A Hybrid Model for Tumor Growth

Tumor growth involves numerous biochemical and biophysical processes whose interactions can only be understood via a detailed mathematical model. In this talk, I will present a new mathematical model of tumor growth that incorporates both continuum and cell-based descriptions, thereby retains the advantages of each descriptions while circumventing some of their disadvantages. In this model, the cell-based description is used in the region where the majority of growth and cell division occurs, while a continuum description is used for the quiescent and necrotic zones of the tumor and for the extracellular matrix. Reaction-diffusion equations describe the transport and consumption of important nutrients throughout the entire domain. Our novel hybrid model can address single cell-cell adhesion, cell growth, cell division and invasive patterning at the cellular level rather than at the continuum level in the proliferating zone, while simplifying computationally the overall system. Free boundaries arising from this model are different from the standard front propagation characteristic of the usual free boundary. We also show that the model can predict a number of cellular behaviors that have been observed experimentally. This project is joint work with Hans Othmer, Yangjin Kim and Magda Stolarska