In vitro investigation of the mechanics of fixed red blood cells based on optical trap micromanipulation and image analysis

Erythrocyte deformability correlates with various diseases. Single-cell measurements via optical tweezers (OTs) enable quantitative exploration but may encounter inaccuracies due to erythrocyte life cycle mixing. We present a three-step methodology to address these challenges. Firstly, density gradient centrifugation minimizes erythrocyte variations. Secondly, OTs measure membrane shear force across layers. Thirdly, MATLAB analyzes dynamic cell areas. Results combined with membrane shear force data reveal erythrocyte deformational capacity. To further characterize the deformability of diseased erythrocytes, the experiments used glutaraldehyde-fixed erythrocytes to simulate diseased cells. OTs detect increased shear modulus, while image recognition indicates decreased deformation. The integration of OTs and image recognition presents a comprehensive approach to deformation analysis, introducing novel ideas and methodologies for investigating erythrocytic lesions.


Introduction
Erythrocyte deformability can be characterized by biomechanical properties such as aggregation, adhesion and elasticity, but changes in these features have been associated with the development of many diseases [1][2][3].For instance, in patients with multiple myeloma, weakened repulsion between erythrocytes leads to increased aggregation, resulting in the formation of erythrocyte stacks and significantly reduced oxygen transport [4,5].Similarly, in sickle cell disease (SCD), the polymerization of deoxyhemoglobin (deoxy-HbS) in erythrocytes reduces their deformability, thereby impacting the efficiency of erythrocyte circulation and contributing to symptoms of anemia [6,7].Additionally, in malaria patients, erythrocytes invaded by Plasmodium falciparum experience a two-to three-fold increase in cellular shear modulus and enhanced adhesion [8].Therefore, a comprehensive understanding of erythrocyte deformation properties is essential for advancing current knowledge of various hematologic disorders.
Common methods for measuring erythrocyte deformation properties include microneedle aspiration (MPA) [9], atomic force microscopy (AFM) [10], osmotic gradient ektacytometry [11] and optical tweezers (OTs) [12].Among them, OTs have emerged as a research hotspot in single-cell detection due to its flexible and contactless operation [13].OTs technologies, based on optical radiation pressure and single-beam gradient forces, allow the trapping and optical manipulation of tiny particles in three dimensions, hence facilitating the study of their mechanical properties.The concept of optical tweezers manipulation was initially proposed by Arthur Ashkin of Bell Labs, USA, in 1970 [14].Due to its non-contact nature, high precision, and mechanical controllability, optical tweezers have found extensive applications in erythrocyte studies [15].Recent major studies in this domain include: (1) Investigation of erythrocyte deformation properties in thalassemia, diabetes mellitus, and sickle cell disease [16][17][18]; (2) Examination of interactions between erythrocytes [19,20]; (3) Assessment of the effects of medical nanomaterials on erythrocytes [21,22].
The manipulation of erythrocytes by OTs consists of two main types.In the first method, the optical tweezers light trap captures erythrocytes directly [23].Erythrocytes, with their homogeneous cytoplasm, are positively lensed and thus stably captured by the OTs.Recently, Yao et al. utilized optical tweezers to directly capture erythrocytes flowing in microchannels, enabling the acquisition of the rheological morphology of the cells [24].However, the irregular shape of erythrocytes in the light trap limits the potential of OTs as a mechanical measurement tool.In the second approach, OTs manipulate erythrocytes using microspheres adhered to them [25].These microspheres have a regular shape and can be easily calibrated for light-trapping mechanics using a thermal motion calibration method [26].Yale et al. obtained the shear modulus of cells by manipulating red blood cells adhered to a carrier stage, squeezing silica microspheres in a light trap [27].In contrast, Liu et al. utilized an acousto-optic deflection (AOD) system to actively manipulate the microspheres for stretching the erythrocytes, a more sensitive manipulation [28].In addition, Sigüenza et al. calculated that the adhesion area of erythrocytes affects tensile measurements, and employing a dual-microsphere adhesion strategy leads to a more stable adhesion area, thereby enhancing measurement accuracy [29].
Despite undergoing numerous optimizations, the stretching procedure for erythrocytes using OTs still exhibits some limitations.Variations in erythrocyte density and shear modulus across different blood circulation cycles may lead to discrepancies in light tweezers measurements, rendering the results less generalizable and representative [30,31].Percoll-based centrifugation enables stratified aggregation of erythrocytes with different densities [32], and thus has great potential for improving sample consistency in OTs assays.Additionally, previous studies have struggled to quantitatively characterize the deformation area of erythrocytes, limited by the single mechanical measurement function of OTs.However, the erythrocyte area serves as an important indicator for disease characterization [33,34].Therefore, further development of area characterization methods during erythrocyte deformation is necessary to broaden the dimension of erythrocyte characterization detected by OTs.
In this study, the first objective was to minimize variations among individual erythrocytes by subjecting them to density gradient centrifugation using Percoll.Subsequently, erythrocyte shear modulus obtained by stretching double microsphere-adherent erythrocytes using an AODdeflected optical pathway.To enable a quantitative analysis of erythrocyte deformation during optical tweezers stretching, MATLAB was also used for identifying erythrocyte stretching images.This facilitated the collection of data on the changes in individual erythrocyte area under stretching conditions.Finally, glutaraldehyde was employed to simulate "diseased" erythrocytes, characterized by increased hardness [35].Mechanical and image changes during the deformation of these "diseased" erythrocytes were then quantitatively analyzed.The findings indicated a significant decrease in the maximum degree of erythrocyte deformation to less than 8% when the erythrocyte shear modulus was increased by more than a factor of two.These results underscore the effectiveness of combining OTs micromanipulation technology with image recognition technology for a comprehensive quantitative study of erythrocyte deformation.In addition, this integrated approach may provide new insights into the behavior of erythrocytic lesions.

