Biomedical Engineering Reference
In-Depth Information
Chapter 21
Multiphysics Modeling of Reactions, Mass
Transport and Mechanics of Tumor Growth
Shiva Rudraraju, Kristen L. Mills, Ralf Kemkemer, and Krishna Garikipati
Abstract
The biochemical dynamics involved in tumor growth can be broadly clas-
sified 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 pro-
gression of cancer. Many of the macroscopic phenomena of physiological relevance,
such as tumor size and shape, formation of necrotic core and vascularization, pro-
liferation 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 mix-
tures 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 non-
linear, coupled multiphysics systems.
21.1 Background
The primary biochemomechanical aspects of tumor growth involve (a) rapid can-
cer cell proliferation leading to formation of solid tumors, (b) metabolism by
which cells consume nutrients like oxygen and glucose and create byproducts,
(c) mechanical interactions between tumor mass, the extracellular matrix (ECM)
and surrounding tissues, and (d) cell migration leading to formation of new tu-
S. Rudraraju
)
Department of Mechanical Engineering, University of Michigan, Ann Arbor, USA
e-mail:
krishna@umich.edu
·
K. Garikipati (
K.L. Mills
·
R. Kemkemer
Max Planck Institute for Intelligent Systems, New Materials and Biosystems, Stuttgart, Germany
