Influence of spatial structure on the success of adaptive therapy in cancer

Resistance evolution is a common problem in cancer therapy, especially for genetically heterogeneous tumors that may harbor resistant subpopulations at the onset of treatment. Thus, designing therapeutic regimens that inhibit the spread of resistance is an important problem. Since higher drug concentrations increase the fitness of resistant cells, drug concentrations below the maximum tolerated dose (MTD) may delay disease progression once resistance has evolved. This strategy was recently termed adaptive therapy. There have been several efforts to model adaptive therapy, but most have used non-spatial models in which limited resources enforce competition between sensitive and resistant cells. We propose that in the absence of resource constraints, space may provide a substrate for competition in solid tumors. Using a spatial Moran model, we show that drug concentrations below the MTD delay disease progression in spatially structured tumors, but only under spatial arrangements defined by the ‘topological containment’ of resistant cells by sensitive cells. We use a toy example of nested resistant and sensitive cell populations to derive an optimal drug concentration and confirm our prediction using stochastic simulations on a 2D and 3D lattice.