1. Introduction

Red blood cell imaging, identification, and counting are the first steps in a rigorous analysis to establish the properties of similar cells exhibiting different development stages, i.e., mature or immature. Automated devices developed for blood cell count, such as flow cytometers and impedance counters, have made work in hospital laboratories easier, offering a fast method for obtaining accurate results. However, it is well established that pathologists can obtain useful information about cell morphology by visualizing the blood smear on a slide, an important diagnostic tool in detecting many diseases. In these procedures, since many cells are transparent in bright-field microscopy, they must use chromatographic agents. For this reason, the procedures remain time-consuming; for example, in the case of immature red blood cells, sample preparation and analysis may take several hours.

In 1865, W. H. Erb [1] described immature red blood cells (IRBCs), also named reticulocytes in their last stage, as transitional forms of mature red blood cells (MRBCs). The reticulocyte is formed in the bone marrow and finishes its development in the peripheral circulation [2]. Reticulocyte maturation into erythrocytes is the final step of erythropoiesis, which occurs in circulating blood [3]. Many biochemical and physical studies or complicated analyses have been conducted to find their properties and their role in the detection, evolution, or treatment of different diseases [4, 5, 6]. Morphological changes in red blood cells can be induced by a variety of factors, including the lethal human malaria parasite [7]; during the development of hemoglobinemia following infection with Leptospira interrorgans serovar bullum [8]; during blood heating [9]; and after UV irradiation [10].

Since IRBCs contain a residual ribosomal RNA, when they are combined with dye agents, they permit fluorescent analysis in laser-based counters or bright-field microscopy analysis on a smear. Reticulocyte maturation into erythrocytes is achieved in about $48\mathrm{h}$ for in vivo conditions, when the IRBC loses its nucleus, changes its shape from oblate spheroid to that of a typical biconcave disk, and minimizes its area and volume. The IRBC percentage in the whole blood has a prominent role in the initial classifying of anemia and in determining the efficiency of chemotherapy treatments. The behavior of the IRBC and MRBC in oxygenation/ deoxygenation cycles gives information that is useful in sickle cell anemia [11].

Mohandas et al. [12] performed one of the first optical analyses of MRBCs using their diffraction pattern by monitoring two points using a photomultiplier. From these intensity values, they deduced the dependence of erythrocyte deformability versus shear stress. In recent years, many analyses based on optical techniques centered on MRBC behavior in different conditions, or diseases have been reported [13, 14, 15, 16, 17].

In this paper, we use a holographic method combined with image processing for IRBC and MRBC identification, counting, and morphological properties measurement in a blood smear on a slide without chromatographic agents. The digital holographic microscopy (DHM) technique offers nanometric resolution along the propagation axis and is used in many laboratories for MRBC analysis [18, 19]. The off-axis DHM technique has the major advantage of reconstructing the MRBC details positioned at various distances along the propagation axis using a single hologram. In recent years, few methods of enhancing the lateral resolution have been reported [20, 21].

Using DHM, we record (on a CCD camera) the interference pattern of the reference and object beams (the last one also carries the diffraction pattern of the object). First, we record the diffraction pattern from IRBCs and MRBCs situated in the same frame. Then, we highlight that, for a given distance between the sample and the objective, their diffraction patterns have complementary central intensity distribution. Next, we develop ellipsoidal models for IRBC and MRBC shapes to use in a propagation simulation analysis in order to establish which of the cell properties has the dominant influence on this behavior.

The reconstructed images from DHM are processed in order to separate edges of the tangential cells, to distinguish IRBCs from the MRBCs, to count automatically, and to further obtain information on their morphological parameters. For accurate numerical values, we remove the background using successive filters. We propose a method based on nonlinear functions applied at threshold intervals and distance transform aiming to separately counting partially overlapping cells. The histograms obtained automatically after simultaneously processing more than six reconstructed images are sub sequently compared with those obtained using the impedance counter.

2. Experimental Procedure

Using Nikon equipment (Eclipse Ti-U, DS-Fi1 5 megapixel CCD camera, and dedicated software, NIS Elements, Nikon Corp., Japan), the experiment includes analyses in bright-field microscopy of the samples with a chromatographic agent and in differential interference contrast (DIC) configuration without a chromatographic agent.

