Tumor Growth Models via Phase-Field Modeling: Vascular and Mechanical aspects

Name: Paulo Wander Barbosa
Type: PhD thesis
Publication date: 10/06/2020

Namesort ascending Role
Lucia Catabriga Advisor *

Examining board:

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Regina Célia Cerqueira de Almeida External Examiner *
Lucia Catabriga Advisor *
Isaac Pinheiro dos Santos Internal Examiner *

Summary: In this work we study tumor growth models based on mixture theory, considering two classes of continuous macroscopic models: a phenomenological and a mechanical one. The former is a hybrid multi-scale partial differential equation model describing vascular solid tumor and capillaries growth, coupled with angiogenic factors and nutrients diffusion. The capillary phase is described by a diffuse-interface model, also known as a phase-field model, giving rise to a fourth-order parabolic partial differential equation. The tip cell dynamics, responsible for the capillary migration, is described by a discrete agent-based model. This model is able to represent the tumor growth and the development of angiogenesis. The mechanical model is developed on a continuum mechanics basis by means of a continuum mixture theory, also giving rise to a system of partial differential equations. Apart from the classical setting, the framework used incorporates the balance of microforces, engendering the possibility to model some of the phases (species) as a diffuse-interface model. A four species thermodynamically consistent mechanical model was developed. With this model, we expect to quantify the influence of stresses on the growth of solid tumors. All models shown in the numerical results were discretized using spline-based Isogeometric Analysis, and implemented in PetIGA, a parallel and high-performance implementation of Isogeometric Analysis on top of the Portable Extensible Toolkit for Scientific Computation, better known by the acronym PETSc.

Keywords: Tumor Growth, Theory of Mixture, Phase-Field, Mathematical Modeling, Isogeometric Analysis.

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