A functionally graded material model for the transmural stress distribution of the aortic valve leaflet

Abstract

Heterogeneities in structure and stress within heart valve leaflets are of significant concern to their functional physiology, as they affect how the tissue constituents remodel in response to pathological and non-pathological (e.g. exercise, pregnancy) alterations in cardiac function. Indeed, valve interstitial cells (VICs) are known to synthesize and degrade leaflet extracellular matrix (ECM) components in a manner specific to their local micromechanical environment. Quantifying local variations in ECM structure and stress is thus necessary to understand homeostatic valve maintenance as well as to develop predictive models of disease progression and post-surgical outcomes. In the aortic valve (AV), transmural variations in stress have previously been investigated by modeling the leaflet as a composite of contiguous but mechanically distinct layers. Based on previous findings about the bonded nature of these layers (Buchanan and Sacks, BMMB, 2014), we developed a more generalized structural constitutive model by treating the leaflet as a functionally graded material (FGM), whose properties vary continuously over the thickness. We informed the FGM model using high-resolution morphological measurements, which demonstrated that the composition and fiber structure change gradually over the thickness of the AV leaflet. For validation, we fit the model against an extensive database of whole-leaflet and individual-layer mechanical responses. The FGM model predicted large stress variations both between and within the leaflet layers at end-diastole, with low-collagen regions bearing significant radial stress. These novel results suggest that the continually varying structure of the AV leaflet has an important purpose with regard to valve function and tissue homeostasis.

A comprehensive pipeline for multi‐resolution modeling of the mitral valve: Validation, computational efficiency, and predictive capability

“…The leaflet tissue response was simulated using a simplified structural model, which provided insight into the tissue‐level response and structural rearrangement. However, this model lacks capability to account for the complex multi‐layer microstructure and composition variations of heart valve leaflet tissue . The mapping of the CFA data is a necessary step, which can only be achieved in an in vitro setting.…”

“…In terms of predicting in vivo biomechanical response of the MV to disease and repair, this study does not take into account the tissue growth and remodeling processes. To better understand the biomechanical response of the tissue, the model needs to be extended to accurately model these phenomena . Furthermore, to elucidate the mechanobiological drivers of the growth and remodeling, it is important to connect the organ‐level tissue response to the cellular‐level response .…”

“…However, this model lacks capability to account for the complex multilayer microstructure and composition variations of heart valve leaflet tissue. 53,54 The mapping of the CFA data is a necessary step, which can only be achieved in an in vitro setting. To address this issue, and we are currently working on building a library of CFA data for a population of ovine MVs, which eventually will be used to generate a representative CFA distribution for in vivo simulations.…”

“…To better understand the biomechanical response of the tissue, the model needs to be extended to accurately model these phenomena. 54 Furthermore, to elucidate the mechanobiological drivers of the growth and remodeling, it is important to connect the organlevel tissue response to the cellular-level response. 55 This would enable us to investigate the changes in phenotypic state of MV interstitial cells and analyze their response to the mechanical stress overloads and surgical interventions.…”

A noninvasive method for the determination of in vivo mitral valve leaflet strains

“…An additional limitation of the present study is that the structural homogenization used in our models restricts what conclusions that can be directly drawn at the tissue and cell levels. For investigations at this scale, a more detailed microstructural model must be used, to account for in‐plane and transmural heterogeneity in composition and fiber architecture throughout the tissue …”