## 3 Results and Discussion
### Contributions of Hematocrit, Flow Rate, and Diluent to Pressure and Equivalent Compliance
Third, to evaluate the contributions of Hct and \(Q_{0}\) to equivalent compliance (\(C_{eq}\)), the blood sample (normal RBCs suspended into 1\(\times\) PBS) was supplied in a periodic on-off fashion (i.e., \(T\) = 480 s, \(Q_{0}\) = 1, 1.5, and 2 mL/h). The hematocrit from blood sample was set to 30-50% within a physiological range. According to the Fahraeus effect, hematocrit distribution varies depending on narrow-sized channels (i.e., capillary mimicked channels). While blood samples flow in the microfluidic channels, hematocrit tends to decrease significantly when compared with hematocrit from the blood sample in the diving syringe. As shown in Figure 3A, temporal variations of \(<\)\(U_{mc}\)\(>\) were obtained with respect to Hct = 30%, 40%, and 50%. As shown in Figure 3B, temporal variations of \(<\)\(U_{mc}\)\(>\) were obtained with respect to Hct and \(Q_{0}\) = 1.5 mL/h. To find out \(\lambda_{off}\), \(<\)\(U_{mc}\)\(>\) was assumed as \(<\)\(U_{mc}\)\(>\)\(=\)\(a_{1}\)\(+\)\(a_{2}\) exp (\(-\)/\(\lambda_{off}\)). Here, the \(\lambda_{off}\) was obtained by conducting non-linear regression analysis with Matlab (version R2018a, Mathworks, Natick, MA, USA). The inset in Figure 3C shows a discrete fluidic circuit used to extract the time constant (\(\lambda_{off}\)) under transient blood flow. The velocity inside the pressure channel was much lower than the blood velocity in the main channel. Under periodic blood flow, the circuit model was modified by including \(Q_{r}\) = 0 and \(Q_{C}\), whereby \(Q_{C}\) represented the flow rate in the compliance element. As shown in Figure 3C, variations of \(\lambda_{off}\) were obtained with respect to \(Q_{0}\) and Hct. The \(\lambda_{off}\) remained unchanged with respect to \(Q_{0}\). However, the time constant tended to increase with higher hematocrit levels. Based on Equation (6), variations of \(C_{eq}\) were obtained with respect to Hct and \(Q_{0}\). As a result, \(C_{eq}\) tended to increase considerably with respect to Hct. However, \(Q_{0}\) did not contribute to varying \(C_{eq}\). Finally, instead of using 1\(\times\) PBS as the diluent, blood samples were adjusted to Hct = 50% by adding normal RBCs into plasma. Figure 4A shows variations of \(P_{x}\) and \(\beta\) with respect to \(Q_{0}\). The inset of Figure 4A shows a linear relationship between \(P_{x}\) and \(\beta\). According to the linear regression analysis, slope (\(k\)) was obtained as \(k\) = 3.2759. When compared with normal RBCs suspended into 1\(\times\) PBS (i.e., \(k\) = 3.1312), the \(k\) of normal RBCs suspended in plasma showed a consistent value within a normalized difference range of 4.6%. Figure 4B shows variations of \(\lambda_{off}\) and \(C_{eq}\) with respect to \(Q_{0}\). The \(\lambda_{off}\) and \(C_{eq}\) remained unchanged with respect to \(Q_{0}\). When compared with the results shown in Figure 3C,D, both \(\lambda_{off}\) and \(C_{eq}\) tended to decrease with respect to \(Q_{0}\). From the results, the blood pressure at the junction (\(P_{x}\)) and the equivalent compliance (\(C_{eq}\)) varied significantly with respect to Hct and \(Q_{0}\). For this reason, for consistent measurement of \(P_{x}\) and \(C_{eq}\), \(Q_{0}\) and Hct were fixed as \(Q_{0}\) = 1.5 mL/h and Hct = 50% throughout all experiments. At the Section S2 (Supplementary Materials), contribution of erythrocyte sedimentation rate (ESR) in driving syringe to pressure and equivalent compliance were evaluated experimentally. In conclusion, blood pressure (\(P_{x}\)) did not provide consistent variations with respect to \(C_{dx}\). Additionally, equivalent compliance (\(C_{eq}\)) gave constant values with respect to \(C_{dx}\). However, as shown in Figure S1(A-b) (Supplementary Materials), the image intensity (\(<\)\(l_{mc}\)\(>\)) showed significant difference with respect to \(C_{dx}\).