## 3 Results and Discussion
### Sinusoidal Flow Rates of Blood Controlled with Syringe Pump
Figure 6C(b) showed variations of \(w_{\tau}\) with respect to \(T\) and diluent. The variation of \(w_{\tau}\) was like that of \(w_{P}\) with respect to \(T\) and the diluent. From the experimental results, the difference in the diluent (i.e., 1\(\times\) PBS, plasma) could be detected by calculating \(w_{P}\) or \(w_{\tau}\). \(T\) had a considerable influence on \(w_{P}\) and \(w_{\tau}\). Thus, it was necessary to fix the period of sinusoidal blood flow to effectively evaluate the difference in blood flow using \(w_{P}\) or \(w_{\tau}\). As the hematocrit of blood had a strong influence on blood flow, the four properties of blood flow (i.e., \(P_{r}\), \(\tau_{r}\), \(w_{P}\), and \(w_{\tau}\)) were obtained by setting Hct = 0, 20%, 30%, 40%, and 50%. Hct = 0 indicates no RBC inclusion. Each hematocrit value was adjusted by adding normal RBCs into the plasma. A driving syringe filled with blood was installed horizontally, as shown in the inset of Figure 7A(b). The period (\(T\)) of the sinusoidal blood flow was fixed at \(T\) = 360 s. As shown in Figure 7A(a), temporal variations in \(\beta\) were obtained with respect to Hct. \(\beta\) tends to increase significantly with increasing hematocrit. Figure 7A(b) showed the temporal variations of \(l_{b}\) with respect to Hct. The inset of Figure 7A(b) showed snapshots of a driving syringe filled with blood (Hct = 30%, and 50%) captured at \(t\) = 0 and \(t\) = 30 min. At lower hematocrit levels ranging from 20% to 40%, the \(l_{b}\) increased significantly over time. Due to RBC sedimentation in the driving syringe, the hematocrit of blood flowing in the guide channel for blood decreased substantially after a certain time. A decrease in hematocrit caused an increase in the \(l_{b}\). The time (\(t_{b}\)), when \(l_{b}\) started to increase substantially, tended to increase with increasing hematocrit (i.e., [a] \(t_{b}\) = 480 s for Hct = 20%, [b] \(t_{b}\) = 870 s for Hct = 30%, and [c] \(t_{b}\) = 1560 s for Hct = 40%). However, at the highest level  
Figure 6: Quantitative evaluation of four parameters (i.e., \(P_{r}\), \(\tau_{r}\), \(w_{P}\), and \(w_{\tau}\)) under sinusoidal flow patterns. Glycerin solution (20%) as reference fluid was supplied at the flow rate of 0.5 mL/h. Blood (Hct = 50%) was prepared by adding normal RBCs into diluent (1\(\times\) PBS, plasma). Blood was delivered at the flow rate of \(Q_{t}\) = 0.9 + 0.7 sin (2 \(\times\)\(\tau\)\(\times\)\(t\)/\(T\)) mL/h. Here, period (\(T\)) was set to \(T\) = 120, 240, 360, and 480 s. (**A**) Contribution of \(T\) to \(P_{r}\) (\(L_{c}\)) and \(\tau_{r}\) for normal RBCs suspended into 1\(\times\) PBS. (a) Temporal variations of \(\beta\) with respect to \(T\). (b) Variations of \(P_{r}\) (\(L_{c}\)) and \(\tau_{r}\) with respect to \(\beta\) and \(T\). (**B**) Contribution of \(T\) to \(P_{r}\) (\(L_{c}\)) and \(\tau_{r}\) for normal RBCs suspended into plasma. (a) Temporal variations of \(\beta\) with respect to \(T\). (b) Variations of \(P_{PS}\) (\(L\) = 7 mm) and \(\tau_{r}\) with respect to \(\beta\) and \(T\). (C) Contribution of diluent (1\(\times\) PBS, plasma) and \(T\) to work (\(w_{P}\), \(w_{\tau}\)). (a) Variations of \(w_{P}\) with respect to \(T\) and diluent (1\(\times\) PBS, plasma). (b) Variations of \(w_{\tau}\) with respect to \(T\) and diluent. of Hct = 50, the \(l_{b}\) remained constant over time. Figure 7B(a,b) showed variations in \(P_{r}\) (\(I_{c}\)) and \(\tau_{r}\) with respect to Hct and \(\beta\). \(P_{r}\) and \(\tau_{r}\) tended to increase at higher hematocrit levels. In addition, \(\beta\) tended to increase with increasing hematocrit levels. Based on the variations of \(P_{r}\) and \(\tau_{r}\) with respect to \(\beta\), temporal variations in \(w_{P}\) and \(w_{\tau}\) were obtained with respect to Hct. Figure 7B(c) showed the temporal variations of \(w_{P}\) with respect to Hct. Plasma (Hct = 0) did not contribute to the variation in \(w_{P}\) over time. For blood with Hct = 20%, \(w_{P}\) decreased gradually over time.