## 3 Results and Discussion  
### Contributions of Hematocrit, Flow Rate, and Diluent to Pressure and Equivalent Compliance  
Before evaluating the performance of the present method, it was necessary to find out the contributions of several factors (hematocrit (Hct), flow rate (\(Q_{0}\)), diluent (1x PBS, plasma)) to blood pressure (\(P_{x}\)), and equivalent compliance (\(C_{eq}\)). First, to evaluate the effects of Hct and \(Q_{0}\) on \(<\)\(U_{mc}\textgreater\) and \(<\)\(U_{pc}\textgreater\), temporal variations of \(<\)\(U_{mc}\textgreater\) and \(<\)\(U_{pc}\textgreater\) were obtained with respect to Hct = 30%, 40%, and 50%. Here, the diluent was fixed at 1x PBS. Blood sample preparation was discussed at the Section S1 (Supplementary Materials). The flow rate of the blood sample was fixed at \(Q_{0}\) = 1 mL/h. According to an analytical formula for the depth of correlation (DOC) [22], the DOC was estimated as 64.1 \(\upmu\)m. As the DOC was much higher than the channel depth (i.e., DOC \(>>\) depth), all RBCs contributed to calculation of the velocity fields of blood flows. Thus, the micro particle image velocimetry (\(\upmu\)PIV) technique measured averaged velocity fields in the depth direction. As shown in Figure 2(A-a), both velocities tended to decrease substantially with respect to the hematocrit. To evaluate the contributions of \(Q_{0}\) to \(<\)\(U_{mc}\textgreater\) and \(<\)\(U_{pc}\textgreater\), temporal variations of both velocities were obtained with respect to \(Q_{0}\) = 1, 1.5, and 2 mL/h. Here, the hematocrit was fixed at Hct = 50%. As shown in Figure 2(A-b), the peak time of \(<\)\(U_{mc}\textgreater\) tended to be short with respect to \(Q_{0}\). Under transient flow conditions, \(<\)\(U_{mc}\textgreater\) could be employed to evaluate the effect of \(Q_{0}\) on dynamic blood flows for up to \(Q_{0}\) = 2 mL/h. Under a steady state condition, \(<\)\(U_{mc}\textgreater\) increased for up to \(Q_{0}\) = 1.5 mL/h. Above \(Q_{0}\) = 2 mL/h, \(<\)\(U_{mc}\textgreater\) did not increase significantly because the high-speed camera could not accurately capture the blood flow in the main channel. As \(<\)\(U_{pc}\textgreater\) was much lower  
flow rate (\(Q_{0}\)). Because the fluidic resistance of the microfluidic channel (\(R_{c}\)) was much higher than that of the polyethylene tubing (\(R_{t}\)) (i.e., \(R_{c}>>R_{t}\)), \(R_{c}\) was only included in the fluidic circuit model. For a rectangular microfluidic channel with a low aspect ratio (i.e., depth (h)/width (w) = 10/250), \(R_{c}\) was approximated as \(R_{c}=\frac{12\mu_{B}L}{w\,h^{\alpha}}\), while \(\mu_{B}\) and \(L\) represented blood viscosity and channel length. \(P_{x}\) was then expressed as \(P_{x}=\frac{12\mu_{B}L}{w\,h^{\alpha}}\,Q_{0}\). Additionally, the shear rate (\(\dot{\gamma}\)) was estimated as \(\dot{\gamma}=\frac{6Q_{0}}{w\,h^{2}}\). In a specific range of \(Q_{0}\) = 1, 1.5, and 2 mL/h, it was estimated that the blood sample behaved as a Newtonian fluid because of \(\dot{\gamma}>10^{3}s^{-1}\). According to coflowing streams reported in a previous study [3], the corresponding blood viscosity for each hematocrit was obtained as \(\mu_{B}=1.66\pm 0.06\) cP for Hct = 30%, \(\mu_{B}=1.75\pm 0.09\) cP for Hct = 40%, and \(\mu_{B}=1.85\pm 0.06\) cP for Hct = 50%. As shown in Figure 2C, variations of \(P_{x}\) were obtained with respect to Hct and \(Q_{0}\). Using a scatter plot, \(P_{x}\) and \(\beta\) were plotted on horizontal and vertical axes, respectively. To find out the proportional constant (\(k\)) between \(P_{x}\) and \(\beta\), a linear regression analysis was conducted with EXCEL(tm) (Microsoft, Redmond, Washington, WA, USA). As shown in Figure 2D, slope (\(k\)) was estimated as \(k\) = 3.1312 (\(R^{2}\) = 0.9568). The result indicated that pressure could be obtained with \(P_{x}\) = 3.1312 \(\beta\) consistently.