# A Coupled Multiscale Approach to Modeling Aortic Valve Mechanics in Health and Disease
###### Abstract  
Mechano-biological processes in the aortic valve span multiple length scales ranging from the molecular and cell to tissue and organ levels. The valvular interstitial cells residing within the valve cusps sense and actively respond to leaflet tissue deformations caused by the valve opening and closing during the cardiac cycle. Abnormalities in these biomechanical processes are believed to impact the matrix-maintenance function of the valvular interstitial cells, thereby initiating valvular disease processes such as calcite aortic stenosis. Understanding the mechanical behavior of valvular interstitial cells in maintaining tissue homeostasis in response to leaflet tissue deformation is therefore key to understanding the function of the aortic valve in health and disease. In this study, we applied a multiscale computational homogenization technique (also known as \"FE2\") to aortic valve leaflet tissue to study the three-dimensional mechanical behavior of the valvular interstitial cells in response to organ-scale mechanical loading. We further considered calcite aortic stenosis with the aim of understanding the likely relationship between the valvular interstitial cell deformations and calcification. We find that the presence of calcified nodules leads to an increased strain profile that drives further growth of calcification. a +
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that investigated this metric in response to the physiological loading of aortic valve leaflet tissue. In an effort to better understand the nature of AV disease, researchers have been exploring the central role of VICs by modeling the inherently multiscale behavior of AV tissue [4; 5; 6; 7]. Numerical simulations that mimic these experiments were carried out but were limited to 2D and uncoupled 3D models (i.e., no interaction between the macroscale and microscale). [PERSON] et al. [6; 8; 9] developed the first 3D, multiscale, transient model of the aortic valve in health and disease, where they coupled the organ-level (whole valve) mechanical strains to tissue and cell-level events, and found agreeable results to the ex vivo experiments that related whole valve deformations to VIC deformations. Missing from the literature, however, are fully coupled multiscale models, i.e., models that allow for _two-way_ interaction between the disparate length scales. Naturally, a meaningful model of the full resolution of the AV, incorporating the cells that make up its microstructure, is a computationally intractable problem. An alternative is computational homogenization, sometimes known as FE\({}^{2}\), where a statistical representation of the microstructure (the \"representative volume element\" or RVE) is embedded into a macroscale model. Computational homogenization is a viable way of coupling multiscale behavior [10]. We use this approach to study the valvular interstitial cell's aspect ratio (VICAR) as a representation of cellular deformations. VICAR is defined as the ratio of the valvular interstitial cell's longest length dimension to its shortest, and it is often used as a suitable metric for cellular shape changes, i.e., the stimuli for mechanotransduction, as proposed by [PERSON] [4]. We are able identify that the perceived aspect ratio from experiments may not be consistent with the actual 3D VIC deformations. With this methodology, we introduce a framework for more complex multiscale and multiphysics AV models. The objective of this study was to apply FE\({}^{2}\) to aortic valve leaflet tissue in 3D to study the mechanical behavior of the VIC in response to organ-scale mechanical loading. The modeling scheme importantly utilizes self-consistent material models based on layer-wise experimental data from aortic valve tissue. Our simulations demonstrate a viable method for the fully multiscale modeling of aortic valve tissue. We find that the \"apparent\" VIC aspect ratio observed in experiments may not necessarily be consistent with the actual 3D deformations of the cells.