# A Coupled Multiscale Approach to Modeling Aortic Valve Mechanics in Health and Disease
###### Abstract
We further consider calcite aortic stenosis, the most prevalent aortic valve disease featuring the calcification of the valve leaflet tissues [11]. The aim here was to understand the relationship between the VIC aspect ratios and calcification. We find behavior that is consistent with previous single-scale studies in the literature, namely that the presence of calcified nodules leads to an increased strain profile that drives the further growth of calcification. _Aortic valve function_: details regarding AV physiology may be found, e.g., in [12]. We briefly revisit them here. The AV complex consists of the aortic root, the sinus, the leaflets, and the ascending aorta, as depicted in Figure 1. Our main focus here are the leaflets (or cusps), shown in color in Figure 1.  
Healthy AVs have three leaflets that open and close to allow blood flow from the ventricle into the ascending aorta and prevent retrograde flow. During the cardiac cycle (illustrated in Figure 2), blood flows in from the left atrium into the left ventricle during diastole, and the AV leaflets open (close) at the beginning (end) of systole. [PERSON] carried out a series of in vitro experiments to measure the VICAR in response to AV tissue loading during the cardiac cycle. AV leaflet samples were fixed in a tank and a pressure head was applied at five different levels, as shown in Table 1. Note that, in [4], the maximum pressure used was 90 mmHg; thus, for comparison purposes, all of our computations were also carried out to this pressure, as opposed to the conventional normal systolic pressure of 120 mmHg. The average VICAR was then measured at each pressure by image processing procedures of sections through the tissue thickness. [PERSON] notes that the VICAR reported was the observed value, i.e., the apparent 2D elliptical aspect ratio that, in general, is not concentric with the presumed ellipsoidal shape. Further details regarding the experimental procedure can be found in [4]. Note that the net pressure load is  
non-random patterns [9]. A few common patterns have been identified, with the two most common being the \"arc\" and \"partial arc\" patterns (Figure 3) [17; 18]. [PERSON] et al. [18] used reverse computed tomography (CT) to classify these patterns and how they progressed temporally and spatially. The calcification occurs more frequently on the aortic side of the valve (fibrosa) and the stiffening results in altered valve function [19; 20; 21; 22]. The underlying cause of calcification is still under investigation, however, tissue strain and hemodynamic shear stresses have been identified as important biomechanical factors driving their growth [23; 24; 25; 26; 27]. These factors result in a biochemical signaling processes between the endothelial cells and the VICs, promoting VIC differentiation into a calcific phenotype [28]. _Multiscale modeling_: in an effort to capture the multiscale feedback inherent to the behavior of AV tissue in health and disease, we will introduce a full 3D coupled multiscale model via FE\({}^{2}\). We first detail the theory and implementation of the model. Then, we calibrate the tissue model to the experimental data. We use the calibrated data to study VIC behavior in response to macroscale pressure loading in two states: healthy and calcified. We further investigate different stages of diseased valves, as mentioned above, to study the evolution of calcification in the tissue. The calcified states are considered by introducing regions of the tissue along the aortic face of the valve leaflet with material properties representing calcification in patterns similar to those observed in the diseased valves. We are able to identify a clear change in the VIC behavior in the non-calcified regions of the tissue which form a basis for the further progression and saturation of the calcified tissue.