Parameter estimation techniques for a chemotaxis model inspired by Cancer-on-Chip (COC) experiments

The present work is inspired by laboratory experiments, investigating the cross-talk between immune and cancer cells in a confined environment given by a microfluidic chip, the so called Organ-on-Chip (OOC). Based on a mathematical model in form of coupled reaction-diffusion-transport equations with chemotactic functions, our effort is devoted to the development of a parameter estimation methodology that is able to use real data obtained from the laboratory experiments to estimate the model parameters and infer the most plausible chemotactic function present in the experiment. In particular, we need to estimate the model parameters representing the convective and diffusive regimes included in the PDE model, in order to evaluate the diffusivity of the chemoattractant produced by tumor cells and its biasing effect on immune cells. The main issues faced in this work are the efficient calibration of the model against noisy synthetic data, available as macroscopic density of immune cells. A calibration algorithm is derived based on minimization methods which applies several techniques such as regularization terms and multigrids application to improve the results, which show the robustness and accuracy of the proposed algorithm.