Experimental and theoretical studies of tumor growth

Abstract

Most biological phenomena commonly involve growth and expansion mechanics. In this work, we propose an innovative model of cancerous growth which posits that an expandable tumor can be described as a poroelastic medium consisting of solid and fluid components. To verify the feasibility of the model, we utilized an established epithelial human breast cancer cell line (MDA-MB-231) to generate an in vitro tumorsphere system to observe tumor growth patterns in both constrained and unconstrained growth environments. The tumorspheres in both growth environments were grown with and without the FDA-approved anti-breast cancer anthracycline, Doxorubicin (Dox), in order to observe the influence small molecule drugs have on tumor-growth mechanics. In our biologically informed mechanical description of tumor growth dynamics, we derive the governing equations of the tumor’s growth and incorporate them with large deformation to improve the accuracy and efficiency of our simulation. Meanwhile, the dynamic finite element equations (DFE) for coupled displacement field and pressure field are formulated. Moreover, the porosity and growth tensor are generalized to be functions of displacement and pressure fields. We also introduce a specific porosity and growth tensor. In both cases, the formalism of continuum mechanics and DFE are accompanied by accurate numerical simulations.