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- Type of Document: M.Sc. Thesis
- Language: Farsi
- Document No: 46363 (02)
- University: Sharif University of Technology
- Department: Mathematical Sciences
- Advisor(s): Fotouhi Firoozabad, Morteza
- Abstract:
- Cancer invasion of tissue is a key aspect of the growth and spread of cancer and is crucial in the process of metastatic spread i.e. the growth of secondary cancers. Invasion consists in cancer cells secreting various matrix degrading enzymes (MDEs) which destroy the surronding tissue or extracellular matrix (ECM). Through a combination of proliferation and migration, the cancer cells then actively spread locally into the surrounding tissue. Thus processes occuring at the level of individual cells eventually give rise to processes occuring at the tissue level. In this thesis we introduce a new type of multiscale model describing the process of cancer invasion of tissue.Our multiscale model is a two-scale model which focusses on macroscopic dynamics of the distributions of cancer cells and of surrounding extracellular matrix, and on the microscale dynamics of the matrix degrading enzymes, produced at the level of the individual cancer cells. These microscale dynamics take place at the interface of cancer cells and ECM and give rise to a moving boundary at the macroscale.On the computational side, in order to approximate the newly proposed model,we have developed a novel computational scheme based on a combination of finite elements at the microscale with a new finite difference technique at the macroscale, linking together in a moving boundary formulation of the problem. This two-scale numerical scheme is organised in such a way that it enables us to accurately model all the key processes of cancer invasion at both the macroscale and microscale
- Keywords:
- Moving Boundary ; Multiscale Method ; Cancer Invasion Model ; Finite Difference Method ; Finite Element Method
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- معرفی
- آشنایی مقدماتی با مفاهیم زیست شناسی مسئله
- تاریخچه مدلسازی حمله سرطانی
- مدل‌های پیوسته
- مدل‌های گسسته
- ابزارها و پیشنیاز ها
- ابزارهای آنالیزی
- ابزارهای آنالیز حقیقی
- ابزارهای معادلات دیفرانسیل با مشتقات جزئی
- قضیه اوریسون
- ابزارهای عددی
- تفاضلات متناهی
- روش پیشگو-اصلاحگر
- روش رونگ-کوتا
- اجزای متناهی
- انتگرالگیری عددی
- تجزیه دوتایی
- تعریف مسئله
- نمادگذاری و پیش فرض‌ها
- مدل چند‌مقیاسه
- قسمت درشت‌مقیاس
- قسمت ریز مقیاس
- خلاصه مدل
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- چند مثال
- تأثیر انتگرالگیری عددی بر جواب معادله سهمی‌وار
- پیشنیازها و نمادگذاری‌ها
- تخمین خطا
- روش پیشگو-اصلاحگر با اندازه گام زمانی متغیر
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