Samples without a chromatographic agent are also studied in a DHM setup based on the Mach–Zehnder interferometer, with the investigated object placed in one arm. Identical microscope objectives are used in the reference and object arms to obtain waves with the same wavefront curvature in the CCD plane. A single recorded hologram (an intensity image) is enough to reconstruct the phase shift introduced by the transparent sample in the optical path. To scan the entire area of the sample, a computer-controlled two-dimensional (2D) motion was performed in a plane perpendicular to the propagation axis. The $40\times$ objective that collects images of the samples allows a $0.9\mathrm{\mu m}$ transversal resolution. Two linear polarizers are used to adjust light intensity, and a neutral density filter in the reference arm ensures proper visibility in the holograms recorded by the CCD (Pike F421, Allied Vision Technologies, Germany, with Kodak sensor $2048\times 2048$ pixels, pixel pitch $\mathrm{\Delta }x=7.4\mathrm{\mu m}$, acquisition rate of $16\mathrm{fps}$ at full resolution). Starting from this pitch, we have chosen the minimum interfringe at $9\mathrm{\Delta }x$, which corresponds to a spatial frequency of $1/(9\mathrm{\Delta }x)$, which is in accordance with the maximum spatial frequency established by the Nyquist–Shannon sampling theorem of $1/(2\mathrm{\Delta }x)$. In this case, the angle between the reference and the object beams is around $0.5\mathrm{deg}$.

Certified phlebotomists collected blood from patients in a hospital, respecting all the appropriate hygienic and legal regulations. The blood was then stored in coated containers at $2–3°\mathrm{C}$, following the standard procedures of in-vitro preservation. Each container was marked uniquely, and all patient personal data were removed. The content of each container was then split into three identical subsamples, for subsequent comparison: one for automatic counts, the second for chromatographic investigations on a slide, and the last for investigations without a chromatographic agent on a slide. A complete blood count for routine analysis was then performed on each first subsample, using the impedance counter in the hospital hematology laboratory (Multisizer 4 Coulter Counter from Beckman Coulter, Inc., USA). The blood from the second and third subsamples was smeared on a microscope slide. A cover slip was placed on top of the blood drop for samples without a chromatographic agent to avoid the cells suffering morphological changes. In this case, the recorded images in the DHM setup and DIC configuration were taken in only few minutes to avoid alterations and drying.

First, we study the blood smear on the microscopic slide using diluted dye agents in bright-field microscopy and the same region in DHM, to visualize which cells are IRBCs or MRBCs. Figure 1 shows the same region of one sample visualized in bright-field microscopy and DHM. In Fig. 1a, the IRBC appears discolored and slightly greater in diameter. In Fig. 1b, the same cell has a different diffractive pattern than neighboring cells, and in Fig. 1c, reconstructed in DHM, it appears as being mountain- shaped, as opposed to the crater-shaped MRBCs.

To avoid the time-consuming procedure with chromatographic agents, we use the third subsample (without a chromatographic agent) in the DHM setup [see Figs. 2a, 2c]. We present images from two regions with at least one IRBC in each, many MRBCs, and one white blood cell [the largest one in Figs. 2c, 2d] being differentiated by its dimension. One can see that the diffractive patterns are different for these three types of investigated cells. Only in the first studies, we observe the same slide in DIC configuration [see Fig. 2b, 2d] to confirm our identification.

Figure 3 presents the holograms recorded when the distance between the sample and the objective is modified (with an actuator step resolution of $0.5\mathrm{\mu m}$). One can observe the differences in the diffraction pattern of these two cell types at different distances between the sample and the microscope objective, which differentiate the IRBC from the MRBC in the preprocessing step. In order to better observe these differences, we record the same region with the reference beam blocked.

The images from Fig. 4 were recorded at different distances between the sample and the objective lens, but without superposing the reference beam onto the object beam. Here, the central maxima and minima in MRBC and IRBC diffraction patterns are more visible and are complementary in the studied interval. The reference distance of $z=0\mathrm{\mu m}$ is chosen in the point where the reconstructed object amplitude has minimum diameter.

3. Diffraction Pattern from Modeled IRBCs and MRBCs

Starting from these experimental observations concerning MRBC and IRBC diffractive pattern behavior, we create models for their shape and refractive index. The phase shift introduced by them is proportional to their thickness $z(x,y)$, thus with the length traveled by the incident monochromatic plane wave within the medium of the sample in every point $(x,y)$,

For the concave shape (which is cropped), different models were considered: semisphere, oblate spheroid, cylindrical or truncated cone, in accordance with experimental images. Similar ellipsoidal models have been introduced in the literature for the study of red blood cell deformability in ektacytometry [22] or for interpreting their spectral response [7].

