INTRODUCTION Both individual and collective cell migration are hallmarks of cancer invasion preceding metastasis and the fatal outcome of the disease.1 To date, basic paradigms of cell migration, including the migration of cancer cells, have been extensively studied in reductionist 2D systems that insuciently reect the complexity of cancer invasion in vivo.2 ese reductionist approaches have been extremely powerful in identifying the genetic and epigenetic factors involved in various stages of tumor development and progression, but are also limited in their capacity to capture the

CONTENTS Introduction 157 Models 159

Force-Based Models 160 Stochastic Random Walk Models 161 Reaction-Diusion-Based Multiple Cell Spheroid Models 163 Monte Carlo Models 164 Integrating Length and Timescales at a Single-Cell Level 167

Discussion 168 Acknowledgments 169 References 170

systems-level behavior seen in vivo. Additionally, the articiality of the substrate, dimensionality, and unrealistic geometric constraints can aect the observed signaling pathways quantied.3 Migration experiments in 2D environments are also blind to biochemical and biomechanical eects of the surrounding matrix, resulting in an incomplete understanding of the tumor cell migration process.