Local maximum entropy approximation-based modelling of the canine heart

 

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dc.contributor.advisor Skatulla, Sebastian en_ZA
dc.contributor.author Rama, Ritesh Rao en_ZA
dc.date.accessioned 2016-02-11T06:55:54Z
dc.date.available 2016-02-11T06:55:54Z
dc.date.issued 2012 en_ZA
dc.identifier.citation Rama, R. 2012. Local maximum entropy approximation-based modelling of the canine heart. University of Cape Town. en_ZA
dc.identifier.uri http://hdl.handle.net/11427/16963
dc.description.abstract Local Maximum Entropy (LME) method is an approximation technique which has been known to have good approximation characteristics. This is due to its non-negative shape functions and the weak Kronecker delta property which allow the solutions to be continuous and smooth as compared to the Moving Least Square method (MLS) which is used in the Element Free Galerkin method (EFG). The method is based on a convex optimisation scheme where a non-linear equation is solved with the help of a Newton algorithm, implemented in an in-house code called SESKA. In this study, the aim is to compare LME and MLS and highlight the differences. Preliminary benchmark tests of LME are found to be very conclusive. The method is able to approximate deformation of a cantilever beam with higher accuracy as compared to MLS. Moreover, its rapid convergence rate, based on a Cook's membrane problem, demonstrated that it requires a relatively coarser mesh to reach the exact solution. With those encouraging results, LME is then applied to a larger non-linear cardiac mechanics problem. That is simulating a healthy and a myocardial infarcted canine left ventricle (LV) during one heart beat. The LV is idealised by a prolate spheroidal ellipsoid. It undergoes expansion during the diastolic phase, addressed by a non-linear passive stress model which incorporates the transversely isotropic properties of the material. The contraction, during the systolic phase, is simulated by Guccione's active stress model. The infarct region is considered to be non-contractile and twice as stiff as the healthy tissue. The material loss, especially during the necrotic phase, is incorporated by the use of a homogenisation approach. Firstly, the loss of the contraction ability of the infarct region counteracts the overall contraction behaviour by a bulging deformation where the occurrence of high stresses are noted. Secondly, with regards to the behaviour of LME, it is found to feature high convergence rate and a decrease in computation time with respect to MLS. However, it is also observed that LME is quite sensitive to the nodal spacing in particular for an unstructured nodal distribution where it produces results that are completely unreliable. en_ZA
dc.language.iso eng en_ZA
dc.subject.other Local maximum entropy en_ZA
dc.title Local maximum entropy approximation-based modelling of the canine heart en_ZA
dc.type Master Thesis
uct.type.publication Research en_ZA
uct.type.resource Thesis en_ZA
dc.publisher.institution University of Cape Town
dc.publisher.faculty Faculty of Engineering and the Built Environment
dc.publisher.department Department of Civil Engineering en_ZA
dc.type.qualificationlevel Masters
dc.type.qualificationname MSc (Eng) en_ZA
uct.type.filetype Text
uct.type.filetype Image
dc.identifier.apacitation Rama, R. R. (2012). <i>Local maximum entropy approximation-based modelling of the canine heart</i>. (Thesis). University of Cape Town ,Faculty of Engineering & the Built Environment ,Department of Civil Engineering. Retrieved from http://hdl.handle.net/11427/16963 en_ZA
dc.identifier.chicagocitation Rama, Ritesh Rao. <i>"Local maximum entropy approximation-based modelling of the canine heart."</i> Thesis., University of Cape Town ,Faculty of Engineering & the Built Environment ,Department of Civil Engineering, 2012. http://hdl.handle.net/11427/16963 en_ZA
dc.identifier.vancouvercitation Rama RR. Local maximum entropy approximation-based modelling of the canine heart. [Thesis]. University of Cape Town ,Faculty of Engineering & the Built Environment ,Department of Civil Engineering, 2012 [cited yyyy month dd]. Available from: http://hdl.handle.net/11427/16963 en_ZA
dc.identifier.ris TY - Thesis / Dissertation AU - Rama, Ritesh Rao AB - Local Maximum Entropy (LME) method is an approximation technique which has been known to have good approximation characteristics. This is due to its non-negative shape functions and the weak Kronecker delta property which allow the solutions to be continuous and smooth as compared to the Moving Least Square method (MLS) which is used in the Element Free Galerkin method (EFG). The method is based on a convex optimisation scheme where a non-linear equation is solved with the help of a Newton algorithm, implemented in an in-house code called SESKA. In this study, the aim is to compare LME and MLS and highlight the differences. Preliminary benchmark tests of LME are found to be very conclusive. The method is able to approximate deformation of a cantilever beam with higher accuracy as compared to MLS. Moreover, its rapid convergence rate, based on a Cook's membrane problem, demonstrated that it requires a relatively coarser mesh to reach the exact solution. With those encouraging results, LME is then applied to a larger non-linear cardiac mechanics problem. That is simulating a healthy and a myocardial infarcted canine left ventricle (LV) during one heart beat. The LV is idealised by a prolate spheroidal ellipsoid. It undergoes expansion during the diastolic phase, addressed by a non-linear passive stress model which incorporates the transversely isotropic properties of the material. The contraction, during the systolic phase, is simulated by Guccione's active stress model. The infarct region is considered to be non-contractile and twice as stiff as the healthy tissue. The material loss, especially during the necrotic phase, is incorporated by the use of a homogenisation approach. Firstly, the loss of the contraction ability of the infarct region counteracts the overall contraction behaviour by a bulging deformation where the occurrence of high stresses are noted. Secondly, with regards to the behaviour of LME, it is found to feature high convergence rate and a decrease in computation time with respect to MLS. However, it is also observed that LME is quite sensitive to the nodal spacing in particular for an unstructured nodal distribution where it produces results that are completely unreliable. DA - 2012 DB - OpenUCT DP - University of Cape Town LK - https://open.uct.ac.za PB - University of Cape Town PY - 2012 T1 - Local maximum entropy approximation-based modelling of the canine heart TI - Local maximum entropy approximation-based modelling of the canine heart UR - http://hdl.handle.net/11427/16963 ER - en_ZA


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