Implementing a micromechanical model into a finite element code to simulate the mechanical and microstructural response of arteries

Risky interpretations across the length scales: continuum vs. discrete models for soft tissue mechanobiology

Modelling and simulation in mechanobiology play an increasingly important role to unravel the complex mechanisms that allow resident cells to sense and respond to mechanical cues. Many of the in vivo mechanical loads occur on the tissue length scale, thus raising the essential question how the resulting macroscopic strains and stresses are transferred across the scales down to the cellular and subcellular levels. Since cells anchor to the collagen fibres within the extracellular matrix, the reliable representation of fibre deformation is a prerequisite for models that aim at linking tissue biomechanics and cell mechanobiology. In this paper, we consider the two-scale mechanical response of an affine structural model as an example of a continuum mechanical approach and compare it with the results of a discrete fibre network model. In particular, we shed light on the crucially different mechanical properties of the 'fibres' in these two approaches. While assessing the capability of the affine structural approach to capture the fibre kinematics in real tissues is beyond the scope of our study, our results clearly show that neither the macroscopic tissue response nor the microscopic fibre orientation statistics can clarify the question of affinity.

Fiber Rearrangement and Matrix Compression in Soft Tissues: Multiscale Hypoelasticity and Application to Tendon

It is widely accepted that the nonlinear macroscopic mechanical behavior of soft tissue is governed by fiber straightening and re-orientation. Here, we provide a quantitative assessment of this phenomenon, by means of a continuum micromechanics approach. Given the negligibly small bending stiffness of crimped fibers, the latter are represented through a number of hypoelastic straight fiber phases with different orientations, being embedded into a hypoelastic matrix phase. The corresponding representative volume element (RVE) hosting these phases is subjected to “macroscopic” strain rates, which are downscaled to fiber and matrix strain rates on the one hand, and to fiber spins on the other hand. This gives quantitative access to the fiber decrimping (or straightening) phenomenon under non-affine conditions, i.e. in the case where the fiber orientations cannot be simply linked to the macroscopic strain state. In the case of tendinous tissue, such an RVE relates to the fascicle material with 50 μm characteristic length, made up of crimped collagen bundles and a gel-type matrix in-between. The fascicles themselves act as parallel fibers in a similar matrix at the scale of a tissue-related RVE with 500 μm characteristic length. As evidenced by a sensitivity analysis and confirmed by various mechanical tests, it is the initial crimping angle which drives both the degree of straightening and the shape of the macroscopic stress-strain curve, while the final linear portion of this curve depends almost exclusively on the collagen bundle elasticity. Our model also reveals the mechanical cooperation of the tissue’s key microstructural components: while the fibers carry tensile forces, the matrices undergo hydrostatic pressure.

Evaluation of affine fiber kinematics in porcine tricuspid valve leaflets using polarized spatial frequency domain imaging and planar biaxial testing

Collagen fibers are the primary load-bearing microstructural constituent of bodily soft tissues, and, when subjected to external loading, the collagen fibers reorient, uncrimp, and elongate. Specific to the atrioventricular heart valve leaflets, the collagen fiber kinematics form the basis of many constitutive models; however, some researchers claim that modeling the affine fiber kinematics (AFK) are sufficient for accurately predicting the macroscopic tissue deformations, while others state that modeling the non-affine kinematics (i.e., fiber uncrimping together with elastic elongation) is required. Experimental verification of the AFK theory has been previously performed for the mitral valve leaflets in the left-side heart; however, this same evaluation has yet to be performed for the morphologically distinct tricuspid valve (TV) leaflets in the right-side heart. In this work, we, for the first time, evaluated the AFK theory for the TV leaflets using an integrated biaxial testing-polarized spatial frequency domain imaging device to experimentally quantify the load-dependent collagen fiber reorientations for comparison to the AFK theory predictions. We found that the AFK theory generally underpredicted the fiber reorientations by 3.1°, on average, under the applied equibiaxial loading with greater disparity when the tissue was subjected to the applied non-equibiaxial loading. Furthermore, increased AFK errors were observed with increasing collagen fiber reorientations (Pearson coefficient r = -0.36, equibiaxial loading), suggesting the AFK theory is better suited for relatively smaller reorientations. Our findings suggest the AFK theory may require modification for more accurate predictions of the collagen fiber kinematics in the TV leaflets, which will be useful in refining modeling efforts for more accurate TV simulations.