The importance of grid size and boundary conditions in discrete tumor growth modeling

Modeling tumour growth has proven a very challenging problem, mainly due to the fact that cancer is a very complex process that spans multiple scales both in time and space. The desire to describe interactions in multiple scales has given rise to modeling approaches that use both continuous and discrete variables, called hybrid. The biochemical processes occurring in tumour environment are usually described by continuous variables. Cancer cells tend to be described as discrete agents interacting with their local neighborhood, which is comprised of their extracellular environment and nearby cancer cells. These interactions shape the microenvironment, which in turn acts as a selective force on clonal emergence and evolution. In this work, we study the effects of grid size and boundary conditions of the continuous processes on the discrete populations. We perform various tests on a simplified hybrid model with the aim of achieving faster execution runtimes. We conclude that we can reduce the grid size while maintaining the same dynamics of a larger domain by manipulating the boundary conditions.