiated groups [START_REF] Fratini | Phylogeography of the threatened crayfish (genus Austropotamobius) in Italy, implications for its taxonomy and conservation[END_REF]: A. i. italicus in the Tuscan-Emilian Apennine (i.e. central Italy); A. i. carsicus in North-eastern Italy; A. i. carinthiacus in Central and and North-western Italy and A. i. meridionalis corresponding to specimens from Latium, Abruzzi, and Southern Italy and also including Slovenian specimens. However, if we take in account the extremely close genetic relationship between A. i. italicus and carinthiacus, it seems to be more reliable to cluster these two subspecies into one A. p. italicus as proposed by Machino in HOLDICH (2002). Actually Austropotamobius italicus is not an official recognised taxon, but the complex phylogenetic structure of the Austropotamobius pallipes supports the necessity of a systematic revision.

The aim of the present study was to investigate the genetic relationships among appennine populations by the analysis of sequences of 16 S RNA gene to determine the subspecific status of specimens. This preliminary study on the genetic characteristics of populations in Marches Region will be used to plan management and recovery programs.

MATERIALS AND METHODS

We collected 50 specimens (five specimens from each population) by hand from ten different rivers of the Umbria-Marches Appennine in six hydrographic drainages of the Adriatic sea (Figure 1). One pereopod was taken per individual and was put in absolute ethanol. Tissues were dehydrated (2 min) in sterile water and ground with plastic pestles in microcentrifuge tubes containing 100 mM Tris, 10 mM EDTA, 100 mM NaCl, 0.1% SDS, 50 mM DTT and 10 µl/ml proteinase K (pH = 8). Samples were incubated at 37°C for 4 hours and DNA extracted twice with phenol/chloroform/isoamyl alcohol (25: 24: 1) followed by an additional extraction with chloroform. The DNA was then precipitated with one volume of isopropanol and 1/10 volume of 3 M (pH = 5.2) sodium acetate. It was then dried and resuspended in sterile water. DNA was collected by centrifugation, dried and diluted in water to a final concentration of 20 ng/µl. The optimal cycling program was 2 min at 94°C, 1 min at 35°C, 2 min at 72°C followed by 1 min at 94°C, 1 min at 35°C and 2 min at 72°C for 44 cycles and a final extension of 5 min at 72°C, using a Trio-Thermoblock (BIOMETRA GmBH, Göttingen, Germany).DNA Alignment-The nucleotide sequences were aligned manually with Se-Al v1.0al (Sequence Alignment Editor Version 1.0 alpha 1; Andrew Rambaut, 1996).

The sequences obtained from this study were combined with other sequences deposited in GenBank and corresponding to Italian, French and Swiss populations; a sequence of A. torrentium from Genbank was also used as outgroup (AF237599; GRANDJEAN et al., 2000a).

Neighbour-Joining (NJ), and Maximum Parsimony (MP) methods were used for phylogenetic reconstructions. The NJ and MP and analyses were conducted on MEGA version 3.0 [START_REF] Kumar | MEGA3: Integrated software for Molecular Evolutionary Genetics Analysis and sequence alignment[END_REF]. MP trees were found by heuristic search using 101 replicates of random stepwise addition. Bootstrap Percentages (BP MP ) were computed after 1,000 replicates. The NJ tree was found using the "p" distance. The pairwise sequence divergence values among haplotypes were used to assess the mean sequence divergence between the two main clusters revealed in phylogeographic analyses.

RESULTS

All the analyses were based on a 301 bp alignment of mitochondrial 16 S sequences. The sequences imported from GenBank were 199 bp shorter than those of 500 bp obtained in this study. The sequence alignments consisted of 301 pb enclosing 62 variable sites, of which 26 are parsimony informative. Among Marches samples three distinct haplotypes M1, M2, M3 were detected (Table I). The geographical distribution of Marches' haplotypes is presented in Figure 1. Among these three haplotypes, M1 and M2 were closely related with a nucleotide distance, pi, between the two haplotypes of 0.6%. These two haplotypes differ from M3 by a mean of 2.3%. These haplotypes show a highly structured geographical pattern of distribution (Figure 1 and Table 1). Haplotype M1 was found in northern locations whereas haplotype M3 was found in southern locations. M2 was specific to one location: Rio Freddo. Two centrally located populations harbour both M1 and M3.

Both phylogenetic analyses from NJ and MP revealed the presence of two subspecies in hydrographic basins of Marches region: A. i. carsicus (M1 & M2 haplotypes) that has been detected up to now only in the North-eastern Italy and in Alpi Orobie and A. i. meridionalis (M3) in the south. Two mixed populations with both subspecies A. i. carsicus and A. i. meridionalis were present in Amandole and Sanguerone from the hydrographic basin of Esino (the middle of Marches region) (Table I).

