Numerical modelling and analysis of the interactions between the left ventricle and the mitral valve
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In order to develop treatments for various heart diseases, a finite element model of the left ventricle and mitral valve apparatus could be of help. The goal of this thesis was to develop a finite element model of the left ventricle and the mitral valve apparatus, taking into account the hyperelastic material properties, as well as the complicated structure of the myocardium of the ventricle, the active contraction of the ventricle, and the fiber orientation of the mitral valve. The ventricle was modeled using a truncated ellipsoid as geometry, and employs a linear distribution of the sheet and fiber angles across its transmural layers. The active contraction of the ventricle was modeled using heat conduction, with the active stress components dependent on a switch function, based around a phase shift temperature. The valves complex geometry was modeled, while a fiber field parallel to the annulus was assumed. The chordae tendineae, modeled with elastic material properties, tethered the valve to the ventricle, disregarding the papillary muscles. The interface between the basal region of the ventricle and the valve was modeled as a stiff elastic part, in attempt to limit the displacement of the mitral valve annulus during the analysis. The goal was to run an analysis from end diastole to end systole, accounting for the systolic pressure distribution, as well as the contraction of the ventricle. The result show that the model had several weaknesses, chief among them the inclusion of the systolic pressure to the contraction model, and the exclusion of the papillary muscles. The model could not represent the contraction of the ventricle accurately when subjected to a systolic pressure, and the stretch the chordae caused on the ventricle activated the contraction, causing an inaccurate contraction process of the ventricle. While parts might be accurate apart, they did not function as a whole.