## 6 Applications to Cardiovascular Medicine
### Arterial Wall  
Changes in mechanical properties of arterial walls have been associated with the onset of multiple cardiovascular pathologies (e.g., atherosclerosis, dissection, stenosis) and remains an important predictor of cardiovascular morbidity and mortality in clinical practice. This motivated the development of early techniques for the non-invasive assessment of arterial stiffness through the evaluation of luminal area change and pulse wave velocity. These techniques, although useful, can only provide a gross estimation of material properties as they introduce many assumptions and simplifications related to homogeneity, perivascular support, and linearized behavior. The image-based resolution of vascular tissue kinematics is technically challenging; the main reason being the relative thinness of vascular walls. For example, the ascending aorta has a typical thickness of about 2.5 mm, which decreases to about 1.5 mm at the abdominal aorta, and the pulmonary artery is only about 0.2 mm thick. These length scales are comparable to the highest resolutions available on imaging techniques, for which luminal area changes (either with or without contrast agents) remained the main input for early inverse analyses of arteries. However, recent developments in ultrasound speckle tracking and DENSE MRI techniques make available arterial wall displacement measurements on a meaningful number of pixels. Most approaches rely on FEM for the solution of the forward problem (summarized in Table 8). \begin{table}
\begin{tabular}{p{42.7 pt} p{113.8 pt} p{113.8 pt} p{113.8 pt} p{113.8 pt} p{113.8 pt}} \hline
**Study** & **Clinical Data** & & **Forward Problem** & & **Inverse Problem** \\ \hline \multirow{4}{*}{[PERSON] et al., 2022, 2021 [14], 280]} & Population & 27H & Reference & Diastole & \multirow{2}{*}{Target function} & Least-squared \\  & Pathology & None & Passive model & Hom. Fung & & \\  & & & & orthotropic & & \\  & Data & Cine and DENSE & & & None & \\  & Data & MRI & & & LP, Het. EF at & & \\  & Anatomy & IAA, DTA, DAA & Boundary & & & \\  & & & & adventitia & & \\ \hline \multirow{4}{*}{[PERSON] et al., 2021 [5]} & Population & 2D & Reference & Diastole & \multirow{2}{*}{Target function} & \multirow{2}{*}{P-V curve error} \\  & Pathology & PAH and CHD & Passive model & & & \\  & & & & & & family \\  & Data & IVP, Cine MRI, PC & & & None & \\  & Data & MRI & & & & \\  & Anatomy & Pulmonary Artery & Boundary & & LP, TF adventitia & \\  & Population & 30D & Reference & Diastole & \multirow{2}{*}{Target function} & \multirow{2}{*}{Systolic shape.} \\  & Pathology & aATA, w BAV and TAV & & Passive model & & \\  & Data & CT scans & Active model & & None & \\  & Anatomy & Thoracic aorta & Boundary & & LP and shape & \\  & & & & change & \\ \hline \multirow{4}{*}{[PERSON] et al., 2019, 2016 [282]} & Population & 30H 65D, 40D & Reference & Unloaded & \multirow{2}{*}{Target function} & \multirow{2}{*}{Displacement error} \\  & Pathology & AAA & Passive model & Hom. Neo-Hookean & & \\  & Data & 4D US, ST, CT scan, Hand cuff pressure & Active model & None & \\  & Anatomy & IAA & Boundary & LP, AP & \\ \hline \multirow{4}{*}{[PERSON] et al., 2018 [284]} & Population & 4D & Reference & Unloaded & \multirow{2}{*}{Target function} & \multirow{2}{*}{Displacement error} \\  & Pathology & Atherosclerosis & Passive model & Het. Neo-Hookean & & \\ \cline{1-1}  & Data & IVUS & Active model & None & \\ \cline{1-1}  & Anatomy & Carotid artery & Boundary & LP, EF at adventitia & \\ \hline \end{tabular}
\end{table} 
Table 8: Literature review of iterative inverse models for the analysis of human arterial wall mechanics. One of the earliest works on inverse arterial mechanics was introduced by [PERSON] et al., in 2008 [288].