Quantification of stored red blood cell fluctuations by time-lapse holographic cell imaging

: We propose methods to quantitatively calculate the fluctuation rate of red blood cells with nanometric axial and millisecond temporal sensitivity at the single-cell level by using time-lapse holographic cell imaging. For this quantitative analysis, cell membrane fluctuations (CMFs) were measured for RBCs stored at different storage times. Measurements were taken over the whole membrane for both the ring and dimple sections separately. The measurements show that healthy RBCs that maintain their discocyte shape become stiffer with storage time. The correlation analysis demonstrates a significant negative correlation between CMFs and the sphericity coefficient, which characterizes the morphological type of erythrocyte. In addition, we show the correlation results between CMFs and other morphological properties such as projected surface area, surface area, mean corpuscular volume, and mean corpuscular hemoglobin.


Introduction
Mature erythrocytes, which are sometimes also referred to as discocytes, are the main cell type in the blood circulation. Their biconcave shape and corresponding deformability are an essential feature of their biological function. Indeed, this configuration, corresponding to the maximum surface area for a given volume, results from their outstanding ability to deform in particular when passing through narrow capillaries during microcirculation. RBCs must adapt to a wide range of capillary sizes, and deform while maintaining their cellular integrity and function. This is made possible by the absence of a three-dimensional (3D) cytoskeleton in RBCs. Their shape and mechanical integrity are maintained instead by a two-dimensional (2D) hexagonal lattice formed of flexible spectrin tetramers, which are linked by actin oligomers. Since the side length of actin (70-80nm) is much smaller than the contour length of a spectrin tetramer (approximately 200nm), it is believed that spectrins are the principal contributors to the bending of membranes or curvature modulus [1][2][3]. The cell-membrane which is more prominent in membrane regions with a small curvature (the dimple region) [4]. The second is linked to the metabolic activity that determines the adenosine triphosphate (ATP) content in the membrane skeleton and to the involvement of actin. The second type of fluctuations is believed to happen in regions of high curvature, such as the ring section of RBCs [5]. As mentioned earlier, different factors influence the deformability of RBCs. However, under storage conditions (e.g., in blood banks), RBCs undergo molecular, metabolic, biochemical and biomechanical changes, which are commonly referred to as storage lesions. Briefly, such processes result primarily in a decrease in energy metabolism, 2,3-diphosphoglycerate (DPG), ATP, and nitric oxide. Furthermore, during storage, the erythrocyte shape alters from deformable discoid to an irreversibly deformed spheroechinocytes. It is due to the irreversible loss of membrane by the formation of micro vesicles, which is the cause of an increased osmotic fragility [6][7][8][9][10][11]. It is understood that these changes are associated with decreased deformability, poor functionality of RBC and consequently with the removal of RBCs from the bloodstream [12][13][14][15]. One important question is regarding the extent to which the RBC biomechanical properties may be altered during the storage time. Considering that CMFs reflect these biomechanical properties, the monitoring of their evolution as a function of storage time could represent an efficient way to address this important question. Specifically, we propose to study the evolution of CMFs within the discocyte RBC subpopulation, i.e. the RBCs having shown the capacity to maintain a biconcave shape over the storage time. Indeed, it has been described that during their transformation into transient echinocytes and finally spherocytes, RBCs exhibit a significant CMF decrease [4,16]. In addition, when transfused the spherocytes do not recover a healthy discoid shape but are subjected to a phagocytic removal. Practically, discocyte RBC morphological properties including projected surface area (PSA), surface area, sphericity coefficient as well as the two clinically relevant parameters, the mean corpuscular volume (MCV) and the mean corpuscular hemoglobin (MCH), were measured at the single-RBC level. Then, the correlations between these morphological parameters and the CMFs, are calculated at different storage times.
In order to address these questions, we propose automated methods for measuring quantitative fluctuations rate, at the single-RBC level, as a function of their storage time, using time-lapse digital holographic microscopy imaging. We also analyze both the ring and dimple regions of the cell separately, according to the observations mentioned above. Quantitative phase images (QPIs) were acquired every few days over a 71-day period to investigate the alterations of RBC parameters over storage time systematically. The erythrocyte concentrate (EC) from which the RBC samples were collected were prepared at the blood center of the Transfusion Interrégionale CRS (Epalinges, Switzerland) as follow: 450 ± 50mL of whole blood were collected and mixed with 63mL citrate-phosphate-dextrose (CPD) anticoagulant. The bags were centrifuged to separate blood components. Then, semiautomated pressure applied to distribute the blood fractions into sterile inter-connected blood bags (Fenwal, Lake Zurich, IL, USA). Finally, to remove residual leukocytes the erythrocytes were filtered and 100mL of saline-adenine-glucose-mannitol (SAGM) additive solution were added. Five mL of each sample were collected using a sampling site every few days during 71 days (the 4 ECs were stored at 4°C) [16]. To prepare the RBCs, the EC samples were washed two times with NaCl 0.9% (centrifugation at 2000g, during 10min at 4°C) and resuspended in HEPA 10mM glucose. The RBCs were then seeded in a 96-well plate coated with poly-L-Ornithine for image acquisition.
Our quantitative analysis reveals some interesting points. First, we demonstrate that older discocytes (71 days storage) exhibit a slightly but statistically significant more pronounced stiffness than younger ones (stored for 4 days). Concretely, the fluctuations rate in the dimple is greater than in the ring section in younger RBCs. Furthermore, the MCV, MCH, PSA, and surface area do not change significantly on these time scales. Interestingly, we show that the CMFs of a whole cell ( (1) pectively. ucted. As allows us g. 2(b)) in ed by the (2) where FFT and IFFT respectively are Fourier and inverse Fourier transforms. Since the final image is a phase-contrasted, the hologram should be multiplied by the digital reference wave R D during the reconstruction process. This is similar to what happens in classical holography in which the recorded hologram is illuminated by the reference wave. Here, we assume that the reference wave is a perfect plane wave and can be shown by: where A R is the amplitude, λ is the laser source wavelength, Δx and Δy are the sampling intervals in the hologram plane (pixel size) and k x and k y are wave vectors which need adjustment to be similar to the experimental reference wave. Another issue is that the MO inserted in the object wave arm introduces phase aberration. This can be numerically resolved by multiplying the reconstructed wave front with the computed complex conjugate of the phase aberration. Eventually the reconstruction of complex amplitude image can be expressed by the Fresnel approximation as following [36]: where A is a constant complex value, k, l, m, and n are integers (-N/2< = k, l, m, n< = N/2; and N × N is the number of pixels in CCD camera 1024 × 1024), F H I is the filtered hologram and ( , ) m n Φ is the digital phase mask for the phase aberrations correction calculated by: Moreover, , ξ η Δ Δ are the sampling intervals in the observation plane expressed by: where d denotes distance between camera plane (hologram plane) and image plane. A fine adjustment of k x , k y and D can be performed in the absence of fringes by removal of residual gradients or curvature of the reconstructed phase distribution in some area of the image where a constant phase is presumed [36]. D is the parameter that must be adjusted to compensate the wave-front curvature according to the distance between MO and specimen, and MO and the image plane evaluated by [36]: where d i is the distance between MO and image plane and d o is the distance between the specimen and MO. Since ( ) , m n Ψ is an array of complex numbers, the intensity of amplitude image ( Fig. 2(e)) can be obtained by: Equation (7)

