A meso-scale layer-specific structural constitutive model of the mitral heart valve leaflets

Abstract

Fundamental to developing a deeper understanding of pathophysiological remodeling in mitral valve (MV) disease is the development of an accurate tissue-level constitutive model. In the present work, we developed a novel meso-scale (i.e. at the level of the fiber, 10–100 μm in length scale) structural constitutive model (MSSCM) for MV leaflet tissues. Due to its four-layer structure, we focused on the contributions from the distinct collagen and elastin fiber networks within each tissue layer. Requisite collagen and elastin fibrous structural information for each layer were quantified using second harmonic generation microscopy and conventional histology. A comprehensive mechanical dataset was also used to guide model formulation and parameter estimation. Furthermore, novel to tissue-level structural constitutive modeling approaches, we allowed the collagen fiber recruitment function to vary with orientation. Results indicated that the MSSCM predicted a surprisingly consistent mean effective collagen fiber modulus of 162.72 MPa, and demonstrated excellent predictive capability for extra-physiological loading regimes. There were also anterior-posterior leaflet-specific differences, such as tighter collagen and elastin fiber orientation distributions (ODF) in the anterior leaflet, and a thicker and stiffer atrialis in the posterior leaflet. While a degree of angular variance was observed, the tight valvular tissue ODF also left little room for any physically meaningful angular variance in fiber mechanical responses. Finally, a novel fibril-level (0.1 to 1 μm) validation approach was used to compare the predicted collagen fiber/fibril mechanical behavior with extant MV small angle X-ray scattering data. Results demonstrated excellent agreement, indicating that the MSSCM fully captures the tissue-level function. Future utilization of the MSSCM in computational models of the MV will aid in producing highly accurate simulations in non-physiological loading states that can occur in repair situations, as well as guide the form of simplified models for real-time simulation tools.

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

“…straightening) of fibres in an ensemble, and is thus referred to as the 'recruitment function'. It has been found that, in normal MV leaflets, D is largely independent of angle [16]. Following anisotropic permanent set and/or growth during pregnancy, however, this assumption is no longer valid if the recruitment function parameters are defined with respect to the natural stress-free reference configuration (b s ) of the tissue.…”

“…In brief, the total stress in the leaflet in this solid mixture model was assumed to be the weighted linear sum of the stresses borne by the underlying collagen fibre network, elastin fibre network and the remainder of the tissue matrix, with each stress being scaled by the mass fraction of its corresponding phase. The matrix phase has been shown to have very low tensile stiffness and thus to contribute very little to the mechanical behaviour of the total tissue [16]. Therefore, in this study, we neglected the matrix phase and instead attributed all the stress in the tissue to the collagen and elastin fibre networks.…”

“…A collagen fibre within the MV leaflet is naturally undulated and bears negligible load for stretch values smaller than some critical 'slack' stretch l slk , above which that fibre is fully straightened [16]. In our MSSCM, the collagen phase was modelled at the level of a fibre ensemble, which exhibits the properties of a unidirectional population of collagen fibres having a bounded distribution of slack stretches with lower bound l lb and upper bound l ub .…”

“…In order to express the mechanical behaviour of each valve leaflet specimen in terms of physically meaningful parameters, we used a recently developed mesoscale structural constitutive model (MSSCM) for MV leaflet tissues [16]. In brief, the total stress in the leaflet in this solid mixture model was assumed to be the weighted linear sum of the stresses borne by the underlying collagen fibre network, elastin fibre network and the remainder of the tissue matrix, with each stress being scaled by the mass fraction of its corresponding phase.…”

“…In particular, we wanted to determine if there is a specific homeostatic endpoint that the MV tissue system attempts to reestablish, similar to vascular tissues [15]. To link the observed structural and morphological information, we used a recently developed comprehensive structural constitutive model specialized for the MV [16]. Moreover, we linked tissue-level and cellular changes by quantifying how MVIC geometry changes throughout pregnancy (figure 1).…”