# A Coupled Multiscale Approach to Modeling Aortic Valve Mechanics in Health and Disease
## 4 Discussion  
### Healthy Valve  
_Macroscale model_: we designed a set of simulations that mimic the experiments of [PERSON] [4] to validate a multiscale modeling approach for AV tissue, namely the pressurization of a \"fixed\" valve leaflet loaded from the aortic side. This corresponds to the region in the cardiac cycle between systole and diastole (Figure 2) where the transvalvular pressure is the largest. These boundary conditions represent in vitro experiments rather than the proper in vivo conditions. They allow us to simulate physiological states in the laboratory. The nature of the fixed boundary conditions, including the \"free\" coaptation edge, results in a \"balloon-inflation\"-like response, as seen in Figure 11. The response is consistent with the material response in Figure 9. The low pressure (load) results in the large deformation of the compliant regime. The tissue quickly stiffens and we see only small changes in the deformation for larger increasing loads. Note that we have not pre-stressed the tissue as in [39]. The initial curvature also plays a role in the response of the tissue, and we also encountered convergence issues for variations of the parameters in (19). However, without \"patient-specific\" geometry, the best we can hope for is an aggregate consistent result, which we observe in Figure 12.  
_Representative volume element (RVE)_: at the heart of our model is the RVE. We first discuss several of the important assumptions we made. [PERSON] et al. [43] argue that due to the averaging process in homogenization, the details of the RVE do not greatly impact the macroscale problem, something we also observe. To facilitate computational efficiency, we downsampled the RVE mesh and use an auxiliary high-fidelity mesh to extract details in a post-processing step (Figure 6). Again, for efficiency purposes, we assume Taylor boundary conditions, which results in an overestimation of stiffness response [44]. We also use Taylor boundary conditions in the VICAR post-processing for consistency. Figure 22 illustrates the difference in VICAR with Taylor and Dirichlet boundary conditions. As expected, the Dirichlet VICAR is on average lower. This is a result of only imposing motions on the boundaries and also allowing for a relaxation of the VIC. Note that although the difference is large for the \"apparent\" VICAR, we did not see a large difference in the actual VICAR. Figure 21: VICAR for mature arc pattern. The error bars represent one standard deviation. Finally, we assume the VIC bonds perfectly with the ECM, which is not physiologically accurate (see [45]). Modeling the discrete attachments via focal adhesions of the VIC requires special attention and is left as a limitation of the current study. Note, however, that by explicitly modeling the VICs in the RVE, such an extension is possible within our framework. _VICAR_: the aspect ratio being measured in the experiments is that of the nucleus, not the cell. We do not make a distinction between the nucleus and the cell in this analysis, i.e., we neglect the cytoskeleton. This is in line with previous analyses [5; 6]. We recommend a more detailed model incorporating this distinction for a future study. The most notable result above is the large discrepancy between the actual and \"apparent\" VICAR, as seen in Figure 12. We observe that the (arithmetic) mean \"apparent\" response is more consistent with the experimental results. We note that there is also large variation in the \"apparent\" ratio. The procedure used to determine the \"apparent\" value, as depicted in Figure 7, is representative of the experiments but not exactly identical. Notwithstanding, the results show that the observed cellular deformation _may_ be significantly different than the true deformation. This is of great importance when developing mechanotransduction models calibrated from experiments.