2.1. Device Concept

RBCs have a biconcave disk shape with a diameter of approximately 7–8 μm and a thickness of approximately 2 μm at the periphery and approximately 1 μm at the central concave region. This characteristic morphology underpins our device concept of a microfluidic channel designed to evaluate RBC deformability by observing its behavior as it passes through a narrow constriction. The device geometry aims to induce measurable deformation while minimizing artifacts, such as cell tilting or wall effects.

Figure 1 illustrates the experimental setup. As shown in Fig. 1(a), the cell suspension flowed from the inlet well on the right side to the outlet well on the left side. An opposing flow was generated from the outlet side, causing the cells to decelerate rapidly or reverse their flow, as shown in Fig. 1(b). This flow manipulation applied a mechanical load to the cells within the microfluidic channel, inducing observable deformations.

2.2. Design Rationale

Based on preliminary experiments and previous reports, the channel height was fixed at 2.0 μm to prevent RBC tilting along the height direction, which complicates the deformation analysis. Although a height of 20 μm suppressed tilt, deformation became less pronounced, complicating evaluation. The RBC deformation is also smaller near the channel walls; therefore, a sufficiently wide channel is preferred to reduce wall effects. However, excessively wide channels risk sagging of the ceiling, which may contact the glass substrate, given the low channel height.

Through prototyping, a channel width of 200 μm was confirmed to maintain a stable height of 2.0 μm without sagging. RBCs were observed in an 80 μm region near the center where wall influence was minimal. The channel had a simple straight geometry with a distance of 10.0 mm between the inlet and outlet wells. Fig. 2(a) shows the channel dimensions, including a height of 2.0 μm, a width of 200 μm, a length of 10 mm, and a central observation region of 80 μm.

2.3. Device Fabrication

Figure 2(b) shows the fabrication process. The device was fabricated using soft lithography. SU-8 2 resist (Kayaku Advanced Materials Inc., Tokyo, Japan) was spin-coated to a thickness of 2.0 μm and patterned via photolithography to define the channel geometry. Polydimethylsiloxane (PDMS) (Silpot 184, DuPont Toray Specialty Materials K.K.) was molded onto the master and peeled off after curing. Inlet and outlet wells (1.5 mm diameter) were created by punching the PDMS. Bonding to a glass substrate was achieved via air plasma treatment using a hydrophilization device (PIB-20, Vacuum Device Inc., Ibaraki, Japan) at a vacuum of 90 Pa and a current of 40 mA for 30 s, followed by thermal bonding at 95 °C for 5 min. To enable a high-magnification observation of RBCs (7–8 μm diameter), a thin glass substrate (0.13–0.16 mm thick) was used to minimize the working distance of the microscope objective.

2.4. Experimental Setup

The experimental system (Fig. 3) consisted of an inverted microscope (IX-73, Evident Corporation, Tokyo, Japan), a microfluidic device, a syringe pump (MSPE-1, AS ONE Corporation, Osaka, Japan), and a high-speed camera (HAS-U2, DITECT Co., Ltd., Tokyo, Japan). The cell suspension was injected into the inlet well via tubing connected to a syringe pump. This setup maintained a steady flow, and air was introduced at the outlet. Imaging was performed at a resolution of \({1280\times 768}\) pixels and 500 fps, with a shutter speed of \(1/10000\) s to avoid motion blur. The spatial resolution was 0.119 μm/pixel, which is sufficient for RBC deformation analysis and comparable to or better than the resolutions reported in previous studies ³⁴, ensuring accurate quantification of subtle morphological changes.

Blood samples were collected from healthy volunteers after informed consent was obtained. The samples were diluted in physiological saline to a concentration of less than \(1/1000\). All the procedures were approved by the Ethics Review Committee for Medical Research Involving Human Subjects at Setsunan University (Approval No.2025-034). Flow reversal was induced by manually pushing the syringe at the outlet well to observe the RBC behavior during deceleration and reverse flow. The dynamics were recorded using a high-speed camera.

