Mathematical modeling of atherosclerosis. (c2019)
Atherosclerosis is a chronic in ammatory cardiovascular disease in which arteries harden through the build-up of plaques. This work is devoted to the mathematical modeling and analysis of the in ammatory process of atherosclerosis. We propose a mathematical model formed by three coupled partial di e...
محفوظ في:
| المؤلف الرئيسي: | |
|---|---|
| التنسيق: | masterThesis |
| منشور في: |
2019
|
| الموضوعات: | |
| الوصول للمادة أونلاين: | http://hdl.handle.net/10725/11585 https://doi.org/10.26756/th.2019.151 http://libraries.lau.edu.lb/research/laur/terms-of-use/thesis.php |
| الوسوم: |
إضافة وسم
لا توجد وسوم, كن أول من يضع وسما على هذه التسجيلة!
|
| _version_ | 1864513489247141888 |
|---|---|
| author | Abi Younes, Ghada |
| author_facet | Abi Younes, Ghada |
| author_role | author |
| dc.creator.none.fl_str_mv | Abi Younes, Ghada |
| dc.date.none.fl_str_mv | 2019-11-27T09:23:27Z 2019-11-27T09:23:27Z 2019 2019-11-27 2019-05-02 |
| dc.identifier.none.fl_str_mv | http://hdl.handle.net/10725/11585 https://doi.org/10.26756/th.2019.151 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 | Lebanese American University -- Dissertations Dissertations, Academic Atherosclerosis -- Mathematical models |
| dc.title.none.fl_str_mv | Mathematical modeling of atherosclerosis. (c2019) |
| dc.type.none.fl_str_mv | Thesis info:eu-repo/semantics/publishedVersion info:eu-repo/semantics/masterThesis |
| description | Atherosclerosis is a chronic in ammatory cardiovascular disease in which arteries harden through the build-up of plaques. This work is devoted to the mathematical modeling and analysis of the in ammatory process of atherosclerosis. We propose a mathematical model formed by three coupled partial di erential equations of reaction-di usion type. We take into account three key-role players: the immune cells (M), the in ammatory cytokines (A) and the oxidized LDL (L). 8>>>>>>>>>>< >>>>>>>>>>: @M @t = d1 @2M @x2 + L + 1A 1 + A= 1 + ML ML 1M @A @t = d2 @2A @x2 + 2A 1 + A= 2 M 2A @L @t = d3 @2L @x2 + M 1 +M= 3 3L A stability analysis of the kinetic system is performed followed by a detailed discussion about the biological interpretation. Several cases may occur ; every case corresponds to a biological situation. Then a holistic conclusion is established. We investigate as well the existence of solutions of traveling waves type along with numerical simulations that show the wave propagation in the di erent cases. These results con rm and generalize previous results published in [1, 2]. |
| eu_rights_str_mv | openAccess |
| format | masterThesis |
| id | LAURepo_7182bb0459faf2a8fd20b05eb6d4072c |
| language_invalid_str_mv | en |
| network_acronym_str | LAURepo |
| network_name_str | Lebanese American University repository |
| oai_identifier_str | oai:laur.lau.edu.lb:10725/11585 |
| publishDate | 2019 |
| publisher.none.fl_str_mv | Lebanese American University |
| repository.mail.fl_str_mv | |
| repository.name.fl_str_mv | |
| repository_id_str | |
| spelling | Mathematical modeling of atherosclerosis. (c2019)Abi Younes, GhadaLebanese American University -- DissertationsDissertations, AcademicAtherosclerosis -- Mathematical modelsAtherosclerosis is a chronic in ammatory cardiovascular disease in which arteries harden through the build-up of plaques. This work is devoted to the mathematical modeling and analysis of the in ammatory process of atherosclerosis. We propose a mathematical model formed by three coupled partial di erential equations of reaction-di usion type. We take into account three key-role players: the immune cells (M), the in ammatory cytokines (A) and the oxidized LDL (L). 8>>>>>>>>>>< >>>>>>>>>>: @M @t = d1 @2M @x2 + L + 1A 1 + A= 1 + ML ML 1M @A @t = d2 @2A @x2 + 2A 1 + A= 2 M 2A @L @t = d3 @2L @x2 + M 1 +M= 3 3L A stability analysis of the kinetic system is performed followed by a detailed discussion about the biological interpretation. Several cases may occur ; every case corresponds to a biological situation. Then a holistic conclusion is established. We investigate as well the existence of solutions of traveling waves type along with numerical simulations that show the wave propagation in the di erent cases. These results con rm and generalize previous results published in [1, 2].N/A1 hard copy: x, 42 leaves: ill. (chiefly col.); 30 cm. available at RNL.Bibliography: (leaves 35-36).Lebanese American University2019-11-27T09:23:27Z2019-11-27T09:23:27Z20192019-11-272019-05-02Thesisinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/masterThesishttp://hdl.handle.net/10725/11585https://doi.org/10.26756/th.2019.151http://libraries.lau.edu.lb/research/laur/terms-of-use/thesis.phpeninfo:eu-repo/semantics/openAccessoai:laur.lau.edu.lb:10725/115852021-03-19T10:47:39Z |
| spellingShingle | Mathematical modeling of atherosclerosis. (c2019) Abi Younes, Ghada Lebanese American University -- Dissertations Dissertations, Academic Atherosclerosis -- Mathematical models |
| status_str | publishedVersion |
| title | Mathematical modeling of atherosclerosis. (c2019) |
| title_full | Mathematical modeling of atherosclerosis. (c2019) |
| title_fullStr | Mathematical modeling of atherosclerosis. (c2019) |
| title_full_unstemmed | Mathematical modeling of atherosclerosis. (c2019) |
| title_short | Mathematical modeling of atherosclerosis. (c2019) |
| title_sort | Mathematical modeling of atherosclerosis. (c2019) |
| topic | Lebanese American University -- Dissertations Dissertations, Academic Atherosclerosis -- Mathematical models |
| url | http://hdl.handle.net/10725/11585 https://doi.org/10.26756/th.2019.151 http://libraries.lau.edu.lb/research/laur/terms-of-use/thesis.php |