Red blood cells (RBCs) are the most common type of blood cells and play the fundamental role of delivering oxygen to the body tissues through the circulatory system (1). The RBC population is characterized by a high heterogeneity in membrane area, cellular volume, and mechanical properties, mainly due to the variety of mechanical and chemical stresses that a red cell undergoes in its entire life span (of about 120 days), resulting in membrane loss and cell aging (2). RBC geometrical parameters are closely related to cell deformability. Indeed, thanks to the membrane excess area [RBC surface area is significantly greater than the surface area of a sphere enclosing a volume equal to RBC volume (3)], RBC can readily deform when flowing in the microcirculation, where cell size is comparable with vessels diameter. In such confined conditions, RBC changes its disk-like shape at rest (diameter of 7–8 μm and thickness of 1–2 μm) into a deformed one, resembling a bullet or a parachute (3, 4). RBC size and deformability are in turn strictly related to cell age, senescent red blood cells being smaller and less deformable than young cells (2, 5). Thus, the resulting scenario is a morphological heterogeneity of the RBC population, consisting most of all in a distribution of values of the membrane area and of the cytosolic volume.
The mean cell volume (MCV) and the distribution of red cell volume (characterized by the red blood cell distribution width or RDW) are routinely measured by the clinical blood cell counter, based on the detection of changes in electrical conductance as cells suspended in a conductive fluid pass through a narrow orifice [Coulter principle (6)]. In particular, RDW is a standard numerical measure of size heterogeneity of circulating erythrocytes, with a normal reference range in human red blood cells of 11–15% (7). In some disorders, RDW provides useful information about health conditions and could be an important prognostic parameter in some cardiovascular pathologies (8, 9): recent studies have reported a strong independent relation between increased RDW and acute myocardial infarction (10, 11) and peripheral artery diseases (12). Moreover, RDW is related to other severe pathologies, such as cancer of colon (13) and heart failure (14). In other cases, instead, RDW, being the measure of the width of the distribution only, is insufficient to adequately describe the whole size distribution and does not provide information about single RBC surface area, volume and shape (15). For example, an important red cell shape parameter is the “sphericity index,” that indicates how much the shape of a cell approaches a sphere (16, 17). This parameter can be useful to discriminate between healthy and pathological cells, for example in some hereditary diseases like spherocytosis. In fact, spherocytic cells, showing at rest spherical shapes rather than the typical biconcave discs, have smaller volumes and are less deformable than biconcave ones, thus hindering RBC flow through narrow capillaries in microcirculation. Moreover, because the spleen breaks down old and worn-out blood cells, those individuals with more severe forms of hereditary spherocytosis can end up with a splenomegaly, eventually treated with a splenectomy (18).
Given the physiopathological relevance of RBC shape, volume and surface area for the diagnosis and the clinical state of a patient, a number of different approaches to measure red cell geometrical parameters are reported in the literature (19), from the pioneering work of Ponder on red cell diameter and thickness (20) to detailed characterization of volume and area (16, 17, 21–25), until the more recent papers based on microfluidic techniques (5, 15) and on digital holographic microscopy (26). Furthermore, a number of numerical models of red cell geometry have been proposed (27–29). The main drawback of the cited experimental techniques is the limited number of cells that can be measured at the same time, thus hindering the acquisition of statistically significant datasets.
In this work, we report on the applicability of a novel technique for the measurement of the surface area and volume of individual red blood cells (RBCs), based on confined and unbounded capillary flow. By using high-speed video microscopy and automated image analysis hundreds of individual healthy human cells have been acquired, and the polydispersity of the distribution of RBC geometrical parameters was evaluated. The obtained values of red cell surface area, volume (MCV), and volume distribution width (RDW) were compared with data from Coulter counter and with reference values from the literature. Moreover, the experimental results demonstrate that the methodology presented in this work is suitable for large-scale measurements of pathological RBCs, thus, allowing to overcome the limits of classical static methods, such as micropipette aspiration, which are not suitable for handling a large number of cells.
