INTRODUCTION Heterogeneous cell proliferation, migration, and death can be caused by genetic damage and in response to the local microenvironment. Diusion gradients of oxygen, glucose, metabolites, and drugs, established in the microenvironment during solid tumor growth and response to treatment, can create varying local conditions for subpopulations of tumor cells. Individual cells possess a broad spectrum of survival and migration mechanisms that can be invoked in response to hostile conditions [1], such as hypoxia and hypoglycemia. e consequences of this heterogeneity and variability can be highly multiscalar. Dierential cell proliferation, migration, and death along the diusion gradients aect cell survival and

CONTENTS Introduction 193 Model 195 Results 198 Discussion 205 Acknowledgments 206 References 206

motility properties as a function of these gradients. At the tumor scale, this can lead to invasive ngering and branching and even fragmentation and migration of cell clusters into the surrounding tissue. us, these diusion gradients have an important role in the stability of the tumor morphology.