Investigating the steady state of multicellular spheroids by revisiting the two-fluid model - Antonio Fasano; Marco Gabrielli; Alberto Gandolfi (Mathematical Biosciences and Engineering)
In this paper we examine the steady state of tumour spheroids consideringa structure in which the central necrotic region contains an inner liquidcore surrounded by dead cells that keep some mechanical integrity.This partition is a consequence of assuming that a finite delayis required for the degradation of dead cells into liquid.The phenomenological assumption of constant local volume fraction ofcells is also made. The above structure iscoupled with a simple mechanical model that views the cell component as aviscous fluid and the extracellular liquid as an inviscid fluid. By imposingthe continuity of the normal stress throughout the whole spheroid, we showthat a steady state can exist only if the forces on cells at the outerboundary (provided e.g. by a surface tension) are intense enough, and in sucha case we can compute the stationary radius. By giving reasonable values tothe parameters, the model predicts that the stationary radius decreases withthe external oxygen concentration, as expected from experimental observations.