MATERIALS AND METHODS
Fresh venous blood samples were withdrawn from healthy consenting donors and used within 4 h from collection. The RBC suspensions used in the experiments were obtained by diluting 1 mL of whole blood with 98 mL of ACD anticoagulant (0.6% citric acid, 1.1% anhydrous dextrose, 2.3% sodium citrate, 96% water) and 1 mL of BSA (bovine serum albumin). The experiments were carried out by using a flow cell made of two Plexiglass plates separated by a rectangular rubber frame (Fig. 1). A glass coverslip was inserted into a window cut in the bottom plate to allow observations with a high magnification oil immersion objective (100×), as described in detail elsewhere (4). Silica cylindrical microcapillaries (Polymicro Technologies) with inner diameter of 4.7, 6.6, 10, and 50 μm were placed on the coverslip in the flow cell. The RBC suspension was fed into the flow cell by using flexible tubing connected to an input glass reservoir and was collected at the exit in an output reservoir. The total pressure drop ΔP across the microcapillaries placed in the flow cell can be taken as proportional to the distance between the liquid menisci in two glass reservoirs (according to Stevino's law), the other pressure losses being negligible. All the experiments were performed at room temperature since no significant differences were found by setting the temperature to 37°C with a microscope cage incubator.
Image Acquisition and Analysis
Bright field observations were performed through a 100× oil immersion objective by using an inverted optical microscope (Zeiss Axiovert 100) in the transmitted light mode equipped with a motorized translating stage and a focus control (Ludl) (without using any autofocusing operations). The large arrays of images (around 10,000 in each run) were recorded by a high-speed camera (Phantom 4.3) operated up to 1,000 frames per second, and processed off-line by custom macros based on the libraries of commercial software packages (Image Pro Plus and Matlab). To measure individual RBC volume and surface area, two kinds of cell shape were considered: (i) the biconcave disk shape, which is found when the cell is at rest or when it slowly flows in a tube three to four times bigger than cell size (such as in the case of a 50 μm ID), i.e., in unbounded flow regime; (ii) the parachute shape, when the cell flows in a capillary with a diameter comparable with its own size (up to 10 μm ID), i.e., under confined flow.
Concerning the unbounded flow condition, where the experiments were carried out in a 50 μm capillary and several cells were found per image, a manual cell selection was carried out due to the presence of (undesired) cells either out of focus or with a nonsymmetrical shape. The analysis of the selected cells was then performed in a semi-automated way (i.e., by choosing a gray level threshold to close the cell contour). An example of image processing is reported in Figure 2. The sequence of consecutive images in the upper panel shows that cells tumble while flowing in such unbounded conditions and thus exhibit different shapes in the plane of observation. So, the first step of image analysis was to select images where the cell edge showed a symmetrical profile (Fig. 2b). Then, just to make area and volume measurements easier, cell image was rotated until a vertical symmetry was obtained (Fig. 2c; of course, such rotation does not affect the area and volume values). As shown in Figure 2b, even if there is a clear visual difference in the gray level of the cell border and that of the surrounding medium, it is hard to define cell contour in an objective, unique way, due to focus and to optical resolution problems. We addressed this problem by using a line profile measurement (i.e., intensity vs distance along a segment crossing cell boundary). The minima of the line profile intensity were taken as the points of belonging to cell contour (Fig. 2f). The coordinates of the so obtained cell contour were recorded on file and were fed to an automated custom macro based on the Rand and Burton (16, 17) method for the area, volume and sphericity index calculation. Concerning the surface area, it was calculated from the area A of a half-cell cross section, A = Σ2πyΔy, that is, the sum of the areas of the surface annular rings generated by rotating each element of length Δy (as taken from the quadrant in Fig. 2d) around the horizontal axis (this is based on the assumption of cell circular symmetry). The total area of the cell cross section was then equal to 2A. The volume V = Σ2πy(xΔy) of a half cell cross section was calculated as the sum of the volumes of the cylindrical shells generated by rotating each element of area xΔy (Fig. 2e) around the horizontal axis. The total volume of the cell cross section was equal to 2 V. The sphericity index is a dimensionless number that indicates how much the shape of a cell approaches a sphere, and was calculate as the ratio between cell volume to the two-thirds power of cell surface area (16, 17). These operations were repeated for two quadrants and average values were taken for the volume and the area of the cell.