The primary objective of this study was to evaluate cell deformability. Therefore, comparative experiments were conducted using RBCs with intentionally reduced deformability. Specifically, adenosine triphosphate (ATP) depletion was induced in RBCs. Previous studies have reported that ATP levels are correlated with deformability and blood-related diseases, such as aging ³⁵, sepsis ³⁶, sickle cell disease ³⁷, diabetes mellitus ³⁸, malaria ³⁹, and chronic kidney disease ⁴⁰. To minimize ATP degradation over time, all the samples were processed within 1 h of blood collection. ATP depletion was achieved by incubating the cell suspensions (adjusted with saline) at 37 °C for 8 h. The experiments were conducted within 1 h of incubation. Samples from the same donor collected on the same day were used to minimize other variations. This approach allows a direct comparison of the mechanical deformability of healthy and disease-mimicking RBCs using the proposed microfluidic technique. Importantly, ATP depletion serves as a widely accepted in vitro model to mimic the impaired deformability observed in pathological conditions, such as sickle cell disease, diabetes mellitus, and other hemorheological disorders ^{35,36,37,38,39,40}.

3.1. Cell Behavior Results

Figure 4 shows a typical example of a cell manipulated within a channel. Time-lapse images at intervals of 10 ms are presented; however, the actual acquisition interval was 2 ms. In the figure, the RBC initially moves from right to left, decelerates, stops, and subsequently reverses direction to move from left to right. The moment at which the direction changes is defined as 0 ms. The scale bar indicates 10 μm.

Before deformation, the RBCs exhibited circular shapes. A magnified image at \(-40\) ms, along with the extracted cell region, is shown. A magnified image at 30 ms, when the cell exhibited maximum deformation, is also presented. As shown in Fig. 4, the RBC does not deform maximally at the instant of flow reversal; rather, the maximum deformation occurs after the cell has traveled approximately 15 μm in the reverse direction. This behavior was consistently observed in all the manipulation experiments, not only in the example shown in Fig. 4. Furthermore, even when varying the initial velocity under steady flow conditions and the magnitude of the manual syringe operation applied from the outlet side, the maximum deformation consistently occurred after the onset of reverse motion.

3.2. Behavioral Analysis

Trajectory analysis was performed based on the acquired time-lapse images. Fig. 5(a) shows the same sample as that shown in Fig. 4. As indicated in the figure, the time at which the direction change occurred was defined as 0 ms, and the position of the cell region closest to the outlet well was set as the origin. The direction toward the inlet well was defined as positive. In all the images, the position of the cell region closest to the outlet well was plotted. Fig. 5(b) shows these positions at intervals of 2 ms. Based on these positional data, the velocity and acceleration were calculated, as shown in Figs. 5(c) and (d), respectively.

3.3. Estimation of Applied Load

Regarding the deformation behavior of the RBCs, the cells maintained a highly circular shape from before load application up to the moment of flow reversal. After reversing this direction, the RBCs gradually deformed into arc-like shapes. In this study, the deformation was evaluated by comparing the cell shape before and at the point of maximum deformation. The numerical calculation software MATLAB was used for the image evaluation. The evaluation method is illustrated in Fig. 6. First, the contour of the RBC before deformation was extracted, and its area was calculated. The reference circle diameter \(D\) is defined as the diameter of a circle with the same area. Similarly, for the deformed RBC, the contour was extracted, and the major axis length \(L\) and minor axis length \(S\) were obtained. In MATLAB, contour extraction was performed using the region of interest method, and the principal axis was determined using principal component analysis (PCA). The accuracy and stability of the PCA-based axis extraction were evaluated by comparing measurements with and without PCA. For instance, the major axis length with PCA was \(9.5{\pm}0.7\) μm and the minor axis was \(7.7{\pm}1.2\) μm, whereas without PCA, they were \(9.6{\pm}0.7\) μm and \(7.5{\pm}1.1\) μm, respectively. The circularity values were \(0.64{\pm}0.16\) with PCA and \(0.77{\pm}0.1\) without PCA. These small differences and low variability indicate that PCA provides stable and reliable axis extraction for shape analysis. Future studies may incorporate additional shape metrics, such as elongation index and circularity, to further validate and complement these findings.

