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Modeling the Growth of Solid Tumors



Tumor growth is a fundamental scientic and societal problem. While much work has been done in the mathematics community on tumor modeling, the state-of-the-art in modeling and numerical simulation lags behind the current understanding of the biophysical processes.

From a materials science perspective, a cancerous tumor is a complex, multiscaled material. There can be strong nonlinear coupling between the nanoscale (genetics), the microscale (cell-signals) and the macroscale (tumor mass).

The goal of our work is to develop a mathematically rigorous, and biologically-justified model of solid tumors that is capable of describing growth through all the known phases of evolution from avascular multicell spheriods to angiogenesis to invasion of malignant tumors.

Tumor growth and tumor-induced angiogenesis

Case 1. Vessels are initiated randomly about 200 microns from the tumor to mimic tumor-induced angiogenesis from a dense background of microvasculature. The random initiation is biased by the level of tumor angiogenic factors (e.g., vascular endothelial cell growth factor, VEGF). The tumor grows in a compact shape because of the nearly isotropic neovasculature distribution.




Case 2. Vessels are initiated randomly about 200 microns from the tumor to mimic tumor-induced angiogenesis from a dense background of microvasculature. The random initiation is biased by the level of tumor angiogenic factors (e.g., vascular endothelial cell growth factor, VEGF). The difference between this and the above simulation is that here, vessels are crushed by the proliferation pressure induced by the tumor. As a result, both the vessels and the tumor regress periodically. Effectively, this induces nearly periodic angiogenic cycles as the regression is associated with increased release of tumor angiogeneic factors.




More details, results and images coming soon...

Collaborators:

Vittorio Cristini UT Health Sci. Center at Houston, M.D. Anderson Cancer Center
Steven Wise UT Knoxville
Fang Jin UC Irvine
Yao-Li Chuang UTHSCH
Herman Frieboes UCI