A Pulsatile Flow-Modulation Microfluidic Sensor for Simultaneous Monitoring of Red Blood Cell Aggregation and Viscosity-Sensitive Time Constant

1. Introduction

Red blood cell (RBC) aggregation is regarded as a key hemorheological phenomenon that has a strong impact on blood viscosity and fluidic resistance, thereby potentially influencing tissue perfusion under low shear rates [1,2,3,4]. Because RBC aggregation modulates microvascular flow resistance and oxygen transport, its quantitative assessment is clinically important for evaluating hemorheological alterations associated with inflammation, cardiovascular and metabolic disorders, and hematological diseases [5,6,7,8]. In addition, RBC aggregation is governed by multiple hematological factors, including plasma protein concentration, hematocrit, RBC morphology [9], cellular deformability [10], and membrane viscoelastic properties [3,6,11]. Therefore, reliable RBC aggregation assessment requires quantifying aggregation while considering key modulatory blood conditions, particularly hematocrit and plasma composition, which can affect disaggregation shear-rate determination and aggregation measurements [12,13,14].

In conventional RBC aggregation assays, test blood is loaded into a measurement chamber and subjected to a high-shear field for a sufficient period to disrupt pre-existing aggregates. The external driving source, such as a vacuum pump [15], syringe pump [13], solenoid valve [16], or vibrational motor [17,18], is then abruptly turned off to stop blood flow, allowing RBC re-aggregation to occur under near-stagnant or low-shear conditions. The resulting aggregation process is subsequently monitored to determine aggregation kinetics or aggregation indices [19]. That is, several detection methods, including optical method (LED or photodiode) [18], electrical impedance [20,21], and ultrasound [14,22], and microscopic imaging [23,24] are adopted to quantify RBC aggregation. The RBC aggregation index (AI) is subsequently determined from the temporal syllectogram recorded during RBC re-aggregation. Although the previous methods can provide quantitative aggregation indices, they are often limited when the hematocrit or suspending medium changes under continuous flow or circulation conditions [13].

More recently, to resolve the critical issues raised by the previous methods, continuous flow-dependent RBC aggregation has been assessed using microfluidic bifurcation channels [13]. Herein, a single blood flow is divided into low-flow and high-flow branches, where RBC aggregation is promoted in the low-flow channel and dispersed in the high-flow channel. The aggregation index is calculated from time-lapse image intensities in both channels. Considering that hematocrit or plasma medium can be varied under continuous blood delivery [25,26,27,28], the previous method has been further improved to simultaneously measure blood viscosity and RBC aggregation [29]. However, the previous method relies on two precision pumps to introduce the reference fluid and test blood sample simultaneously. Continuous infusion of 1× PBS can gradually dilute the test blood, making it difficult to distinguish true RBC alterations from hemodilution-induced changes during continuous blood flow [30,31,32]. To overcome this limitation, direct viscosity measurement using a reference fluid should be replaced by indirect viscosity-sensitive parameters [33,34].

In this study, we propose a microfluidic sensing method for simultaneous assessment of RBC aggregation and a viscosity-sensitive time constant under continuous pulsatile blood flow. The proposed device is designed to generate two distinct flow environments: a low-flow test chamber for inducing and measuring RBC aggregation and a high-flow main channel for analyzing transient velocity responses. A single syringe pump is adopted to generate a pulsatile blood-flow profile. In particular, in the low-flow test chamber, RBC aggregation is quantified using a position-dependent aggregation index derived from image intensity along the test chamber. This approach allows spatially resolved evaluation of RBC aggregation. In the high-flow main channel, the time-dependent velocity of blood flow is measured and analyzed by regression to obtain a viscosity-sensitive time constant, which reflects changes in the state of blood delivered from the syringe.

Compared with previous methods that measure RBC aggregation alone [35], estimate viscosity using co-flow interface tracking [29,30], or perform sequential pressure or aggregation analysis, the proposed method enables simultaneous assessment of RBC aggregation and a viscosity-sensitive time constant in a single microfluidic platform under continuous pulsatile blood flow. By combining position-dependent image-based aggregation analysis in a low-flow test chamber with velocity-based regression analysis in a high-flow main channel, the method can monitor both aggregation behavior and flow-response changes without reference-fluid infusion. Therefore, it reduces hemodilution-related artifacts and provides a practical sensing strategy for detecting hemorheological alterations caused by hematocrit or medium-dependent changes in continuously delivered blood.

2. Materials and Methods

2.1. Microfluidic Chip Fabrication and Experimental Setup

A novel microfluidic platform was suggested for probing viscosity-sensitive time constant and RBC aggregation index in continuous pulsatile blood flow.

As shown in Figure 1A, the experimental setup consisted of a microfluidic chip, a single syringe pump, and a microscopic imaging system. As shown in Figure 1A-i, the microfluidic chip comprised a single inlet, a rectangular main channel (mc) (width = 1 mm, length = 14.9 mm), a bifurcation channel, and a large outlet. The main and bifurcation channels were connected to the outlet. The bifurcation channel contained a large test chamber (tc) (width = 1 mm, length = 2 mm) positioned between two narrow guide channels (width = 0.1 mm, length = 6.89 mm). The channel depth was fixed at h = 50 μm throughout the device.

The microfluidic device was fabricated by PDMS replica molding from a silicon master, which was patterned using conventional photolithography and etched by deep reactive ion etching, following standard soft-lithography and MEMS micromachining procedures [36,37]. For PDMS replica molding, Sylgard 184 elastomer base and curing agent (Dow Corning, Midland, MI, USA) were mixed at a 10:1 weight ratio. The uncured PDMS mixture was degassed in a vacuum chamber for 1 h and subsequently cured at 65 °C for 2 h. After curing, the PDMS replica was gently peeled off from the silicon master, trimmed to the required dimensions, and punched to form an inlet port with an outer diameter of 2 mm. A large outlet port was also created using a punch with an outer diameter of 3 mm. Finally, the PDMS layer was irreversibly sealed onto a glass substrate after oxygen plasma activation using a plasma treatment system (CUTE-MPR, Femto Science Co., Ltd., Hwaseong-si, Republic of Korea). The assembled chip was further heated at 120 °C for 10 min for enhancing bonding strength between the PDMS and glass surfaces.

As shown in Figure 1A-ii, a single syringe equipped with a 20-gauge needle was loaded with blood (V_b = 0.5 mL). To introduce air compliance into the blood-delivery system, an air cavity (V_air) was maintained above the blood column inside the syringe [38]. A trapped gas volume can function as a hydraulic capacitor that absorbs flow fluctuations and modifies the transient response of syringe-pump-driven microfluidic systems [39,40,41,42,43]. The needle tip was connected to one end of polyethylene tubing (inner diameter = 0.25 mm, length = 200 mm), while the other end of the tubing was inserted into the inlet port of the microfluidic device. To minimize nonspecific protein adsorption, the microchannels were pretreated with 0.2% bovine serum albumin (BSA) for 10 min. The channels were then rinsed with 1× PBS to remove residual BSA before blood infusion. The syringe was mounted on a syringe pump (neMESYS, Cetoni Gmbh, Korbussen, Germany). The pump was programmed to generate a pulsatile blood flow rate profile. The flow rate (Q_sp) was set to Q_sp = Q_h for the high-flow interval (0 < t < t_h) and Q_sp = Q_l mL/h for the low-flow interval (t_h < t < T), with one cycle period defined as T = t_h + t_l.

