Simultaneous measurement method of erythrocyte sedimentation rate and erythrocyte deformability in resource-limited settings

In accordance with the ethics committee of Chosun University Hospital (CUH), all the experiments were performed while ensuring that the procedures were appropriate and humane. Concentrated RBCs and fresh frozen plasma (FFP) were purchased from the Gwangju-Chonnam blood bank (Gwangju, Korea), and were stored at 4 °C and  −20 °C, respectively. Blood was prepared by adding concentrated RBCs into phosphate-buffered saline (PBS) solution (1×, pH 7.4, Gibco, Life Technologies, Korea). Using a centrifugal separator, pure RBCs were collected by removing the buffer layer and PBS. The washing procedure was conducted three times for all blood samples. After the FFP thawed at room temperature, a syringe filter of mesh size 5 µm (Minisart, Sartorius, Germany) was applied to remove debris included in the plasma. Several suspended bloods were prepared by adding normal RBCs into base solutions (i.e. PBS, plasma, and dextran solution).

First, to evaluate the effect of the hematocrit on the ESR and RBC deformability, the hematocrit (Hct) was adjusted to Hct  =  20%, 30%, 40%, and 50% by adding normal RBCs into a dextran solution of specific concentration (15 mg ml⁻¹). Second, to stimulate the ESR of blood, four different concentrations of dextran solution (C_dex  =  5, 10, 15, and 20 mg ml⁻¹) were prepared by mixing dextran (Leuconostoc spp., MW  =  450–650 kDa, Sigma-Aldrich, USA) with PBS solution. Subsequently, bloods (Hct  =  30%) were prepared by adding normal RBCs to dextran solutions of specific concentrations. As a control, normal blood (Hct  =  30%) was prepared by adding normal RBCs into plasma. Third, to vary the RBC deformability, four different concentrations of glutaraldehyde (GA) solution (C_GA  =  2, 4, 6, and 8 µl ml⁻¹) were diluted by mixing GA solution (Grade II, 25% in H₂0, Sigma-Aldrich, USA) into PBS solution. Homogeneous hardened RBCs were prepared by exposing normal RBCs to each concentration of GA solution for 10 min. Hardened bloods (Hct  =  30%) were then prepared by adding hardened RBCs into PBS solution. Because the PBS solution did not induce the ESR inside the ACS, hardened blood was only prepared to evaluate variations in the RBC deformability. To detect minor hardened RBCs in heterogeneous RBCs, heterogeneous blood was prepared by adding hardened blood to normal blood. For convenience, to reduce the duration of the ESR substantially, the hematocrit was reduced. Plasma was replaced with a dextran solution of a specific concentration (15 mg ml⁻¹). In other words, normal blood was adjusted to Hct  =  30% by adding normal RBCs into a dextran solution of a specific concentration (i.e. V_NB). Hardened blood was prepared by adding RBCs fixed by GA solution (8 µl ml⁻¹) into PBS solution (V_HB). The mixing ratio (φ) was defined as the ratio of the hardened blood volume (V_HD) to the total blood volume (V_HB  +  V_NB) (i.e. $\varphi =\frac{{{V}_{HB}}}{{{V}_{NB}}~+~{{V}_{HB}}~}$. Various mixing ratios (φ  =  0, 5%, 10%, 20%, and 100%) were obtained by adding hardened blood to normal blood. Here, φ  =  0 and φ  =  100% denote pure normal blood and pure hardened blood, respectively.

The fabricated microfluidic device for sequentially measuring the RBC deformability and ESR consisted of an inlet, an outlet, and multiple micropillar channels, as shown in figure 1(A(a)). The straight channel (width  =  250 µm) was connected to the micropillar channels from the inlet and outlet. As shown in figures 1(A(b)) and S1 (supplementary materials), the micropillar channels were composed of multiple narrow channels (N  =  43, gap  =  4 µm, and channel length  =  50 µm). The channel depth of the microfluidic device was fixed at 10 µm. Conventional micro-electromechanical-system fabrication techniques, such as photolithography and deep reactive iron etching (RIE) were employed to fabricate a silicon-master mold. PDMS (Sylgard 184, Dow Corning, Midland, MI, USA) was mixed with a curing agent at a ratio of 10:1. The PDMS mixture was poured into the mold. Air bubbles in the PDMS were removed completely by operating a vacuum pump for 1 h. After curing the PDMS mixture in a convective oven at 70 °C for 1 h, the PDMS block was peeled off from the mold and was cut with a razor blade. An inlet and outlet were punched with a biopsy punch (outer diameter  =  1.0 mm). After the surfaces of the PDMS block and a glass slide were treated with an oxygen plasma system (CUTE-MPR, Femto Science Co. South Korea), the microfluidic device was finally prepared by bonding the PDMS block onto the glass slide.

