Deciphering circulating tumor cells binding in a microfluidic system thanks to a parameterized mathematical model.

The spread of metastases is a crucial process in which some questions remain unanswered. In this work, we focus on tumor cells circulating in the bloodstream, the so-called Circulating Tumor Cells (CTCs). Our aim is to characterize their trajectories under the influence of hemodynamic and adhesion forces. We focus on already available in vitro measurements performed with a microfluidic device corresponding to the trajectories of CTCs - without or with different protein depletions - interacting with an endothelial layer. A key difficulty is the weak knowledge of the fluid velocity that has to be reconstructed. Our strategy combines a differential equation model - a Poiseuille model for the fluid velocity and an ODE system for the cell adhesion model - and a robust and well-designed calibration procedure. The parameterized model quantifies the strong influence of fluid velocity on adhesion and confirms the expected role of several proteins in the deceleration of CTCs. Finally, it enables the generation of synthetic cells, even for unobserved experimental conditions, opening the way to a digital twin for flowing cells with adhesion.