Mathematical modeling of cell movement and tumor spheroid growth in vitro

The aim of this study is to address the mechanism underlying cell movement through the extracellular matrix (ECM) and tumor spheroid growth through mathematical modeling.;The mathematical model involves the finite element model for cell migration through the ECM and a hybrid model for tumor spheroid growth. This hybrid model consists of a cell-based model in the proliferating zone outside of spheroids and a continuum mechanics model inside spheroids and in outer gel.;This study provides a way to explore the mechanical interaction between cells and the ECM. We focus on cell migration through the ECM while many existing models investigate the cell movement on a hard substrate.;Tumor growth models heavily rely on computational techniques and multi-scale modeling because of the different time and space scales in each region. Despite the existence of many mathematical models on this subject this hybrid model provides a unique approach to deal with several issues that appear in ordinary differential equation models, single and multi-component models, and cell-based models. This hybrid model provides the solution to the limitation of modeling in other type of models: (a) heavy computational cost and inability to deal with continuum materials of cell-based models (b) non-realistic description of cellular processes such as cell-cell interaction and cell degradation in continuum models (single and multi-component models). Our results highlight the delicate interaction between cells and between cells and the ECM, and furthermore asymmetric growth of spheroids and growth control by stress as experimentally observed.