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

TL;DR

This paper develops a continuum mathematical model to estimate free energy rates in growing tumor spheroids, integrating biochemical and mechanical processes at the tumor scale to understand cancer progression thermodynamically.

Contribution

It introduces a novel thermodynamics-based modeling framework for tumor growth, linking biochemical dynamics and mechanics to free energy changes.

Findings

Preliminary estimates of free energy rates in tumor spheroids.

Model aligns with available single-cell and spheroid data.

Provides a basis for system-level understanding of tumor energetics.

Abstract

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.