The microfluidic chip was mounted on an inverted microscope (IX81, Olympus, Tokyo, Japan) equipped with a 4× objective lens (NA = 0.1). Microscopic images of blood flow were acquired at 5000 frames per second (fps) using a high-speed camera (FASTCAM MINI, Photron, Tokyo, Japan). Image acquisition was triggered at 0.5 s interval using a function generator. All experiments were performed at room temperature (25 °C).

2.2. Quantification of Blood Velocity and Microscopic Image Intensity

Blood velocity was measured separately in the main channel and test chamber. The velocity response in the main channel was used to determine the viscosity-sensitive time constant, while the velocity in the test chamber was used to estimate the low-shear-rate condition for RBC aggregation. RBC aggregation was then quantified from the spatial distribution of image intensity along the test chamber.

First, as shown in Figure 1B-i, to obtain the average velocity in each channel, the region-of-interest (ROI) (1.7 mm²) was defined in the upper portion of the main channel and in the straight section of the test chamber, respectively. Velocity fields were obtained from time-lapse image sequences using PIVlab (version 3.12) [44] with an interrogation window of 129 × 129 µm² and 50% overlap. The calculated velocity vectors were subsequently filtered using local median and standard-deviation filters. For the optical measurement system used in this study, the depth of correlation (DOC) was estimated to exceed 300 µm, which was substantially greater than the channel depth of 50 µm [45]. According to the micro-PIV depth-of-correlation theory [46,47], all RBCs located through the illuminated depth direction could contribute to the recorded correlation signals. Therefore, the measured velocity vectors were regarded as depth-averaged velocities across the channel depth. Within each channel, the velocity vectors were spatially averaged over the selected ROI. The resulting time-dependent mean velocities in the main channel and test chamber were defined as U_mc and U_tc, respectively.

Second, the initial background image was subtracted from each acquired image, and the resulting images were analyzed using MATLAB (version 2025b, MathWorks, Natick, MA, USA). As shown in the upper panel of Figure 2B-ii, a small ROI (0.04 mm²) was selected within the straight region of the test chamber and translated along the x-direction from the left boundary to the right boundary. The mean grayscale intensity at each position was defined as (I_tc [x]). The arrow indicated blood flow direction left to right. As blood moved from the narrow guide channel into the wider test chamber, local shear rate decreased substantially. RBC aggregation was continuously induced under low-shear conditions. As shown in the lower panel of Figure 2B-ii, the I_tc (x) gradually increased along the 2-mm chamber length, reflecting the progression of RBC aggregation. The spatial intensity distribution was then used to determine two parameters (S_a, S_b), following the conventional aggregation-index definition [18,21,48], and the RBC aggregation index was calculated as (AI = Sa/(S_a + S_b).

2.3. A Lumped Parameter Modeling for Estimating Time Constant and Shear Rate

As shown in Figure 1C, a simplified mathematical model was established to estimate viscosity-dependent time-constant and shear rate in test chamber, under pulsatile blood flow conditions.

As shown in Figure 1C-i, air cavity was maintained above blood volume inside the syringe. Q_sp and Q_m denoted flow rate of syringe pump and flow rate through tubing, respectively. From the mass conservation law [49], the temporal change in air cavity could be expressed as,

$${\displaystyle \frac{\mathit{d}}{\mathit{d}\mathit{t}}}\left({\mathit{V}}_{\mathit{a}\mathit{i}\mathit{r}}\right)={-\mathit{Q}}_{\mathit{s}\mathit{p}}+{\mathit{Q}}_{\mathit{m}}$$

(1)

Assuming that the air cavity follows the ideal-gas law [50], the relationship between the initial and instantaneous air cavity volume was given by P₀ V₀ = P_s V_air, where P₀ was the atmosphere pressure, V₀ was initial air cavity, P_s was air pressure inside the syringe. Thus, the instantaneous air cavity was written as V_air = P₀V₀/P_s. Differentiating V_air with respect to time gave the Eqn (2) [43],

$$\begin{gathered} {\displaystyle \frac{\mathit{d}}{\mathit{d}\mathit{t}}}\left({\mathit{V}}_{\mathit{a}\mathit{i}\mathit{r}}\right)={\displaystyle \frac{\mathit{d}}{\mathit{d}{\mathit{P}}_{\mathit{s}}}}\left({\displaystyle \frac{{\mathit{P}}_0{\mathit{V}}_0}{{\mathit{P}}_{\mathit{s}}}}\right){\displaystyle \frac{\mathit{d}{\mathit{P}}_{\mathit{s}}}{\mathit{d}\mathit{t}}}, \\ =-{\mathit{C}}_{\mathit{f}}{\displaystyle \frac{\mathit{d}{\mathit{P}}_{\mathit{s}}}{\mathit{d}\mathit{t}}} \end{gathered}$$

(2)

In Eqn (2), compliance coefficient (C_f) was defined as,

$${\mathit{C}}_{\mathit{f}}={\displaystyle \frac{{\mathit{P}}_0{\mathit{V}}_0}{{{\mathit{P}}_{\mathit{s}}}^2}}$$

(3)

The Eqn (1) was then simplified as the Eqn (4) as,

$${\mathit{Q}}_{\mathit{s}\mathit{p}}={\mathit{Q}}_{\mathit{m}}+{\mathit{C}}_{\mathit{f}}{\displaystyle \frac{\mathit{d}{\mathit{P}}_{\mathit{s}}}{\mathit{d}\mathit{t}}}$$

(4)

Equation (4) indicated that the imposed syringe-pump flow rate was divided into the flow delivered through the tubing and the flow associated with compression or expansion of the air cavity [51]. Based on this relationship, the air cavity was represented as a compliance element in the equivalent fluidic circuit shown in the left panel of Figure 1C-i. In the circuit, GND (▼) denoted zero value of gauge pressure. P_j represented pressure at the junction point where the bifurcation channel was branched from the main channel. Q_b denoted the flow rate through the bifurcation channel. Based on Hagen-Poiseuille law (pressure drop [ΔP] = flow rate [Q] × fluidic resistance [R]) [49], frictional loss in channel or tubing was represented as a fluidic resistance element (R). As shown in Figure 1C-ii, a lumped fluidic circuit model was established for the proposed microfluidic system. The model consisted of a syringe pump, a tubing, and a microfluidic channel. The syringe pump was represented by a flow-rate source coupled with a compliance element (C_f), whereas the tubing was modeled as a hydraulic resistance (R_t). The microfluidic channel was described using the hydraulic resistances of the main channel and bifurcation channel, which were denoted as R_m and R_b, respectively. Herein, R_b represented the equivalent hydraulic resistance of the two guide channels and the large test chamber connected in series. By applying mass conservation at junction (j), the transient flow response through the main channel could be expressed as

$${\mathit{\lambda }}_1{\displaystyle \frac{\mathit{d}}{\mathit{d}\mathit{t}}}\left({\mathit{Q}}_{\mathit{m}}\right)+{\mathit{Q}}_{\mathit{m}}={\mathit{Q}}_{\mathit{s}\mathit{p}}$$

(5)

where Q_sp was the flow rate imposed by the syringe pump and Q_m was the flow rate through the main channel. The corresponding time constant was given by

$${\mathit{\lambda }}_1={\mathit{C}}_{\mathit{f}}({\mathit{R}}_{\mathit{m}}+{\mathit{R}}_{\mathit{t}}+{\displaystyle \frac{{\mathit{R}}_{\mathit{m}}{\mathit{R}}_{\mathit{b}}}{{\mathit{R}}_{\mathit{m}}+{\mathit{R}}_{\mathit{b}}}})$$

(6)

Since the equivalent hydraulic resistance was directly dependent on the apparent viscosity of blood, an increase in blood viscosity led to an increase in the flow-response time constant under the same air compliance. Therefore, the flow-response time constant could provide a physically grounded and experimentally accessible index for assessing viscosity-related hemorheological variations in the proposed microfluidic system.