Cell thickness
After single-cell QPIs extraction and applying morphological operators, the thickness, at a single cell level can be calculated. The data provided by QPIs in this study are in the form of phase values, from which cell thickness images were obtained: where h(x, y) is the RBC thickness, and n RBC and n m are the refractive indices of the RBC and HEPA medium, respectively. The value for n RBC is previously obtained by the method called decoupling technique [32,38] and it is reported to be 1.418 ± 0.012 over a spherocyte population. This assumption is valid if the hemoglobin content remains stable in time, we observed within the same EC. The refractive index of HEPA (1.3334 ± 0.0002) is measured at room temperature precisely with Abbe-2WAJ refractometer at the wavelength similar to the DHM laser diode.

Membrane fluctuation rate
Different techniques have been proposed to measure fluctuations in RBC membranes [3-5, 13, 39-46]. However, their separate applications to the ring and dimple sections remain to be carried out, since the sources of their respective fluctuations could be distinct [4]. To calculate the fluctuations rate, we consider the statistical model of Rappaz et al. [5]. Briefly, this requires the definition of a region of interest (ROI) and two independent variables: std(h cell + h background ), the temporal deviation within the RBC area (combining both the cell fluctuations and noise), and std(h background ), the mean temporal deviation calculated over all the pixels located outside the RBC area (see Fig. 3). The measured standard deviations for one pixel outside the cell (  Fig. 4 and Visualization 1). Accordingly, the fluctuations at each single pixel CMF(x,y) can be evaluated as [5].  ,