Red blood cell extraction
To assess the validity of the erythrocyte density gradient separation method, two distinct sets of erythrocytes were prepared.The control group involved a washing procedure of whole blood, performed in three cycles, and this was followed by resuspension in PBS.To wash and resuspend the erythrocytes, phosphate buffer solution (PBS) containing 8 mM Na 2 HPO 4 , 1.8 mM KH 2 PO 4 ,137 mM NaCl, and 2.7 mM KCl at pH 7.2-7.4was used.In the experimental group, whole blood was centrifuged using a Percoll gradient, and after extracting the upper and lower erythrocyte fractions, they were subsequently washed and resuspended.Ex vivo whole blood were preserved in anticoagulation tubes, with the anticoagulant showing no visible effects on erythrocyte separation within the Percoll gradient [36].Percoll, which can induce cell separation through density gradient centrifugation within the 1.02-1.13g/ml range, was subjected to gradient dilutions based on the following density proportioning formula: where, V 0 is the volume of undiluted Percoll, V is the volume of the final solution, ρ is the desired density of the target solution, ρ 0 is the density of the original percoll (1.13 g/ml) and ρ 1 is the density of the PBS solution used to dilute the percoll solution (1.058 g/ml).
Based on the buoyant density distribution of erythrocytes which ranged from 1.08 g/ml to 1.11 g/ml [37], the density gradients of the target solution were configured at 1.075 g/ml, 1.085 g/ml, 1.095 g/ml, 1.105 g/ml, and 1.115 g/ml, with each gradient having a volume of 1.5 ml.Gradient centrifugation of erythrocytes isolated for 1 day, 7 days, and 14 days, respectively, was performed according to the above method, and the results are shown in Fig. 1.With the passage of time in vitro, the dense area of red blood cells gradually moved from the upper low density layer to the lower high density area, since the average cell density increased due to the decay of red blood cells.Following the separation process, the upper (UL) and lower (LL) layers of erythrocytes were isolated and resuspended separately.

Co-processing of SiO 2 with erythrocytes
An amino-modified silica stock solution was combined with the resuspended erythrocyte.In this case, the amino groups which are present on the surface of silicon dioxide and carry positive charges established a strong electrostatic interaction with the negatively charged glycoproteins on the surface of cell membranes.This interaction facilitated the attachment of the silicon dioxide optical handle [38].

Fixation of erythrocytes
Control group erythrocytes were prepared by washing whole blood and resuspending the cells.For the experimental group, the erythrocytes were extracted from the upper layer after Percoll centrifugation and fixed using varying concentrations of glutaraldehyde.A 50% glutaraldehyde solution was then diluted in PBS to yield three concentration gradients (0.005%, 0.01% and 0.015%).These diluted solutions were subsequently added to the silica-erythrocytes mixture, and left to stand for 10 minutes.

Experimental design for stretching red blood cells with optical tweezers
The shear modulus of erythrocytes was measured with an optical tweezer system (Tweez250si, Aresis, Slovenia), as illustrated in Fig. 2 (left).This system involved a laser light, emitted and directed through a computer-controlled acousto-optic deflector (AOD) module, and after being expanded by a beam expander, it was eventually reflected through a dichroic mirror and into a high-numerical-aperture microscope objective lens (Nikon Ti, Japan).This laser light was precisely focused to generate an optical trap within the sample chamber.The power of the laser reaching the beam waist via optical path loss is about 100 mW.It has been demonstrated in the literature that the temperature rise of the laser trapping silica microspheres in aqueous solution is 0.79 °C/100 mW and does not cause thermal damage to red blood cells [39].