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As shown in figure 1(A(c)), to remove the bulky syringe pump, an ACS partially filled with air and blood was prepared by assembling a disposable syringe (~1 ml), fixture, and plastic needle (PN18G-1/2, ESR Co., Korea). As shown in figure S2(A) (supplementary materials (stacks.iop.org/PM/41/025009/mmedia)), the dimensions of the fixture were determined to fix the plunger in the syringe securely. The fixture was then fabricated by using a 3D printer (Ultimaker 2+, Ultimaker B.V., Netherlands). The needle of the ACS was tightly fitted to the inlet of the microfluidic device. Owing to air compression inside the ACS, blood was supplied to the microfluidic device from the ACS. To stop or run blood flows in the microfluidic channel, a stopper was tightly fitted into the outlet or removed from the outlet. As shown in figure S2(B) (supplementary materials), the stopper was fabricated by using a 3D printer.

To remove air bubbles in the channels and avoid nonspecific binding of plasma proteins to the inner surface of the channels, the channels were manually filled with bovine serum albumin (BSA) solution of 2 mg ml⁻¹ through the outlet with a disposable syringe. After the elapse of 5 min, a stopper was tightly fitted into the outlet and the plastic needle of the ACS was inserted into the inlet of the microfluidic device. When the cell-rich volume inside the ACS was reduced to a specific value of V_CR  =  0.2 ml, the stopper inserted into the outlet was removed and blood flowed into the microfluidic channel from the ACS. The V_B inside the ACS decreased gradually with time.

As shown in figure 1(A(d)), an Open-Camera application installed in a smartphone camera (Galaxy A5, Samsung, Korea) was employed to capture snapshot images of the ACS over time. The snapshot images were sequentially captured at intervals of 5 s, for a specific duration. The variations in V_B, V_CF, and V_CR were then quantified from the images. All the experiments were conducted at a room temperature of 25 °C.

As shown in figure 1(B), the ACS was suggested for delivering blood into a microfluidic device. The operation of the ACS was divided into five stages. First, air (~0.4 ml) was secured by moving the plunger backward (figure 1(B(a))). Second, blood (~0.6 ml) was suctioned by moving the plunger backward (figure 1(B(b))). Third, to close the outlet of the microfluidic device, the stopper was tightly fitted into the outlet (figure 1(B(c))). Fourth, by securing the end of the plunger and syringe with the fixture, the air cavity inside the ACS was compressed to a specific value of V_comp (i.e. V_comp  =  0.2, 0.3, and 0.4 ml) (figure 1(B(d))). Finally, a smartphone camera was employed to capture snapshot images (figure 1(B(e))). When the V_CR had decreased to 0.2 ml, the outlet was closed. The variations in V_CF and V_CR were monitored over time. After removing the stopper from the outlet, snapshot images were captured sequentially for a specific duration. The temporal variations in V_B were then obtained from the snapshot images.

As a preliminary study, suspended blood (Hct  =  30%) was prepared by adding normal RBCs to a dextran solution of a specific concentration (C_dex  =  15 mg ml⁻¹). The ACS was partially filled with blood and air. The air inside the ACS was compressed to 0.4 ml. Figure 1(C(a)) shows snapshot images captured at specific time (t) (t  =  0, 184, 246, 345, and 460 s) by closing the outlet. As time elapsed, the ESR caused V_CF to increase and V_CR to decrease. On the contrary, by removing the stopper from the outlet, blood was supplied to the microfluidic device from the ACS. Figure 1(C(b)) illustrates snapshot images captured at specific time (t) (t  =  497, 632, and 883 s) by opening the outlet. The V_B inside the ACS decreased over time. The V_CR also decreased with time. In other words, by inserting the stopper into the outlet, the ESR was evaluated by inspecting the V_CF in the ACS. Next, by removing the stopper from the outlet, the RBC deformability was quantified by monitoring the variation in the blood volume (ΔV_B) in the ACS.

