  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.
