The continuum physics of tumor growth

The dynamical processes of chemistry, transport and mechanics that govern tumor growth can be broadly classified into three distinct spatial scales: the tumor scale, the cell-extracellular matrix (ECM) interactions and the sub-cellular processes. In this work, we focus on tumor scale investigations, and model the emergent morphology of tumors to gain system-level insights into their progression. At this scale, the complex interactions between physical processes are more broadly observable than in single-cell studies. We have developed a continuum framework for modeling the phenomena of physiological relevance such as cell metabolism, cell proliferation and death, formation of necrotic cores, external mechanical interactions, cell migration and the resulting tumor morphology. The evolution of various constituents (cancer cells, stem cells, necrotic cells, nutrients, byproducts, etc) is modelled with reaction-advection-diffusion equations coupled with finite strain mechanics. The multiplicative decomposition of the deformation gradient into growth and elastic components is the basis of our kinematic representation of growth, and dilatation/contraction at the tumor scale is a consequence of changes in cell and ECM densities. These interactions are parametrized using quantitative experimental observations from in the literature, and the model has been validated by comparison with in vitro observations of growth in human colon adenocarcinoma tumors performed by our collaborators at the Max Planck Institute for Intelligent Systems in Stuttgart, Germany: Prof. Kristen Mills, now at Rensselaer Polytechnic Institute, and Prof. Ralf Kemkemer, now at University of Reutlingen. In earlier work we had laid out a free energy-based comparison of the many bio-chemo-mechanical processes that are in play during tumor growth. More recently we have been focused on the processes that determine tumor shape, but are reuniting this line of study with the free energy rates in growing tumors.


H. Narayanan, S.N. Verner, K.L. Mills, R. Kemkemer, K. Garikipati, ``In silico estimates of the free energy rates in growing tumor spheroids'', Journal of Physics: Condensed Matter, (Special Issue on Cell-Substrate Interactions), Vol. 22(19) 194122, 2010. [journal]

S. Rudraraju, K.L. Mills, R Kemkemer, K. Garikipati, ``Multiphysics Modeling of Reactions, Mass Transport and Mechanics of Tumor Growth'' Computer Models in Biomechanics, Pages 293-303, 2013. [journal]

K.L.Mills, R Kemkemer, S. Rudraraju, K. Garikipati, ``Elastic free energy drives the shape of prevascular solid tumors'', PLoS ONE, 9(7), 2014. [journal] [arXiv]

Shown here are the experimentally observed growth of human colon adenocarcinoma tumors and the simulations of tumor growth in 2D and 3D.

[Click images to enlarge/play]