## 3 Results and Discussion
### Quantitative Comparison of the Present Method and Previous Method  
To evaluate the performance of the present method, two quantities obtained at a constant flow rate and transient flow rate were compared with those obtained with the previous method. In other words, under a constant blood flow rate, pressure (\(P_{x}\)) obtained by the present method was compared with blood viscosity (\(\mu_{B}\)) obtained by the previous method. Additionally, under the transient blood flow rate, the equivalent constant (\(C_{eq}\)) obtained by the present method was compared with the elasticity (\(G_{B}\)) obtained by the previous method [23]. Figure 4: Quantitative evaluations of pressure (\(P_{x}\)) and equivalent compliance (\(C_{eq}\)) for the blood sample (normal RBCs in plasma, hematocrit (Hct) = 50%). (**A**) Variations of \(\beta\) and \(P_{x}\) with respect to flow rate (Q\({}_{0}\)). (**B**) Variations of time constant (\(\lambda_{\textit{off}}\)) and \(C_{eq}\) with respect to \(Q_{0}\). Figure 3: Quantitative evaluation of compliance coefficient (\(C_{eq}\)). (**A**) Temporal variations of averaged blood velocity in main channel (\(<\)\(U_{mc}\)\(>\)) with respect to hematocrit (Hct) = 30%, 40%, and 50%. (**B**) Variations of \(<\)\(U_{mc}\)\(>\) under transient blood flows. (**C**) Variations of time constant (\(\lambda_{\textit{off}}\)) with respect to Hct and flow rate (Q\({}_{0}\)). (**D**) Variations of \(C_{eq}\) with respect to Hct and \(Q_{0}\). First, blood pressure (\(P_{x}\), present method) and blood viscosity (\(\mu_{B}\), previous method) were measured simultaneously for the same fixed blood sample. To vary the RBC deformability, normal RBCs were fixed chemically with various concentrations of glutaraldehyde(GA) solution (\(C_{GA}=0,2\), 4, 6, 8, and 10 \(\mu\)L/mL). \(C_{GA}=0\) denoted 1\(\times\) PBS as the diluent. The fixed blood sample (Hct = 50%) was prepared by adding homogeneous fixed RBCs into 1\(\times\) PBS. As shown in Figure 5A, after setting the blood flow rate from \(Q_{0}=1.5\) mL/h to \(Q_{0}=0\), temporal variations of \(<\)\(U_{pc}\)\(>\) for a half period were obtained with respect to \(C_{GA}=0\), 6, and 10 \(\mu\)L/mL. Higher concentrations of the GA solution contributed to substantially increasing the magnitude of \(<\)\(U_{pc}\)\(>\). Bases on Equations (1) and (2), variations of \(\beta\) and \(P_{x}\) were obtained with respect to \(C_{GA}\). As shown in Figure 5B, \(\beta\) and \(P_{x}\) tended to increase distinctively with higher concentrations of the GA solution. The variations of \(\beta\) and \(P_{x}\) exhibited consistent trends because the GA solution contributed to stiffening the plasma membranes of the RBCs. When compared with the blood pressure obtained with the present method, blood viscosity for the same blood sample was quantified with coflowing streams, as in the previous method [4]. As shown in the inset of Figure 5C, the blood sample and the 1\(\times\) PBS were supplied into a T-shaped channel at the same flow rate (i.e., \(Q_{B}=Q_{PBS}=1.5\) mL/h) with two syringe pumps. According to the coflowing method, blood viscosity (\(\mu_{B}\)) was approximately derived as \(\mu_{B}=\mu_{PBS}\cdot C_{f}\cdot a_{B}/(1-\alpha_{B})\). To compensate for the model error resulting from difference in the boundary condition between the simple mathematical model and real physical model, the correction factor (\(C_{f}\)) was included as \(C_{f}=1.4929\ \alpha_{B}{}^{4}-2.9858\ \alpha_{B}{}^{3}+2.6301\ \alpha_{B}{}^{2}-1.1372\ \alpha_{B}+1.1971\ (R^{2}=0.9874)\). Blood viscosity was then estimated by monitoring the blood-filled width (\(\alpha_{B}\)). As shown in Figure 5C, the corresponding viscosity for each \(C_{GA}\) was obtained as \(\mu_{B}=1.427\ \pm 0.016\) cP (\(C_{GA}=0\)), \(\mu_{B}=1.485\ \pm 0.0.026\) cP (\(C_{GA}=2\ \mu\)L/mL), \(\mu_{B}=1.499\ \pm 0.025\) cP (\(C_{GA}=4\ \mu\)L/mL), \(\mu_{B}=1.611\ \pm 0.034\) cP (\(C_{GA}=6\ \mu\)L/mL), \(\mu_{B}=2.071\ \pm 0.106\) cP (\(C_{GA}=8\ \mu\)L/mL), and \(\mu_{B}=2.460\ \pm 0.1\) cP (\(C_{GA}=10\ \mu\)L/mL).