On the Presence of Affine Fibril and Fiber Kinematics in the Mitral Valve Anterior Leaflet

Abstract

In this study, we evaluated the hypothesis that the constituent fibers follow an affine deformation kinematic model for planar collagenous tissues. Results from two experimental datasets were utilized, taken at two scales (nanometer and micrometer), using mitral valve anterior leaflet (MVAL) tissues as the representative tissue. We simulated MVAL collagen fiber network as an ensemble of undulated fibers under a generalized two-dimensional deformation state, by representing the collagen fibrils based on a planar sinusoidally shaped geometric model. The proposed approach accounted for collagen fibril amplitude, crimp period, and rotation with applied macroscopic tissue-level deformation. When compared to the small angle x-ray scattering measurements, the model fit the data well, with an r 2 ¼ 0.976. This important finding suggests that, at the homogenized tissue-level scale of~1 mm, the collagen fiber network in the MVAL deforms according to an affine kinematics model. Moreover, with respect to understanding its function, affine kinematics suggests that the constituent fibers are largely noninteracting and deform in accordance with the bulk tissue. It also suggests that the collagen fibrils are tightly bounded and deform as a single fiber-level unit. This greatly simplifies the modeling efforts at the tissue and organ levels, because affine kinematics allows a straightforward connection between the macroscopic and local fiber strains. It also suggests that the collagen and elastin fiber networks act independently of each other, with the collagen and elastin forming long fiber networks that allow for free rotations. Such freedom of rotation can greatly facilitate the observed high degree of mechanical anisotropy in the MVAL and other heart valves, which is essential to heart valve function. These apparently novel findings support modeling efforts directed toward improving our fundamental understanding of tissue biomechanics in healthy and diseased conditions.

Mitral valve leaflet remodelling during pregnancy: insights into cell-mediated recovery of tissue homeostasis

“…MV leaflet tissue is composed of four morphologically distinct layers: (i) the atrialis, which faces the left atrium; (ii) the spongiosa, which is made up primarily of hydrated glycosaminoglycans (GAGs) and proteoglycans; (iii) the fibrosa, which consists mainly of collagen; and (iv) the ventricularis, which contains not only some collagen, but also a substantial amount of elastin. Elastin in MV leaflets has been shown to consist of two highly aligned subpopulations of fibres, oriented circumferentially in the ventricularis and radially in the atrialis [7]. Similarly, collagen in MV leaflets is also highly aligned, with the majority of fibres pointing within +158 of the circumferential direction.…”

“…Similarly, collagen in MV leaflets is also highly aligned, with the majority of fibres pointing within +158 of the circumferential direction. Collagen fibres are also highly undulated (crimped) and thus bear no load until after they have been stretched enough to be completely straightened [7,8]. While native valve properties have been extensively studied, we have comparatively little knowledge regarding how these functional aspects of heart valve leaflet tissues adapt and remodel to altered stresses induced by changes in valvular and ventricular geometry from various surgical procedures and cardiac pathologies.…”

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

“…The latter question is especially raised with regards to past studies, revealing non-affine collagen kinematics [5,10,29,31], illustrating the complexity of arterial microstructure properties. Whether they are attributed to the decrimping process [34], to fiberfiber interactions [13] or to fiber-matrix interactions [5,50], non-affine collagen kinematics are currently taken into account in a novel generation of multiscale and micromechanical modelling approaches [48,16,56,37], but their microstructural and micromechanical origin has not yet been experimentally documented nor understood, which constitutes a limit for further refined multi-scale formulations. Specifically, few studies investigate the dependence of fiber kinematics on the loading type [52,12], and to the authors' knowledge, none have quantitatively compared fiber rotations for the same tracked fibers undergoing different loading scenarii, while comparing them to affine predicted reorientations.…”

Computational modeling of the arterial wall based on layer-specific histological data

“…In contrast, the nonaffine fiber kinematics assumes that the primary load transfer happens among fiber chains and each fiber chain deforms independently of the matrix (Chandran and Barocas 2006;Stylianopoulos and Barocas 2007). One of the fundamental assumptions of the EF and AI approaches presented in this paper is the affine fiber kinematics, which is shown to be a valid assumption for pericardial collagenous tissues (Fan and Sacks 2014) and mitral valve anterior leaflet (Lee et al 2015). On the other hand, there is evidence suggesting that the nonaffine fiber kinematics may be a more realistic assumption for other types of fibrous biomaterial such as bovine annulus fibrous tissue (Head et al 2003;Chandran and Barocas 2006;Huyghe and Jongeneelen 2012;Lake et al 2012).…”

“…The affine fiber kinematics is shown to be a valid assumption for many biological tissues including pericardial collagenous tissues (Fan and Sacks 2014) Fig. 3 Influence of the relative angle between segments θ r ∼ unif(−θ max , θ max ) on the level of fiber dispersion introduced by fiber waviness and mitral valve anterior leaflet (Lee et al 2015). Figure 4 shows a rectangular arterial wall layer sample with two families of fibers synthetically generated by the random walk algorithm.…”