In silico estimates of the free energy rates in growing tumor spheroids

Details In silico estimates of the free energy rates in growing tumor spheroids In silico estimates of the free energy rates in growing tumor spheroids

2010-02-07

arxiv.org/abs/1002.1428v2

Journal of Physics: Condensed Matter, Special Issue on Cell-Substrate Interactions. 22 (2010), 194122.

Biology

Quantitative Biology

Cell Behavior

27 pages with 5 figures and 2 tables. Figures and tables appear at the end of the paper

Scientific paper

10.1088/0953-8984/22/19/194122

The physics of solid tumor growth can be considered at three distinct size scales: the tumor scale, the cell-extracellular matrix (ECM) scale and the sub-cellular scale. In this paper we consider the tumor scale in the interest of eventually developing a system-level understanding of the progression of cancer. At this scale, cell populations and chemical species are best treated as concentration fields that vary with time and space. The cells have chemo-mechanical interactions with each other and with the ECM, consume glucose and oxygen that are transported through the tumor, and create chemical byproducts. We present a continuum mathematical model for the biochemical dynamics and mechanics that govern tumor growth. The biochemical dynamics and mechanics also engender free energy changes that serve as universal measures for comparison of these processes. Within our mathematical framework we therefore consider the free energy inequality, which arises from the first and second laws of thermodynamics. With the model we compute preliminary estimates of the free energy rates of a growing tumor in its pre-vascular stage by using currently available data from single cells and multicellular tumor spheroids.

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