As shown in figure 1(C(c)), from inspection of the captured snapshot images, the variations in V_B, V_CF, and V_CR were obtained with respect to time. The ESR and RBC deformability were then quantified by analyzing the temporal variations in the V_CF and V_B. First, by closing the outlet, the variations in the V_CF were obtained for a specific duration (t  =  t₁) until the V_CR had decreased to 0.2 ml. The ESR index proposed in this study (i.e. ESR_PM) was then quantified by dividing the V_CF (t  =  t₁) by the duration (t  =  t₁) (i.e. ESR_PM  =  V_CF [t  =  t₁]/t₁). Second, by opening the outlet, the ΔV_B (i.e. ΔV_B  =  V_B [t  =  t₁]  −  V_B) was monitored as time passed. Owing to the ESR of the blood sample, the V_CF increased continuously with time. For this reason, instead of the V_CF or V_CR, the ΔV_B was employed to detect changes in the RBC deformability. To fit the ΔV_B with respect to time, a two-term exponential model (i.e. $\Delta {{V}_{B}}=a{{e}^{bt}}-c{{e}^{-dt}}$) was newly proposed. The fitting model consisted of an increasing exponential term and a decreasing exponential term. The coefficients (a) and (b) in the rising exponential term denote the amplitude and variation rate, respectively. In addition, the coefficients (c) and (d) in the decreasing exponential term represent the amplitude and variation rate, respectively. By conducting a regression analysis with a commercial software package (MATLAB, version R2019, MathWorks, USA), the four regression coefficients (a)–(d) were obtained and employed to detect changes in the RBC deformability.

A previous method with the ability to measure the RBC aggregation (Kang et al 2018b, Kang 2018c, 2018d, 2018e, 2019) or RBC deformability (Kang 2018a, 2018b) using microscopic image-based analysis was employed to evaluate the performance of the proposed method. As shown in figure S3(A) (supplementary material), the experimental setup consisted of an ACS, a microfluidic device, and an image acquisition system. Unlike the previous method that used a syringe pump (Kang 2018a, 2018c, 2018d, 2018e), the ACS was employed to deliver the blood sample into a microfluidic device. The ends of a polyethylene tube (L₁, inner diameter  =  500 µm and length  =  300 mm) were connected to the needle of the ACS and the inlet of the microfluidic device. The other tube (L₂, inner diameter  =  500 µm and length  =  200 mm) was connected to the outlet of the microfluidic device. Because the method required sequential microscopic images of blood flows, the microfluidic device was positioned on an optical microscope (BX51, Olympus, Japan) equipped with a 4×  objective lens (NA  =  0.1). A high-speed camera (FASTCAM MINI, Photron, USA) captured microscopic images of blood flows. The camera had a spatial resolution of 1280  ×  1000 pixels, where each pixel corresponded to 10 µm. With a function generator (WF1944B, NF Corporation, Japan), a pulse signal of period 1 s triggered the high-speed camera. Microscopic images were then sequentially captured at a frame rate of 5 kHz. To quantify the RBC aggregation in the microfluidic channel, the image intensity of the blood flows ($\left\langle I \right\rangle$) was averaged by analyzing the RBCs distributed within a region of interest (ROI) (300  ×  810 pixels) within the multiple micropillar channels, as shown in figure S3(B) (supplementary material). To quantify the blood velocity influenced by the RBC deformability, a specific ROI (110  ×  80 pixels) was selected appropriately within the downstream of the micropillar channels. The velocity fields of blood flows were obtained by conducting a time-resolved micro-PIV technique. The size of the interrogation window was 16  ×  16 pixels. The window overlap was 50%. The obtained velocity fields were validated with a median filter. The averaged blood velocity ($\left\langle U \right\rangle$) was then calculated by conducting an arithmetic average of the blood velocity fields over the ROI.

The statistical significance was evaluated by conducting statistical analyses with a commercial software package (SPSS Statistics version 24, IBM Co., USA). An analysis of variance (ANOVA) test was used to verify significant differences between comparative results quantitatively. If the P-value was less than 0.05 (i.e. P-value  <  0.05), the results exhibited significant differences within a 95% confidence interval.

Before testing the performance of the proposed method, it is necessary to evaluate the effect of several factors (i.e. V_comp, Hct) on the ESR and RBC deformability. Here, to reduce the duration of the ESR test substantially, a specific concentration of dextran solution (15 mg ml⁻¹) was employed as a suspension solution, rather than plasma.

