Multiphysics Modeling of Reactions, Mass Transport and Mechanics of Tumor Growth

Abstract

The biochemical dynamics involved in tumor growth can be broadly classified into three distinct spatial scales: the tumor scale, the cell-ECM interactions and the sub-cellular processes. This work presents the tumor scale investigations, which are expected to eventually lead to a system-level understanding of the progression of cancer. Many of the macroscopic phenomena of physiological relevance, such as tumor size and shape, formation of necrotic core and vascularization, proliferation and metastasis of cell populations, external mechanical interactions, etc., can be treated within a continuum framework by modeling the evolution of various species involved by transport equations coupled with mechanics. This framework is an extension of earlier work (Garikipati et al. in J. Mech. Phys. Solids 52:1595–1625, 2004; Narayanan et al. in Biomech. Model. Mechanobiol. 8:167–181, 2009, J. Phys. Condens. Matter. 22:194122, 2010) based on the continuum theory of mixtures for modeling biological growth. Specifically, the focus is on demonstrating the effectiveness of mechano-transport coupling in simulating tumor growth dynamics and explaining some in vitro observations like mechanics-induced ellipsoidal tumor shapes. Additionally, this work also seeks to demonstrate the effectiveness of tools like adaptive mesh refinement and automatic differentiation in handling highly nonlinear, coupled multiphysics systems.