Pairwise mt16S sequence divergence was reported in Table II. The level of genetic variation within A. italicus subspecies is represented by the pairwise p-distance extimation (expressed as percentage) in Table II.

DISCUSSION

Our results showed that two subspecies overlap in Marches Region of Italy, A. i. carsicus and A. i. meridionalis. The distribution of A. i. carsicus in the central-northern part of the region was in accordance with the Italian ichthyogeographic Padan-Venetian (PV) district identified by [START_REF] Bianco | L'Ittiofauna continentale dell'Appennino umbro-marchigiano, barriera semipermeabile allo scambio di componenti primarie tra gli opposti versanti dell'Italia centrale[END_REF]. It could be explained by the extension of the Po River basin as far as the border of the meso-adriatic ditch, capturing water from a large number of rivers on both sides of the Adriatic Sea. In fact during glaciations the lowering of the sea level determined confluences of water between rivers flowing into the epicontinental area of the Mediterranean sea [START_REF] Cattauto | Lo studio dei corsi minori dell'Italia Appenninica come mezzo di indagine sulla tettonica del Plio/Pleistocene[END_REF]. A. i. meridionalis, recently described by [START_REF] Fratini | Phylogeography of the threatened crayfish (genus Austropotamobius) in Italy, implications for its taxonomy and conservation[END_REF] from molecular data, and to the Apennine cluster defined by TRONTELJ et al., 2005 is located in Central-Southern Italy from both side of the Apennines chain. According to these authors, its presence in Slovenia could result from recolonization events from glacial refugial area during the Pleistocene due to the lowering of the sea level and the consequent confluence of some Adriatic rivers [START_REF] Bianco | Mediterranean endemic freshwater fishes in Italy[END_REF]. In this study, we showed that its northern distribution reaches the central Marches Region where this subspecies is in contact with A. i. carsicus in the hydrographic basin of Esino. Two hypotheses could be drawn to explain the existence of mixed populations in central Marches region. They could be the result of a natural secondary contact between the two species during their spreading from different refugia after the last glacial period of the Pleistocene. According to the distribution of A. i. meridionalis, the refugial area during the last glaciation period could be located in the south of Italy, and from that area postglacial recolonisation events had taken place towards the north. Translocations by humans may also be the explanation for the presence of populations exhibiting both haplotypes in Amandole and Sanguerone. Humans have had a major impact on organism distribution by transporting animals, especially Crayfish, to many other geographical areas. According to [START_REF] Laurent | Les écrevissses en France[END_REF], [START_REF] Reynolds | Ireland's freshwaters[END_REF]LARGIARDER et al. (2000), these practices occurred until recently on both the local and larger scales across Europe.

The case of Spanish white-clawed crayfish is one of the best examples. Before the application of molecular markers, all authors ascribed a specific or subspecific status to Spanish crayfish, as either Austropotamobius lusitanicus or A. italicus lusitanicus. However, the molecular data provide a robust phylogeny which does not support this specific or subspecific status (GRANDJEAN et al., 2000and 2002b[START_REF] Trontelj | Phylogenetic and phylogeographic relationships in the crayfish genus Austropotamobius inferred from mitochondrial COI gene sequences[END_REF]. These authors explained the origin of the Spanish stock by a translocation of specimens from Italy. Also the analysis of nine Irish populations of Austropotamobius pallipes supported the evidence of the introduction in Ireland from western French specimens [START_REF] Gouin | Population genetic structure of the endangered freshwater crayfish Austropotamobius pallipes, assessed using RAPD markers[END_REF].

It was surprising to note that A. i. italicus while present in the northern and northeastern Marches border regions, Emilia Romagna and Tuscany, does not appear in Marches region [START_REF] Fratini | Phylogeography of the threatened crayfish (genus Austropotamobius) in Italy, implications for its taxonomy and conservation[END_REF]. This could be explained by restricted gene flow between the Adriatic and Mediterranean sides of the Apennine chain.

CONCLUSIONS

Our study confirmed that the application of molecular markers is a prerequisite before considering a management program, in helping taxonomic decisions, especially at specific and intraspecific levels where taxonomic recognition is based on limited numbers of morphological traits. The lack of a precise knowledge of genetic structure could have resulted in establishing populations of allochthonous taxa, and in the genetic contamination of local populations contrary to good conservation management. In terms of conservation genetics, two separated ESU (Evolutionary Significant Units according to Moritz's definition, 1994) occur in Marches. Each should be given conservation priorities and should be managed separately. However, one advantage of such mixed populations is the opportunity to test reproductive isolation between these lineages by the use of nuclear markers.