The deformation rate is defined by the following equation:

In the example shown in Fig. 4, the deformation rate is 39.11%. The experiments were conducted under various initial velocity and syringe operation conditions. For the 16 samples, the deformation rate was \(31.11{\pm}5.40\)%. The relationship among the applied load originating from the inertial force, shear stress, and deformation rate was also analyzed. The inertial force can be expressed using Eq. (2) below.

Here, \(m\) represents the mass of a single RBC, calculated as 90 pg (\({9.0\times 10^{-14}}\) kg). The acceleration \(\alpha\) was approximated at the point of directional change. For example, in Fig. 5(d), an acceleration of 0.036 m/s\(^2\) was obtained from an approximation curve, resulting in an inertial force of 3.64 fN. Similar calculations were performed for all 16 samples. The relationship between the inertial force and the deformation rate is shown in Fig. 7.

To quantitatively verify that the shear stress dominates the inertial forces, we calculated the relevant dimensionless numbers. Using a channel height of approximately 2 μm, a flow velocity of approximately 2 mm/s, a fluid viscosity of approximately 1 mPa \(\cdot\) s, and a fluid density of approximately 1000 kg/m\(^3\), the Reynolds number (\(\mathit{Re}\)) is estimated as follows:

Instead, the dominant factor is the wall shear stress generated between the channel and the RBCs. In previous experiments with a channel height of 1 μm, direct physical contact between the RBCs and the channel walls was observed, confirming that the RBC thickness (\(\sim\)2 μm) can lead to contact in sufficiently narrow channels ⁴⁴. Experimental observations in the current study confirmed that there is no physical contact between the RBCs and the channel walls at the channel height of 2 μm. Although both the RBC thickness and channel height are approximately 2.0 μm, a thin lubrication gap of approximately 10–100 nm is presumed to exist based on microscopic observations and cell deformation behavior.

The viscosity \(\mu\) is assumed to be 1 mPa \(\cdot\) s, which approximates the viscosity of water at 25 °C under the experimental conditions. The gap was set to 100 nm. Using the initial steady flow velocity of 2.012 mm/s from Fig. 5, the shear rate (velocity gradient) near the wall is estimated as follows:

Thus, the wall shear stress \(\tau\) can be approximated as

In the example shown in Fig. 5, the initial steady flow velocity was 2.012 mm/s, and the projected cell area was 56.65 μm\(^2\). Based on these values, the load owing to the shear force was estimated to be 1140 pN. Similar calculations were performed for all 16 samples. The relationship between the shear-stress-derived load and the deformation rate is shown in Fig. 8. The shear stress is the dominant factor compared with the inertial force. However, the magnitude of the shear-induced load does not significantly affect the deformation rate. For example, the deformation rate showed a value of approximately 30% in a wide range from below 200 pN to above 2000 pN. This indicated that variations in the steady flow velocity and manual syringe operation did not significantly influence the results. Therefore, the proposed method can be implemented using a relatively simple experimental setup.

A sensitivity analysis involving repeated measurements of the same RBC under varying load conditions was not performed in this study. This is mainly due to the inherent heterogeneity in cell size and shape, as reflected by the projected cell area of 62.18\(\pm\)8.4 μm\(^2\) across the 16 samples. Even among cells of similar sizes, variability in the deformation rate was observed, indicating significant individual differences in mechanical response. The ability to detect cell–cell heterogeneity is a notable feature of this method. Consequently, although no significant variation in the deformation rate was observed within the estimated load range of 200–2000 pN, it appears that biological variability, rather than load variation, predominantly contributed to the observed spread in deformation rates. Future studies will focus on controlled sensitivity analyses to more precisely quantify the effect of the applied load magnitude on RBC deformability and to separate load effects from intrinsic cellular variability.

