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Tumor Growth Dynamics: A Deterministic and Stochastic Analysis of the Interaction Between Normal and Abnormal Cells

We study the interactions between normal and abnormal cell populations as they occur in a tumorous growth. The purpose of our research is determine whether the spatial arrangement of abnormal cells in a tissue is a significant factor governing the spread of the tumor. To this end, we model how normal and abnormal cells compete for nutrients using a deterministic model and a spatial stochastic model. We vary nutrient competition rates as well as drug treatment effects for the two cell populations. The deterministic model indicates how the populations interact without consideration of spatial arrangement, while the stochastic model includes this factor. Our results show that different spatial arrangements of cells may cause significant differences in the growth dynamics of the cells even if the initial population sizes are kept constant. We have found that the spatial model reveals some growth dynamics that the deterministic model overlooks. Therefore it is of interest to obtain more realistic spatial models. For this, we need to focus research on the most distinctive factor of the spatial model: how normal and malignant cells on the boundary of a tumor compete for nutrients.

Article Number:
BU-1425-M

Year:
1997

Authors:
Brendaliz Acosta, Universidad de Puerto Rico-Cayey
Jaime H. Barrera, Texas A&M University
Ernesto S. Clarke II, Pitzer College
Nicolas Davidenko, Harvard University
Derek Ting, Cornell University

tumor_growth_dynamics_a_deterministic_and_stochastic_analysis_of_the_interaction_between_normal_and_abnormal_cells_.pdf