Modelling geometric patterns of cancer progression

Throughout the years the morphological characteristics of malignant tumours have played a major role to perform cancer staging, which in turn determines the selection of therapy [1]. Studies that quantify the geometry of tumours have shown that tumours progress towards less smooth boundaries with strands of cells invading in surrounding tissues [2,3,4], thus, resulting in poor therapeutic outcomes [5,6]. Mathematical models can provide useful insights towards the understanding the morphological progression of cancer as well as improve their therapeutic outcomes. In this context, a computational framework that focuses on the modelling of complex geometric patterns is presented. The framework utilizes hybrid spatiotemporal models that describe cancer growth in terms of both tumour and cellular levels. Model validation is performed with 3D cell culture experiments of triple negative breast cancer cells (MDA-MB-231) grown in Matrigel. The model is calibrated to the experimental data with the use of combined approximate bayesian computation and monte carlo techniques (ABC-MCMC). Spatial statistical analysis methods are then utilized towards the identification of geometric patterns across tumour volumes, formed in both experiments and simulations. Results so far indicate cell organization into clusters that progressively tend to accumulate in the boundaries of the examined space. The resulted collective migration pattern suggests cell-cell cooperativity and combined with increased mobility leads to the escape from the examined space.