As shown in Figure 1C-iii, the time-dependent syringe pump flow rate (Q_sp) was defined as Q_sp = Q_h for 0 < t < t₁ and Q_sp = Q_l for t₁ < t < T. To minimize the influence of RBC aggregation on the blood viscosity, the time constant was determined under sufficiently high shear rate conditions ($\dot{\mathit{\gamma }}$ > 10³ s^-1). Therefore, within one period (T), the analytical solution for Q_m was derived for the transient interval, when the Q_sp was changed from Q_h to Q_l. Under this transient flow-rate condition, solving the Eqn (5) provided Q_m as,

$${\mathit{Q}}_{\mathit{m}}\left(\mathit{t}\right)=({\mathit{Q}}_{\mathit{h}}-{\mathit{Q}}_{\mathit{l}})\mathit{e}\mathit{x}\mathit{p}(-{\displaystyle \frac{\mathit{t}-{\mathit{t}}_1}{{\mathit{\lambda }}_1}})+{\mathit{Q}}_{\mathit{l}}$$

(7)

In the Eqn (7), ${\mathit{Q}}_{\mathit{m}}\left(\mathit{t}\right)$ in the main channel could be expressed as ${\mathit{Q}}_{\mathit{m}}\left(\mathit{t}\right)={\mathit{U}}_{\mathit{m}\mathit{c}}\left(\mathit{t}\right){\mathit{A}}_{\mathit{m}\mathit{c}}$, where U_mc was the time-dependent mean velocity and A_mc was the cross-sectional area of the main channel. The time constant (λ₁) was obtained by regression analysis of the time-lapse U_mc (t) data during the flow-rate transition from Q_h to Q_l.

To estimate shear rate in the test chamber, the syringe flow rate was assumed as a constant value of Q_sp = Q₀. Based on mass conservation at the junction point (‘j’), pressure at the junction (P_j) was derived as,

$${\mathit{P}}_{\mathit{j}}={\displaystyle \frac{{\mathit{R}}_{\mathit{m}}{\mathit{R}}_{\mathit{b}}}{{\mathit{R}}_{\mathit{m}}+{\mathit{R}}_{\mathit{b}}}}{\mathit{Q}}_{\mathit{s}\mathit{p}}$$

(8)

Dividing P_j with R_b gave the expression of Q_b as,

$${\mathit{Q}}_{\mathit{b}}={\displaystyle \frac{{\mathit{Q}}_{\mathit{s}\mathit{p}}}{1+\frac{{\mathit{R}}_{\mathit{b}}}{{\mathit{R}}_{\mathit{m}}}}}$$

(9)

With regard to microfluidic channel proposed in this study, the fluidic resistance ratio (R_b/R_m) was calculated as R_b/R_m = 18.76. As shown in left panel of Figure 1C-iv, variations of flow rate in the bifurcation (Q_b) were estimated by increasing Q_sp ranging from 0.5 mL/h to 9.5 mL/h. As expected, the Q_b was linearly proportional to Q_sp. In the inset of Figure 1C-iv, the arrow (‘←’) denoted blood flow direction in the bifurcation channel. The right-side panel depicted the corresponding shear rate profiles in test chamber and guide channel, respectively. Considering that RBC aggregation was mainly promoted under low shear rate conditions ($\dot{\mathit{\gamma }}<100{\mathit{s}}^{-1}$) [5,25,52,53,54], RBC aggregation could be observed in the yellow region, which corresponded to Q_sp < 3 mL/h. In contrast, no appreciable RBC aggregation was detected within the selected range of Q_sp.

2.4. Test Blood Preparation

A packed RBC unit was provided by the Gwangju–Chonnam Blood Bank (Gwangju, Republic of Korea) and maintained at refrigerated temperature before experiments. For sample preparation, normal RBCs were collected using an established washing protocol [55,56]. After centrifugation, the supernatant containing the storage medium and washing buffer was carefully aspirated, and the buffy coat layer was subsequently removed to minimize leukocyte and platelet contamination. The RBC pellet was then resuspended in 1× PBS, and this washing procedure was repeated twice to minimize residual storage solution in the RBC suspension.

To systematically characterize the flow-response time constant and RBC aggregation, two different sets of test blood were prepared by varying hematocrit and blood medium. First, the effect of hematocrit (ϕ_vol) was examined using normal RBCs suspended into 1% dextran solution, where hematocrit was set from 20% to 60%. The dextran solution was prepared by dissolving dextran powder (Leuconostoc spp., MW 450–650 kDa, Sigma-Aldrich, St. Louis, MO, USA) into 1× PBS. Second, medium-dependent response was evaluated by varying the dextran concentration from 1% to 4% at a fixed hematocrit of ϕ_vol = 50%.

2.5. Statistical Analysis

Statistical analyses were performed using MINITAB software (version 22.4, Minitab Inc., State College, PA, USA) and Microsoft Excel 365 (Microsoft, Redmond, WA, USA). Assuming normal distribution, all measured values were presented as mean (x̅) ± standard deviation (σ). Sample size was denoted as n. 95% confidence interval (CI) was estimated calculated using x̅ − 1.96 σ/$\sqrt{\mathit{n}}$ and x̅ + 1.96 σ/$\sqrt{\mathit{n}}$ as the lower and upper limits, respectively. Difference among groups were evaluated using one-way ANOVA. Statistical significance was defined as p-value < 0.05. Linear regression analysis was performed to assess the correlation between paired variables.

3. Results and Discussion

3.1. Demonstration of the Proposed Method

To demonstrate the proposed method, viscosity-sensitive time constant and RBC aggregation index (AI) were obtained for control blood and test blood. Herein, hematocrit of both bloods (test blood, control blood) was adjusted to ϕ_vol = 0.5 by adding normal RBCs into dextran (C_dex = 2%) and 1× PBS, respectively. Air cavity (V_air = 0.1 mL) was maintained above blood column (V_b = 0.5 mL) inside the syringe. The syringe pump was set to generate a pulsatile flow profile (i.e., Q_h = 6 mL/h for 0 < t < 2 min, Q_l = 1 mL/h for 2 min < t < 6 min, and T = 6 min).

As shown in Figure 2A, time-lapse RBC aggregation index was obtained for control and test bloods. Figure 2A-i showed temporal variations of blood velocity and RBC aggregation index for control blood. The left panel represented temporal variations of blood velocity (U_mc, U_tc) and Q_sp. The middle panel depicted temporal variations of RBC aggregation index (AI) and Q_sp. The right panel showed microscopic blood-flow images in test channel captured at t = 50 s and 290 s. As control blood did not induce RBC aggregation in test chamber, microscopic image did not exhibit substantial variations. In contrast, control blood was replaced by test blood. As shown in Figure 2A-ii, temporal variations of blood velocity and RBC aggregation index were acquired for test blood. The left panel represented timelapse U_mc, U_tc, and Q_sp. When the syringe flow rate was switched from Q = 6 mL/h to Q = 1 mL/h, test blood exhibited a longer transient response than the control blood. The middle panel depicted time-dependent AI and Q_sp. The aggregation index (AI) increased substantially under the low flow condition (Q = 1 mL/h), whereas it remained relatively low at the high flow rate (Q = 6 mL/h). The right panel showed microscopic blood-flow images in test channel captured at t = 50 s and 290 s. At the high flow rate (t = 50 s), no appreciable morphological difference was observed between the test and control bloods. However, at the low flow rate (t = 290 s), pronounced RBC aggregation led to a marked increase in cell-free void regions.

