## 1 Introduction  
As cancer remains one of the main risk factors to human health, researchers are continually seeking effective therapy methods to avoid death [1, 2, 3]. Tumor metastasis is a multi-step process involving not only the tumor cells themselves, but also other blood cells (e.g., white blood cells and platelets) and soluble proteins [4, 5, 6, 7]. There are several theories to explain tumor metastasis, one of which was developed by [PERSON] et al. and named the \"two-step theory\". It proposed that polymorphnuclear neutrophils (PMNs) acted as bridges between tumor cells (TCs) and endothelial cells (ECs), which facilitated TC adhesion on the blood vessel wall [8]. A series of studies showed that the involvement of PMNs significantly increased tumor cell adhesion and extravasation under flow, which was regulated by shear force and shear rate, as well as tumor microenvironment [8, 9, 10, 11, 12]. These studies revealed the importance of targeting the adhesion of circulating tumor cells in tumor metastasis [6, 13].  
Studies showed that soluble fibrinogen (Fg) and fibrin (Fn) affected the initial adhesion of circulating melanoma cells. The potential procoagulant effect of melanoma cells is closely connected with a transmembrane protein tissue factor (TF) they secrete. It is reported that TF expression level on the surface of high metastatic tumor cells was 1000 times higher than that on the surface of nonmetastatic tumor cells [14], and TF could trigger coagulation by promoting thrombin formation [15; 16]. Thrombin is one kind of serine protease with multiple functions, which could transfer Fg to Fn and activate several intracellular signal pathways [17; 18]. It could also cause a cellular immune response, such as a change of intercellular adhesion molecule-1 (ICAM-1) expression level on an endothelial monolayer and the activation of white blood cells [19; 20; 21].  
Parallel plate flow chamber experiments by [PERSON] et al. elucidated that the adhesion between melanoma cells and an endothelial monolayer was mediated by soluble Fn (sFn) via ICAM-1 (on TC)-Fn-ICAM-1 (on EC) and \(\alpha_{v}\beta_{3}\) (on TC)-Fn-ICAM-1 (on EC). Thus, sFn acted as a bridge not only to promote the adhesion between melanoma cells and PMNs, but also to help melanoma cells directly adhere to the endothelial monolayer [22]. Soluble Fg (sFg) exists in the blood of healthy human beings, while the change of sFn expression is usually related to diseases [23; 24; 25]. Studies showed that sFg and sFn, especially sFn, could highly enhance the number of adhered melanoma cells, particularly the firmly adhered ones, on an endothelial monolayer. Moreover, sFg promoted a short adhesion time (1 s < t < 3 s) between melanoma cells and endothelial cells mediated by PMNs, while sFn promoted both short adhesion and long firm adhesion (t > 5 s) between melanoma cells and endothelial cells mediated by PMNs under high shear conditions [22; 26].  
Although the adhesion efficiency, adhesion time period, and adhesion kinetics were well studied, the change of local hydrodynamic environment during the process of PMNs facilitating TC adhesion on ECs in the presence of sFg and sFg was rarely understood. A better understanding of local hydrodynamic environment changes in a neutrophil-tumor cell-endothelial cell adhesion system with the presence of sFg or sFn would enrich the \"two-step theory\". Our previous studies indicated that both cell deformation and cell relative positions would affect the local hydrodynamic environment to promote the firm adhesion of TCs on the substrate [27]. Therefore, in the current study, we proceed to improve the side-view micro-particle imaging velocimetry (micro-PIV) technique to investigate the local hydrodynamic environment of adhesion between TCs and ECs mediated by PMNs with sFg and sFn in blood flow. The purpose is to explore the hydrodynamic mechanism and to reveal the effect of sFg and sFn by combining the adhesion efficiency, adhesion time, and adhesion kinetics.