| Summary: | Mathematical modelling is an essential and convenient tool to understand the systemic mechanism of human bodies and to assist the diagnosis and/or the treatment of various diseases. The main objective of this thesis is to develop soft tissue mechanics models and use these to address a number of particular clinical topics, namely, the human iris, the artery and the mitral valve. Important modelling aspects such as fluid-structure interaction, fibre reinforcement, material anisotropy and organ-organ interaction are included. To avoid the acute closed-angle glaucoma and the buckling of floppy iris syndrome in Descemet’s stripping endothelial keratoplasty, three-dimensional linear human iris is studied and the intraocular pressure is found to be a critical factor in determining the involving complications. Human arteries usually consist of two or more families of collagen fibres in each of the three distinct layers (the intima, the media and the adventitia). One challenge is to explain the recent experimental observation that only one family of (circumferential) fibres exists in the media of the iliac artery. Using an invariant-based fibre-reinforced nonlinear constitutive model, we are able to provide a plausible explanation from the mechanics viewpoint, and show that such fibre architecture achieves the optimal energy or stress distributions. We also find that the axial pre-stretch plays a vital role in different fibre structures. We finally develop a patient-specific human mitral valve model using the immersed boundary finite element method. A major advantage of this approach is that we can incorporate experimentally based constitutive laws for material properties in a coupled three-dimensional fluid-structure interaction framework. This mitral valve model is ex- tended by coupling with a contractile left ventricular model and a comparative analysis is further conducted.
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