Stress generation, relaxation and size control in confined tumor growth

• Main Authors: Lowengrub, J. (Author), Ramirez-Guerrero, D. (Author), Wu, M. (Author), Yan, H. (Author)
• Format: Article
• Language: English
• Published: Public Library of Science 2021
• Subjects: anisotropy; Anisotropy; article; biology; Biomechanical Phenomena; biomechanics; cancer growth; cancer model; cancer size; cell density; Cell Line, Tumor; cell proliferation; Cell Proliferation; cell size; Computational Biology; controlled study; cytology; diffusion; feedback system; growth rate; human; Humans; leisure; mechanical stress; microenvironment; multicellular spheroid; neoplasm; Neoplasms; pathology; pathophysiology; physiological stress; physiology; rigidity; Spheroids, Cellular; Stress, Mechanical; tumor cell culture; tumor cell line; Tumor Cells, Cultured; tumor growth; tumor spheroid; viscoelasticity
• Online Access: View Fulltext in Publisher

 Experiments on tumor spheroids have shown that compressive stress from their environment can reversibly decrease tumor expansion rates and final sizes. Stress release experiments show that nonuniform anisotropic elastic stresses can be distributed throughout. The elastic stresses are maintained by structural proteins and adhesive molecules, and can be actively relaxed by a variety of biophysical processes. In this paper, we present a new continuum model to investigate how the growth-induced elastic stresses and active stress relaxation, in conjunction with cell size control feedback machinery, regulate the cell density and stress distributions within growing tumors as well as the tumor sizes in the presence of external physical confinement and gradients of growth-promoting chemical fields. We introduce an adaptive reference map that relates the current position with the reference position but adapts to the current position in the Eulerian frame (lab coordinates) via relaxation. This type of stress relaxation is similar to but simpler than the classical Maxwell model of viscoelasticity in its formulation. By fitting the model to experimental data from two independent studies of tumor spheroid growth and their cell density distributions, treating the tumors as incompressible, neo-Hookean elastic materials, we find that the rates of stress relaxation of tumor tissues can be comparable to volumetric growth rates. Our study provides insight on how the biophysical properties of the tumor and host microenvironment, mechanical feedback control and diffusion-limited differential growth act in concert to regulate spatial patterns of stress and growth. When the tumor is stiffer than the host, our model predicts tumors are more able to change their size and mechanical state autonomously, which may help to explain why increased tumor stiffness is an established hallmark of malignant tumors. © 2021 Yan et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.