As shown in Figure 2B, the time constant and RBC aggregation index (AI) of the control and test bloods were quantitatively evaluated during the first and second periods. Figure 2B-i exhibited time constant obtained from the time-lapse U_mc data over two consecutive periods. The left panel showed the temporal variation in U_mc for both bloods during the stepwise decrease in the syringe-pump flow rate from Q_h to Q_l. The results indicated that the decrease in U_mc was slower for the test blood than for the control blood. Compared with the control blood, the test blood exhibited a slower decrease in U_mc, indicating a longer transient response in the test blood. To accurately describe the transient behavior of U_mc, the time-lapse velocity data were fitted using a two-exponential model as $U_{mc}\left(t\right)=U_{1}exp(-{\displaystyle \frac{t}{{\lambda }_1}})+U_{2}exp(-{\displaystyle \frac{t}{{\lambda }_2}})$. Non-linear curve-fitting was performed using a curve-fitting toolbox in Matlab. The resulting fitting equations were expressed as $U_{mc}\left(t\right)=18.41\mathrm{e}\mathrm{x}\mathrm{p}(-{\displaystyle \frac{t}{9.88}})+7.41\mathrm{e}\mathrm{x}\mathrm{p}(-{\displaystyle \frac{t}{476.19}})$ for control blood and $U_{mc}\left(t\right)=18.44\mathrm{e}\mathrm{x}\mathrm{p}(-{\displaystyle \frac{t}{11.49}})+8.45\mathrm{e}\mathrm{x}\mathrm{p}(-{\displaystyle \frac{t}{312.5}})$ for test blood, respectively. Because ${\lambda }_1$was much smaller than ${\lambda }_2$, ${\lambda }_1$was selected as the representative time constant characterizing the dominant rapid transient response. The higher ${\lambda }_1$ value of the test blood indicated that its transient flow response was slower than that of the control blood. The middle panel showed the λ₁ values obtained for the two bloods during the first period. Each blood was tested with n = 4 ~ 8 replicates. The mean value and 95% confidence interval (CI) were superimposed on the raw data points. The λ₁ value of the test blood was substantially higher than that of the control blood. One-way ANOVA confirmed a statistically significant difference between two groups (p-value = 0.003). The right panel presented the λ₁ values obtained for the two bloods during the second period. One-way ANOVA revealed a statistically significant difference between the control and test bloods (p-value = 0.011). Similarly, as shown in Figure 2B-ii, the RBC aggregation index (AI) of the control and test bloods was quantitatively evaluated during two consecutive periods. The left panel showed time-dependent AI and Q_sp for both bloods during the first period. Herein, the mean AI (<AI>) was calculated by averaging the AI values within the plateau regions observed at both Q_h and Q_l. The middle panel presented the mean AI values (<AI>) of the control and test bloods at Q_h and Q_l during the first period. One-way ANOVA confirmed statistically significant differences between the two bloods at both flow rates (p-value < 0.001). Notably, the difference in <AI> between two bloods was more pronounced under low flow rate (Q_l). The right panel exhibited the mean AI (<AI>) values for both samples at Q_h and Q_l during the second period. One-way ANOVA indicated significant differences between two bloods at both flow rates (p-value < 0.001).

The preliminary results showed that the proposed a single syringe pump microfluidic method could simultaneously assess viscosity-related flow dynamics and RBC aggregation under periodically modulated flow conditions. Compared with the control blood, the test blood exhibited a significantly higher time constant (λ₁) and aggregation index (AI), indicating increased flow resistance and enhanced RBC aggregation, particularly under the low-flow-rate condition (Q_l).

3.2. Correlation Between Blood Viscosity and Time Constant

In this subsection, to probe the linear relationship between time constant and blood viscosity, the blood flow rate was adjusted to ensure a sufficiently high shear condition of $\dot{\gamma }$ > 10³ s^-1. Under these high shear regimes, blood viscosity could be reasonably treated as constant. According to Eqn (6), the time constant (λ₁) was linearly proportional to blood viscosity. That is, the hydraulic resistance of a fixed microfluidic channel was linearly proportional to fluid viscosity under laminar flow, while the transient response of a compliant fluidic system was governed by a hydraulic resistance–compliance time constant [42,57,58,59,60]. When the air volume and channel geometry were maintained constant, the compliance term remained nearly unchanged and the measured time constant (λ₁) was expected to vary linearly with blood viscosity. The linear relationship between the time constant and blood viscosity was experimentally validated by varying the infusion flow rate, hematocrit, and dextran concentration. Herein, air cavity inside a syringe was fixed at V_air = 0.1 mL.

As shown in Figure 3A, time constant and blood viscosity were acquired as a function of flow rate (Q_sp) (Q_sp = 1 ~ 6 mL/h). Herein, test blood (ϕ_vol = 0.5) was prepared by adding normal RBCs into dextran (C_dex = 2%). Syringe pump was abruptly stopped from the plateau value of Q_sp = 1, 2, 4, and 6 mL/h. As shown in Figure 3A-i, time constant of test blood was obtained quantitatively from time-lapse blood flow rate in the main channel (Q_m). The left panel exhibited time-dependent Q_m with respect to plateau value of Q_sp = 2, 4, and 6 mL/h. As shown in the middle panel, time-lapse Q_m was redrawn from the onset of transient blood flow. Herein, the plateau value of Q_sp was set to Q_sp = 2 mL/h. Based on one -exponential model as $Q_m\left(t\right)=Q_0\mathrm{e}\mathrm{x}\mathrm{p}(-{\displaystyle \frac{t}{{\lambda }_1}}$), the time-lapse Q_m was best described by $Q_m\left(t\right)=1.92\mathrm{e}\mathrm{x}\mathrm{p}(-{\displaystyle \frac{t}{27.62}}$). Amplitude and time constant were obtained as Q₀ = 1.92 mL/h and λ₁ = 27.62 s, respectively. The right panel showed variations of λ₁ and Q₀ with respect to plateau value of Q_sp. Experiment at each flow rate was repeated five times (n = 5). The Q₀ increased linearly with respect to plateau flow rate of Q_sp (p-value < 0.001), while λ₁ decreased gradually for up to Q_sp = 4 mL/h and dropped substantially at the plateau flow rate of Q_sp = 6 mL/h (p-value < 0.001). As shown in Figure 3A-ii, coflowing stream method was adopted to measure blood viscosity at plateau value of Q_sp = 1 ~ 6 mL/h. The left panel showed experimental setup and microscopic image for measuring blood viscosity (μ_b). According to the previous study [29], viscosity formula of test fluid was given as,

$${\mu }_b={\mu }_r\left({\displaystyle \frac{{\alpha }_b}{1-{\alpha }_b}}\right)\left({\displaystyle \frac{Q_r}{Q_b}}\right)C_f\left({\alpha }_b\right)$$

(10)

where viscosity of reference fluid (1× PBS) was denoted as ${\mu }_r=1cP.$ The formula of correction factor: C_f (α_b) was obtained experimentally and derived as polynomial expression,

$$C_f=12.038{{\alpha }_b}^4+26.171{{\alpha }_b}^3-20.77{{\alpha }_b}^2+7.156{\alpha }_b+0.014.$$

(11)

Herein, test blood was set to Q_b = 2 mL/h. To relocate interface near the channel center, flow rate of reference fluid (1× PBS) was adjusted to Q_r = 6 mL/h. Then, blood viscosity was obtained by substituting blood-filled width (α_b) into the Eqn (10). The middle panel showed time-dependent blood viscosity with respect to constant flow-rate of Q_b = 1, 2, 4, and 6 mL/h. Blood viscosity remained constant over time and decreased at higher flow rate of Q_b. The right panel exhibited variation of μ_b and $\dot{\gamma }$ with respect to Q_b. Herein, shear rate formula of a rectangular microfluidic channel was given as $\dot{\gamma }$= ${\displaystyle \frac{6Q_b}{w{h}^2}}$. From the results, the μ_b was decreased gradually for up to Q_b = 4 mL/h, where the $\dot{\gamma }$ was calculated as about 5089 s^-1. Blood viscosity was remained constant at Q_b = 4 ~ 6 mL/h.

