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Acquired resistance is one of the major barriers to successful cancertherapy. The development of resistance is commonly attributed to geneticheterogeneity. However, heterogeneity of drug penetration of the tumormicroenvironment both on the microscopic level within solid tumors as well ason the macroscopic level across metastases may also contribute to acquired drugresistance. Here we use mathematical models to investigate the effect of drugheterogeneity on the probability of escape from treatment and time toresistance. Specifically we address scenarios with sufficiently efficienttherapies that suppress growth of all preexisting genetic variants in thecompartment with highest drug concentration. To study the joint effect of drugheterogeneity, growth rate, and evolution of resistance we analyze a multitypestochastic branching process describing growth of cancer cells in twocompartments with different drug concentration and limited migration betweencompartments. We show that resistance is more likely to arise first in the lowdrug compartment and from there populate the high drug compartment. Moreover,we show that only below a threshold rate of cell migration does spatialheterogeneity accelerate resistance evolution, otherwise deterring drugresistance with excessively high migration rates. Our results provide newinsights into understanding why cancers tend to quickly become resistant, andthat cell migration and the presence of sanctuary sites with little drugexposure are essential to this end.

Spatial heterogeneity in drug concentrations can facilitate the emergence of resistance to cancer therapy