First, the effect of the V_comp on the ESR and RBC deformability was quantified by varying the V_comp (V_comp  =  0.2, 0.3, and 0.4 ml). A blood sample with Hct  =  30% was prepared by adding normal RBCs into the specific dextran solution. Figure 2(A) shows the temporal variations in the V_CF and ΔV_B with respect to the V_comp. The higher value of the V_comp caused the V_CF to reduce substantially compared with the lower value of the V_comp. By setting the V_comp as 0.2 ml, the V_CF increased to 0.3 ml after an elapsed time of approximately 1046 s. However, by increasing the V_comp from 0.2 to 0.4 ml, the V_CF increased to 0.28 ml after an elapsed time of 460 s. On the contrary, because the V_comp caused the air pressure inside the ACS to increase, blood flowed faster at a higher value of V_comp. In other words, at the higher value of V_comp  =  0.4 ml, the ΔV_B increased to 0.2 ml in a shorter time. However, at the lower value of V_comp  =  0.2 ml, the ΔV_B did not increase to 0.2 ml, owing to the lower air pressure inside the ACS. Figure 2(B) shows variations in the ESR_PM with respect to the V_comp. At the lower value of V_comp  =  0.2 ml, it took a longer time for the V_CF to increase to 0.3 ml in comparison with the higher value of the V_comp. By referring to the definition of the ESR_PM (i.e. ESR_PM  =  V_CF [t  =  t₁]/t₁), the higher value of the V_comp contributed to the increased ESR_PM. According to the statistical analysis, the ESR_PM was increased significantly with respect to the V_comp (i.e. P-value  =  0.001). At the blood-air interface, the surface tension hindered the RBCs' sedimentation inside the ACS. When increasing the V_comp range from V_comp  =  0.2 ml to V_comp  =  0.4, the pressure inside the ACS tended to increase substantially. The pressure reduced the contribution of the surface tension to the ESR. From the results, it was found that the ESR was accelerated significantly with the increasing V_comp. Based on the temporal variations in ΔV_B, the change in ΔV_B was best fitted by using the two-term exponential model (i.e. $\Delta {{V}_{B}}=a{{e}^{bt}}-c{{e}^{-dt}})$. Figure 2(C(a)) shows variations in the coefficients (a) and (c) with respect to the V_comp. From the statistical analysis, the coefficient (a) showed significant variations with respect to the V_comp (i.e. P-value  =  0.071). However, the coefficient (c) remained constant with respect to the V_comp (i.e. P-value  =  0.938). This result indicates that the coefficient (a) in the rising exponential term (i.e.$~a{{e}^{bt}}$) varied considerably with respect to the V_comp when compared with the coefficient (c) in the decreasing exponential term (i.e. $c{{e}^{-dt}}$). Figure 2(C(b)) shows variations in the coefficients (b) and (d) with respect to the V_comp. From the statistical analysis, the coefficients (b) and (d) of the variation rate in the exponential terms remained constant with respect to the V_comp (i.e. P-value  =  0.435–0.955). From the experimental results, the V_comp caused the ESR and the coefficient (a) in the rising exponential term to vary. For consistent measurement of the ESR and RBC deformability, the V_comp was fixed as V_comp  =  0.4 ml for all of the experiments. In other words, as V_comp  =  0.4 ml showed the maximum value of ESR_PM, it was selected carefully to reduce the elapsed time for measurement of the ESR considerably.

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Second, according to previous studies, a higher value of hematocrit contributed to a significant decrease in the ESR (Kang et al 2014, 2018b, Kang 2018c, 2017b]. In addition, the blood flow decreased at a higher value of the hematocrit, because the fluidic resistance was increased substantially by the hematocrit. When the RBC deformability was quantified by evaluating the blood flows through narrow channels (Kang et al 2016a, 2016b, Kang 2017a, 2018a, 2018b), it was necessary to verify the effect of the hematocrit on the RBC deformability. For these reasons, the effect of the hematocrit on the ESR and RBC deformability was quantified by varying the hematocrit. The hematocrit was adjusted to Hct  =  30%, 40%, and 50% by adding normal RBCs into the dextran solution. Figure 3(A) shows temporal variations in the V_CF and ΔV_B with respect to the Hct. When the outlet was closed, the V_CF was increased substantially at the lower value of the hematocrit. When the outlet was opened, the ΔV_B was increased considerably at the lower value of the hematocrit. Figure 3(B) shows variations in the ESR_PM with respect to the Hct. From the statistical analysis, the ESR_PM was decreased significantly by increasing the hematocrit (i.e. P-value  =  0.027). Figures 3(C(a)) and (C(b)) show variations in the regression coefficients (a)–(d) in the two-term exponential model with respect to the Hct. From the statistical analysis, the coefficient (a) in the rising exponential term was increased significantly with respect to the Hct (i.e. P-value  =  0.02). Except for the coefficient (a), the other three coefficients (b)–(d) remained constant with respect to the hematocrit. This result indicated that the amplitude in the rising exponential term (i.e. the coefficient (a)) had a strong relation to the hematocrit. From the results, to decrease the experimental time of the ESR and RBC deformability, a lower hematocrit was preferable. The hematocrit was then fixed as Hct  =  30% for all the experiments.

