Biological tissue mechanics with fibres modelled as one dimensional Cosserat continua: applications to cardiac tissue in healthy and diseased states
Master Thesis
2014
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University of Cape Town
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Abstract
Classically, the elastic behaviour of cardiac tissue mechanics is modelled using anisotropic strain energy functions capturing the averaged behaviour of its fibrous microstructure. The strain energy function can be derived via representation theorems for anisotropic functions where a suitable nonlinear strain tensor, e.g. the Green strain tensor, describes locally the current state of strain [57, 150, 158]. These kinds of approaches, however, are usually of phenomenological nature and do not elucidate on the complex heterogeneous material composition of cardiac tissue characterized by different fibre hierarchies interwoven by collagen, elastin and coronary capillaries [61, 115]. Thus, pathological changes of microstructural constituents, e.g. with regards to the extra cellular matrix, and their implications on the macroscopically observable material behaviour cannot be directly investigated. In this research the fibrous characteristics of the myocardium are modelled by one dimensional Cosserat continua. This additionally allows for the inclusion of fibre motion relative to the matrix representing the non-local material response due to twisting and bending of fibres. In this sense, a so-called characteristic scaling parameter associated with the micro structure, becomes a material parameters of the formulation. The ability to explicitly account for torsion and bending in the constitutive law gives this approach a natural advantage over classical formulations. Moreover, the additional degrees of freedom in the kinematic description allow for more complex, realistic deformations. The assumed hyperelastic material behaviour of myocardial tissue is represented by a nonlinear strain energy function which includes the contributions linked to the Cosserat fibre continuum and the complementary terms which refer to the extra-cellular matrix. Utilizing the element-free Galerkin method, simulations of the left ventricle undergoing various stages of the cardiac cycle are introduced to investigate ventricular tissue mechanics.
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Includes bibliographical references.
Reference:
Sack, K. 2014. Biological tissue mechanics with fibres modelled as one dimensional Cosserat continua: applications to cardiac tissue in healthy and diseased states. University of Cape Town.