As far as the confined flow is concerned, RBCs flowing in a 4.7, 6.6, and 10 μm capillary were considered. In this case, the image analysis was fully automated (30,31), thanks to the fact that most cells, in such confined condition, assumed an axisymmetric shape and laid essentially in only one focal plane (since the diameter of the capillaries was comparable with that of the cells). The measurements in the confined case were carried out by using a two-step fully automated procedure. The first step is used to: (i) select images containing RBCs (it should be pointed out that, due to low cell concentration, most images are empty and only one cell at a time is found at most in the field of view) by applying a gray level threshold, i.e., by comparing the average gray level of each image to the background value; (ii) extract and record on file cell contour coordinates. By this way, it was possible to analyze about 30 cells per minute. Starting from the so-obtained values of cell contour coordinates (solid line in Fig. 3a), in the second step, RBC volume and surface area was evaluated in the second step by regarding the cell as an axisymmetric solid of revolution around the x axis (Fig. 3a). The surface of revolution was created by the revolution of a curve about an arbitrary axis [first theorem of Pappus, or Guldin's first rule (32)]. The area S of a surface of revolution is equal to the product of the arc length dS of the generating curve and the distance dx traveled by the curve's geometric centroid.
It can be shown that , where the term is equal to the length of the circumference of radius f(x), (where f(x) is a function of the capillary centerline) and the term corresponds to an element of curve dS (Fig. 3a). The whole surface area of the upper part of the cell was equal to . The volume V of a solid of revolution is created by the revolution of an arbitrary shape about an arbitrary axis [second theorem of Pappus, or Guldin's second rule (32)]. In our case, the volume of a single disc of height dx was equal to the product of the area of a circle of radius f(x) and the distance traveled by the shape's geometric centroid dx (Fig. 3a). The whole volume of the upper part of the cell was then equal to .
A continuous profile representing cell contour was obtained by the interpolation of the cell contour coordinates. It has to be noticed that two different values of the y-coordinate may be associated with the same value of an x-coordinate in the trailing edge of the cell. Because of this problem, the cell contour coordinates were interpolated by using four polynomials, as shown in Figure 3b. Moreover, to avoid possible shape asymmetry problems, the upper part (i.e., the one above the x axis) and the lower part of a cell were separately analyzed, and the obtained results were compared one to each other. This comparison was used to verify cell axisymmetry, and to screen out the RBCs for which the difference between the volume and area of the two parts was >5%. In particular, the difference between the upper and lower part of the cell is <5% for 30% of the analyzed cells in surface measurements, and for 60% of the analyzed cells in volume measurements.
RESULTS AND DISCUSSION
Unbounded Capillary Flow
Figure 4 shows the volume and the sphericity index distributions of RBCs (only data from one donor are shown for the sake of brevity) flowing in unbounded conditions in a 50 mm capillary, in which the cell shape is a biconcave disc.
The RBC volume distribution (Fig. 4a) was considerably Gaussian (R2 = 0.8791, where R2 is the coefficient of determination, the most common measure of how well a regression model describes the data). The closer R2 is to one, the better the independent variables predict the dependent variable. R2 is computed as 1 - ΣSr/ΣSm, (where ΣSr is the sum of squared deviations from the regression line, and ΣSm is the sum of squared deviations from the mean). The MCV was quite lower (by ≈20%) than the normal range (90 fL) (16) being equal to 70 ± 13. We could explain this discrepancy based on the procedure to obtain the cell contour (as explained above; see Fig. 2). In fact, even small gray level threshold variations would significantly change the calculated volume. The same explanation can be applied to the sphericity index distribution shown in Figure 4b, where once again the mean value was lower (by ≈20%) than the one from the literature (16).
