Biological tissue mechanics with fibres modelled as one dimensional Cosserat continua: applications to cardiac tissue in healthy and diseased states

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dc.contributor.advisorSkatulla, Sebastianen_ZA
dc.contributor.authorSack, Kevinen_ZA
dc.date.accessioned2014-11-05T03:33:46Z
dc.date.available2014-11-05T03:33:46Z
dc.date.issued2014en_ZA
dc.descriptionIncludes bibliographical references.en_ZA
dc.description.abstractClassically, 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.en_ZA
dc.identifier.apacitationSack, K. (2014). <i>Biological tissue mechanics with fibres modelled as one dimensional Cosserat continua: applications to cardiac tissue in healthy and diseased states</i>. (Thesis). University of Cape Town ,Faculty of Engineering & the Built Environment ,Department of Civil Engineering. Retrieved from http://hdl.handle.net/11427/9079en_ZA
dc.identifier.chicagocitationSack, Kevin. <i>"Biological tissue mechanics with fibres modelled as one dimensional Cosserat continua: applications to cardiac tissue in healthy and diseased states."</i> Thesis., University of Cape Town ,Faculty of Engineering & the Built Environment ,Department of Civil Engineering, 2014. http://hdl.handle.net/11427/9079en_ZA
dc.identifier.citationSack, 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.en_ZA
dc.identifier.ris TY - Thesis / Dissertation AU - Sack, Kevin AB - 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. DA - 2014 DB - OpenUCT DP - University of Cape Town LK - https://open.uct.ac.za PB - University of Cape Town PY - 2014 T1 - Biological tissue mechanics with fibres modelled as one dimensional Cosserat continua: applications to cardiac tissue in healthy and diseased states TI - Biological tissue mechanics with fibres modelled as one dimensional Cosserat continua: applications to cardiac tissue in healthy and diseased states UR - http://hdl.handle.net/11427/9079 ER - en_ZA
dc.identifier.urihttp://hdl.handle.net/11427/9079
dc.identifier.vancouvercitationSack K. Biological tissue mechanics with fibres modelled as one dimensional Cosserat continua: applications to cardiac tissue in healthy and diseased states. [Thesis]. University of Cape Town ,Faculty of Engineering & the Built Environment ,Department of Civil Engineering, 2014 [cited yyyy month dd]. Available from: http://hdl.handle.net/11427/9079en_ZA
dc.language.isoengen_ZA
dc.publisher.departmentDepartment of Civil Engineeringen_ZA
dc.publisher.facultyFaculty of Engineering and the Built Environment
dc.publisher.institutionUniversity of Cape Town
dc.titleBiological tissue mechanics with fibres modelled as one dimensional Cosserat continua: applications to cardiac tissue in healthy and diseased statesen_ZA
dc.typeMaster Thesis
dc.type.qualificationlevelMasters
dc.type.qualificationnameMScen_ZA
uct.type.filetypeText
uct.type.filetypeImage
uct.type.publicationResearchen_ZA
uct.type.resourceThesisen_ZA
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