Glioblastoma multiforme (GBM
) is the most common and aggressive brain cancer [1
]. Statistics show that it has the worst prognosis of all central nervous system malignancies [3
]. However, with the resolution of functional magnetic resonance imaging (fMRI
], currently limited to around 2-3 mm, even the most experienced clinical personnel cannot accurately forecast GBM
progression. The difficulties of making such forecasts motivated computational biologists to develop multiscale mathematical models to explore the expansion and invasion of GBM
Cancer behaves as a complex, dynamic, adaptive and self-organizing system [10
], and agent-based models (ABM
) are capable of describing such a system as a collection of autonomous and decision-making agents, which represent the cells. Therefore, computational biologists hope that with the ABM
approach they can surpass the current limitations of imaging technology and predict tumor progression [11
]. Our previous studies [15
] developed various multiscale ABMs
to simulate GBM
progression. In these models, a cell's intracellular epidermal growth factor receptor (EGFR
) signaling pathway is stimulated by a chemoattractant (such as transforming growth factor α
)), which diffuses at the tissue level. We also assumed that the transient rate of change of phospholipase Cγ
), an important molecule in the EGFR
pathway, will result in cancer cell migration, whereas a smooth rate of change of PLCγ
will result in cancer cell proliferation [11
]. At the intercellular scale, the behaviors of cells (such as the autocrine or paracrine secretion of chemoattractants and migration or proliferation phenotypes) remodel the tumor microenvironment and affect the overall tumor dynamics at the tissue level.
An important advantage of multiscale agent-based modeling (MABM
] is that we can employ multiscale analysis to investigate the incoherent connections among various scales. For example, we can depict the intracellular (molecular) profiles that lead to phenotypic switches at any cell's dynamic cross points (migration cell number crosses with proliferation cell number) [15
] or in the interesting tumor regions [16
]. Thus, MABM
] can be used as tools for generating experimentally testable hypotheses. The consequent validation experiments may reveal potential therapeutic targets.
approaches have a great potential for investigating GBM
progression, their complexity necessitates immense computational resources [15
], which becomes forbidding for real-time simulations of spatio-temporal GBM
progression. In fact, two problems prevent MABM
doing real-time simulation. The first is that the computation time required for intracellular pathway computing for cancer cells will become huge, since a real cancer system may consist of millions of cells. The second is that it is impossible to employ a conventional sequential numerical solver to model the real-time diffusion of chemoattractants in a large extracellular matrix (ECM
) with relatively fine grids.
To overcome the computation time problems, this study incorporates a graphics processing unit (GPU
)-based parallel computing algorithm [18
] into a multi-resolution design [16
] to speed up the previous MABM
]. The multi-resolution design [16
] classified the cancer cells into heterogeneous and homogeneous clusters. The heterogeneous clusters consisted of migrating and proliferating cancer cells in the region of interest, whereas the homogeneous clusters comprised dead or quiescent cells. The limited computational resource was concentrated on the heterogeneous clusters to investigate the molecular profiles of migrating and proliferating cancer cells, while the quiescent and dead cells in the homogeneous clusters were treated with less of the resource. The GPU
-based parallel computing algorithm can not only model the diffusion of chemoattractants in a large ECM
with relatively fine grids in real time, but also process computing queries concerning the intracellular signaling pathways of millions of cancer cells in a real cancer progression system.
The results presented in this paper demonstrate that the GPU
-based multi-resolution MABM
has certain novel features that can help cancer scientists to explore the mechanism of GBM
cancer progression. First, it is able to simulate real-time cancer progression in a large ECM
with relatively fine grids. Second, since multiscale analysis [15
] can reveal the correlations between GBM
tumor progression and molecular concentration changes, we can tell which molecular species are the important biomarkers that impact tumor progression. Third, a multi-resolution design [16
] not only allows us to visualize cancer progression by displaying all the cancer cell clusters in the tissue, but also enables us to track each cancer cell's trajectory.
In the following sections, we will introduce the previously-developed multiscale and multi-resolution ABM, describe how to use GPU to accelerate the simulation of the model, and finally illustrate the advantages of the model that can be used to analyze important biomarkers to inhibit GBM expansion and predict GBM progression.