As shown in Figure 3B, correlation between blood viscosity and time constant was validated by varying hematocrit (ϕ_vol). Herein, hematocrit of test blood was adjusted to ϕ_vol = 0.3 ~ 0.6 by adding normal RBCs into dextran (C_dex = 2%). To probe time constant consistently, blood flow rate was abruptly stopped from plateau value of Q_b = 2 mL/h. Under transient blood flow, as shown in Figure 3B-i, time constant (λ₁) was obtained as a function of ϕ_vol. Multiple experiments for each hematocrit were carried out (n = 3 ~5). The time constant (λ₁) increased remarkedly with respect to hematocrit (p-value = 0.003). In addition, as shown in Figure 3B-ii, blood viscosity (μ_b) was obtained with respect to ϕ_vol. To examine the relationship between two parameters, time constant (λ₁) and blood viscosity (μ_b) were plotted on y-axis and x-axis, respectively. As shown in Figure 3B-iii, λ₁ tended to increase with increasing μ_b. Linear regression analysis yielded the following relationship: λ₁ = 8.2722 μ_b − 2.9861 (R² = 0.7376, p-value = 0.141). Although the correlation did not reach statistical significance, the result suggested a positive association between λ₁ and μ_b, supporting the potential use of the time constant as a viscosity-related parameter.

As shown in Figure 3C, correlation between blood viscosity and time constant was evaluated as a function of dextran concentration (C_dex). For this analysis, test blood (ϕ_vol = 0.5) was prepared by suspending normal RBCs into dextran solution (C_dex = 0.5 ~ 3%). Under transient blood flow conditions, as shown in Figure 3C-i, time constant (λ₁) was determined as a function of dextran concentration (C_dex). The time constant (λ₁) increased remarkedly with increasing dextran concentration, showing a statistically significant dependency on dextran concentration (p-value = 0.012). Under steady blood flow conditions, as represented in Figure 3C-ii, blood viscosity (μ_b) was measured with respect to C_dex. Linear regression formula was obtained as μ_b = 0.8349 C_dex + 2.1811 (R² = 0.9586, p-value = 0.001), indicating that the μ_b increased significantly with respect to C_dex. As shown in Figure 3C-iii, the λ₁ was plotted against μ_b. According to linear analysis, linear regression analysis yielded λ₁ = 4.7749 μ_b + 10.468 (R² = 0.9326, p-value = 0.002).

From experimental results, including variations in infusion flow rate, hematocrit, and dextran concentration, the time constant (λ₁) increased with blood viscosity (μ_b). Strong correlations between (λ₁) and (μ_b), particularly under hematocrit- and dextran-dependent changes, demonstrated that (λ₁) could be regarded as a reliable viscosity-related parameter.

3.3. Validation of the Proposed RBC Aggregation Index Against the Previous Methods

To validate RBC aggregation index (AI) proposed in this study, its performance was compared with those of the previously reported methods [17,21,29]. As shown in Figure 4A, the AI values obtained from the three methods were quantitatively evaluated under different blood flow conditions. Test blood with a volume fraction of ϕ_vol = 0.5 was prepared by suspending normal RBCs in dextran solution at C_dex = 2%. To examine the influence of blood flow rate on AI, the plateau blood flow rate (Q_b) was systematically varied from 1 to 6 mL/h.

As the first previous method, RBC aggregation index (AI_p1) was obtained by analyzing temporal variation in microscopic image intensity at stasis [15,17,21]. As shown in Figure 4A-i, the left panel presented time-resolved microscopic images acquired at t = 200, 230, 260, 290, 320, and 360 s. Blood flow was suddenly stopped at 200 s after reaching a plateau flow rate of Q_on = 1 mL/h. After blood flow was stopped, RBCs gradually formed aggregates over time, resulting in a pronounced reduction in image intensity. The middle panel showed time-lapse image intensity (I), measured at plateau flow rates of Q_on = 1, 2, 4, and 6 mL/h. According to the conventional definition of RBC aggregation index (AI_p1), the two characteristic parameters (S_a, S_b) were calculated from temporal intensity profile during the first 120 s after the onset of stasis. The conventional RBC aggregation index was then computed as AI_p1 = S_a/(S_a + S_b). The right panel summarized variations of AI_p1 as a function of Q_on. A substantial rise in AIp1 was observed as Qon increased from 1 to 2 mL/h, and this change was found to be statistically significant (p-value < 0.001). At higher flow rates (Q_on > 2 mL/h), the AI _p1 showed only a gradual increased, and no statistically significant difference was observed among the specific flow rate conditions.

More recently, our group suggested another RBC aggregation index (AI_p2) which could be measured under continuous blood flow [13,29]. Unlike the conventional method, this approach did not require repeated stopping of blood flow. Instead, blood was continuously supplied into a microfluidic device at a constant flow rate using a syringe pump. The microfluidic device comprised a main channel and a test channel. Blood flowing through the main channel was exposed to relatively high shear conditions, under which RBC aggregates were largely dispersed. In contrast, blood entering the test channel experienced a substantially lower shear rate, promoting continuous RBC aggregation. The RBC aggregation index (AI_p2) was then calculated based on the difference in image intensity between the two channels. The left panel showed microscopic image captured at t = 240 s, when blood flow rate was maintained at Q_b = 1 mL/h. The red arrow (→) indicated the direction of blood flow in the channels. To quantify the image intensity in the main and test channels (i.e., I_m: main channel, and I_t: test channel), the ROI size in each channel was set to 3.63 mm² and 2 mm², respectively. The AI_p2 was then determined as AI_p2 = (I_{m −} I_t)/I_m.

The second panel showed time-dependent I_m, I_t, and AI_p2 at Q_b = 1 mL/h. From the results, the I_m remained nearly constant throughout the measurement period. In contrast, the I_t decreased gradually during the initial time, and increased slowly after reaching its minimum value. The AI_p2 increased progressively from the initial time, reached a maximum value, and decreased gradually over time. The third panel presented time-dependent variations of AI_p2 at different flow rates of Q_b = 1, 2, 4, and 6 mL/h. The results clearly indicated that the Q_b had a strong influence on AI_p2. In particular, the AI_p2 showed a relatively high value at the low flow rate of Q_b =1 mL/h, whereas it decreased markedly at the higher flow rate of Q_b = 6 mL/h. This trend suggested that RBC aggregation was enhanced at the lower flow rates, whereas it was suppressed at the higher flow rates. The last panel depicted variations of AI_p2 as a function of Q_b. For each flow condition, the measurement was repeated about n = 4 ~ 5. The results showed that the AI_p2 decreased remarkedly as Q_b increased from 1 mL/h to 4 mL/h (p-value < 0.001). However, no substantial difference in AI_p2 was observed between Q_b = 4 and Q_b = 6 mL/h.