Mechanical characterization
The stiffness of the optical trap was determined by analyzing the thermal motion of individual silica microspheres within the trap [25].The microsphere exhibited irregular thermal motion at the central region of the light trap and the probability density of its position distribution adhered to Boltzmann's law as follows: In the equation, k B is the Boltzmann constant, T is the absolute temperature, a is a normalized constant, and E(x) is the potential field at the center of the optical tweezers.A harmonic potential field was taken into account in the vicinity of the optical trap's center, with the expression for E(x) being as follows: In the equation, k x is the optical trap stiffness, and ∆x is the distance of the microsphere from the center of the light trap.For light trap calibration, a silica microsphere is captured using the light trap.The deviation distance of the microsphere from the center of the light trap during thermal motion is recorded by a CMOS sensor.Subsequently, the potential of the light trap on the particle in both the horizontal (X) and vertical (Y) directions within the capture plane is fitted, as illustrated in Fig. 3. Combining Eq. ( 3) and based on the potential energy curve, the optical trap stiffness can be found to be 3.18 pN/µm in the X direction and 3.51 pN/µm in the Y direction.Throughout this set of experiments, the laboratory room temperature was maintained at 25 °C.
While the microspheres were in motion, causing the stretching of the erythrocytes, they were set to move at a low speed of < 0.2 µm/s.Applying Stokes' law, we can calculate the viscous resistance of the liquid to the movement of the microspheres: In the equation, η is the viscosity coefficient of the liquid, µ is the velocity of the microspheres relative to the liquid, and R is the radius of the microsphere.It is calculated that the viscous resistance received by the ball is two orders of magnitude smaller than the light trap force at a speed of 200 µm/s, which is negligible.Hence, the microspheres experienced only the light-trapping force and the reaction force exerted by the erythrocyte membrane.As depicted in Fig. 2 (right), there was a disparity between the displacement of the light trap (∆x 1 ) and the displacement of the silica sphere (∆x 2 ) due to the erythrocyte membrane's reaction force that was pulling the sphere away from the center of the light trap.
By incorporating the calibrated curve for the stiffness of the light trap center, the value of the light trap force acting on the sphere was determined, and it was equal to the stretching force applied to the erythrocyte.

Deformation characterization
To measure the stretching and deformation process of red blood cells, video images were processed using MATLAB based on information captured by CMOS.Initially, the image was sharpened to produce a binarized version.Expansion, filling and erosion algorithms were subsequently applied to generate a comprehensive binarized image that depicted cell stretch deformation.Finally, a threshold segmentation method was employed to isolate pixels within the cell area, thereby facilitating the extraction of precise data on the dynamic area changes of erythrocytes during stretching.

Erythrocyte density gradient centrifugation
Erythrocytes exhibit varying shear moduli at different stages of maturation [32].Additionally, the densities of erythrocytes also differ based on their age.To further validate the effect of density gradient centrifugation on the enhancement of sample homogeneity, shear modulus was measured on density-separated erythrocytes.Optical tweezers were used to stretch erythrocytes by controlling the horizontal movement of SiO 2 , as depicted in Fig. 4. The stretching force applied during this process was quantified, with the resulting data presented in Fig. 5.In that figure, the vertical axis represents the extension ratio, calculated by dividing the stretched length of the cell membrane by the cell diameter, while the legend corresponds to the different diameters of red blood cells, as determined through image processing of recordings from the CMOS camera.The shear modulus of erythrocytes was then calculated using the formula [40]: where d is the diameter of the red blood cell, and B is the torsional modulus of elasticity which was equal to 2 × 10 −19 N•m.A linear fit to the scatter plot provided the slope k, which was subsequently used to calculate the shear modulus of the cell membrane.Shear modulus measurements were conducted on freshly ex vivo erythrocytes from both the upper layer (UL) and lower layer (LL) post-centrifugation, and these values were compared with a control group (CG) comprising freshly ex vivo erythrocytes that did not undergo gradient centrifugation.For each group, measurements were taken from ten erythrocytes, and the results are depicted in the bar chart of Fig. 5(B).Statistical analysis revealed that the mean shear modulus of control (CG) erythrocytes fell within the ra 3nge of shear moduli observed for upper (UL) and lower (LL) erythrocytes after centrifugation.Differences between groups were calculated using two-sample t-tests: In the equation, X is the sample mean, s is the sample standard deviation, and n is the sample size.A t-test was conducted to compare the upper (UL) and lower (LL) erythrocytes with the control erythrocytes, yielding results of 3.35 and 7.36, respectively.The level of significance is usually set at 0.05.A query of the t-test table reveals that the t-value corresponding to a significance level of 0.05 is 2.23(bilateral testing).The t-value for both UL and LL groups was greater than 2.23, indicating that the P-value for both groups was lower than 0.05.Specifically, the mean shear modulus value of the upper layer (UL) and the lower layer (LL) were significantly different from that of the control group (CG) (p < 0.05).
These statistically significant results indicated that the gradient centrifugation technique could effectively segregate low-density erythrocyte populations with a consistent density distribution.In the high-density zone, erythrocytes experience some degree of mixing within the centrifuged layer [32].This, coupled with potential mechanical damage incurred as the cells traverse from the top to the bottom of the centrifuge solution, leads to an elevated standard deviation in the measurements.Thus, the results suggest that the consistency of the samples can be enhanced and the accuracy of the light tweezers assay results can be further improved by de-screening the high density of aged erythrocytes.

