## 6 Applications to Cardiovascular Medicine
### Arterial Wall
#### 6.4.2 Atherosclerotic Plaques  
Atherosclerosis is a chronic inflammatory disease that manifests as the hardening and occlusion of arteries due to the build-up of plaque on the lumen of the arterial wall. Atherosclerotic plaque is a mixture of fatty substances, cholesterol, calcium, and cellular waste, usually enclosed in a fibrous cap. Atherosclerotic lesions are generated at specific regions of the arterial tree, mostly in the vicinity of branch points, the outer wall of bifurcations, and the inner wall of curves [157]. Among many possible associated complications, plaque can break and detach, generating thrombosis, acute myocardial infarction, and stroke. Thus, the in vivo evaluation of the mechanical properties of atherosclerotic plaques and their mechanical environment could support the assessment of risk associated with plaque rupture. One of the earliest inverse analyses of atherosclerotic plaques was proposed by [PERSON] et al., in 2012 [286]. This study was performed on 12 patients with carotid artery atherosclerosis. For each patient, a set of cine MRI, 3D multi-contrast MRI, and sphyg-momanometry were collected. Two-dimensional models of the diseased sections were built from MRI images at diastole, including lipid pools resolved by multi-contrast MRI. The arterial wall and plaque were assumed uniform and to behave as a Mooney-Rivlin hyperelastic material, while the lipid pools were assumed to be isotropic linear elastic. An L-BFGS-B optimization method was applied to fit the material properties of the wall plaque until the error between the simulated and measured diastole-to-systole area change was minimized. Each iteration included the estimation of the unloaded configuration by the shrink-and-fit algorithm, and a forward FEM problem for the inflation from the unloaded configuration to the systolic configuration applying uniform luminal pressurization. The authors found the estimations of material stiffness show reasonable agreement with reported data from experimental studies. An analysis of stress distribution indicated that, for all cases, peak stress was located at the thin cap covering the lipid core. This study was further refined by [PERSON] et al., in 2017 [285], with similar imaging and functional data acquired for 8 patients with carotid atherosclerosis with follow-up tests after 18 months. The material models, optimization algorithm, target function, and iteration steps were the same as previously; however, a total of eight slices were analyzed from each carotid artery and modeled as a 3D thin layer so that axial prestretch could be included in the estimation of the unloaded configuration. Results revealed high patient-to-patient variability on plaque stiffness, which was significantly larger in the hypertensive cases. The authors also found that estimations of material properties of the plaque can significantly change over time, with stiffness increments being the most common scenario. [PERSON] et al. further explored these results with FSI simulations based on patient-specific estimations of atherosclerotic tissues with patient-specific measurements of pressure gradients by explanation tonometry and confirmed that flow and pressure-induced stresses peak at the fibrous cap that covers the lipid core, which could offer support to explain the main mechanisms of plaque rupture [296]. The main limitation of previous studies is that the current resolution of non-invasive imaging techniques is insufficient to resolve the displacement of atheroma plaques in small vessels such as the carotid artery. To overcome this, [PERSON] et al. utilized intravascular ultrasound technology [284]. This work analyzed data from 4 atherosclerotic lesions which were modeled as 3D thin cross-sectional slices. Each model was single-layered and divided into six circumferential sections, each portion being assumed materially homogeneous and following the Neo-Hookean hyperelastic material model. Perivascular tethering was modeled as a homogeneous elastic media of fixed stiffness.