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.
Tissue-Intrinsic Shape Mechanics in Growing Pre-Migratory Tumor Spheroids
Faculty of Mathematics and Physics, University of Ljubljana（卢布尔雅那大学数学物理学院）；Jožef Stefan Institute（约瑟夫·斯蒂芬研究所）；School of Physics, Indian Institute of Science Education and Research Thiruvananthapuram（印度科学教育与研究学院特里凡得琅物理学院）
Development and cytotoxic response of two proliferative MDA- MB-231 and non-proliferative SUM1315 three-dimensional cell culture models of triple-negative basal-like breast cancer cell lines