3.4. Evaluation of Deformation

Based on the findings in Section 3.3, no significant variation in the deformation rate was observed within the load range of 200–2000 pN. The deformation rate was calculated experimentally when a load was applied within this range. In the present study, experiments were conducted using normal and ATP-depleted RBCs. Six samples were analyzed for each condition. The results are shown in Fig. 9. The deformation rate for normal RBCs was \(31.5{\pm}11.8\)%, whereas that for ATP-depleted RBCs was \(11.1{\pm}5.3\)%. These results confirmed that ATP depletion reduced deformability. A statistical analysis was performed using an independent two-sample \(t\)-test, assuming equal variances, because tests for the equality of variances support this approach. Additionally, 95% confidence intervals were calculated to assess the variability of group means: for normal RBCs, \(31.5{\pm}16.38\)% (95% CI: 15.12 to 47.88), and for ATP-depleted RBCs, \(11.1{\pm}7.33\)% (95% CI: 3.77 to 18.43). The \(p\)-value between the two groups was 0.025, indicating a statistically significant difference. The calculated Cohen’s \(d\) value was 1.86, indicating a significant effect. Although the sample size was limited to six per group, the observed significant difference and large effect size suggest meaningful biological relevance. Future studies with larger sample sizes are warranted to confirm and generalize these findings. Before deformation, both had high circularity and no significant difference was confirmed, even when using the reference circle diameter as an indicator. Therefore, the deformability of individual RBCs can be evaluated by applying a load.

Additional experiments were conducted using a channel height of 3.6 μm to investigate the effect of microchannel dimensions on RBC deformability. Under these conditions, the deformation rates for normal RBCs was \(11.4{\pm}6.9\)%, and ATP-depleted RBCs were \(10.3{\pm}8.3\)%. No statistically significant differences were observed between the two groups (\({p>0.05}\)). This suggests that increasing the channel height reduces the wall shear stress applied to the RBCs, thereby decreasing the effective mechanical loading and limiting cell deformation. These findings highlight the importance of precise control of microchannel dimensions when designing experiments to evaluate the mechanical properties of RBCs.

4.1. RBC Deformation Mechanism and Response Delay

The deformation behavior observed in this study suggests that wall shear stress, rather than inertial force, is the dominant factor contributing to RBC deformation. It is possible that the wall shear stress generated during steady flow was released upon flow cessation, thereby inducing deformation. However, the maximum deformation did not occur immediately during the flow reversal but after a short period during reverse motion.

This delay may have resulted from several interacting factors. First, the elastic properties of the silicone materials used in tubing and microfluidic devices may cause a temporal lag in force transmission ⁴⁵. Second, transient flow dynamics, such as fluid inertia and pressure wave propagation within the microchannel, can contribute to the temporal delay. Third, RBCs exhibit viscoelastic behavior by combining elastic and viscous properties, which likely contribute to the delayed deformation response ⁴⁶. Additionally, slight variations in channel height from the nominal value of 2.0 μm owing to pressure changes induced by syringe operation may affect the deformation. Although the precise quantification of these factors is difficult, considering them provides a more comprehensive understanding of the observed deformation dynamics. However, these explanations remain speculative interpretations based on plausible physical reasoning and relevant literature. No direct experimental measurements were conducted to quantitatively verify the individual contributions of tubing elasticity, transient flow dynamics, or RBC viscoelasticity to the observed delay. Future studies involving detailed flow and pressure measurements, mechanical characterization of device materials, and rheological studies of RBCs under dynamic conditions are necessary to substantiate and refine these hypotheses.

