Simulation of Multispecies Desmoplastic Cancer Growth via a Fully Adaptive Non-linear Full Multigrid Algorithm

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 fourt...

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Published in:Frontiers in physiology Vol. 9; p. 821
Main Authors: Ng, Chin F., Frieboes, Hermann B.
Format: Journal Article
Language:English
Published: Switzerland Frontiers Media S.A 12.07.2018
Subjects:
adaptive mesh refinement
cancer
computational simulation
diffuse interface model
mathematical model
non-linear 3D tumor growth
Physiology
computational simulation
diffuse interface model
non-linear 3D tumor growth
mathematical model
cancer
adaptive mesh refinement
full multigrid
full approximation scheme
ISSN:1664-042X, 1664-042X
Online Access:Get full text
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Summary: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.
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Edited by: Luca Mesin, Politecnico di Torino, Italy
This article was submitted to Computational Physiology and Medicine, a section of the journal Frontiers in Physiology
Reviewed by: Luigi Preziosi, Politecnico di Torino, Italy; Silvina Ponce Dawson, Universidad de Buenos Aires, Argentina
ISSN:1664-042X
1664-042X
DOI:10.3389/fphys.2018.00821