Inverse Reconstruction of Cell Proliferation and Mutation Laws in Cancer Invasion Modelling

  • Maher Alwuthaynani

Student thesis: Doctoral ThesisDoctor of Philosophy

Abstract

The process of local and nonlocal cancer cells invasion of the surrounding tissue is key for the overall tumour growth and spread within the human body. The past three decades have witnessed intense mathematical modelling efforts in these regards. However, in order to gain a deep understanding of the cancer invasion process and to contribute in prevention, diagnosis and treatment of cancer, we need to expand these modelling studies and to complement them with inverse problems data assimilation approaches.

While being of crucial importance in assimilating potential clinical data, the inverse problems approaches in cancer modelling are still in their early stages. This study deals with the identification and reconstruction of the usually unknown cancer cell proliferation and mutation laws, which lead to the transformation of a primary into a mutated tumour cell population, more aggressive cell population. We focus on local and nonlocal mathematical models for cell dynamics and movement, and identify these proliferation and mutation laws from macroscopic tumour snapshot data collected at some later stage in the tumour evolution. Considering two basic tumour configuration, associates with the case of one cancer cells population and two cancer cells sub-populations that exercise their dynamics within the extracellular matrix, we combine Tikhonov regularisation and gaussian mollification approaches with finite element and finite differences approximations to reconstruct the proliferation and mutation laws for each of these sub-populations from both exact and noisy measurements. Our inverse problem formulation is accompanied by numerical examples for the reconstruction of several proliferation and mutation laws used in cancer growth modelling.
Date of Award2022
Original languageEnglish
SupervisorDumitru Trucu (Supervisor) & Raluca Eftimie (Supervisor)

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