In particular, the observed delay between flow reversal and maximum deformation likely arises from multiple interacting factors. The elasticity of the silicone tubing and microfluidic device may act as a mechanical filter, causing a time lag between the sudden change in flow direction and shear stress transmitted to the cells. Thus, although the flow reverses instantaneously, the effective mechanical load on the RBCs builds over a short period owing to the elastic deformation and relaxation of the device materials. Additionally, transient flow dynamics, such as fluid inertia and pressure wave propagation within the microchannel, may contribute to this temporal delay by delaying the establishment of steady shear stress conditions after reversal. The viscoelastic nature of RBCs further compounds this delay, as the cells require a finite time to respond to changing mechanical stimuli owing to cytoskeletal remodeling and membrane viscosity. Together, these mechanisms explain why the maximum deformation occurs shortly after flow reversal rather than immediately after. Although the precise quantification of each contribution is challenging, considering these factors provides a comprehensive understanding of the observed deformation dynamics.

4.2. Experimental Setup Robustness and Practicality

Despite these complexities, the current experimental setup is simple and enables a relatively high-throughput application of mechanical loads in the piconewton to nanonewton range, making it a practical tool for assessing RBC deformability under controlled stimuli. Manual syringe operation to induce reverse flow introduces some variability; however, the direct observation and quantification of cell deformation via high-speed imaging at the single-cell level effectively accounts for these variations in the results. Our results show consistent deformation despite minor manual differences, demonstrating the practical robustness of the proposed method. Although automation can improve reproducibility, the current approach offers a simple and reliable method for assessing RBC deformability.

4.3. Channel Geometry and Mechanical Loading Limitations

Although this method is simple and robust, it has some limitations. Mechanical loading and the resulting deformation are sensitive to the channel geometry, particularly the channel height, which determines the gap between the cells and the channel walls. The channel height was set considering the flattened shapes of the RBCs. When a larger channel height of 3.6 μm was tested, smaller deformation was observed, suggesting that the channel geometry should be adjusted to match the target cell size and shape. Although the gap estimations were based on nominal dimensions, slight variations in fabrication or pressure may have affected the actual geometry and mechanical load. The assumptions in the gap and shear stress calculations simplify the complex fluid–cell interactions in confined microchannels. Although this study focused on RBCs owing to their high deformability and clinical relevance, the method could potentially be applied to other cell types by tailoring the channel geometry accordingly. Future studies should explore these adaptations to broaden the applicability of this approach.

4.4. Biological Variability and ATP Depletion Model Considerations

Furthermore, our findings highlight the inherent biological variability among RBCs, as indicated by the spread of deformation responses under similar loading conditions. This emphasizes the importance of single-cell analysis for capturing heterogeneity that bulk measurements may overlook. The ability of the present method to detect such cell-to-cell differences could prove valuable for diagnostic applications, for example, in identifying pathological changes in RBC mechanics associated with diseases such as sickle cell anemia and malaria.

However, ATP depletion is a simplified surrogate model for the impaired RBC deformability observed in various diseases. Although it mimics the metabolic abnormalities seen in conditions such as diabetes and sickle cell disease, the actual pathological states involve multiple complex factors, including oxidative stress, membrane protein alterations, and inflammatory responses that are not captured by ATP depletion alone. Therefore, although our findings are promising, they remain preliminary until they can be validated using clinical patient samples. Future studies should test this method using pathological specimens to confirm its diagnostic relevance. Additionally, evaluating the sensitivity and specificity for detecting subtle clinical variations in RBC deformability is crucial.

Future studies should focus on refining the load control, possibly through automated syringe pumps or microfluidic flow controllers, to reduce variability and enable systematic sensitivity analyses. Integrating molecular or biochemical markers with mechanical measurements can provide deeper insights into the mechanisms underlying RBC deformability. Extending this approach to other cell types or cells under different physiological or pathological conditions may broaden its applicability and impact in biomedical research.