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Modeling Tumor Growth and Radiation Response with a Multi-Population, Diffusion-Based Model

E Dahlman*, Y Watanabe , University of Minnesota, Minneapolis, MN


(Tuesday, 7/16/2019) 1:15 PM - 1:45 PM

Room: Exhibit Hall | Forum 2

Purpose: To develop a mathematical model that simulates tumor growth and predicts the tumor’s response to radiation therapy. The model can be used to tailor the treatment regimen to each patient. Consequently, this approach may lead to improved outcomes of radiation therapy.

Methods: The proposed model simulates tumor growth using a set of diffusion equations. Cancer cells were grouped into three populations: 1) dividing (or proliferating) cells (“Dividing cells�); 2) cells that have been irradiated and are still dividing but have received fatal damage that prevents their division for more than a few generations (“Doomed cells�); and 3) cells that are no longer dividing (“Dead cells�). Each population of cells must satisfy the continuity equation. Hence, there are a set of three time-dependent non-linear partial differential equations to be solved. The solution provides the growth, death, and removal of cancer cells in each population as a function of time. These equations were solved using a Crank-Nicolson method for a spherically-symmetric geometry.

Results: The model was used to predict the temporal variation of the volume of mouse tumors which were not irradiated (or control) or irradiated with a single dose of 10, 20, 30, or 40 Gy. Model parameters for the growth rate and diffusion rate were estimated from the tumor growth data of the control. The plots of tumor volume vs. time showed good agreement with the experimentally measured volume changes.

Conclusion: The three-population model was validated by simulating mice experiments. The model accounted for the presence of irradiated cells in a tumor before they were removed by biologic processes. These cells are an important part of the volume of the tumor and are often left out of other models. By tracking all three cell populations in the tumor, an accurate picture of the volume over time can be developed.


Diffusion, Modeling, Linear Quadratic Model


TH- Dataset analysis/biomathematics: Informatics

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