Quantitat
In this paper correlation an adopted a 95% plots represen Fig [30,31]. In the case of older RBCs, the STD value of the sphericity coefficient is significantly larger ( ± 0.12). We believe that reflects the early phase of the gradual discocyte-spherocyte transformation process. In contrast the MCH does not change over the time of storage and only fluctuates around its average value of 32 ± 0.6pg (See Fig.  9), consistent with earlier reports [3,30,31,38]. Moreover, MCH is in agreement with the value obtained by Sysmex KX-21 in the present study (See Fig. 9). This constancy indicates that, while biconcave RBCs undergo morphological changes during storage, they do not leak hemoglobin into the storage solution [3,13]. The CMF amplitude fluctuates over the storage time. However, the general trend of the CMF amplitudes as a function of the storage time of the whole RBC, the ring, and the center are to decrease (F-statistics suggest that the linear regression line has a slope that is significantly different from zero; p-value <0.05), consistent with earlier findings [3]. Our experimental reflecting that RBC membranes stiffen with storage time, in agreement with the reported decrease in deformability [3,12,13,46]. According to Fig. 8, fluctuation amplitude at the dimple are generally larger than in the ring region (p<0.05; two-sample Kolmogorov-Smirnov test), as expected and in agreement with the results of Rappaz et al. [5] (Age of RBC is 4 days). Figure 10 shows the correlation analyses of the fluctuation amplitudes -the whole RBC membrane and the dimple section -of young RBCs (stored for 4 days; n = 33) as functions of the morphological and MCH parameters. The ring section exhibits the same trend as the whole RBC membrane. We therefore decided to exclude ring-section results from our correlation analysis results shown in Fig. 10. Interestingly, the CMF amplitude of the whole RBC exhibits a strong negative correlation with the sphericity coefficient (p<0.05; Pearson product-moment correlation test). The greater k is the CMF amplitude of the whole RBC is fewer. This can rise from the fact that the more spherical RBCs are, the stiffer they become [12,46]. On the other hand, there is a significant positive correlation between the CMF amplitude in the dimple region and the k factor ( Fig. 10(a)). The lower the PSA of a RBC, the larger the observed CMF amplitude (Fig. 10(b)). The fluctuation amplitudes of both the whole RBC membrane and dimple region (Fig. 10(c)) have no significant correlation with the MCH, consistent with previous findings [4,46]. Figure 10(d) and 10(e) shows that CMF amplitudes are not correlated with the MCV and surface area value. We also evaluated the correlation between the CMF amplitudes and k factor and MCH parameters of RBC for two storage times namely 43 and 71 days (See Fig. 11). Our statistical model for evaluating CMF amplitudes suggests that both the ring and dimple regions differ between young and old  During circulation, normal RBCs must deform to pass through capillaries having a diameter almost half the size of a typical RBC. Their resistance to deformation may not, therefore, be substantial but not too small either, lest it compromise the integrity of the cell in normal circulation [45]. Previous experiments [3,12,13,42] have revealed that RBCs become less deformable and much stiffer over longer storage periods. The consequences of this loss of RBC deformability are significant and potentially seriously detrimental to human organs. It is more difficult, if not impossible, for stiff RBCs to traverse a microcapillary system. Obstructed capillaries cause pain and damage to tissues and organs including infarction and necrosis. Longer transit times through capillaries, resulting from lower RBC deformability, can also hinder oxygen delivery and carbon-dioxide absorption. This increase in stiffness with the aging of the RBC can be explained in several ways. The membrane area is reduced due to the release of microvesicles [51]. Also, ATP is crucial for preserving the biconcave shape, since the depletion of ATP caused a change from the biconcave to the echinocyte shape and finally yielded a spherocyte. This change of shape suggests that ATP and membrane loss stiffen the cytoskeleton and hence constrains the bilayer to a smaller cytoskeleton-projected area. The underlying physical origin of this effect is the change in the number of released spectrin filaments with the reduction in the number of defects as the ATP concentration is reduced [42][43][44]. Interestingly, it has been shown that the ATP concentration in RBCs decreases with increasing RBC age, or near the end of the RBC lifespan [48]. It is presumed that lower ATP concentrations linked to increasing age should correspond to a denser cytoskeleton, a higher shear modulus, and a drop in fluctuations rate [52]. Figure 12 shows two different discocyte RBCs, imaged after different storage times. Figure 12(a) displays a smaller sphericity coefficient and larger amplitude of fluctuations. In contrast, the older RBCs have a greater sphericity coefficient and a smaller fluctuation amplitude. (See Fig. 12(b)).