All these equations become matrices, implemented in MATLAB, which digitally describe cell transmission functions. The phase objects are considered as diffractive elements in a circular aperture of radius $R_i$ with the transmittance function

To calculate the Fresnel diffraction pattern, we have considered a monochromatic plane wave of wavelength λ, normally illuminating the structure of the samples with the transmittance function described by Eq. (3) situated in the input plane. The diffracted field in the output plane at the distance z from the sample, $U(x_0,y_0,z)$, can be expressed using the 2D convolution operator [23]:

Consequently, the complex amplitude of the diffracted field is given by:

For the numerical evaluation, these functions are sampled at the Nyquist frequency and Eqs. (7, 8) are implemented in discrete forms using 2D matrices and the fast Fourier transform routines in MATLAB. The values for equatorial radii were measured experimentally. The values for the refractive index depend on the hemoglobin concentration of the cell [13]:

Simulations performed in MATLAB, in Fresnel approximation, confirm the diffraction pattern observed experimentally (Fig. 4). As in the experimental case, we also consider five distances, and the simulated diffraction patterns after propagation can be seen in Fig. 5 for $a_I=b_I=4.5\mathrm{\mu m}$, $a_M=b_M=3.5\mathrm{\mu m}$, $c_I=2\mathrm{\mu m}$, and the height of the MRBC after concave cropping $3.3\mathrm{\mu m}$. The intensity values and corresponding gray levels are arbitrary in all figures, normalized at the maximum value in each. For this reason, some backgrounds appear brighter than others.

To study the influence of cell parameters on their diffractive patterns, we scan different characteristic values for IRBCs and MRBCs at two given distances, $z_i$ and $z_{i+1}$. Figure 6 illustrates the central intensity dependence on the equatorial and polar radii of the spheroid. The increment i, $i+1$ designates all distances where we found in the central intensity of the diffracted patterns maximum values for MRBC and minimum values for IRBC or vice versa.

4. Automated Procedure for Cell Separation, Identification, and Counting

In this procedure, the starting points are holograms of the transparent cells in plasma, recorded in hospital conditions in a DHM configuration. An algorithm for object image reconstruction and aberration compensation is used [29]. The sample images corresponding to the phase shift introduced by each cell (samples without a chromatographic agent) and their three-dimensional (3D) representations are given in Fig. 7. We apply a low-pass filter in the Fourier plane to remove small, unwanted details. In Fig. 7a, one can see that the entire sample plane is elevated in the back right corner. To adjust this, we use morphological structuring elements, which scan all pixels with their center and probe the neighboring area using a binary block. Its dimension can be scanned until the proper tilt is achieved [the background values are similar in all regions from Fig. 7c.] In Fig. 7b, the removed background is shown in a resized manner only for representation reasons (the indexing syntax is applied to view only one out of eight pixels in each direction; otherwise the surface plot would be too dense). In this sample, a white blood cell (of the largest radius), two IRBCs (the mountain shapes), and many MRBCS (crater shapes) are visible.

Some typical profiles are subtracted from these reconstructions (see Fig. 8). Their shapes prove that our choice to model the cells as oblate ellipsoids was appropriate. All these reconstructions are obtained from the hologram recorded in the in-focus plane, corrections at nanometric scale being achieved using the reconstruction algorithm (to find the minimum cell radius in amplitude reconstructions).

For automated cell–edge separation, identification, and volume calculation for IRBCs and MRBCs, we built a MATLAB code. It can read many images simultaneously and in the end exhibits the histograms, which include information extracted from these images for at least 1000 cells. To design this code, after background corrections presented in the previous paragraph, we use “the distance transform” which provides a metric or calculates the separation points in the image. The aim is to separate all cell images and detect their edges, centroids, radius, eccentricity, and volume. The resultant output images are shown in Fig. 9 (the input images are those of the reconstructed holograms). Notice that partial cell images are excluded (look at the edge for both samples). The distance transform individually identifies cells when they are far apart, but not when some cells are partially overlapped or adhere to each other (see the right region of Fig. 9).

To remove this shortcoming, we propose the following scheme based on several steps. Initially, we enhance the contrast using nonlinear functions applied to the image from Fig. 10a in threshold intervals. We apply an exponential decay for low-value pixels and a logarithmic function for large-value pixels (the commercial programs for contrast enhancement did not give good results). The threshold value is computed statistically for each image based on its pixel weights [Fig. 10b]. However, these functions enhance unwanted details as well, which are further removed through convolution with a Gaussian filter applied on $5\times 5$ neighboring pixels [Fig. 10c].