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As the proposed method had the ability to measure the ESR and RBC deformability simultaneously, it was necessary to verify each function (i.e. ESR and RBC deformability) independently. According to previous studies (Sherwood et al 2012, Kang et al 2018b, 2018e, Kang 2019), dextran solutions were widely employed to vary the degree of the ESR or RBC aggregation. In other words, to stimulate the ESR of bloods, dextran solutions of various concentrations (C_dex  =  5, 10, 15, and 20 mg ml⁻¹) that were diluted with PBS solution were prepared. The control (C_dex  =  0) indicated plasma. Individual blood (Hct  =  30%) was then prepared by adding normal RBCs into a dextran solution of a specific concentration. Figure 4(A(a)) shows the temporal variations in the V_CF and ΔV_B with respect to the C_dex. When compared with the control, the dextran solution contributed to the decrease in the elapsed time of the ESR significantly. In addition, the ΔV_B was decreased substantially at higher dextran solution concentrations. Figure 3(A(b)) shows variations in the ESR_PM and the coefficient (a) in the rising exponential term with respect to the C_dex. From the statistical analysis, the ESR_PM was increased considerably with respect to the C_dex. When compared with the previous results (Kang et al 2014, 2018b), the proposed method gave consistent variations with respect to the dextran solution concentration. On the contrary, by conducting a regression analysis for each ΔV_B with respect to time, the four regression coefficients (a)–(d) in the two-term exponential model were obtained, as shown in figure S3 (supplementary material). From the statistical analysis, the regression coefficient (a) in the rising exponential term showed a statistically significant decrease with respect to the C_dex (i.e. P-value  =  0.001). In addition, the regression coefficient (b) in the rising exponential term showed a statistically insignificant increase with respect to the C_dex (i.e. P-value  =  0.082). However, the remaining two coefficients (c, d) in the decreasing exponential term remained constant with respect to the C_dex (i.e. P-value  =  0.17 for the coefficient (c) and 0.559 for the coefficient (d)). From these results, the amplitude in the rising exponential term only showed a strong relation to ΔV_B.

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As shown in figure S3(A) (supplementary material), the microscopic imaging approach reported in previous studies was employed for comparison with the performance of the proposed method. Initially, by removing the PV that clamped the tube (L₁), blood was supplied to the microfluidic channel for 30 s. After this, the middle position of the tube (L₁) was clamped with the PV for 5 min. The blood flow stopped immediately. Under blood stasis, the RBC aggregation index (i.e. AI_MI) was quantified by analyzing the image intensity of the blood. Figure S3(C) (supplementary material) shows temporal variations in $\left\langle I \right\rangle$ with respect to the C_dex  =  0, 5, 10, 15, and 20 mg ml⁻¹. Here, C_dex  =  0 denoted plasma. Below C_dex  =  5 mg ml⁻¹, the dextran solution did not contribute to varying Δ$\left\langle I \right\rangle$. Above C_dex  =  5 mg ml⁻¹, the ΔI was increased substantially at the higher concentrations of the dextran solution. The AI_MI was then calculated by averaging Δ$\left\langle I \right\rangle$ (i.e. Δ$\left\langle I \right\rangle$  =  <I (t)  >  −<I (t  =  0)>) for 300 s (i.e. AI_MI  =  $\frac{1}{300}\int_{t=0}^{t=300\,{\rm s}}{\Delta \left\langle I \right\rangle dt}$. By removing the PV, the blood flowed continuously for 10 min. Figure S3(D) (supplementary material) shows temporal variations in $\left\langle U \right\rangle$ with respect to the C_dex. Above C_dex  =  5 mg ml⁻¹, $\left\langle U \right\rangle$ was decreased significantly. The RBC deformability index (i.e. DI_MI) was then quantified by integrating the average blood velocity from t  =  300 s to t  =  900 s (i.e. DI_MI  =  A_c x $\int_{t=300\,{\rm s}}^{t=900\,{\rm s}}{\left\langle U \right\rangle dt}$). Here, A_c denotes the cross-sectional area of a rectangular channel (i.e. A_c  =  w  ×  h, w  =  250 µm, and h  =  10 µm). As shown in figure 4(B), variations in AI_MI and DI_MI obtained by the microscopic imaging approach were obtained by varying the C_dex. From the results, the dextran solution contributed to the increase in the AI_MI substantially (i.e. P-value  =  0.001). Because the dextran solution contributed to the increase in the blood viscosity, the blood velocity decreased at higher dextran solution concentrations (Kang 2018d, 2018e). Therefore, the DI_MI was decreased significantly above C_dex  =  5 mg ml⁻¹ (i.e. P-value  =  0.001).

