Off-campus Michigan Tech users: To download campus access theses or dissertations, please use the following button to log in with your Michigan Tech ID and password: log in to proxy server

Non-Michigan Tech users: Please talk to your librarian about requesting this thesis or dissertation through interlibrary loan.

Date of Award


Document Type


Degree Name

Doctor of Philosophy in Computational Science and Engineering (PhD)

College, School or Department Name

Department of Mathematical Sciences

First Advisor

Le Zhang


This dissertation presents how to use parallel computing algorithms on the basis of graphics processing unit (GPU) technology to speed up a well developed multi-scale, multi-resolution agent based (MMABM) brain cancer (Glioblastoma multiforme (GBM)) model. The improved cancer model shows great potentiality to simulate real progression of brain cancer cells.

MMABM includes three various scales, such as intracellular scale, intercellular scale and tissue scale. It employs a system of ordinary differential equations to describe the intracellular molecular pathway at the intracellular level, which determines the cell's phenotypic switch, such as from migration to proliferation and vice versa. At the intercellular level, a discrete module is used to describe cell's behaviors such as cell-cell interactions, cell's migration and proliferation which will remodel the tissue scale of the cancer system. At the tissue level, MMABM models the diffusion of chemoattractants with the partial differential equations. These chemoattractants also can be considered as the input of the system of ordinary differential equations in the intracellular scale. In addition, multi-scale analysis can explore which molecules are essential to determine the cellular phenotypic switch and drive the whole GBM progression. However, limited to the computational resources, previous MMABM is a theoretical model which employs relatively coarse grids to simulate a few cancer cells' progression in a small slice of brain cancer tissue. To relive the heavy compute request, the multi-resolution design is developed. Indicated by cancer scientists, many cancer cells are quiescent and dead.Thus, we classify the simulated cancer cells into heterogeneous or homogeneous clusters. Active cancer cells which are in proliferation or migration status are set into heterogeneous clusters, whereas the inactive cancer cells which are dead or quiescent are put into homogeneous clusters. After that, we only employ limited computation resource to interrogate each cell's phenotype switch for heterogeneous clusters. The aim of the multi-resolution design is to relieve heavy compute cost by sacrificing the accuracy of the simulation results.

However, since the multi-resolution design is still not enough to simulate and predict actual and real-time GBM cancer progression, we have to employ GPU-based parallel computing algorithms to accelerate the former MMABM.

At the beginning, we employ GPU technology to speed up the diffusion module in the tissue scale of MMABM. Three parallel algorithms are developed based on the latest Fermi GPU. Our studies demonstrate these proposed algorithms can quickly obtain the numerical solutions of diffusion equations, around folds faster than the classical sequential algorithm.

Next, we develop a GPU-based parallel algorithm to accelerate the systems of ordinary differential equations describing the intracellular molecular pathway, and then we combine it with the optimal parallel diffusion module to speed up the entire model. The simulation results turn out that the GPU-based, multi-resolution and multi-scale model can accelerate the previous MMABM by around 30 folds with relatively fine grids in a large extracellular matrix. Thus, the revised MMABM model shows great potential to simulate and predict millions of GBM cells' progression in real time by incorporating real experimental data.