Mathieu Nierenberger

A new multiscale model for the mechanical behavior of vein walls

The purpose of the present work is to propose a new multiscale model for the prediction of the mechanical behavior of vein walls. This model is based on one of our previous works which considered scale transitions applied to undulated collagen fibers. In the present work, the scale below was added to take the anisotropy of collagen fibrils into account. One scale above was also added, modeling the global reorientation of collagen fibers inside the vessel wall. The model was verified on experimental data from the literature, leading to a satisfactory agreement. The proposed multiscale approach also allows the extraction of local stresses and strains at each scale. This approach is presented here in the case of vein walls, but can easily be extended to other tissues which contain similar constituents.

Assessing the three-dimensional collagen network in soft tissues using contrast agents and high resolution micro-CT: Application to porcine iliac veins

The assessment of the three-dimensional architecture of collagen fibers inside vessel walls constitutes one of the bases for building structural models for the description of the mechanical behavior of these tissues. Multiphoton microscopy allows for such observations, but is limited to volumes of around a thousand of microns. In the present work, we propose to observe the collagenous network of vascular tissues using micro-CT. To get a contrast, three staining solutions (phosphotungstic acid, phosphomolybdic acid and iodine potassium iodide) were tested. Two of these stains were showed to lead to similar results and to a satisfactory contrast within the tissue. A detailed observation of a small porcine iliac vein sample allowed assessing the collagen fibers orientations within the medial and adventitial layers of the vein. The vasa vasorum network, which is present inside the adventitia of the vein, was also observed. Finally, the demonstrated micro-CT staining technique for the three-dimensional observation of thin soft tissues samples, like vein walls, contributes to the assessment of their structure at different scales while keeping a global overview of the tissue.

Investigation of the human bridging veins structure using optical microscopy

In this paper, we investigated the brain–sinus junction and especially the bridging veins linking these two organs. Two types of optical microscopy were used: conventional optical microscopy and digital microscopy. We used thin histological sections prepared from a human brain, and stained with Masson’s trichrome, hemalun and orcein. Finally we observed the path of the bridging vein inside the brain–skull interface. At smaller scales, wavy collagen fiber bundles were found and characterized inside the vein walls. Taking into account the orientations of the different sections with reference to frontal planes, we found that the bridging vein has a very complex geometry, which increases the difficulty to determine fiber orientations in its walls. Nevertheless, we found that collagen fiber bundles are mainly circumferentially oriented in the superior sagittal sinus walls. In this paper, we were able to characterize precisely the path of the bridging vein from the brain to the sinus, with different magnifications.

Evolution of the three-dimensional collagen structure in vascular walls during deformation: An in situ mechanical testing under multiphoton microscopy observation

The collagen fibers’ three-dimensional architecture has a strong influence on the mechanical behavior of biological tissues. To accurately model this behavior, it is necessary to get some knowledge about the structure of the collagen network. In the present paper, we focus on the in situ characterization of the collagenous structure, which is present in porcine jugular vein walls. An observation of the vessel wall is first proposed in an unloaded configuration. The vein is then put into a mechanical tensile testing device. As the vein is stretched, three-dimensional images of its collagenous structure are acquired using multiphoton microscopy. Orientation analyses are provided for the multiple images recorded during the mechanical test. From these analyses, the reorientation of the two families of collagen fibers existing in the vein wall is quantified. We noticed that the reorientation of the fibers stops as the tissue stiffness starts decreasing, corresponding to the onset of damage. Besides, no relevant evolutions of the out of plane collagen orientations were observed. Due to the applied loading, our analysis also allowed for linking the stress relaxation within the tissue to its internal collagenous structure. Finally, this analysis constitutes the first mechanical test performed under a multiphoton microscope with a continuous three-dimensional observation of the tissue structure all along the test. It allows for a quantitative evaluation of microstructural parameters combined with a measure of the global mechanical behavior. Such data are useful for the development of structural mechanical models for living tissues.

Towards Building a Multiscale Mechanical Model for the Prediction of Acute Subdural Hematomas

Acute subdural hematoma (ASDH) is a potentially devastating, yet curable, extra axial fluid collection within the subdural space situated between the skull and the cortex. It is often due to rupture of bridging veins crossing this subdural space, caused by the brain-skull relative motion. To be able to predict ASDH, a numerical model reflecting the mechanical properties of vascular walls is attractive. With this in mind, a suitable approach consists in modeling the material microstructure at different scales. In a former work [1, 2], R. Abdel Rahman studied the mechanical properties of the bridging veins – superior sagittal sinus junction when a human head is submitted to shock. This work showed the apparition of ASDH over a given value of head rotational acceleration. But lacks in the knowledge of microstructure and of the constituents mechanical properties were put forward in understanding the relations between material mechanical behavior and the apparition of ASDH. Therefore we chose to adopt a multiscale approach to model ASDH apparition. In the current work, several experimental observations have been set up to obtain a sufficient knowledge of the vein wall microstructure which was imprecisely documented to date. Stained thin slices of human brain were observed by optical microscopy. In addition, microtomography was used to assess the collagen fibers orientations. These observations allowed the identification of the different scales needed for modeling the microstructure. Many authors [3–6] deal with the mechanical behavior of vascular walls and of their various constituents but none of them consider multiple scales for modeling [7]. The next step of this work consists in improving the predictive capabilities of the existing model by going down the scales and taking microstructure into account. This methodology enabled the introduction of only physical parameters into the model, which is essential for future predictive capabilities. Finally, a failure criterion for the bridging veins taking into account the different scales has been created and is still being improved. It allows the evaluation of specific disease influence like collagen damage due to physiology. Besides it provides a prediction tool for ASDH useable for optimization of various shock absorbers.Copyright