The variations in the ESR (or RBC aggregation) or RBC deformability obtained by using both methods (the proposed method and the previous method) for dextran-included bloods are overlapped in an X–Y plot. Figure 4(C(a)) shows the relationship between the ESR_PM and AI_MI, which are strongly correlated (i.e. R²  =  0.9199 and P-value  =  0.01). The results indicate that the ESR_PM can be used effectively for measuring the ESR of blood. Figure 4(C(b)) shows the relationship between the regression coefficient (a) and DI_MI. The indices had a significant linear relationship (i.e. R²  =  0.9076 and P-value  =  0.013). From the result, the coefficient (a) in the rising exponential term can be effectively employed to quantify the change in the RBC deformability. According to a previous measurement of viscoelasticity (Kang 2016), the blood elasticity remained constant with respect to the concentration of the dextran solution. Because the blood elasticity is strongly related to the RBC deformability, the previous result indicated that the RBC deformability remained constant within the specific concentrations of the dextran solution. However, the blood viscosity increased significantly at higher concentrations of dextran solution. In other words, the DI_MI of dextran-included blood was changed substantially by the blood viscosity, rather than the blood elasticity. By referring to the results obtained by the present method, the coefficient (a) decreased considerably with respect to the C_dex. However, the coefficient (b) was increased slightly with respect to the C_dex. Thus, it was inferred that both deformability indices (i.e. the coefficient (a) and DI_MI) were changed considerably by the blood viscosity. RBCs with poor deformability contributed to the increase in the blood viscosity. Furthermore, it was inferred that the coefficient (b) in the rising exponential term might be increased by the degree of the RBC deformability. From the experimental results, the proposed method had the ability to measure the ESR and RBC deformability of dextran-included blood with sufficient consistency. As shown in figures 2 and 3, the ESR and deformability varied linearly with respect to the Hct or V_comp. From the results, it was estimated that the proposed method could provide consistent results for a blood sample with Hct  =  40% or 50%, or V_comp  =  0.2 or 0.3 ml.

Homogeneous hardened blood was employed to evaluate the physical representation of the regression coefficients (a) and (b) in the two-term exponential model. In other words, to remove the effect of the RBC aggregation completely, PBS solution was added to each blood sample instead of plasma or dextran solution. Normal RBCs were chemically fixed using GA solution. The normal RBCs were dipped into specific concentrations of GA solution (C_GA  =  2, 4, 6, and 8 µl ml⁻¹), which were diluted with PBS solution. Then, homogeneous hardened blood (Hct  =  30%) was prepared by adding RBCs fixed by the same concentration of GA solution to the PBS solution. As a control, normal RBCs were added to PBS solution (C_GA  =  0). Because the PBS solution did not include plasma proteins, each hardened blood did not contribute to induction of the ESR. In each experiment, after the air compression inside the ACS, the V_CF was monitored for 200 s. The result confirmed that there was negligible variation in the V_CF for each blood sample. Based on these results, the ESR measurement was not conducted for homogeneous hardened blood. Thereafter, when removing the stopper from the outlet, the blood inside the ACS was supplied to the microfluidic device immediately. As time passed, the ΔV_B varied by the degree of the RBC deformability. Temporal variations in the ΔV_B were then employed to understand the regression coefficients in the two-term exponential model. Figure 5(A(a)) shows temporal variations in the ΔV_B with respect to the C_GA. From the results, the ΔV_B was increased considerably at lower concentrations of GA solution. After an elapse of 400 s, the ΔV_B was saturated at ΔV_B  =  0.14 ml for C_GA  =  6 µl ml⁻¹ and ΔV_B  =  0.1 ml for C_GA  =  8 µl ml⁻¹. The results indicated that normal RBCs easily passed through the micropillar channels when compared with chemically fixed RBCs. Because blood composed of RBCs fixed by C_GA  =  6–8 µl ml⁻¹ did not pass through the micropillar channels at all, the ΔV_B remained constant after 400 s. Four regression coefficients (a)–(d) were obtained by best-fitting the ΔV_B with the two-term exponential model. As shown in figures S5(A) and (B) (supplementary material), the four regression coefficients were obtained with respect to the C_GA. The coefficients (c) and (d) in the decreasing exponential term remained constant with respect to the C_GA (i.e. P-value  =  0.313 for the coefficient (c) and P-value  =  0.7 for the coefficient (d)). As shown in figure 5(A(b)), the coefficient (a) in the rising exponential term was decreased slightly with respect to the C_GA (i.e. P-value  =  0.111). The coefficient (b) in the rising exponential term was decreased substantially with respect to the C_GA (i.e. P-value  =  0.043). The coefficient (b) varied substantially up to C_GA  =  6 µl ml⁻¹. Above C_GA  =  6 µl ml⁻¹, there was no difference in coefficient (b). The results indicated that the upper threshold was about C_GA  =  6 µl ml⁻¹. In other words, the present method did show significant differences in deformability for RBCs fixed with GA solution below C_GA  =  6 µl ml⁻¹. The microscopic imaging-based approach suggested in a previous study was employed to verify the results obtained by the present method. Figure 5(B) shows variations in the DI_MI (ΔV) with respect to the C_GA. From the results, the DI_MI remained constant below C_GA  =  2 µl ml⁻¹. Above C_GA  =  2 µl ml⁻¹, the DI_MI decreased substantially with respect to the C_GA (i.e. P-value  =  0.0001). By referring to figure 4(B), the DI_MI obtained by the previous method only varied with the suspension solution (i.e. concentration differences in the dextran solution). From the results, it was found that the DI_MI would be altered by the suspension solution or individual RBC deformability.

