Abstract
A fully adaptive non-linear full multigrid (FMG) algorithm is implemented to computationally simulate a model of multispecies desmoplastic tumor growth in three spatial dimensions. The algorithm solves a thermodynamic mixture model employing a diffuse interface approach with Cahn-Hilliard-type fourth-order equations that are coupled, non-linear, and numerically stiff. The tumor model includes extracellular matrix (ECM) as a major component with elastic energy contribution in its chemical potential term. Blood and lymphatic vasculatures are simulated via continuum representations. The model employs advection-reaction-diffusion partial differential equations (PDEs) for the cell, ECM, and vascular components, and reaction-diffusion PDEs for the elements diffusing from the vessels. This study provides the details of the numerical solution obtained by applying the fully adaptive non-linear FMG algorithm with finite difference method to solve this complex system of PDEs. The results indicate that this type of computational model can simulate the extracellular matrix-rich desmoplastic tumor microenvironment typical of fibrotic tumors, such as pancreatic adenocarcinoma.
Highlights
The process of cancer progression is driven by the communication between tumor cells and their surroundings
A dynamic tumor microenvironment typically consists of highly proliferating neoplastic cells of different phenotypes, necrotic tumor cells, infiltrating innate and adaptive immune inflammatory cells, cancer-associated fibroblasts, cancer stem cells, extracellular matrix (ECM), blood and lymphatic vessels, pericytes, healthy host cells, and a variety of soluble molecules (Hanahan and Weinberg, 2000; de Visser and Coussens, 2006; Tlsty and Coussens, 2006; Whiteside, 2008; Perez-Moreno, 2009)
Mathematical modeling of cancer progression including its associated microenvironment may be a useful tool for predicting tumor dynamics and cancer response to therapy
Summary
The process of cancer progression is driven by the communication between tumor cells and their surroundings. A dynamic tumor microenvironment typically consists of highly proliferating neoplastic cells of different phenotypes, necrotic tumor cells, infiltrating innate and adaptive immune inflammatory cells, cancer-associated fibroblasts, cancer stem cells, extracellular matrix (ECM), blood and lymphatic vessels, pericytes, healthy host cells, and a variety of soluble molecules (Hanahan and Weinberg, 2000; de Visser and Coussens, 2006; Tlsty and Coussens, 2006; Whiteside, 2008; Perez-Moreno, 2009). These cellular and molecular elements dictate the tumor progress from unregulated neoplastic growth to potential metastasis. To study the desmoplastic tumor microenvironment, we recently presented a tumor model (Ng and Frieboes, 2017) as a continuum scale multicomponent-multispecies system consisting
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