Numerical modeling of diffusion in extracellular space of biological cell clusters and tumors

Biological cluster of cells may be seen as porous media, where the cells are the “solid grains” and the extracellular space (ECS) the “pores”. It is often the case in dense clusters of cells that the flow rate of liquid inside the extracellular space is negligible in front of the molecular diffusion. In the particular case of tumoral cells, the extra-cellular path is the tumor interstitial matrix (IM) and the apparent (or effective) diffusion coefficient (ADC) determines the speed of delivery of drugs into the tumor. It is then of great importance to be able to estimate the value of the apparent diffusion coefficient. We present here a numerical approach, based on a Monte Carlo modeling to estimate the ADC in irregular, non repetitive morphologies of cell clusters.