The next step of this work will be to investigate the genetic variability within populations with more polymorphic mtDNA gene or molecular markers in relation to the hydrographic basins, to improve our knowledge of these populations with the aim to plan conservation projects including restocking and restoration operations in this region. Given the taxonomic unit differences between Emilia Romagna and Marches regions, it would be interesting to verify the probable presence of A. i. carsicus in Emilia Romagna, too.

Figure 1

 1 Figure 1Geographical distribution of haplotypes of Austropotamobius italicus subspecies in Marches region.

Figure 1

 1 Figure 1Distribution géographique des haplotypes des sous-espèces de Austropotamobius italicus dans la région des Marches.

Table I For each site, data are reported of: water body and its hydrographic drainage; region or country; sample size; mitochondrial haplotypes (in parentheses, the number of individuals for each haplotype). Some sequences are downloaded from GeneBank. Tableau I Pour chaque site, les données suivantes sont reportées: cours d'eau, bassin hydrographique, région ou pays, taille de l'échantillon, haplotypes mitochondriaux (entre parenthèses, le nombre d'individus pour chaque haplotypes). Quelques séquences ont été téléchargées à partir de GeneBank. Code Water body Hydrographic drainage Sampling location Sample size Haplotype 16S(n) Genebank accession number, original source and taxonomic reference

 I

	REF genebank (present paper): A. i. carsicus	A. i. carsicus	A. i. carsicus	REF genebank (present paper): A. i. meridionalis	A. i. meridionalis & A. i. carsicus	A. i. meridionalis & A. i. carsicus	REF genebank (present paper): A. i. carsicus	A. i. meridionalis	A. i. meridionalis	A. i. meridionalis	AY611201 (FRATINI et al., 2004): A. pallipes	AY611185 (FRATINI et al., 2004): A. italicus carinthiacus	AY611198 (FRATINI et al., 2004): A. italicus carsicus	AY611186 (FRATINI et al., 2004): A. italicus carsicus	AY611189 (FRATINI et al., 2004): A. italicus italicus	AY611187; AY611188 (FRATINI et al., 2004): A. italicus italicus	AY611193 (FRATINI et al., 2004): A. italicus meridionalis	AF237590 (GRANJDEAN et al., 2000): A. i. italicus	AF237598 (GRANJDEAN et al., 2000): A. pallipes	APA242708 (LARGIADER et al., 2000): A. i. carinthiacus	APA242709 (LARGIADER et al., 2000): A. i. carinthiacus
	M1 (5)	M1 (5)	M1 (5)	M3 (5)	M3 (2); M1(3)	M3 (3); M1 (2)	M2 (5)	M3 (5)	M3 (5)	M3 (5)	A5 (5)	A3 (3)	A18 (1)	A4 (2)	A8 (2)	A6 (1); A7 (1)	A14 (1)	A19	F33	SW1	SW2
	5	5	5	5	5	5	5	5	5	5	2	3	1	2	2	2	1	/	/	/	/
	Marche	Marche	Marche	Marche	Marche	Marche	Marche	Marche	Marche	Marche	Piemonte	-	Trentino	Friuli	Emilia	Romagna	Toscana	Umbria	Emilia	Romagna	France	Switzerland	Switzerland
	Metauro	Metauro	Cesano	Esino	Esino	Esino	Esino	Aso	Tronto	Tenna	Po	Po	Brenta	Rosandra	Bidente-Ronco	Arno	Tevere	Reno	Clain	Rhone	Rhone
	Meta	Auro	Cesano	Pozzatoio	Amandole	Sanguerone	Rio Freddo	Cannavì	Lago	Lera	Varaita	Ticino	Lake	Caldonazzo	Rosandra	Lama	Farfereta	Nera	Samoggia	La gace	multiple	samplings	multiple	samplings
	1	2	3	4	5	6	7	8	9	10	11	14	20	21	22	23	27	31	40	43	44

For each site data reported are: water body and its hydrographic drainage, Italian region and/or country, sample size; mitochondrial 16S haplotype. Number 1-10 correspond to the populations sampled for this study; other eleven populations are sequences downloaded from GeneBank with their access number, original source and taxonomic reference; 43-44 are haplotype of more than one water body.

Polymerase chain reaction (PCR) amplification of of a rDNA 16S portion about 500 base pairs (bp) long was carried out in a Progene thermocycler using primers available inGRANDJEAN et al. (2002).

ACKNOWLEDGEMENTS

We are grateful to Prof. ssa Maria Balsamo for her skilful scientific and organisational support. A fundamental role, for their technical assistance in sample collection, was played by Patricia Viviana Masini and Maurizio Fusari. Many thanks for their support to the Ente Parco Nazionale dei Monti Sibillini and to the Amministrazioni Provinciali of Pesaro e Urbino, Ancona, Macerata, Ascoli Piceno.

 I.