A mechanobiological model for tumor spheroids evolution: application to glioblastoma

Abstract

Spheroids are in vitro spherical structures of cell aggregates, eventually cultured within a hydrogel matrix, that are used, among other applications, as a technological platform to investigate tumor formation and evolution. Several interesting features can be replicated using this methodology, such as cell communication mechanisms, the effect of gradients of nutrients, or the creation of realistic 3D biological structures. In this paper, we propose a continuum mechanobiological model which accounts for the most relevant phenomena that take place in tumor spheroids evolution under in vitro suspension, namely, nutrients diffusion in the spheroid, kinetics of cellular growth and death, and mechanical interactions among the cells. The model is qualitatively validated, after calibration of the model parameters, versus in vitro experiments of spheroids of different glioblastoma cell lines. This preliminary validation allowed us to conclude that glioblastoma tumor spheroids evolution is mainly driven by mechanical interactions of the cell aggregate and the dynamical evolution of the cell population. In particular, it is concluded that our model is able to explain quite different setups, such as spheroids growth (up to six times the initial configuration for U-87 MG cell line) or shrinking (almost half of the initial configuration for U-251 MG cell line); as the result of the mechanical interplay of cells driven by cellular evolution. Indeed, the main contribution of this work is to link the spheroid evolution with the mechanical activity of cells, coupled with nutrient consumption and the subsequent cell dynamics. All this information can be used to further investigate mechanistic effects in the evolution of tumors and their role in cancer disease. Author summarySpheroids structures of cell aggregates are an available experimental platform to analyze the evolution and drug response of solid tumors. In particular, the dynamics of different glioblastoma cell lines have been studied in this work using spheroids. Interestingly, very different behaviors were observed, from a half of the initial configuration shrinking for U-251 MG cell line to six times the initial configuration growth for U-87 MG cell line. These results were replicated by means of a coupled mathematical model which accounts for nutrients diffusion in the spheroid, kinetics of cellular growth and death, and mechanical interactions among the cells. Tumor growth or shrinkage can be explained from a continuum mechanics view driven by cell activity and nutrients availability. This modeling put the focus on mechanistic effects and is aligned with novel experimental techniques to quantify the mechanical microenvironment in tumors. These techniques may be combined with the approach presented in this work to further investigate the role of mechanics in cancer disease.