As shown in Figure 4A-iii, the RBC aggregation index (AI) proposed in this study was obtained as a function of blood flow rate. The first panel showed blood image intensity (I) across the test chamber under a constant flow rate of Q_b = 1 mL/h. The inset showed a microscopic image captured at t = 250 s, where the red arrow (←) indicated the direction of blood flow through the main and bifurcation channels. Two parameters (S_a, S_b) were obtained from the spatial variation in I and were subsequently used to calculate the RBC aggregation index as AI = S_a/ (S_a + S_b). The second panel presented time-dependent variation of AI at Q_b = 1 mL/h. When compared with AI_p2, the proposed AI remained relatively stable during measurement period of 250 s. The AI value was expressed as mean ± standard deviation. At Q_b = 1 mL/h, AI was measured as AI = 0.123 ± 0.016 (n = 514). The third panel depicted time-lapse AI with respect to Q_b = 1, 2, 4, and 6 mL/h. The corresponding AI values of each flow rate was obtained as AI = 0.103 ± 0.008 (n = 446) at Q_b = 2 mL/h, AI = 0.073 ± 0.006 (n = 211) at Q_b = 4 mL/h, and AI = 0.061 ± 0.008 (n = 214) at Q_b = 6 mL/h. The last panel summarized variations of AI with respect to Q_b. The results indicated that the constant flow rate (Q_b) had a significant influence on AI over the tested flow rate range (p-value < 0.001). Compared with previous method (AI_p2), the proposed AI showed lower absolute values under the same flow rate conditions. However, because its temporal variation was much smaller, the proposed AI provided more stable measurements and more consistent trends with respect to the infusion flow rate.

As the first demonstration, as shown in Figure 4B, the performance of the proposed AI was evaluated by comparing three aggregation indices (i.e., AI_p1, AI_p2, and AI) as a function of hematocrit (ϕ_vol). The hematocrit of test blood was adjusted from ϕ_vol = 0.3 to ϕ_vol = 0.6 by suspending normal RBCs into dextran solution (C_dex = 2%). The plateau flow rate was fixed at Q_b = 2 mL/h. Figure 4B-i presented variation of AI_p1 with respect to ϕ_vol. The results indicated that AI_p1 decreased substantially with increasing hematocrit (p-value < 0.001). For each hematocrit condition, experiments were repeated about n = 4 ~ 6. Figure 4B-ii exhibited variation of AI_p2 with respect to ϕ_vol. Similar to AI_p1, the AI_p2 decreased significantly as hematocrit increased (p-value < 0.001). When compared with AI_p1, the AI_p2 exhibited lower absolute values under the same hematocrit conditions. None-the-less, both indices showed a consistent decreasing trend with increasing hematocrit. Figure 4B-iii depicted the variation of the proposed AI with respect to ϕ_vol. The proposed AI also showed a significant dependence on hematocrit (p-value < 0.001). Importantly, it showed a similar trend to the two previous indices (AI_p1, AI_p2), supporting the reliability of the proposed AI for evaluating hematocrit-dependent changes in RBC aggregation.

As the second demonstration, as shown in Figure 4C, three RBC aggregation indices (i.e., AI_p1, AI_p2, and AI) were compared quantitatively as a function of dextran concentration (C_dex). Test blood (ϕ_vol = 0.5) was prepared by suspending normal RBCs into dextran solution with different concentrations (C_dex = 0.5 ~ 3%). The plateau flow rate was fixed at Q_b = 2 mL/h. Figure 4C-i presented variation of AI_p1 with respect to C_dex. The results indicated that the AI_p1 increased significantly as the dextran concentration increased from 0.5% to 2% (p-value < 0.001). However, it remained nearly constant when C_dex was further increased between C_dex = 2% and C_dex = 3%. Figure 4C-ii depicted variation of AI_p2 as a function of C_dex. Unlike AI_p1, the AI_P2 continued to increase significantly over the entire tested dextran concentration range from C_dex = 0.5% to C_dex = 3% (p-value < 0.001). Figure 4C-iii depicted variation of proposed AI with respect to C_dex. The proposed AI showed a statistically significant difference across the tested dextran concentration (p-value < 0.001). In particular, its increasing trend was similar to that of AIp2, indicating that the proposed AI could effectively reflect dextran-induced enhancement of RBC aggregation.

From the experimental investigation, the proposed AI provided a reliable and stable quantification of RBC aggregation when compared with the previous indices (AI_p1, AI_p2). The proposed AI showed consistent and statistically significant trends with respect to both hematocrit and dextran concentration. In particular, it decreased with increasing hematocrit and increased with increasing dextran concentration, in agreement with the established behavior of RBC aggregation [27,29,56,61]. These results demonstrate that the proposed AI could serve as a robust and reproducible index for quantifying RBC aggregation under continuous blood flow.

3.4. Optimization of Infusion Pulsatile Blood Flow Profile

In this subsection, a pulsatile blood flow profile was optimized to enable effective measurement of time constant and RBC aggregation index. Herein, air cavity inside the syringe was adjusted to V_air = 0.1 mL. Test blood (ϕ_vol = 0.5) was prepared by suspending normal RBCs into dextran solution (C_dex = 2%). The minimum infusion flow rate was fixed at Q_l = 1 mL/h. Three design variables (i.e., Q_h: maximum flow rate, t_h: delivery time for Q_h, and t_l: delivery time for Q_l) were then determined by evaluating time constant and RBC aggregation.

First, the suggested method was employed to examine the effect of maximum flow rate (Q_h) and overall period (T = t_h + t_l) on time constant and aggregation index (AI). As presented in Figure 3A-ii, blood velocity remained nearly constant above Q_b = 4 mL/h, where shear rate was estimated as $\dot{\gamma }$ = 2,667 s^-1 in the main channel and $\dot{\gamma }$ = 135 s^-1 in the test chamber, respectively. The maximum flow rate was selected as Q_h = 4, and 6 mL/h. Period of pulsatile flow rate was set to T = 120 ~ 480 s. As shown in Figure 5A-i, time-dependent U_mc and AI was measured at T = 120, 240, and 360 s under the flow rate condition (Q_h = 4 mL/h, Q_l = 1 mL/h). At T = 120 s, both U_mc and AI did not reach plateau values during each pulsatile flow period. When period was set to 240 s or longer, the U_mc reached a plateau value in each period. Additionally, the AI showed a stable plateau response. Under the conditions, the AI was obtained about 0.3 at Q_l = 1 mL/h and 0.1 at Q_h = 4 mL/h, respectively. Furthermore, the U_mc decreased gradually from its plateau value when flow rate was changed from Q_h to Q_l. Analytical expression of the Eqn (7) could be subsequently used to determine time constant under a well-defined transient blood flow profile. Figure 5A-ii presented time-resolved U_mc and AI as function of T under the flow-rate condition (Q_h = 6 mL/h, Q_l =1 mL/h). When the pulsatile flow period was set to 240 s or longer, the AI reached a stable plateau value. In particular, a longer period produced a more stable AI response, indicating that sufficient delivery time at each flow rate condition was required for reliable aggregation measurement. As shown in Figure 5A-iii, variations of time constant (λ₁) and AI were summarized as a function of T under the flow rate conditions. The left panel showed variations of λ₁ as a function of T under the flow rate condition (Q_h = 4 mL/h, Q_l = 1 mL/h). Experiment for each period was repeated about n = 2 ~ 5. The results indicated that the λ₁ tended to increase substantially with respect to T (p-value = 0.05). The middle panels exhibited variations of λ₁ as functions of T under the flow rate condition (Q_h = 6 mL/h, Q_l = 1 mL/h). For each period, experiment was repeated about n = 2 ~ 4. The results showed that the λ₁ increased significantly with increasing T (p-value = 0.014). In addition, the λ₁ exhibited more consistent values when compared with those obtained at Q_h = 4 mL/h. The right panel depicted variations of AI as a function of T at Q_max = 4 and 6 mL/h. Herein, the AI was calculated by averaging plateau values obtained at Q_l = 1 mL/h. Compared with the flow rate of Q_h = 4 mL/h, the AI exhibited lower values at Qh = 6 mL/h over the tested range of T.

