## 2 Materials and Methods
### Quantification of Blood Pressure and Compliance Properties  
As a preliminary demonstration, the blood sample (normal RBCs in 1\(\times\) PBS, Hct = 50%) was supplied into inlet with single syringe pump (i.e., \(T\) = 480 s, \(Q_{0}\) = 1.5 mL/h). Figure 1(C-a) shows a microscopic image captured at specific time (\(t\) = 0, 60, 120, 180, 240, 300, 360, and 420 s) during a single period. After turning on the syringe pump (\(Q_{0}\) = 1.5 mL/h), the blood pressure at the junction increased over time. Then, the blood sample flowed forward in the pressure channel. After 60 s, the pressure reached equilibrium in the pressure channel. The RBCs then stopped moving forward over time. Because there was no existence of RBCs in the pressure channel, it was impossible to visualize blood flows. After turning off the syringe pump (\(Q_{0}\) = 0), the blood pressure decreased over time. The blood sample flowed backwards for the remaining time of the period (\(240\) s \(<t<480\) s). As the pressure channel was filled with the blood sample sufficiently, velocity fields of blood flows (\(U_{pc}\)) were obtained accurately with respect to time. Figure 1(C-b) shows temporal variations of \(<\)\(U_{mc}\)\(>\) and \(<\)\(U_{pc}\)\(>\) during the single period. Backward blood flow gave more consistent values of \(<\)\(U_{pc}\)\(>\) than forward blood flow. Thus, \(<\)\(U_{pc}\)\(>\) obtained under a backward blood flow was used to estimate pressure. Based on the mathematical formula of the compliance element, the pressure at junction (\(P_{x}\)) can be derived as:  
\[P_{x}=\left(\frac{A_{c}}{C_{f}}\right)\beta=k\cdot\beta \tag{1}\]  
In Equation (1), \(A_{c}\) and \(C_{f}\) mean the cross-sectional area and coefficient of compliance, respectively; \(\beta\) is expressed as Equation (2):  
\[\beta=\int\limits_{0.5T}^{T}|U_{pc}|dt \tag{2}\]  
Because \(k=A_{c}/C_{f}\) has a constant value in Equation (1), pressure (\(P_{x}\)) was only determined by \(\beta\). Here, a microfluidic system was modeled with discrete fluidic circuit elements, including the flow rate (\(Q_{B}\), \(Q_{m}\)), resistance (\(R_{c}\)), and equivalent compliance (\(C_{eq}\)). \(Q_{B}\) and \(Q_{m}\) indicate the blood flow rate supplied from the syringe pump and the blood flow rate flowing in the main channel, respectively. \(R_{c}\) represents the fluidic resistance of the main channel filled with the blood sample. The fluidic resistance of the microfluidic channel (\(R_{c}\)) was much higher than that of the tubing (\(L_{2}\)) (\(R_{t}\)) connected to outlet (a) (i.e., \(R_{c}>>R_{t}\)). For this reason, \(R_{c}\) was only included in the fluidic circuit model. The equivalent compliance represents the summation of the tube compliance (\(C_{t}\)), channel compliance (\(C_{c}\)), and RBC compliance (\(C_{RBCs}\)) (i.e., \(C_{eq}=C_{t}+C_{c}+C_{RBCs}\)). Based on mass conservation at the junction (\(x\)), Equation (3) was derived as:  
\[Q_{B}=\frac{P_{x}}{R_{c}}+C_{eq}\frac{d}{dt}\ (P_{x}) \tag{3}\]  
In Equation (3), if \(P_{x}/R_{c}\) is replaced with \(Q_{m}\) (i.e., \(P_{x}/R_{c}=Q_{m}\)), Equation (1) can be simplified as:  
\[R_{c}\text{-}C_{eq}\frac{d}{dt}\ (Q_{m})+Q_{m}=Q_{B} \tag{4}\]  
Because \(Q_{m}\) is expressed as \(Q_{m}=A_{c}\text{-}\text{<}U_{mc}\textgreater\), Equation (4) becomes Equation (5):  
\[\lambda_{off}\frac{d}{dt}\ (<U_{mc}>)+<U_{mc}>\ =\frac{Q_{B}}{A_{c}} \tag{5}\]  
In Equation (5), the time constant (\(\lambda_{off}\)) is represented as \(\lambda_{off}=R_{c}\text{-}C_{eq}\). Because \(P_{x}\) is expressed as \(P_{x}=R_{c}\text{-}Q_{0}\), an equivalent compliance (\(C_{eq}\)) can be derived as:  
\[C_{eq}=\lambda_{off}\cdot Q_{0}/P_{x} \tag{6}\]  
According to Equation (6), three factors (i.e., \(\lambda_{off}\), \(Q_{0}\), and \(P_{x}\)) were used to estimate equivalent compliance. As shown in Figure 1(C-b), using transient behaviors of \(<\)\(U_{mc}\textgreater\), \(\lambda_{off}\) was obtained by conducting regression analysis with the model (i.e., \(<\)\(U_{mc}\textgreater\) = \(a_{1}+a_{2}\) exp (\(-\)\(t/\lambda_{off}\))).