## 2 Materials and Methods  
### Microfluidic Device and Experimental Setup  
As shown in Figure 1A, the microfluidic device consisted of two guiding microchannels for two fluids (width [\(W\)] = 250 \(\upmu\)m), a coflowing channel (\(W\) = 250 \(\upmu\)m), two inlets (a, b), and one outlet. The depth (\(h\)) of all channels is set to \(h\) = 20 \(\upmu\)m. A polydimethylsiloxane (PDMS) block was replicated from a silicon master mold using microfabrication procedures, such as photolithography and soft lithography [52]. Figure 1: Proposed method for monitoring blood flows with several parameters (i.e., blood pressure, blood shear stress, blood pressure-driven work, and blood shear stress-driven work) using coflowing streams. (**A**) A microfluidic device for monitoring blood flows. The microfluidic device consists of two inlets (a, b), one outlet, guide channels for two fluids, and coflowing channels (width [\(W\)] = 250 \(\upmu\)m, and depth [\(h\)] = 20 \(\upmu\)m). Test fluid (i.e., flow rate [\(Q_{t}\)] and viscosity [\(\mu_{t}\)]: unknown) was supplied into the inlet (a). Reference fluid (i.e., flow rate [\(Q_{t}\)] and viscosity [\(\mu_{t}\)]: known) was injected into the inlet (b) with a syringe pump. (**B**) Quantification of image intensity of blood flow and interface in the coflowing channel. (a) Two regions of interest (ROIs) were selected for quantifying image intensity (\(I_{b}\)) and interface (\(\beta\)). (b) Image conversion from gray-scale image to binary-scale image for detecting the interface (\(\beta\)). \(\beta\) was defined as blood-filled width (\(W_{b}\)) in relation to channel width (\(W\)) (i.e., \(\beta\) = \(W_{b}/W\)). (**C**) Mathematical representation of coflowing streams. (a) A simple mathematical model for two streams (i.e., reference fluid stream [r] and test fluid stream [t]) using a discrete circuit model. (b) The relationship between shear stress (\(\tau\)) and pressure (\(P\)) for each compartment is decoupled with a virtual wall. (**D**) As a preliminary demonstration, glycerin (20%) was selected as a reference fluid. Blood (Hct = 30%) as test fluid was prepared by adding normal RBCs into autologous plasma. Flow rates of reference fluid (\(Q_{r}\)) and test fluid (\(Q_{t}\)) were controlled as \(Q_{r}\) = 0.5 mL/h and \(Q_{t}\) = 0.7 + 0.5 \(\sin\) (2 \(\pi\) \(t\)/360) mL/h. (a) Microscopic images captured over time (\(t\) = 84, 434, 793, 1166, 1526, and 1898 s). (b) Temporal variations of \(\beta\) and \(I_{b}\) over time. Two inlets and one outlet of the PDMS block were punched with a biopsy punch (outer diameter = 0.75 mm). Using an oxygen plasma system, a microfluidic device was fabricated by bonding the PDMS block onto a glass substrate. The microfluidic device was positioned on an inverted microscope (IX53, Olympus, Tokyo, Japan) with a 4\(\times\) objective lens (NA = 0.1). The ends of two polyethylene tubing (inner diameter = 250 \(\upmu\)m, length = 300 mm) were connected to each inlet (a, b). The end of the polyethylene tubing (inner diameter = 250 \(\upmu\)m, length = 200 mm) was tightly fitted to the outlet. To remove air from the microfluidic channels and avoid the non-specific binding of plasma proteins inside microfluidic channels, 2 mg/mL bovine serum albumin solution was supplied through the outlet. After 10 min, the microfluidic channels were filled with 1\(\times\) PBS (pH 7.4, Gibco, Life Technologies, Carlsbad, CA, USA). Two disposable syringes (~1 mL) were filled with glycerin 20% (reference fluid) and blood (test fluid). Each needle of the syringe was fitted to the open end of the individual tubing inserted into the inlet. Two syringes were then installed in a syringe pump (neMESYS, Cetoni Gmbh, Korbussen, Germany). The syringe pump was set to the flow rate of the test fluid (\(Q_{t}\)) for supplying blood in a constant or sinusoidal pattern. The viscosity of the test fluid (\(\mu_{t}\)) is not specified. The flow rate of the reference fluid remained unchanged over time (\(Q_{r}\)).