Morphological Stability for in silico Models of Avascular Tumors

by Erik Blom & Stefan Engblom

We develop a simple, stochastic model of an avascular tumor that displays known behavior at the considered scales. In parallel we develop, analyze, and simulate a surrogate PDE model to explain the growth pattern and shape of the stochastic model. 

We investigate the emergent tumor morphology of the stochastic model (Fig. a) through the PDE model and through comparisons of respective model’s numerical experiments. The stochastic model displays the three characteristic avascular tumor regions -- the proliferative rim, quiescent annulus, and necrotic center -- and sigmoidal volumetric growth pattern in line with the PDE model under radial symmetry (Fig. b). The analysis predicts morphological instability under low oxygen and cell-cell adhesion conditions, as well as an ever-present creeping effect where the tumor as a whole migrates towards the oxygen source -- an effect observed during simulations of both models (Fig. c). The analysis further displays a capacity to predict non-trivial morphological patterns of the model tumor (Fig. d).