## 4 Discussion  
In this paper, we measured the velocity profiles around adherent cells in the presence of sFg and sFn at different PMN-to-TC position states to calculate local shear rates and relative shear rates above adherent cells and the corresponding cell Reynolds number. The results showed that both sFg and sFn affected the curves of relative shear rates above an adherent cell under different shear conditions: (1) the curves of relative shear rates above the same type of adherent cell under different shear conditions were overlapping; (2) the curves of relative shear rates above an adherent cell became flatter in the presence of sFn. Furthermore, the curves of the cell Reynolds numbers of an adherent cell showed fluctuation under high shear condition, and the value ranges of cell Reynolds numbers became smaller in the presence of sFn. Soluble fibrin(ogen), endothelial monolayer, PMN  
Figure 5: Drag force acting on adherent cells in the presence of soluble fibrin (ogen). (**A**) Above an adherent PMN; (**B**) Above an adherent TC. Solid squares (\(\bullet\)) represent a low shear condition (91.25 \(\mu\)L min\({}^{-1}\)) with sFg, solid circles (\(\bullet\)) represent a high shear condition (292 \(\mu\)L min\({}^{-1}\)) with sFg, open squares (\(\circ\)) represent a low shear condition (91.25 \(\mu\)L min\({}^{-1}\)) with sFn, and open circles (\(\circ\)) represent a high shear condition (292 \(\mu\)L min\({}^{-1}\)) with sFn. to-TC position states, and different shear conditions all contributed to PMN-facilitated TC adhesion on ECs. Besides the effect of an endothelial monolayer on the local hydrodynamic environment, soluble fibrin(ogen) acted as a bridge to form extra molecule bonds between three pairs of cells: PMNs and ECs, TCs and ECs, and PMNs and TCs. The increase of collision frequency among these three types of cells affected the contact area and contact time, and further enhanced tumor cells' firm adhesion on an endothelial monolayer. Both in vivo and in vitro studies showed that there was a strong connection between hemostasis and tumor metastasis. For example, cancer patients usually have a coagulation abnormality with a higher concentration of Fg and fibrinopeptide [31, 32]. Tissue factors secreted by melanoma cells could promote the formation of Fn, which could increase the adhesion time of melanoma cells to endothelial cells [14]. Fg could facilitate the adhesion between PMNs and endothelial cells by forming molecular bonds to ICAM-1 [33, 34]. Animal experiments indicated that a lack of Fg reduced the firm adhesion of tumor cells, while adding Fn increased the number of adhered tumor cells in pulmonary microcirculation [31, 35, 36]. In the presence of Fg and Fn, the adhesion between PMNs and melanoma cells would happen in a similar way, which is ICAM-1 (on TC)-fibrin(ogen)-\(\beta_{2}\) integrin (on PMN). \(\alpha_{\
u}\beta_{3}\) Integrin expressed on the surface of melanoma cells could also bind to Fg and Fn in blood flow [37, 38]. [PERSON] et al. studied the adhesion between melanoma cells and PMNs, and the results indicated that sFg and sFn enhanced the adhesion between tumor cells and PMNs with different kinetic mechanisms. It was also found that ICAM-1 was responsible for initial adhesion and \(\alpha_{\
u}\beta_{3}\) integrin played a role in firm adhesion [39]. PMNs enhanced melanoma cells' adhesion to endothelial cells in the blood flow, and the concentration of sFn in cancer patients increased due to thrombin [32, 35]. In the process of PMN-facilitated tumor cell adhesion to endothelial cells, there were several factors that affected the final adhesion efficiency of tumor cells, such as collision efficiency, contact area, and contact time. In the \"two-step theory\", collisions first occurred between PMNs and an endothelial monolayer, then between melanoma cells and adherent PMNs, and finally between tethering melanoma cells and the endothelial monolayer.