## 6 Applications to Cardiovascular Medicine
### Summary
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**Section** & **Highlights** \\ \hline
6. & The development of patient-specific inverse analyses of cardiovascular mechanics has advanced considerably recently thanks to continuous technological improvements in imaging hardware and software, decreasing cost, increased imaging availability, improvements in image-based kinematics acquisition and postprocessing, simulation engineering, and significant increases in computational power. \\ \hline
6. & Blood vessels, in particular those of the arterial tree, function under physiological pressure load at all times and are axially pre-stretched; thus, none of the patient-specific configurations resolved by in vivo imaging is truly a stress-free or zero-strain configuration. \\ \hline  & The unloaded configuration of cardiovascular tissue is not truly stress-free. The residual stress is hypothesized to be the product of heterogeneous growth and remodeling of tissue. \\  & For patient-specific analyses, the material properties and zero-stress configuration are unknown. Thus, the solution to this problem requires the specification of at least two deformed and loaded states as input data. \\
6.1 & Direct methods for the solution of inverse elastostatic problems to determine the unloaded configuration of the heart and arteries have been incorporated into FEM solvers for hyperelastic and fiber-family material models. \\  & Several iterative methods for the solution of the unloaded configurations have been proposed. All these methods have in common that a single point or a collection of points on the surface are fixed, while forward inflation problems from unloaded configuration iterations to the known loaded configurations are solved until a convergence criterion is satisfied. Unloaded configuration iterations are estimated either by shrinking the known loaded configuration or by taking “backward” inflation steps. \\  & An alternative iterative approach is to solve the strain and stress distribution that balances the applied loads acting on the image-derived anatomic configurations without the resolution of the unloaded geometry. \\ \hline  & The inverse modeling of the heart as a whole is currently unfeasible due to the complexity of the system and computational limitations. \\  & An accurate understanding of myocardial mechanics is key for the diagnosis and treatment of diverse cardiac pathologies, and potentially, to predict and stratify the risk of heart failure after infarct. \\  & The assumption of material homogeneity is a common and convenient simplification for forward and inverse models. Homogeneous models may be deemed to be adequate for the study of healthy hearts, or when the aim of the analysis is not centered on the study of focalized lesions. \\  & Homogeneous models can quantify the stiffening effect of infarct lesions and predict the natural compensation of the active component of the heart to maintain cardiac function after infarction. \\
6.2 & Modeling of material heterogeneity of the heart can provide better fits to kinematic data, can resolve property changes, and identify the location and severity of myocardial lesions. This comes with an increment of model complexity and computational expense. \\  & A common approach is to approximate spatial variations of myocardial properties and microstructure with region-wise heterogeneities. AHA standard division of the left ventricle is often used to define region-wise heterogeneity. \\  & Heterogenous models of the myocardium can identify the material properties of the infarcted zone, the border zone, and the unaffected tissue. \\  & Heterogeneous models can accurately predict how impaired activation of the myocardium affects the cardiac function in patients with left bundle branch block (LBBB). \\  & Inverse analyses with heterogeneous models have been used to predict the effect of ischemia on cardiac function, and its recovery after revascularization treatment. \\ \hline
6.3 & Heart valves and leaflets are thin structures with complex motion that are difficult to resolve through in vivo imaging techniques. \\  & Owing to this, most studies on these structures are carried out in vitro. \\  & Recent developments in US imaging of heart valves are the first steps toward the in vivo inverse modeling of these structures. \\ \hline  & Changes in mechanical properties of arterial walls have been associated with the onset of multiple cardiovascular pathologies and remain an important predictor of cardiovascular morbidity and mortality in clinical practice. \\  & The image-based resolution of vascular tissue kinematics is technically challenging due to the relative thinness of vascular walls. \\  & Inverse analyses of healthy arteries have been used to assess the stiffening effect of aging and to explore the effect of perivascular interaction on aortic mechanics. \\  & Aneurysms are a potentially fatal condition that consist of the enlargement of blood vessels caused by the remodeling of its wall. \\  & Aneurysmal rupture risk increases with maximum diameter on average for the entire population, although diameter alone struggles to predict rupture for any given individual. \\  & Inverse modeling has been used to obtain heterogeneous maps of mechanical stress and strain in thoracic and abdominal aneurysms and to assess the effect of disease progression on tissue stiffening. \\  & 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. \\  & The in vivo evaluation of the mechanical properties of atherosclerotic plaques and their mechanical environment through inverse modeling could support the assessment of risk associated with plaque rupture. \\ \hline
6.5 & Computational modeling of hemodynamics is more resource consuming than tissue mechanics. \\  & Statistical analyses have shown that outputs of the inverse methods yield smaller uncertainties than CFD or 4D flow MRI data analysis alone. \\  & Inverse modeling of the fluid–structure interaction of the blood flow in the pulmonary arteries has been used to identify relevant markers of pulmonary artery hypertension. Among these markers are wall stiffness, wall shear stress and oscillation, pulse wave velocity, and regurgitant flow. \\ \hline \end{tabular}
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