Analyzing model inaccuracy and relative importance of parameters of discrete model of adhesion of circulating tumor cells for investigating metastatic dynamics.

Metastasis is strongly influenced by the ability of cancerous cells to adhere to endothelial cells, facilitating their extravasation to distant organs; however, how uncertainty in cellular and adhesion properties propagates to observable dynamics remains unclear. A key finding is that a physiological "speed limit" imposed by Poiseuille flow fundamentally constrains this uncertainty: although input variability reaches a coefficient of variation (CV) of 20%, the resulting variability in CTC velocity saturates at ∼12%, revealing a bounded, nonlinear response rather than a linear error amplification. Coupling the stochastic LBM-DEM-IBM adhesive dynamic model with a high-fidelity Random Forest surrogate enables time-resolved global sensitivity analysis (Sobol' and E-FAST). This coupled model shows that parameter importance is stage-dependent: early attachment is dominated by membrane/link elasticity, whereas stable rolling is governed by bond spring stiffness and rupture mechanics. These insights explain why velocity variability attenuates while adhesion outcomes can still diverge (rolling vs detachment). In contrast, adhesion behavior remains highly sensitive to parameter variability. Machine learning (XGBoost) enables accurate classification of CTC rolling or detachment states with 95.62% accuracy, providing a predictive framework for assessing detachment likelihood under uncertainty. Together, these results establish a unified physics-to-mechanism perspective in which flow-imposed limits, stage-dependent control, and sparse parameter interactions govern CTC adhesion dynamics to enhance predictive models for metastasis.