Hélène Magoariec

A comprehensive study of layer-specific morphological changes in the microstructure of carotid arteries under uniaxial load

The load bearing properties of large blood vessels are principally conferred by collagen and elastin networks and their microstructural organization plays an important role in the outcomes of various arterial pathologies. In particular, these fibrous networks are able to rearrange and reorient spatially during mechanical deformations. In this study, we investigate for the first time whether these well-known morphological rearrangements are the same across the whole thickness of blood vessels, and subsequently if the underlying mechanisms that govern these rearrangements can be predicted using affine kinematics. To this aim, we submitted rabbit carotid samples to uniaxial load in three distinct deformation directions, while recording live images of the 3D microstructure using multiphoton microscopy. Our results show that the observed realignment of collagen and elastin in the media layer, along with elastin of the adventitia layer, remained limited to small angles that can be predicted by affine kinematics. We show also that collagen bundles of fibers in the adventitia layer behaved in significantly different fashion. They showed a remarkable capacity to realign in the direction of the load, whatever the loading direction. Measured reorientation angles of the fibers were significantly higher than affine predictions. This remarkable property of collagen bundles in the adventitia was never observed before, it shows that the medium surrounding collagen in the adventitia undergoes complex deformations challenging traditional hyperelastic models based on mixture theories. STATEMENT OF SIGNIFICANCE The biomechanical properties of arteries are conferred by the rearrangement under load of the collagen and elastin fibers making up the arterial microstructure. Their kinematics under deformation is not yet characterized for all fiber networks. In this respect we have submitted samples of arterial tissue to uniaxial tension, simultaneously to confocal imaging of their microstructure. Our method allowed identifying for the first time the remarkable ability of adventitial collagen fibers to reorient in the direction of the load, achieving reorientation rotations that exceeded those predicted by affine kinematics, while all other networks followed the affine kinematics. Our results highlight new properties of the microstructure, which might play a role in the outcomes of vascular pathologies like aneurysms.

Viscoelastic properties of rabbit osteoarthritic menisci: A correlation with matrix alterations

The aim of this study was to evaluate the effect of early osteoarthritis (OA) on the viscoelastic properties of rabbit menisci and to correlate the mechanical alterations with the microstructural changes. Anterior Cruciate Ligament Transection (ACLT) was performed in six male New-Zealand White rabbits on the right knee joint. Six healthy rabbits served as controls. Menisci were removed six weeks after ACLT and were graded macroscopically. Indentation-relaxation tests were performed in the anterior and posterior regions of the medial menisci. The collagen fibre organization and glycosaminoglycan (GAG) content were assessed by biphotonic confocal microscopy and histology, respectively. OA menisci displayed severe macroscopic lesions compared with healthy menisci (p=0.009). Moreover, the instantaneous and equilibrium moduli, which were 2.9±1.0MPa and 0.60±0.18MPa in the anterior region of healthy menisci, respectively, decreased significantly (p=0.03 and p=0.004, respectively) in OA menisci by 55% and 57%, respectively, indicating a global decrease in meniscal stiffness in this region. The equilibrium modulus alone decreased significantly (p=0.04) in the posterior region, going from 0.60±0.18MPa to 0.26±012MPa. This induced a loss of tissue elasticity. These mechanical changes were associated in the posterior region with a structural disruption of the superficial layers, from which the tie fibres emanate, and with a decrease in the GAG content in the anterior region. Consequently, the circumferential collagen fibres of the deep zone were dissociated and the collagen bundles were less compact. Our results demonstrate the strong meniscal modifications induced by ACLT at an early stage of OA and highlight the relationship between structural and chemical matrix alterations and mechanical properties.

The concept of frozen elastic energy as a consequence of changes in microstructure morphology

Constitutive modelling of soft biological tissues has been the topic of abundant literature. These biological tissues, made of variously oriented and crimped fibers embedded in a soft matrix, exhibit a highly nonlinear anisotropic behavior with the ability to sustain large reversible strains. The existing constitutive models are mainly phenomenological hyperelastic models developed at the macroscopic scale (Holzapfel & Gasser 2000). Experimental mechanical tests performed on soft tissues and coupled to confocal microscopic imaging (Schrauwen et al. 2012) reveal that this nonlinear behavior originates in geometrical changes in the microstructure, such as progressive decrimping and re-alignement of the fibers along the load direction. This confirms the growing need to understand the relationship between phenomena taking place in the microstructure and macroscopic mechanical response; subsequently driving forward multi-scale approaches (Morin & Hellmich 2014). We here propose to model the reorientation of the fibers within the matrix through extension of the framework of continuum micromechanics (Zaoui 2002) and Eshelby’s inclusion problems (Eshelby 1957). We investigate the ability of the proposed model to capture, through microstructure morphology changes, the non-linear mechanical response of soft tissues, the possible path dependence of their response to multiaxial loading, and a remaining frozen elastic energy after complete unloading of the tissue.

