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cancer-invasion-model
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Existence of Global Solution for Two Models of Cancer Invasion
, M.Sc. Thesis Sharif University of Technology ; Hesaaraki, Mahmoud (Supervisor)
Abstract
In this thesis we investigating two models of cancer invasion .First, a general mathematical model of cancer invasion is presented. In this model there are three factors: tumor cell, extracellular matrix and enzyme. The model consists of a parabolic partial differential equation (PDE) describing the evolution of tumor cell density , an ordinary differential equation modeling of extracellular matrix and a parabolic PDE governing the evolution of the matrix degrading enzyme concentration. This model is investigated in two special versions for existence and uniqueness of global solutions. In the first model we neglect the remodeling term, this model is named the chemotaxis-haptotaxis model....
A Multiscale Moving Boundary Model For Cancer Invasion
, M.Sc. Thesis Sharif University of Technology ; Fotouhi Firoozabad, Morteza (Supervisor)
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...