Second, although the condition of T = 360 s and Q_h = 6 mL/h provided stable values for time constant and aggregation index, the 180 s delivery at Q_h = 6 mL/h resulted in considerable blood loss because measurement was not performed during the high flow rate interval. To minimize blood loss at Q_h = 6 mL/h, it was further necessary to determine the delivery duration at Q_h (t_h). As shown in Figure 5B, the contribution of t_h to both time constant and AI was quantitatively examined under the flow rate condition (Q_h = 6 mL/h, Q_l = 1 mL/h). As shown in Figure 5B-i, the effect of delivery duration at Q_h on both AI and time constant (λ₁) was quantitatively examined. The delivery duration of Q_h was set to t_h = 30, 60, 90, and 120 s. The left panel showed time-resolved U_mc as a function of t_h, where t_l denoted the delivery duration at Q_l. Except for the condition of t_h = 30 s, the U_mc reached a plateau value during the high flow rate interval. The middle panel presented time-lapse AI with respect to t_h. The results indicated that a longer t_h contributed to increasing AI. The right panel exhibited variations of λ₁ as a function of t_h. Unlike AI, the λ₁ did not show a substantial difference with respect to t_h (p-value = 0.45).

Based on the results, delivery duration at Q_h was set to t_h = 60 s or longer. As show in Figure 5B-ii, variations of λ₁ and AI were obtained at specific delivery condition (i.e., t_h = 60 s, t_l = 300 s, and T = 360 s). The left panel showed time-resolved U_mc and AI. As a plateau interval at Q_h was short, the AI did not show a plateau value. However, the AI exhibited a plateau value at longer delivery duration at Q_l.

The middle panel showed variations of λ₁ during the first and second periods. For each period, measurement was repeated about n = 3. The results showed that the λ₁ increased remarkedly after an elapsed period (p-value = 0.002). The right panel presented variations of AI between the first and second periods. In contrast to λ₁, the AI decreased after an elapsed period, with marginal statistical significance (p-value = 0.054). Because the λ₁ increased remarkedly at t_h = 60 s, the delivery duration at Q_h was extended to t_h = 120 s. The delivery duration at Q_l was then adjusted to t_l = 240 s (i.e., T = 360 s). As shown in Figure 5B-iii, λ₁ and AI were measured under this optimized delivery condition (i.e., t_h = 120 s, t_l = 240 s). The left panel showed time-lapse U_mc and AI. Both U_mc and AI showed stable plateau values at Q_h and Q_l. The middle panel presented variations of λ₁ during the first and second periods. For each period, measurement was repeated about n = 6. The results indicated that the λ₁ remained nearly constant after an elapsed period (p-value = 0.598). The right panel showed variations of AI between the first and second periods. According to the results, AI showed a decreasing tendency after an elapsed period, the difference was not statistically significant (p-value = 0.328).

From the experimental investigation, the pulsatile blood flow profile was optimized to reliably measure both the time constant (λ₁) and RBC aggregation index (AI) while reducing unnecessary blood consumption. The final condition was set to Q_h = 6 mL/h, Q_l = 1 mL/h, t_h = 120 s, and t_l = 240 s. Under this delivery condition, U_mc and AI reached stable plateau values, and λ₁ remained reproducible across repeated periods, confirming that the optimized profile could provide a robust condition for simultaneous assessment of transient blood flow response and RBC aggregation.

3.5. Contribution of Air Compliance to Time Constant

Because the air cavity secured inside the syringe acts as a compliance element [42], it could dampen flow fluctuations while increasing the transient response time of the microfluidic system [57,62]. Consequently, the compliance-induced delay may affect the plateau value of AI by altering the time required to establish a stable low-shear condition for RBC aggregation measurement.

As shown in Figure 6A, the effect of flow rate on time constant was examined by measuring λ₁ as a function of plateau flow rate. Instead of test blood, glycerin (C_gl = 30%) was used as test fluid. Air cavity above glycerin inside the syringe was set to V_air = 0.1 mL.

Fluid flow was abruptly stopped from a plateau value of Q_on = 1, 2, 4, and 6 mL/h. The left panel showed time-dependent U_mc as a function of Q_on. In middle panel, the U_mc was replotted from the onset of transient flow. The results showed that the U_mc decreased more slowly at higher flow rates. Based on single exponential model, the transient velocity was fitted using $U_{mc}\left(t\right)=U_0\mathrm{e}\mathrm{x}\mathrm{p}(-{\displaystyle \frac{t}{{\gamma }_1}})$ for estimating the time constant (λ₁). The right panel exhibited variations of λ₁ with respect to Q_on. The λ₁ did not show substantial difference below Q_on = 4 mL/h. However, when Q_on increased from 4 mL/h to 6 mL/h, the λ₁ increased remarkedly (p-value = 0.01). This trend for the glycerin solution was similar to that observed for control blood as shown in Figure 3A-i.

As shown in Figure 6B, time constant was evaluated as a function of glycerin concentration (C_gl) during the first and second periods. Herein, glycerin solution was infused under the optimized pulsatile flow profile, and air cavity inside a syringe was fixed at V_air = 0.1 mL. The left panel showed time-lapse U_mc as a function of C_gl = 10% ~ 50%. Herein, λ_1-T1 and λ_1-T2 denoted time constants obtained during the first and second periods, respectively. The middle panel presented variations of λ_1-T1 and λ_1-T2/λ_1-T1 with respect to C_gl. The λ_1-T1 increased significantly with increasing C_gl (p-value = 0.001). In contrast, λ_1-T2/λ_1-T1 did not show significant dependence on C_gl (p-value = 0.316), indicating that the time constant remained consistent between two periods. To examine the correlation between time constant (λ_1-T1) and viscosity (μ_gl) [63], λ_1-T1 was plotted against μ_gl in the right panel. Linear regression analysis showed a strong proportional relationship between the time constant and viscosity, expressed as λ_1-T1 = 1.7123 μ_gl + 5.768 (R² = 0.9703, and p-value = 0.002). The results indicated that the time constant could be effectively used to monitor viscosity variations.

As 6. C, time constants for glycerin and control blood were measured as a function of air cavity (V_air). Both fluids were infused under the optimized flow profile. The air cavity inside the syringe was set to V_air = 0, 0.1, and 0.2 mL. Figure 6C-i depicted the time constant for glycerin (C_gl = 30%) as a function of V_air. The left panel presented time-lapse U_mc with respect to V_air. By analyzing transient flow response during the first and second periods, two time constants (λ_1-T1, λ_1-T2) were calculated for each period.

