Cancer is a complex illness that affects millions of people every year. Amongst the most frequently encountered variants of this illness are solid tumours. The growth of solid tumours depends on a large number of factors such as oxygen concentration, cell reproduction, cell movement, cell death, and vascular environment. The aim of this thesis is to provide further insight in the interconnections between these factors by means of numerical simulations. We present a multiscale model for tumor growth by coupling a microscopic, agent-based model for normal and tumor cells with macroscopic mean-field models for oxygen and extracellular concentrations. We assume the cell movement to be dominated by Brownian motion. The temporal and spatial evolution of the oxygen concentration is governed by a reaction-diffusion equation that mimics a balance law.To complement this macroscopic oxygen evolution with microscopic information, we propose a lattice-free approach that extends the vascular distribution of oxygen. We employ a Markov chain to estimate the sprout probability of new vessels. The extension of the new vessels is modeled by enhancing the agent-based cell model with chemotactic sensitivity. Our results include finite-volume discretizations of the resulting partial differential equations and suitable approaches to approximate the stochastic differential equations governing the agent-based motion. We provide a simulation framework that evaluates the effect of the various parameters on, for instance, the spread of oxygen. We also show results of numerical experiments where we allow new vessels to sprout, i.e. we explore angiogenesis. In the case of a static vasculature, we simulate the full multiscale model using a coupled stochastic/deterministic discretization approach which is able to reduce variance at least for a chosen computable indicator, leading to improved efficiency and a potential increased reliability on models of this type.
| Identifer | oai:union.ndltd.org:UPSALLA1/oai:DiVA.org:kau-85077 |
| Date | January 2021 |
| Creators | Luna, René Edgardo |
| Publisher | Karlstads universitet, Institutionen för matematik och datavetenskap (from 2013) |
| Source Sets | DiVA Archive at Upsalla University |
| Language | English |
| Detected Language | English |
| Type | Student thesis, info:eu-repo/semantics/bachelorThesis, text |
| Format | application/pdf |
| Rights | info:eu-repo/semantics/openAccess |
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