To show any correlation between the individual size parameters presented above, the plots of volume vs. cell diameter (Fig. S2a in the Supporting Information), area vs. cell diameter (Supporting Information Fig. S2b), and area vs volume (Supporting Information Fig. S2c) were prepared and are shown for one subject (The graphs for all the three subjects investigated in this work show the same trend and they have not been presented here for the sake of brevity). In all the cases, a linear fit (with correlation coefficients about 0.8) was found to well represent the data, in agreement with the results by Canham and Burton (16). These results can be explained by the less than one average value of the sphericity index, corresponding to the disk-like shape found in the unbounded flow geometry. Indeed, one would expect area and volume to be proportional to the diameter squared and cubed, respectively, and area to be proportional to volume2/3 only for a shape close to a spherical one.
Confined Capillary Flow
In this section, data resulting from experiments about RBC under confined flow have been reported. When a red cell flows in a microcapillary with diameter comparable with its own size it deforms according to the so-called parachute shape or bullet shape (4), which is observed in microcirculation in vivo (33). However, to our knowledge, there are no previous reports of RBC geometrical measurements in confined flow. We will show that this analysis can provide data on RBC volume, RDW, and surface area, the latter not being available from the routine clinical tests.
The measurements were carried out in microcapillaries with the following inner diameters: 4.7, 6.6, and 10 μm. It should be noticed that a cell size screening effect was found in the 4.7 and 6.6 μm capillaries, i.e., only RBCs below a certain size were able to enter such capillaries. This effect has been also observed in vivo at the capillary entrance in microcirculation (34–36), and has been attributed to the collision between cells or between cells and the capillary entrance rim. In our experiments, the area and volume data show a decrement (with respect to the 10 μm ID) of 15 and 20%, respectively, in 6.6 μm capillaries and of 22 and 35% in 4.7 μm capillaries (see Fig. S1 in the Supporting Information). These results were used in the choice of the best capillary diameter for our technique, as red blood cell selection is of course undesirable. Hence, we selected 10 μm capillaries for our measurements as this diameter was at the same time small enough to ensure cell deformation and big large enough to avoid cell size screening.
In Figure 5a, the volume distribution is shown. The data refer to cells coming from the same donor of Figure 4 and Supporting Information Figure S2, and were taken at three different imposed pressure drops (65, 50, and 35 mm Hg) close to the physiological range (37). Pooling of data was used to increase the number of cells, as area and volume are independent on the flow field, being intrinsic properties of the red cells.
The distribution was well represented by a Gaussian fit (R2 = 0.96). The MCV was higher than the one obtained in the unbounded case (85 instead of 70 μm3) and it was closer to the one measured by the Coulter counter cell analyzer (equal to 88 μm3 for this subject). Such good agreement with the routine blood tests shows that our techniques are indeed capable of correctly measuring RBC size parameters. In Figure 5b, the surface area distribution is shown. The distribution was again Gaussian (R2 = 0.76), with an average value of 125 μm2, quite smaller than the one (134 μm2) known from the literature (16). RBC surface area plays a fundamental role in modified red cell aggregability and deformability in some pathological states (38), such as spherocytosis (18) and elliptocytosis (39), and in aging phenomena (2). Because of the importance that surface area has in RBC deformability and aggregation processes (40), a large amount of work on RBC area measurements is reported in the literature (16, 22–24). In all these studies, however, a limited number of cells was measured at the same time, thus hindering the acquisition of statistically significant datasets. Thus, the possibility to measure the area of a large number of cells in conditions very close to the physiological ones represents one of the main novelties of the technique presented in this work.
Concerning the relation between RBC area and volume shown in Figure S3 in the Supporting Information, the same linear trend of the one in Supporting Information Figure S2c (i.e., in the unbounded case) is observed, confirming the hypothesis of Canham and Burton (15, 16) about the existence of a minimum cylindrical diameter. The minimum cylindrical diameter represents the diameter of the thinnest capillary through which each RBC could theoretically pass without lysis, area and volume staying constant (16) [in analogy with multilamellar vescicles (41)]. The linear trend was also found for RBCs flowing in capillaries smaller than their own size in microcirculation in vivo (31).