Kinematics of collagen fibers in carotid arteries under tension-inflation loading

Biomechanics of the extracellular matrix in arteries determines their macroscopic mechanical behavior. In particular, the distribution of collagen fibers and bundles plays a significant role. Experimental data showed that, in most arterial walls, there are preferred fiber directions. However, the realignment of collagen fibers during tissue deformation is still controversial: whilst authors claim that fibers should undergo affine deformations, others showed the contrary. In order to have an insight about this important question of affine deformations at the microscopic scale, we measured the realignment of collagen fibers in the adventitia layer of carotid arteries using multiphoton microscopy combined with an unprecedented Fourier based method. We compared the realignment for two types of macroscopic loading applied on arterial segments: axial tension under constant pressure (scenario 1) and inflation under constant axial length (scenario 2). Results showed that, although the tissue underwent macroscopic stretches beyond 1.5 in the circumferential direction, fiber directions remained unchanged during scenario 2 loading. Conversely, fibers strongly realigned along the axis direction for scenario 1 loading. In both cases, the motion of collagen fibers did not satisfy affine deformations, with a significant difference between both cases: affine predictions strongly under-estimated fiber reorientations in uniaxial tension and over-estimated fiber reorientations during inflation at constant length. Finally, we explained this specific kinematics of collagen fibers by the complex tension-compression interactions between very stiff collagen fibers and compliant surrounding proteins. A tensegrity representation of the extracellular matrix in the adventitia taking into account these interactions was proposed to model the motion of collagen fibers during tissue deformation.

Granular Materials: Mesoscale Structures and Modeling

Abstract: A straightforward and reliable modeling of granular materials currently remains an open issue. The difficulty lies in the very discrete nature of these materials composed of grains in contact. In this chapter, we explore a new upscaling approach including a mesoscale.

Effects of a viscosupplementation therapy on rabbit menisci in an anterior cruciate ligament transection model of osteoarthritis

The aim of this study was to evaluate the morphological, microstructural, and mechanical effects of a viscosupplementation therapy on rabbit menisci at an early stage of osteoarthritis (OA). Anterior cruciate ligament transection (ACLT) was performed in twelve male New-Zealand White rabbits on the right knee joint. Six of these twelve rabbits received a mono intra-articular injection of high molecular weight hyaluronic acid (HA) two weeks after ACLT. Six additional healthy rabbits served as controls. Medial menisci were removed from all right knees (n=18) six weeks after ACLT and were graded macroscopically. Indentation-relaxation tests were performed in the anterior and posterior regions of the menisci. Collagen fiber organization and glycosaminoglycan (GAG) content were assessed by biphotonic confocal microscopy and histology, respectively. Viscosupplementation significantly (p=0.002) improved the surface integrity of the medial menisci compared to the operated non-treated group. Moreover, the injection seems to have an effect on the GAG distribution in the anterior region of the menisci. However, the viscoelastic properties of both operated groups were similar and significantly lower than those of the healthy group, which was explained by their modified collagen fiber organization. They displayed disruption of the tie fibers due to structural alterations of the superficial layers from which they emanate, leading to modifications in the deep zone. To conclude, the viscosupplementation therapy prevents macroscopic lesions of the menisci, but it fails to restore their collagen fiber organization and their viscoelastic properties. This finding supports the role of this treatment in improving the lubrication over the knee.

Change of Scale Based on Phenomenological Modeling at the Meso-scale

The aim of this chapter is to demonstrate that the knowledge of the mechanical behavior of granular materials at the meso-scale allows the mechanical behavior at the macro-scale to be forecast for any stress path. To this end, we first propose a phenomenological modeling of the mechanical behavior of the phases, which has been analyzed. Then, we analyze relations between the model parameters defined for each phase and two characteristics of these phases: their orientation with respect to the loading direction 1′, and their induced anisotropy defined by the component X 1′ of the anisotropy tensor considered in the phenomenological model. We then propose a simple model to define the evolution of the volumetric amount of each phase related to the loading. Finally, we show that the mechanical behaviors of the considered phases and of the global sample can be forecast on a different stress path from the one used for the identification of the model parameters at the meso-scale. All the analyses presented in this chapter were based on DEM simulations on sample B.

Texture, Stress and Strain at the Meso-scale

In this chapter, we will describe the internal state at the meso-scale and define stress and strain tensors at this scale. The heterogeneity of the internal state, of stress and of strain at this scale is also presented.

Previous Approaches and Motivation for the Use of the Meso-scale

In this chapter we present, in a synthetic form, some previous change of scale approaches for the definition of the mechanical behavior of granular materials. The change of scale approach based on the microscopic scale is described and limitations of this approach are put into evidence. To this end, we first present the change of scale for texture variables and then the average and localization operators for static and kinematic variables (these operators will be represented schematically).

Texture–Stress–Strain Relationship at the Meso-scale

In the following, different variables characterizing structure, stress and strain of the six phases W 1 ′ W 1 ′ , W 0 ′ W 0 ′ , W 2 ′ W 2 ′ , S 1 ′ S 1 ′ , S 0 ′ S 0 ′ and S 2 ′ S 2 ′ are defined as the average of their counterpart over all the meso-domains belonging to each phase. The definition of porosity ϕ p , stress tensor σ p , and strain tensor δe p for each phase p makes use of the volume-weighted average, while the definition of mean valence r p , makes use of the arithmetic average.