(23f) Discretized Reaction-Diffusion Model of the Transport of Drugs in 3D Cancer Cell Spheroids for Informed Drug Screening

Cancers are a heterogeneous class of diseases that not only vary between each instance but also over the course of disease. Many novel and innovative strategies have been developed to treat different forms of cancer. Yet, significant challenges remain in establishing effective standardized treatments. Chief amongst these is the problem of standardized drug screening. The standard has advanced from using representative 2D cell cultures to 3D cell spheroids. These new methodologies provide more biologically informed approaches that capture in vivo characteristics of cell morphology, ECM interactions, and transport limitations. Yet with these new approaches, in vitro experiments fail to recapitulate in vivo results for therapeutics – even targeted precision medicine.

In this work, we develop a discretized, reaction-diffusion model of a cancer spheroid to investigate the heterogeneity found in the current body of work. In particular, dose-response curves and reported IC50 values for the same drug and cell combination vary wildly for different spheroid preparations and drug dosing methodologies. By approximating the spheroid as a spherical catalyst, we explain the differences in IC50 between different sizes of cell spheroids. Additionally, we explain dose-responsive plateauing using discretization of the spheroid into multiple layers of cells. With this approach, we are able to collapse dose-response curves generated for several different drug-cell combinations from several different groups by normalization to two key dimensionless system parameters respectively corresponding to cell-spheroid size ratio and the Thiele modulus. Asymptotic analyses with respect to both parameters indicate the IC50 scales exponentially with respect to spheroid size beyond a critical size.

These findings recapitulate what we know of in situ tumors. Solid tumors operate in microenvironments built around themselves. Densely packed tumors consisting of cancer cells, healthy cells, and extracellular matrix form over time where rogue cells recruit surrounding tissues for nutrients and protection. Smaller spheroids approximate early cancers well and have been shown to respond well to direct application of chemotherapy. Later into disease, angiogenesis occurs to the recruit surrounding endothelial cells and fibroblasts to create vasculature for the intake. However, proper vascularization of tumors is necessary for the perfusion of applied therapies to the tumor itself. This is shown in our model as passive diffusion from the spheroid boundary is insufficient to fully treat the disease. Our work emphasizes the necessity of vascularization and consideration for heterogeneity in larger 3D cell spheroid models to better inform drug screening efforts.