## 6 Applications to Cardiovascular Medicine
### The Heart
#### 6.2.1 Properties of the Healthy and Infarcted Ventricular Wall
An idealized truncated ellipsoid matching MRI-derived averaged dimensions of a human LV was used as a computational domain. Fiber orientations were assumed helical with the linear transmural distribution established from DT-MRI data from [PERSON] et al. [258]. The myocardium was modeled as a homogeneous fiber-reinforced Ogden hyperelastic material. The active tension of myofib was assumed to be proportional to the pressure load, the \begin{table}
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**Study** & **Clinical Data** & & **Forward Problem** & **Inverse Problem** & \\ \hline \multirow{6}{*}{[PERSON] et al., 2017 [253]} & Population & 27H 11D & Reference & End of diastole & Target & Volume error and strain error. \\  & Pathology & Acute myocardial infarction & Passive model & Het. Holzapfel-Ogden & & \\  & Data & Cine MRI, GE MRI, Hand-cuff pressure & Active model & 2 eq. active stress & & Gaussian processes and automatic relevance \\  & Anatomy & & LV in 17 AHA regions with RBPO by [PERSON] et al. & Boundary & ICP, TF epicardium & Opt. algorithm & \\ \hline \multirow{6}{*}{[PERSON] et al., 2014 [110]} & Population & 5H & Reference & Early diastole & Target & Least-squared-error to normalized Klotz P-V curve \\  & Pathology & None & Passive model & Hom. Guccione & & \\  & Data & Cine MRI, TT & Active model & Hom. 1 eq. active stress & & Derivative-free quadratic approximation algorithm \\  & Anatomy & LV with fiber orientation from canine histology & Boundary & Volume change, TF epicardium, Constrained base. & Opt. algorithm & \\ \hline \multirow{6}{*}{[PERSON] et al., 2013 [254]} & Population & 8H 3D & Reference & End of diastole & & Volume change error \\  & Pathology & HFrEF & Passive model & Region & Target & \\  & Data & Cine MRI, ICP, Electrophysiology & Active model & 2 eq. active stress & & \\  & Anatomy & BV divided in 17 regions with RBPO by [PERSON] et al. & Boundary & ICP, TF epicardium, Constrained base & & \\ \hline \multirow{6}{*}{[PERSON] et al., 2013, 2011a [254]} & Population & 1H 2D & Reference & Unloaded & Target & \\  & Pathology & HFrEF & Passive model & Hom. Guccione & function & \\  & Data & Cine MRI, TT, ICP & Active model & 1 eq. active stress & & \\  & Anatomy & LV with fiber orientation from canine histology & & ICP, TF epicardium, Constrained base & & \\ \hline \multirow{6}{*}{[PERSON] et al., 2013, 2011a [255, 256]} & Abbreviations and acronyms: Clinical data: AHA, American Heart Association, BV, biventricular; D, diseased; GE, gadolinium enriched; H, healthy; ICP, intracardiac pressure; LV, left ventricle; MRI, magnetic resonance imaging; TT, tissue tagging; RBFO, ruled-based fiber orientation; US, ultrasound; USST, ultrasound speckle tracking. Pathologies: CI, cardiac infarction; FMR CAD: functional mitral regurgitation associated to coronary artery disease; HFrEF, heart failure with preserved ejection fraction; HFrEF, heart failure with reduced ejection fraction; LBBB, left bundle branch block. Forward problem: EF, elastic foundation; eq., equation; Het., heterogeneous; Hom., homogeneous; ICP, intracardiac pressure; TF, traction free. & \\ \hline \end{tabular}
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Table 7: _Cont._latter being prescribed as a boundary condition at the endocardial surface. A uniform elastic foundation was applied to the pericardium to simulate the interaction of the heart with the surrounding organs, and all displacements were fixed on a lateral node. All material parameters were fixed except for the bulk modulus, which was optimized to fit a measured pressure-volume curve. The authors conceptually divided the cardiac cycle into the following consecutive stages: atrial systole, isovolumetric contraction, rapid ejection, isovolumetric relaxation, rapid filling, and reduced filling. This study suggested that the volume of the myocardium changed slightly during the cardiac cycle.