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According to the present method, the RBC deformability was quantified by using two regression coefficients (a) and (b) in the two-term exponential model. It was necessary to verify the linear relationship between the present method (regression coefficients (a) and (b)) and the previous method (DI_MI (ΔV)). Figure 5(C) shows the regression coefficients (a) and (b) and DI_MI (ΔV) overlapped in an X–Y plot. According to the linear regression analysis, the regression coefficient (a) and DI_MI had a statistically insignificant linear relationship (i.e. R²  =  0.5788, P-value  =  0.138). However, the regression coefficient (b) and DI_MI had a statistically significant linear relationship (i.e. R²  =  0.8953, P-value  =  0.015). From the linear relationship analysis, the regression coefficient (b) represented variations in the RBC deformability. In other words, because normal RBCs were chemically fixed and added to the same PBS solution, it was inferred that the RBC membrane fixation could be detected by means of the regression coefficient (b). In addition, by referring to figure 4(A(a)), the coefficient (a) was determined by the change in the suspension solution (i.e. dextran solution, PBS solution, and plasma). These results lead to the conclusion that the two coefficients (a) and (b) can effectively be used to detect changes in the suspension solution or individual RBC.

For the early detection of diseases related to hematological disorders, it was required to detect subpopulation differences in large populations of RBCs. In other words, it was necessary to verify that the proposed method had the ability to detect minor differences in whole blood. To mimic subpopulation differences in normal blood, heterogeneous blood was prepared by adding hardened blood to normal blood. Thus, the proposed method was employed to detect heterogeneous blood by means of two properties, the ESR and RBC deformability.

From the experimental results represented in figure 5, hardened blood was prepared by adding chemically fixed RBCs with GA solution (C_GA  =  8 µl ml⁻¹) to PBS solution (i.e. V_HB). In addition, to reduce the duration of the ESR experiments significantly, plasma was replaced with a specific dextran solution of 15 mg ml⁻¹. Normal blood was then prepared by adding normal RBCs into the specific dextran solution (i.e. V_NB). Heterogeneous blood was prepared by mixing normal blood with hardened blood. The mixing ratio (φ) was defined as the ratio of the hardened blood volume to the total blood volume (i.e. $\varphi =\frac{{{V}_{HB}}}{{{V}_{NB}}~+~{{V}_{HB}}~}$). Blood with the specific mixing ratios (φ  =  0, 5%, 10%, 20%, and 100%) was prepared by adding hardened blood to normal blood. Here, φ  =  0 and φ  =  100% denote pure normal blood and pure hardened blood, respectively.

First, as shown in figure 6(A(a)), variations in the ESR_PM were obtained by varying φ  =  0, 5%, 10%, 20%, and 100%. Below φ  =  5%, the ESR_PM remained constant. However, above φ  =  10%, the ESR_PM was decreased substantially by increasing the mixing ratio (i.e. P-value  =  0.01). In other words, when hardened blood (i.e. PBS as the suspension solution) was partially added to normal blood (i.e. dextran solution as the suspension solution), the concentration of the dextran solution in the normal blood was diluted considerably with respect to the mixing ratio. It was certain that the ESR_PM decreased substantially due to the dilution effect of the normal blood. In addition, hardened RBCs in heterogeneous blood did not contribute to the RBC aggregation. Thus, the ESR_PM showed significant differences when heterogeneous blood included at least 10% volume of hardened blood, when compared with the control (i.e. pure normal blood).