Data from all the donors in our experiments, including both unbounded (five donors) and confined (three donors) flow, are reported in Table 1, where values of RBC volume (MCV), distribution width (RDW), surface area, and sphericity index are shown. The volume values measured by experiments on RBC in unbounded and confined conditions were compared with the Coulter counter values and with data from the literature (16). It can be seen that volume measured by the confined capillary flow method was the closest to the one obtained by the Coulter counter, with an error <5%.
Table 1. Data on RBC volume, RDW, area and sphericity index from different methods for five healthy subjects
The red blood cell distribution width (RDW) was calculated as the standard deviation (SD) of the cell volume distribution divided by the MCV (7). Once again, the measured values of RDW in the case of confined flow were in very good agreement with the Coulter counter data. Concerning the surface area, the measurements in the case of confined flow provided values smaller (about 10%) than the ones available in the literature by different experimental techniques, such as micropipette (25), interference microscopy (22), and geometrical characterization of RBC aggregates (rouleaux) (24), all based on RBC disk-like biconcave shape. The lower values of surface area in confined flow obtained here could be explained by the fact that cell shape in our conditions cannot be fully described as a revolution body, due to the presence of thin extensions of the cell's membrane protracting behind, which have been documented in previous works (4, 42, 43). Such extensions give some additional contribution to the cell surface area which is neglected in our measurements.
To sum up, the method which turns out to be in better agreement with clinical tests is confined flow in 10 μm microcapillaries. Measurements in unbounded flow provided values of MCV smaller than the ones obtained by Coulter counter (whereas data of Canham and Burton are larger). The worse performance of the unbounded flow analysis can be explained by optical problems, such as focus and threshold selection, and by the fact that the disk-like biconcave shape of RBCs at rest or under slow flow conditions is not really symmetric. To evaluate such possible shape asymmetry, we calculated volume and area based on each of the four quadrants in which cell projection can be divided (see Figs. 2d and 2e, where the upper right quadrant is shown). Significant, though small differences (>5%) between the volume and area values corresponding to the four quadrants were found, thus showing that the biconcave cell shape is indeed not perfectly symmetric in the side view (although the shape is quite circular in the top view). The variation in thickness in the side view could be due to non-uniform distribution of cell cytoplasm.
On the other hand, when RBCs flow in 10-μm microcapillaries, the strong confinement elicits a more axisymmetrical shape, as shown by the low variations (<5%) between the area and volume values calculated from the two halves of the cell body (see Fig. 3a). Furthermore, optical focusing is easier in these capillaries due to the smaller size as compared to the 50 μm microcapillaries which are used in the unbounded flow case, allowing fully automated image processing.
In this article we described a novel methodology to measure either individual RBC geometric parameters and the RBC distribution width (RDW), based on the image analysis of red blood cells flowing in microcapillaries, either in unbounded and confined conditions. On the basis of comparison with Coulter counter cell analyzer data, we show that high-speed imaging of 10 μm microcapillary flow provides a reliable way of measuring RBC size parameters. In particular, measurements on RBC surface area, lacking in routine clinical tests, are also obtained. Unlike impedance measurements, our technique is well suited for monitoring and measuring individual RBC geometrical parameters, such as volume (MCV), RDW and surface area at a single cell level. It does not require suspending cells in electrolyte solutions and being a noninvasive technique could be used to analyze images of flowing RBCs from in vivo experiments (44, 45) as well.
In summary, this technique is useful for the analysis of RBC size polydispersity and can provide both distributions of single parameters and relationships between them. Advantages of this method include the reproducibility of the results, the small amount of blood sample required and the large number of cells that can be analyzed.
The authors thank Giuseppe Fatigati and Luigi Marano for help in the experimental part. The authors do not have any conflict of interest to declare.