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Evaluation of a discrete dynamic systems approach for modeling the hierarchical relationship between genes, biochemistry, and disease susceptibility
Dynamics of a model for brain tumors reveals a small window for therapeutic intervention
1.  Department of Pathology, Harborview Medical Center, and Department of Applied Mathematics, University of Washington, Seattle, WA, United States 
2.  Department of Pathology, Harborview Medical Center, Seattle, WA, United States 
3.  Department of Applied Mathematics, University of Washington, Seattle, WA, United States 
Mathematical modeling has presented itself as a viable tool for studying complex biological processes (Murray, 1993, 2002). We have developed a mathematical model that portrays the growth and extension of theoretical glioblastoma cells in a matrix that accurately describes the brain's anatomy to a resolution of 1 cu mm (Swanson, et al, 1999, 2000, 2002, 2003a, 2003b). The model assumes that only two factors need be considered for such predictions: net growth rate and infiltrative ability. The model has already provided illustrations of theoretical glioblastomas that not only closely resemble the MRIs (magnetic resonance imaging) of actual patients, but also show the distribution of the diffusely infiltrating cells.
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