Mathematical Modeling of Atherosclerosis
In this thesis, we suggest a one and two dimensional mathematical models of reaction-diffusion type that study the inflammatory process of atherosclerosis in the intima. They consider the concentration of five main agents: LDL, free radicals, oxidized LDL, macrophages and cytokines. The existence an...
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| Format: | masterThesis |
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2021
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| Online Access: | http://hdl.handle.net/10725/13645 https://doi.org/10.26756/th.2022.267 http://libraries.lau.edu.lb/research/laur/terms-of-use/thesis.php |
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| _version_ | 1864513490830491648 |
|---|---|
| author | Salloum, Elissa |
| author_facet | Salloum, Elissa |
| author_role | author |
| dc.creator.none.fl_str_mv | Salloum, Elissa |
| dc.date.none.fl_str_mv | 2021 2021-06-01 2022-06-14T05:42:20Z 2022-06-14T05:42:20Z |
| dc.identifier.none.fl_str_mv | http://hdl.handle.net/10725/13645 https://doi.org/10.26756/th.2022.267 http://libraries.lau.edu.lb/research/laur/terms-of-use/thesis.php |
| dc.language.none.fl_str_mv | en |
| dc.publisher.none.fl_str_mv | Lebanese American University |
| dc.rights.*.fl_str_mv | info:eu-repo/semantics/openAccess |
| dc.subject.none.fl_str_mv | Atherosclerosis -- Mathematical models Free radicals (Chemistry) -- Pathophysiology Inflammation -- Pathophysiology Lebanese American University -- Dissertations Dissertations, Academic |
| dc.title.none.fl_str_mv | Mathematical Modeling of Atherosclerosis |
| dc.type.none.fl_str_mv | Thesis info:eu-repo/semantics/publishedVersion info:eu-repo/semantics/masterThesis |
| description | In this thesis, we suggest a one and two dimensional mathematical models of reaction-diffusion type that study the inflammatory process of atherosclerosis in the intima. They consider the concentration of five main agents: LDL, free radicals, oxidized LDL, macrophages and cytokines. The existence and stability analysis of fixed points for the kinetic system is performed. All obtained results are analyzed and compared to those in [1] in order to provide an appropriate biological interpretation. We prove the existence of solution of traveling wave type which decribes the set up of the in ammatory reaction as a reaction-diffusion wave inside the intima. This result is shown theoretically and numerically. We prove as well the convergence of the 2D model to the 1D case in the thin domain. |
| eu_rights_str_mv | openAccess |
| format | masterThesis |
| id | LAURepo_50fe68f504f7d83d6db09944c70970df |
| language_invalid_str_mv | en |
| network_acronym_str | LAURepo |
| network_name_str | Lebanese American University repository |
| oai_identifier_str | oai:laur.lau.edu.lb:10725/13645 |
| publishDate | 2021 |
| publisher.none.fl_str_mv | Lebanese American University |
| repository.mail.fl_str_mv | |
| repository.name.fl_str_mv | |
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| spelling | Mathematical Modeling of AtherosclerosisSalloum, ElissaAtherosclerosis -- Mathematical modelsFree radicals (Chemistry) -- PathophysiologyInflammation -- PathophysiologyLebanese American University -- DissertationsDissertations, AcademicIn this thesis, we suggest a one and two dimensional mathematical models of reaction-diffusion type that study the inflammatory process of atherosclerosis in the intima. They consider the concentration of five main agents: LDL, free radicals, oxidized LDL, macrophages and cytokines. The existence and stability analysis of fixed points for the kinetic system is performed. All obtained results are analyzed and compared to those in [1] in order to provide an appropriate biological interpretation. We prove the existence of solution of traveling wave type which decribes the set up of the in ammatory reaction as a reaction-diffusion wave inside the intima. This result is shown theoretically and numerically. We prove as well the convergence of the 2D model to the 1D case in the thin domain.1 online resource (x, 44 leaves) : ill. (some col.)Bibliography: leaf 28-29.Lebanese American University2022-06-14T05:42:20Z2022-06-14T05:42:20Z20212021-06-01Thesisinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/masterThesishttp://hdl.handle.net/10725/13645https://doi.org/10.26756/th.2022.267http://libraries.lau.edu.lb/research/laur/terms-of-use/thesis.phpeninfo:eu-repo/semantics/openAccessoai:laur.lau.edu.lb:10725/136452023-02-20T13:33:45Z |
| spellingShingle | Mathematical Modeling of Atherosclerosis Salloum, Elissa Atherosclerosis -- Mathematical models Free radicals (Chemistry) -- Pathophysiology Inflammation -- Pathophysiology Lebanese American University -- Dissertations Dissertations, Academic |
| status_str | publishedVersion |
| title | Mathematical Modeling of Atherosclerosis |
| title_full | Mathematical Modeling of Atherosclerosis |
| title_fullStr | Mathematical Modeling of Atherosclerosis |
| title_full_unstemmed | Mathematical Modeling of Atherosclerosis |
| title_short | Mathematical Modeling of Atherosclerosis |
| title_sort | Mathematical Modeling of Atherosclerosis |
| topic | Atherosclerosis -- Mathematical models Free radicals (Chemistry) -- Pathophysiology Inflammation -- Pathophysiology Lebanese American University -- Dissertations Dissertations, Academic |
| url | http://hdl.handle.net/10725/13645 https://doi.org/10.26756/th.2022.267 http://libraries.lau.edu.lb/research/laur/terms-of-use/thesis.php |