On the Ability of Structural and Phenomenological Hyperelastic Models to Predict the Mechanical Behavior of Biological Tissues Submitted to Multiaxial Loadings

Medical surgery is currently rapidly improving and requires modeling faithfully the mechanical behavior of soft tissues. Various models exist in literature; some of them created for the study of biological materials, and others coming from the field of rubber mechanics. Indeed biological tissues show a mechanical behavior close to the one of rubbers. But while building a model, one has to keep in mind that its parameters should be loading independent and that the model should be able to predict the behavior under complex loading conditions. In addition, keeping physical parameters seems interesting since it allows a bottom up approach taking into account the microstructure of the material. In this study, the authors consider different existing hyperelastic models based on strain energy functions and identify their coefficients successively on single loading stress-stretch curves. The experimental data used, come from a paper by Zemanek dated 2009 and concerning uniaxial, equibiaxial and plane tension tests on porcine arterial walls taken in identical experimental conditions. To achieve identification, the strain energy function of each model is derived differently to provide an expression of the Cauchy stress associated to each loading case. Firstly the parameters of each model are identified on the uniaxial tension curve using a least squares method. Then, keeping the obtained parameters, predictions are made for the two other loading cases (equibiaxial and plane tension) using the associated expressions of stresses. A comparison of these predictions with experimental data is done and allows evaluating the predictive capabilities of each model for the different loading cases. A similar approach is used after swapping the loading types.Since the predictive capabilities of the models are really dependent on the loading chosen to determine their parameters, another type of identification procedure is set up. It consists in adding the residues over the three loading cases during identification. This alternative identification method allows a better agreement between each model and the various types of experiments. This study evaluated the ability of some classical hyperelastic models to be used for a predictive scope after being identified on a specific loading type. Besides it brought to light some existing models which can describe at best the mechanical behavior of biological tissues submitted to various loadings.Copyright

Optical line generation using a 3D-printed component: application for a force sensor (Conference Presentation)

Additive manufacturing is more and more used in optics to produce opto-mechanical components as well as light transmission mediums, either for prototype evaluation or for functional part generation. It was previously shown that optical systems can benefit from the geometrical accuracy of the printed parts. Intrinsic defects such as surface roughness or volume birefringence can also be exploited for optical component design. We here present such use of particular properties of an additive manufacturing process based on photopolymerization. The final goal of the work is the design of a force sensor for collaborative robotics. More precisely, the aim is to design an optical force sensor to control the contact force between a human body and a magnetic source controlled by a robot for medical purpose. Optical sensors are known to have major interests in harsh environments where classical electrical sensors cannot be used due to, like here, electromagnetic compatibility issues. Two 3D-printed designs of optical force sensors are compared. The first one, conceptually developed in a previous work, is using polarization modulation due to force-induced birefringence to modify optical transmission in a sensor based on a monolithic original geometry. For such a case, additive manufacturing appears as a powerful production technique as the 3D part must be transparent and at the same time obtained with an accurate complex geometry. The second design is based on the volume scattering properties of printed transparent parts. For the first time to our knowledge, we show that the optical system made out of a beam expander and a cylindrical lens, necessary to achieve an optical line, can be replaced by a simple prismatic 3D-printed element. Using the Polyjet technology developed by Stratasys Ltd, a line can simply be obtained using the 1D volume light scattering inside the printed medium. The variation of line properties is then related to the mechanical strain induced by the force to be measured. In other words, the optical properties we rely on are linked to the bulk liquid material, its photopolymerization during printing and finally the impact of mechanical stress on the printed component. The sensitive element in the force sensor can be seen as a metamaterial with properties which depend on its micrometric structuration. The micro-structuration size is not related to the standard minimum feature size as claimed by the manufacturer but to the additive manufacturing process itself. In our case, a Stratasys Connex 350 printer has been used with an acrylate transparent material. Opto-mechanical properties such as birefringence, surface roughness, elasto-optic coefficients have been measured. The ability to generate an optical line using natural 1D volume light scattering in a printed parallelepiped with polished surfaces is experimentally demonstrated. As potential application, the parallelepiped is used to replace a cylindrical lens in an amplitude modulation force sensor. The sensor response is measured. Thus, additive manufacturing appears to be a promising technique to achieve optical components and to integrate optical sensors in future 3D-printed mechatronic systems.