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Second, four regression coefficients (a)–(d) were obtained by best-fitting the ΔV_B with the two-term exponential model. As shown in figures S6(A) (supplementary material), the regression coefficients (a) and (c) in the two-term exponential model were obtained by increasing the mixing ratio. The coefficient (a) was decreased considerably above φ  =  20% (i.e. P-value  =  0.037). The coefficient (a) showed a statistically insignificant decrease below φ  =  20% (i.e. P-value  =  0.576). When setting the mixing ratio (Φ) as Φ  =  10% or 20%, the RBC deformability and ESR showed a significant difference. For this reason, the author did not test above Φ  >  20%. The coefficient (c) did not show a significant change with respect to φ (i.e. P-value  =  0.815). Figure S6(B) (supplementary material) shows variations in the regression coefficients (b, d) with respect to φ. The coefficient (b) remained constant below φ  =  10% (i.e. P-value  =  0.901). Above φ  =  10%, the coefficient (b) decreased substantially (i.e. P-value  =  0.049). The coefficient (d) had a statistically insignificant increase with respect to φ (i.e. P-value  =  0.305). Figure 6(A(b)) shows the coefficients (a, b) in the rising exponential term redrawn with respect to φ. From the results, the coefficients (a) and (b) showed a significant difference when heterogeneous blood included at least 20% by volume of hardened blood, when compared with the control (i.e. pure normal blood).

Finally, the previous method that used a microscopic imaging approach was employed to verify the results obtained by the proposed method. As shown in figure 6(B), variations in the ESR (AI_MI) and RBC deformability (DI_MI) were obtained by varying the mixing ratio (φ). Below φ  =  10%, the AI_MI remained constant with respect to φ. Above φ  =  10%, the AI_MI decreased substantially (i.e. P-value  =  0.001). In addition, above φ  =  5%, the DI_MI showed a statistically significant change, when compared with the control (i.e. P-value  =  0.001). From the results, the previous method was able to detect heterogeneous blood that includes at least 10% by volume of hardened blood.

These results lead to the conclusion that the proposed method had the ability to detect heterogeneous blood with at least 10% hardened blood by measuring the ESR and RBC deformability. The proposed method could give comparable results to the previous method. The ESR_PM and the two coefficients (a) and (b) in the rising exponential term could be effectively employed to detect subpopulations in heterogeneous blood.

In this study, while opening the outlet by removing the stopper, the V_B inside the ACS tended to decrease over time. As the blood sample flowed into the micropillar channel, the V_B tended to decrease and varied depending on the RBC deformability. The net blood volume (i.e. ΔV_B) which was supplied to the microfluidic device was estimated as ΔV_B (t)  =  V_B (t  =  t₁)  −  V_B (t). The ΔV_B was best fitted using the two-term exponential model (i.e. ΔV_B (t)  =  axexp [bt]  −  cxexp [−dt]). Three different blood samples (i.e. dextran-included blood sample, GA-induced homogeneous blood sample, and heterogeneous blood sample) were prepared to test the feasibility of the proposed method. First, as shown in figure 4(A(b)), the coefficient (a) was varied substantially with respect to the concentration of the dextran solution. The result indicated that the coefficient (a) represented the contribution of the base solution (i.e. dextran solution) to the RBC deformability. Second, a homogeneous hardened blood sample was prepared by adding RBCs fixed with the same concentration of GA solution into 1×  PBS solution. The results indicated that the coefficient (a) remained constant with respect to the C_GA. However, coefficient (b) tended to decrease substantially with respect to the C_GA. Considering that the blood sample had different degrees of RBC deformability in the same base solution, the coefficient (b) represented contributions of RBCs to RBC deformability. At last, the heterogeneous blood sample was prepared by partially adding a hardened blood sample to a normal blood sample. As the heterogeneous blood sample had simultaneous variations in the base solution and RBCs, it was estimated that two coefficients (a) and (b) tended to vary substantially with respect to the mixing ratio. According to the experimental results, the coefficient (a) tended to decrease substantially above a mixing ratio of 20%. Additionally, the coefficient (b) tended to decrease substantially above a mixing ratio of 10%. When compared with the microscopic imaging-based technique suggested in a previous study, the present method showed consistent results. Thus, it was certain that the proposed method could be employed to detect differences in RBC deformability.

However, the proposed method was not applied to clinical tests. As future work, it will be necessary to verify the performance of the proposed method for clinical samples, such as CVDs or malaria-infected bloods. Furthermore, from various experimental results, one will be required to understand the distinctive trends of the ESR and RBC deformability with respect to various diseases.