Microstructure-Based Constitutive Modelling Of Soft Biological Tissues
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To date, patient specific finite element models of the left ventricle fail to apply appropriate boundary conditions to capture the key physics of the cardiac cycle. In the literature there are two main approaches; (i) the application of a pressure boundary condition 1, and (ii) the application of a displacement boundary condition 2 to the myocardial wall. Not accounting for the interaction of the heart wall and blood volume is a critical omission of the physics of the system. In reality, both pressure and volume are outputs of the model, due to the active contractility acting against the blood volume as valves open and close. In this study we highlight the importance of considering the ventricular blood volume in capturing the key physics of the cardiac cycle. We begin by building a patient specific finite element model of the left ventricle directly from triplanar CINE ECHO scan data, using a custom-built framework generated using MATLAB & GIBBON 3. We model both the ventricular myocardium and the ventricular blood volume using continuum elements. We simulate an Inferior Vena Cava Occlusion (IVCO) experiment, and also highlight the effects of including non-linear aortic compliance on the pressure-volume relationship of the ventricle. Capturing 2-Ch, 3-Ch and 4-Ch ECHO planes results in three image datasets each separated by 60⁰ (Figure 1). The end diastolic frames in each of the datasets is used for mesh generation. The internal surface mesh is then offset to form the solid ventricular wall mesh. The space enclosed by the myocardial wall is also meshed using C3D8 elements as the blood volume. For the ventricular myocardium we employ a rule of mixtures approach developed previously for arteries 4 where each component of the wall undergoes the same strain, but the stresses are additive, and the sum of constituent densities equals unity. For the blood volume we employ a Windkessel formulation during ejection that solves for both pressure and volume, while a standard volumetric formulation with high bulk modulus is used in both isovolumetric contraction and relaxation phases. Transmurally varying fibre directions are included based on the local surface normal of each element. The active contractility waveform of the cardiomyocytes is prescribed and the resulting pressure-volume (PV) loop is shown for a range of applied filling pressures. Simulations capture the Frank-Starling effect with a decreased end diastolic volume resulting in a decreased stroke volume.