Mechanical characterization of the shear modulus of fixed red blood cells
To examine the deformability of diseased erythrocytes, the red blood cells were treated with glutaraldehyde to modify their shear moduli, thereby simulating "diseased" erythrocytes.The erythrocyte cell membrane consists of a phospholipid bilayer and a cell membrane protein backbone on its inner surface [41].Upon exposure to glutaraldehyde, the fluidity of the phospholipid bilayer decreases, leading to the cross-linking of cell membrane proteins into dimers or trimmers [42] as well as an elevated shear modulus of erythrocytes.
In this experiment, three different concentrations of glutaraldehyde were selected, and the shear modulus of individual erythrocytes was measured over time for each concentration.Controls are erythrocytes from the UL layer after gradient centrifugation.The results, depicted in Fig. 6(A), revealed a direct correlation between the rate of erythrocyte curing by glutaraldehyde and the concentration applied.Specifically, at glutaraldehyde concentrations of 0.005%, 0.01% and 0.015%, the shear moduli of the erythrocytes after 30 minutes incubation increased by 1.49, 2.98 and 5.2 times, respectively, compared with that of the original cell.In fact, at the highest concentration (0.015%), there was an excessively rapid cell curing rate which hindered statistical analysis of mean cell shear modulus.Conversely, at the lower concentration (0.005%), it took over half an hour to observe any significant changes in the shear modulus.This was coupled with potential erythrocyte aggregation that compromised the efficiency of optical tweezer stretching.Overall, the findings indicated that a glutaraldehyde concentration of 0.01% was optimum for simulating diseased erythrocytes in the optical tweezer study of mechanical parameters.To further investigate the impact of glutaraldehyde on erythrocytes at various stages of aging, the shear moduli of cells in 0.01% of glutaraldehyde solution were measured at different ex vivo time points using optical tweezers.In his case, the control consisted of naturally senescent ex vivo erythrocytes that were not exposed to glutaraldehyde.The results, presented in Fig. 6(B), showed that the mean shear modulus of ex vivo erythrocytes increased progressively with prolonged ex vivo time.
In the experimental group, all erythrocytes exhibited a significant increase in shear modulus due to the effects of the 0.01% glutaraldehyde.The line graph in Fig. 6 represents the ratio of the mean shear modulus of the control group to that of the experimental group.The results suggested that, with prolonged isolation time, the modification of erythrocyte shear modulus by glutaraldehyde decreased during erythrocyte senescence.It is established that membrane proteins in senescent erythrocytes form macromolecular aggregates, while concurrently, the surface area of the cell membrane gradually diminishes during erythrocyte decay [43].These changes could lead to reduced cross-linking efficiency of glutaraldehyde as well as diminished effectiveness in fixing erythrocyte membranes by glutaraldehyde.

