## 3 Results and Discussion
### Sinusoidal Flow Rates of Blood Controlled with Syringe Pump  
Instead of glycerin solutions as the test fluid, the present method was applied to quantify four properties of blood flows (i.e., pressure, shear stress, pressure unit volume work, and shear stress unit volume work) under sinusoidal flow rates. To clearly detect the interface in the coflowing channel, a glycerin solution (20%) was supplied as a reference fluid. The flow of the reference fluid was set to 0.5 mL/h. Blood (Hct = 50%) as the test fluid was prepared by adding normal RBCs into a diluent (1\(\times\) PBS, plasma). The blood flow rate set to \(Q_{t}\) = 0.9 + 0.7 sin (2 \(\times\)\(\pi\times t/T\)) mL/h. The period (\(T\)) set to \(T\) = 120, 240, 360, and 480 s. The contributions of the period to \(P_{r}\) (\(L_{c}\)) and \(\tau_{r}\) were evaluated for normal RBCs suspended in 1\(\times\) PBS and plasma. Figure 6A(a) showed the temporal variations of \(\beta\) with respect to \(T\). When \(T\) increased from 120 s to 480 s, the alternating amplitude of \(\beta\) (\(\Delta\beta\)) (i.e., \(\Delta\beta\) = maximum value of \(\beta\)--minimum value of \(\beta\)) tended to decrease gradually. Figure 6A(b) showed the variations of \(P_{r}\) (\(L_{c}\)) and \(\tau_{r}\) with respect to \(\beta\) and \(T\). Four trajectories represented between \(P_{r}\) and \(\beta\) overlapped nearly with respect to \(T\). \(\tau_{r}\) showed similar trends to \(P_{r}\) with respect to \(T\). On the other hand, while replacing 1\(\times\) PBS with plasma as a diluent, contributions of \(T\) to \(P_{r}\) (\(L_{c}\)) and \(\tau_{r}\) were obtained for normal RBCs suspended in plasma. Figure 6B(a) showed the temporal variations of \(\beta\) with respect to \(T\). When compared with 1\(\times\) PBS as diluent, plasma as diluent contributed substantially to increasing \(\beta\). The \(\Delta\beta\) tended to decrease at higher values of \(T\). Figure 6B(b) showed  
Figure 5: Quantitative evaluations of four parameters (i.e., pressure, shear stress, pressure-unit volume work, and shear stress-unit volume work) under the sinusoidal fluid flow of test fluid. 1\(\times\) PBS as reference fluid was supplied at the flow rate of 1 mL/h. Glycerin solution (\(C_{glycerin}\) = 30%) as test fluid was supplied at the flow rate of \(Q_{t}\) = 0.9 + 0.7 sin (2 \(\times\)\(\pi\times t/T\)) mL/h. (**A**) Variations of \(P_{r}\) and \(\tau_{r}\) with respect to \(T\) = 120, 240, 360, and 480 s. (a) Temporal variation of \(\beta\) with respect to \(T\). (b) Variation of \(P_{s}\) (\(L_{c}\)) with respect to \(T\) and \(\beta\). (c) Variations of \(\tau_{r}\) with respect to \(T\) and \(\beta\). (**B**) Definition of work per unit volume (\(w_{p}\), and \(w_{\tau}\)) obtained from \(P_{r}\) and \(\tau_{r}\) during a single period. (a) Variations of \(P_{r}\) (\(L_{c}\)) and \(\tau_{r}\) with respect to \(\beta\). Based on variations of \(P_{r}\) and \(\tau_{r}\), pressure-unit volume work (\(w_{p}\)) and shear stress-unit volume work (\(w_{\tau}\)) were calculated as \(w_{p}=\int_{\beta_{1}}^{\beta_{2}}P_{r}\delta\) and \(w_{\tau}=\int_{\beta_{1}}^{\beta_{2}}\tau_{r}\delta\), respectively. (b) Variations of \(w_{p}\) with respect to \(T\). (c) Variations of \(w_{\tau}\) with respect to \(T\). variations in \(P_{r}\) (\(L_{c}\)) and \(\tau_{r}\) with respect to \(\beta\) and \(T\). When compared with Figure 6A(b), the pressure (\(P_{r}\)) and shear stress (\(\tau_{r}\)) increased substantially. However, \(P_{r}\) and \(\tau_{r}\) did not show substantial differences in trajectories (i.e., \(P_{r}\) vs. \(\beta\), \(\tau_{r}\) vs. \(\beta\)). Furthermore, two works (\(w_{P}\), \(w_{\tau}\)) were obtained by analyzing \(P_{r}\) and \(\tau_{r}\) with respect to \(\beta\). Figure 6C(a) showed variations in \(w_{P}\) with respect to \(T\) and diluent (1\(\times\) PBS, plasma). Plasma as a diluent caused a significant increase _in_\(w_{P}\) when compared with 1\(\times\) PBS as a diluent. Additionally, \(w_{P}\) increased potentially with respect to \(T\).