Towards uncertainty quantification of a model for cancer-on-chip experiments

This study is a first step towards using data-informed differential models to predict the dynamics of cancer-on-chip experiments. We consider a conceptualized one-dimensional device, containing a cancer and a population of white blood cells. The interaction between cancer and cells is described by a chemotaxis model inspired by Keller-Segel-type equations, solved by a Hybridizable Discontinuous Galerkin method. Our goal is using (synthetic) data to tune the parameters of the model and assessing the uncertainty on the predictions of the dynamics due to the uncertainty on the parameters remaining after the tuning procedure. To this end, we first perform a sensitivity analysis using both Sobol and Morris indices to assess how parameters impacts model predictions, and fix the value of parameters with negligible impact. Subsequently, we conduct an inverse uncertainty quantification analysis by Bayesian techniques to compute a data-informed probability distribution of the remaining parameters. Finally, we carry out a forward uncertainty quantification analysis to compute the impact of the residual parametric uncertainties on the quantities of interest of the model. The whole procedure is sped up by sparse-grids surrogate models approximating the mapping of the uncertain parameters to the quantities of interest.