Analysis of erythrocyte stretch images
The binarized image of a stretched red blood cell, derived from a CMOS camera recording in the y-axis direction during red blood cell stretching, is presented in Fig. 7(A).Regions 1 and 3 display binarized images of the silica microspheres, while region 2 shows a binarized image of erythrocytes in a state of stretch deformation.Initially, the number of pixel points in region 2 was tallied.This was followed by a calculation of the scale relationship between the number of pixel points and the area of the binary image.Eventually, the dynamic area of the erythrocyte during stretching was determined through scale transformation.To investigate the dynamic changes in erythrocytes under stretching conditions, information on changes in the area of both control and experimental (0.01% glutaraldehyde cured) erythrocytes during multiple stretching deformations was gathered, as illustrated in Fig. 7 B and C. The legend indicates the original diameter of the red blood cells, while statistical analysis indicated that the erythrocyte morphology reached its maximum value at 10 seconds from the onset of stretching, with the entire stretching process lasting for 20 seconds.The difference between the peak and original area during erythrocyte stretching was also calculated, and the value was normalized to characterize the maximum degree of deformation of the erythrocyte area.
By controlling the light trap force, erythrocytes from both the experimental and control groups were stretched, and the maximum degree of change in the erythrocyte area was calculated to generate the box line statistical graph shown in Fig. 7(D).Based on the results of this plot, the mean value for the degree of deformation of normal erythrocytes during stretching with the same light trapping force was 11.93%, while the mean value for erythrocytes cured by glutaraldehyde was 6.62%.This implied that a two-fold increase in erythrocyte shear modulus can be accompanied by a 50% decrease in the degree of its maximum deformation.Drawing from the pathological erythrocyte model, which incorporates a twofold increase in shear modulus, we've achieved a quantitative calibration of its deformation area.This calibration is achieved by integrating image recognition detection during the stretching process, where the degree of deformation remains under 8%.This calibrated value serves as a criterion for identifying erythrocyte lesion sclerosis.

Conclusion
This study quantitatively characterized and analyzed the deformability of both normal and fixed in vitro erythrocytes, and for this purpose, an optical trap micromanipulation system was used along with a MATLAB image processing program.Overall, precise mechanical measurements were achieved by applying gradient centrifugation of red blood cells followed by the micromanipulation of erythrocytes using optical tweezers.Dynamic area measurements of the cells during stretching were also conducted using MATLAB image recognition techniques.This enabled an accurate characterization of area changes and quantification of deformation during cell stretching.The deformability of simulated diseased erythrocytes was finally characterized through a combination of optical trap micromanipulation and MATLAB image recognition techniques.In this case, the results revealed that simulated diseased erythrocytes could exhibit less than 8% deformation, in line with clinical results.
The density gradient centrifugation technique used in this study effectively overcame individual differences in low-density erythrocytes, thereby enhancing the representativeness of optical tweezers-based measurements.The mechanical and image-based measurements proposed in the study involves micromanipulation of optical traps, and this provides a versatile measurement approach for precisely quantifying the deformability of erythrocytes Diminished erythrocyte deformability is recognized to be present in various diseases such as sickle cell anemia, diabetes, and malaria.In line with this study, conducting further accurate quantitative calibration of erythrocyte deformability across different diseases is anticipated to provide a significant contribution to disease detection and development.

Fig. 1 .
Fig. 1. Results of erythrocyte gradient centrifugation, with left, center and right images showing the results at 1, 7, and 14 days, respectively.

Fig. 2 .
Fig. 2. Schematic diagram of the AOD scanning optical tweezers used for the experiment (left).Schematic diagram of the erythrocyte stretching process within the sample chamber (right).

Fig. 4 .
Fig. 4. CMOS shot of a single erythrocyte bound to a silica pellet and stretched by light tweezers.Top and bottom images were taken before and after light tweezers stretching, respectively.

Fig. 5 .
Fig. 5. Mechanical measurements of the erythrocyte stretching process.(A) Linear fit plot of the stretch force versus cell elongation.(B) Statistical plot of cellular shear modulus.The control group (CG) referred to erythrocytes not treated by gradient centrifugation, while UL and LL corresponded to the shear modulus of the upper and lower cell layers after gradient centrifugation; ⋆ represents statistically significant differences in means at p < 0.05.

Fig. 6 .
Fig. 6. (A) Shear modulus of erythrocytes in glutaraldehyde solutions of different concentration gradients (0.005%, 0.01%, 0.015%).(B) Values for the shear moduli of cell membranes in the control (non-glutaraldehyde-treated erythrocytes) and experimental (0.01% glutaraldehyde-treated) erythrocytes at different ex vivo time periods.The folded line is the ratio of the mean shear modulus of the control to that of the experimental groups.

Fig. 7 .
Fig. 7. Dynamic identification and area statistics of erythrocyte deformation processes.(A) binarized image of the erythrocyte stretching process.(B) Scatter plot of erythrocyte area versus stretching time for the control group.(C) Scatter plot showing the area of erythrocytes affected by glutaraldehyde solution versus stretching time.(D) Statistical results of the maximum degree of change in erythrocyte area in the control and experimental groups.

Funding.
The Postgraduate Research & Practice Innovation Program of Jiangsu Province General Universities (KYCX22_2846); Natural Science Research of Jiangsu Higher Education Institutions of China (19KJA510003, 20KJA430003); National Natural Science Foundation of China (61971207, 62005108).