## 3 Results  
sFg and sFn Regulated the Local Shear Rates above an Adherent PMN and an Adherent TC on an Endothelial Monolayer  
In order to simulate the process of PMN-mediated TC adhesion on an endothelial monolayer under physiological conditions, 1.5 mg ml\({}^{-1}\) sFg was added to the solution. Local shear rates above an adherent PMN and an adherent TC at six different PMN-to-TC position states were calculated. Comparing the local shear rates above an adherent PMN with those above an adherent TC at the same PMN-to-TC position state, the data show that the local shear rates above an adherent PMN are all lower than those above an adherent TC under both low (91.25 mL min\({}^{-1}\)) and high (292 mL min\({}^{-1}\)) shear conditions, respectively (Figure 2). The results were consistent with previous studies [22]. It was also found that the differences between the local shear rates above an adherent TC and those above an adherent PMN are very small at two PMN-to-TC position states in the presence of sFg: (1) a TC detaches from an adherent PMN under low shear flow condition; (2) a TC forms transient aggregates with an adherent PMN under high shear condition. The corresponding heights of a PMN are 4.65 \(\upmu\)m and 6.7 \(\upmu\)m, while those of a TC are 11.85 \(\upmu\)m and 13.5 \(\upmu\)m (as shown in Table 1). Although the height of a PMN is much smaller than that of a TC, the local shear rates above adherent cells are very close, which might due to the \"peak\" and \"valley\" of endothelial monolayer. If a PMN adheres to the \"peak\" and a TC adheres to the \"valley\", the effect of endothelial monolayer morphology on flow field might compensate for the effect of cell height on flow field. Therefore, besides the height of an adherent cell, the position on the endothelial monolayer where it stays also becomes an import factor that can affect the local hydrodynamic environment.  
Since the increase of sFn in blood flow may reflect the occurrence of disease, we intended to investigate the local hydrodynamic environment around adherent PMNs and  
Figure 2: Comparison of local shear rates above adherent PMNs and those above adherent melanoma cells in the presence of soluble fibrin(ogen). (**A**) Under low shear flow condition (91.25 mL min\({}^{-1}\)); (**B**) Under high shear flow condition (292 mL min\({}^{-1}\)). Solid squares (\(\blacktriangle\)) represent local shear rates above an adherent PMN in soluble fibrinogen (sFg) solution, solid circles (\(\bullet\)) represent local shear rates above an adherent TC in soluble fibrin (sFn) solution, open squares (\(\cdot\)) represent local shear rates above an adherent PMN in sFg solution, and open circles (\(\circ\)) represent local shear rates above an adherent TC in sFn solution.  
TCs on an endothelial monolayer with sFn in the solution. Thrombin (2 U mL\({}^{-1}\)) was mixed with sFg (1.5 mg mL\({}^{-1}\)) solution to convert sFg to sFn, while Gly-Pro-Arg-Pro amide (GPRP) was also added to prevent self-aggregation of sFn. As shown in Figure 2, local shear rates above an adherent TC are much higher than those above an adherent PMN under both low and high shear conditions, which also agreed with previous results [22]. Regarding the cell dimensions in Table 2, when a TC collides with an adherent PMN, the PMN shows the largest deformation (the heights decrease to 4.2 \(\upmu\)m and 5.001 \(\upmu\)m under low shear and high shear conditions, respectively). Besides the deformation of PMNs, the relative positions of TCs with respect to PMNs (TCs stand upstream of PMNs) contributed to the lowest local shear rates above an adherent PMN as well. However, the highest local shear rates above an adherent PMN and the extreme local shear rates (both the lowest and the highest) above an adherent TC appear at different PMN-to-TC position states, which might be explained by the effect of both an endothelial monolayer and sFn.