Abstract 2006: Mathematical and computational models for cellular space in cancer growth

Abstract

Abstract This study investigates the dependency of tumor cell growth on specific spatial regulations for both normal and tumor cells. In general it is known that cellular growth is affected by contact inhibition, but many models fail to include this aspect explicitly. Our work studies the extent to which spatial constraints and interactions between normal and tumor cells affect tumor growth. We model spatial constraints via a set of differential equations, modified from the classic logistic equation. These equations represent the hallmarks of cancer, with the addition of spatial rules based on the ratio of living tumor to normal cells in the tissue. Four different sets of equations are analyzed and compared, each representing a different potential scenario of how tumor and normal cells differ in their views of space. Most computational models of cancer do not investigate the interactions between normal cells and tumor cells, and our approach demonstrates that these interactions are crucial for modeling and understanding cancer growth. Our results provide a delineation of when tumor growth will take over an area versus when it will be slowed or stopped for each type of spatial constraint. Our results indicate that different combinations of spatial regulations cause different outcomes in tumor growth. They also demonstrate that cells following the same set of rules for proliferation, death, and mutation meet different outcomes given a change in spatial constraints. Thus, an accurate modeling of spatial interactions between two cellular populations is crucial to adequately examine tumor cells. Our results suggest that a treatment assuming one set of rules will fail if another set of rules is in place. Further, if we learn to modify these spatial rules in a tissue then tumor growth could be decreased. Our work also implies that to be able to use computational models for evaluating options for treatment proper spatial rules must be taken into account in the model. In conclusion, we recognize that the influence of contact inhibition on different populations of cells can drive one cancer to take over the system, while it can significantly slow the growth of another. Such spatial constraints are extremely crucial to modeling and understanding cancer growth and in evaluating options for treatment. Citation Format: {Authors}. {Abstract title} [abstract]. In: Proceedings of the 101st Annual Meeting of the American Association for Cancer Research; 2010 Apr 17-21; Washington, DC. Philadelphia (PA): AACR; Cancer Res 2010;70(8 Suppl):Abstract nr 2006.