Neuroblastomas are solid tumors and represent the most common extracranial tumors in children, with no known cause to date. The analysis of tumoroid data (artificial organoids capable of reproducing neuroblastoma growth) has revealed a distinctive spatial organization: cancer stem cells tend to cluster at the center of the tumor. A multiscale agent-based neuroblastoma tumoroid model was developed to simulate neuroblastoma growth. Data provided by this computational model represent a unique opportunity to investigate the genetic causes of neuroblastoma tumors’ spatial structures. Our goal is to build a mathematical model that can reproduce the growth of neuroblastoma based on these data, in order to better understand and capture the particular spatial distribution as the result of the stochastic interaction of genes promoting stem or differentiated phenotypes and non-local interactions based on gene dynamics, and ultimately propose more targeted treatments.

We combined an existing deterministic model of tumor growth, which accounts for cell proliferation, diffusion, and differentiation, with a Piecewise Deterministic Markov Process (PDMP) representing the stochastic gene regulatory network. We conducted a mathematical analysis of this model to prove that it is well-posed, using semigroup theory and stochastic process theory. We also performed numerical simulations in both 1D and 2D to observe whether the expected spatial distribution emerges.

Results show that cell proliferation and diffusion occur as expected for each cell type, but the specific clustering of stem cells is not yet reproduced. The model needs to be further refined to better capture this spatial organization, which will be the focus of the next steps of this work.

This work has been done in collaboration with Olivier Gandrillon (Inria, ENS de Lyon) and Thi Nhu Thao Nguyen (Université Paris Cité, Inria, ENS de Lyon).