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Local maximum entropy approximation-based modelling of the canine heart
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 Leas...
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| Format: | Thesis |
| Language: | English |
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Department of Civil Engineering
2016
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| _version_ | 1867614430435475456 |
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| access_status_str | Open Access |
| author | Rama, Ritesh Rao |
| author2 | Skatulla, Sebastian |
| author_browse | Rama, Ritesh Rao Skatulla, Sebastian |
| author_facet | Skatulla, Sebastian Rama, Ritesh Rao |
| author_sort | Rama, Ritesh Rao |
| collection | Thesis |
| description | 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. |
| format | Thesis |
| id | oai:open.uct.ac.za:11427/16963 |
| institution | University of Cape Town (South Africa) |
| language | eng |
| last_indexed | 2026-06-10T12:51:55.256Z |
| license_str | Not specified — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UCTD — University of Cape Town Open Access Repository |
| publishDate | 2016 |
| publishDateRange | 2016 |
| publishDateSort | 2016 |
| publisher | Department of Civil Engineering |
| publisherStr | Department of Civil Engineering |
| record_format | dspace |
| source_str | UCTD — University of Cape Town Open Access Repository |
| spelling | oai:open.uct.ac.za:11427/16963 Local maximum entropy approximation-based modelling of the canine heart Rama, Ritesh Rao Skatulla, Sebastian Local maximum entropy 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. 2016-02-11T06:55:54Z 2016-02-11T06:55:54Z 2012 Master Thesis Masters MSc (Eng) http://hdl.handle.net/11427/16963 eng application/pdf Department of Civil Engineering Faculty of Engineering and the Built Environment University of Cape Town |
| spellingShingle | Local maximum entropy Rama, Ritesh Rao Local maximum entropy approximation-based modelling of the canine heart |
| thesis_degree_str | Master's |
| title | Local maximum entropy approximation-based modelling of the canine heart |
| title_full | Local maximum entropy approximation-based modelling of the canine heart |
| title_fullStr | Local maximum entropy approximation-based modelling of the canine heart |
| title_full_unstemmed | Local maximum entropy approximation-based modelling of the canine heart |
| title_short | Local maximum entropy approximation-based modelling of the canine heart |
| title_sort | local maximum entropy approximation based modelling of the canine heart |
| topic | Local maximum entropy |
| url | http://hdl.handle.net/11427/16963 |
| work_keys_str_mv | AT ramariteshrao localmaximumentropyapproximationbasedmodellingofthecanineheart |