The middle panel exhibited variations of λ_1-T1 with respect to V_air. As expected, the λ_1-T1 increased remarkedly with respect to V_air (p-value < 0.001), confirming the strong influence of air compliance on the transient flow response. The right panel presented variations of λ_1-T2/λ_1-T1 with respect to V_air. From the results, the ratio did not show significant dependence on V_air (p-value = 0.597), indicating that the time constant remained consistent between the two periods. As shown in Figure 6C-ii, the time constant for test blood (normal RBCs into 1× PBS, ϕ_vol = 0.5) was measured as a function of V_air. The left panel showed time-lapse U_mc with respect to V_air. The middle panel exhibited variations of λ_1-T1 with respect to V_air. The λ_1-T1 increased significantly with increasing air cavity (p-value < 0.001). The right panel showed variations of λ_1-T2/λ_1-T1 with respect to V_air. The results indicated that the ratio did not show significant difference with respect to Vair (p-value = 0.157), suggesting that the time constant remained reproducible between the two periods.

From the experimental investigation, the air cavity (V_air) significantly increased the time constant (λ_1-T1) in both glycerin solution and control blood, confirming that syringe air compliance strongly delayed the transient flow response. However, the λ_1-T2/λ_1-T1 remained nearly unchanged with respect to V_air, indicating good reproducibility between repeated periods.

3.6. Monitoring Variation in Blood During Continuous Blood Infusion

Because RBC aggregation accelerates sedimentation in syringe [27,56,61,64,65], hematocrit of delivered blood could vary continuously during blood infusion. As the final demonstration, the proposed method was applied to detect these changes in supplied blood by simultaneously monitoring two parameters, including time constant and RBC aggregation index. Herein, for consistent measurement, air cavity inside the syringe was fixed at V_air = 0.1 mL. Test blood (normal RBCs into dextran solution) was then infused into a microfluidic device under the optimized pulsatile flow profile.

First, as shown in Figure 7A, to examine the effect of hematocrit on both time constant and RBC aggregation index, time constant (λ₁) and AI were measured by varying hematocrit (ϕ_vol). Herein, hematocrit of test blood was adjusted to ϕ_vol = 0.2, 0.3, 0.4, 0.5, and 0.6 by suspending normal RBCs into a dextran solution of C_dex = 1%. Figure 7A-i showed variations of time constant as a function of hematocrit during the first and second periods. The first panel presented time-lapse U_mc as a function of ϕ_vol = 0.2 ~ 0.6. Herein, λ_1-T1 and λ_1-T2 were obtained by analyzing transient flow response during the first and second periods. The second panel depicted snapshots of the syringe captured at the completion of blood delivery. From the results, RBC-depleted layer increased significantly at lower hematocrit. At ϕ_vol = 0.6, RBC-depleted layer was not detected clearly. The third panel exhibited variations of λ_1-T1 as a function of ϕ_vol. For each hematocrit, the measurement was repeated three times (n = 3). As expected, hematocrit contributed to significantly increasing λ_1-T1 (p-value < 0.001), which was consistent with previous hemorheological studies showing that hematocrit was a major determinant of whole-blood viscosity and flow resistance [66,67,68]. Therefore, a higher hematocrit could prolong the transient flow response in a compliant microfluidic system. The last panel showed variations of λ_1-T2/λ_1-T1 with respect to ϕ_vol. The ratio did not show substantial dependence on hematocrit (p-value = 0.287), indicating that time constant remained consistent between two periods. As shown in Figure 7A-ii, RBC aggregation index (AI) was measured as a function of hematocrit during the first and second periods. The left panel showed time-dependent AI as a function of ϕ_vol. Herein, AI₁ and AI₂ were determined by averaging the plateau values at Q_l during the first and second periods, respectively. The middle panel represented variations of AI₁ with respect to ϕ_vol. The AI₁ decreased remarkedly with increasing hematocrit (p-value < 0.001). The right panel depicted variations of AI₂/AI₁ as a function of ϕ_vol. The ratio increased significantly up to ϕ_vol = 0.4 (p-value < 0.001), whereas no substantial difference was observed from ϕ_vol = 0.4 to ϕ_vol = 0.6. From the results, RBC sedimentation occurred during blood delivery and significantly reduced AI, particularly at lower hematocrit (ϕ_vol = 0.2 ~ 0.4).

Second, to examine the contribution of dextran concentration to time constant and AI, as shown in Figure 7B, time constant and AI were probed as a function of dextran concentration. Herein, test blood (ϕ_vol = 0.5) was prepared by adding normal RBCs into dextran solution (C_dex = 1% ~ 4%). Figure 7B-i presented variations of time constant as a function of dextran concentration during the first and second periods. The first panel showed time-lapse U_mc as a function of C_dex. The second panel depicted snapshots of the syringe captured at the completion of blood delivery. At C_dex = 1%, RBC-depleted layer was much smaller than those observed at higher concentration of dextran solution (C_dex = 2% ~ 4%). The third panel exhibited variations of λ_1-T1 as a function of C_dex. The results indicated the dextran concentration significantly increased the time constant (p-value < 0.001). The last panel showed variations of λ_1-T2/λ_1-T1 with respect to C_dex. Although the ratio tended to decrease from C_dex = 2% to C_dex = 4%, the change was not statistically significant (p-value = 0.497). Figure 7B-ii exhibited variations of AI as a function of dextran concentration during the first and second periods. The left panel showed time-dependent AI as a function of C_dex. The results indicated that the AI increased remarkedly at higher concentration of dextran solution. The middle panel represented variations of AI₁ with respect to C_dex. The AI₁ increased significantly with increasing dextran concentration (p-value < 0.001). The right panel depicted variations of AI₂/AI₁ as a function of C_dex. The ratio showed a significant dependence on dextran concentration (p-value < 0.048), indicating that the AI varied substantially between the two periods.

From the experimental investigation, the proposed method enabled effective monitoring of time-dependent changes in blood properties during continuous infusion. By simultaneously measuring the time constant (λ₁) and RBC aggregation index (AI), the method detected infusion-induced variations in the delivered blood. Specifically, λ₁ reflected changes in flow resistance and viscosity-related properties, whereas AI quantified variations in RBC aggregation. These results demonstrated that the proposed approach could provide a practical and sensitive platform for real-time assessment of blood property changes during continuous delivery.

The proposed method has several limitations for practical applications. First, it was validated mainly under controlled laboratory conditions using prepared blood samples with defined hematocrit and dextran concentration. Second, the current platform still depends on external syringe-pump control, which may limit its immediate clinical translation. Further validation using fresh clinical blood samples and integration with a portable fluid-delivery system will be necessary to improve its robustness and practical applicability.

4. Conclusions

In this study, the proposed microfluidic method enabled simultaneous evaluation of viscosity-related transient flow behavior and RBC aggregation under continuous pulsatile blood delivery. The time constant (λ₁) showed a strong correlation with fluid viscosity, supporting its use as a sensitive indicator of flow resistance and viscosity-related changes. The proposed aggregation index (AI) exhibited consistent trends with hematocrit and dextran concentration when compared with two previous indices (AI_p1 and AI_p2), while providing improved temporal stability under continuous-flow conditions. By optimizing the pulsatile-flow profile, reliable measurements of both λ₁ and AI were achieved with reduced blood consumption. The air cavity inside the syringe acted as a compliance element and significantly influenced the time constant, confirming the importance of controlling system compliance. Finally, the method successfully detected time-dependent changes in delivered blood during continuous infusion, demonstrating its potential as a practical and sensitive platform for real-time monitoring of hemorheological variations.