Images obtained by applying the distance transform after contrast enhancement and Gaussian filter convolution are shown in Fig. 11. The improvement is less spectacular for spaced-out cells [see Fig. 11a], but highly visible for closely packed cells [compare the central right side of the Fig. 10b with the right side of Fig. 11b, where four cells are separately identified]. Comparing the border regions from Figs. 9b, 11b one can see that the incompletely pictured cells are excluded. As the whole image enlarges, the same cells are complete and visible enough to consider these cells in the counting process.

Because the contrast enhancement modifies the values of the pixels, to compute the morphological parameters, we consider the initial images only with Fourier filters for small details and tilt adjustment. Next, finding the properties of the individual cells in our image implies determining the coordinates of the centroids and the contained pixels based on the images with distance transform and edge detection using the “canny” operator from MATLAB. Based on this information and on the profile shapes, we can establish which cells are MRBCs and which are IRBCs by calculating a gradient from their centroids. For each cell, we add up the differences between the height of its centroid and the height of every other constituent pixel. These calculations are performed on the input images in the projected areas delimited after edge detection. For immature cells, which have profiles as plotted in Fig. 8b, the slope will be positive, summing up to a very large number. For mature cells [profiles as in Fig. 8a], the slope will be negative for the first points, starting from their centroid, then positive. Assuming that there is at least one immature cell in the image (our original images have $2048\times 2048$ pixels and contain approximately 200 cells), the cell with the largest gradient number will certainly be an IRBC (or a white blood cell, but white blood cells will be excluded by the scheme, because they have greater radii). To identify the other immature cells, we chose, based on empirical results, those cells whose gradient numbers amount to at least one-third of the maximum. To go from phase shift to thickness values, we consider Eq. (1) and $n_s=n_{\text{plasma}}=1.3515$ [30].

In the same iterations, while calculating the gradient for each cell, we also determine its volume by adding up the heights of all the pixels inside the cell projection. Using this parameter, the IRBCs are well-differentiated by the MRBCs. At a 95% confidence limit, the percentage of reticulocytes is $1.65\%\pm 0.05\%$ [see Fig. 12a] for a healthy person and $1.22\%\pm 0.05\%$ for a suspected patient [see Fig. 12b]. These results were consistent with other measurement techniques: $1.72\%\pm 0.05\%$ and $1.18\pm 0.05\%$ (impedance counter) and $1.70\%\pm 0.07\%$ and $1.23\%\pm 0.07\%$ (bright-field microscopy) performed on the first and second subsamples from each blood sample.

5. Discussion and Conclusions

Besides being used for automated counts, correct blood smear investigation is important in a wide range of diseases. Chromatographic agents are used to visualize and identify different cell types, but some procedures are time-consuming. This is also the case for the classical method for finding the percentage of IRBCs in the total number of red blood cells. For this reason, methods to simultaneously image, and identify/count are sought by scientists.

We experimentally revealed that at different distance intervals between the sample and the objective lens, IRBCs and MRBCs exhibit complementary central maxima and minima in their diffractive patterns. To simulate the propagation in Fresnel approximation, we model IRBCs and MRBCs as oblate spheroids with experimentally established dimensions. We use a mean value for the refractive index, which takes into account hemoglobin concentration. One can observe the succession of the central maxima and minima, which is similar to that seen in the experimental diffraction pattern. The dependencies of the central intensity with regard to the spheroid parameters reveal that the transversal dimensions have a more dominant influence on the diffractive pattern than the longitudinal ones. Between the mean radius of MRBCs and the mean radius of IRBCs there is only one central intensity maximum in their respective diffractive patterns. The equatorial and polar radii do influence the central intensity in the same manner: for both we have a maximum at MRBC parameters and a minimum for IRBCs at a given $z_i$ and vice versa at $z_{i+1}$. We find few values for the distance $z_i$ within the studied interval. Between these values are transition zones, but we never find maximum central intensity for both IRBC and MRBC radii. These preliminary data will be used as preprocessing observations in our microfluidic applications, where every cell has its own distance to the focal plane.

Next, we developed a MATLAB code for combining the advantage of a less time-consuming cell identification-count procedure with the acquisition of other morphological parameters, for discriminating similar cells. The input images are obtained in the re construction step of the DHM technique. Since the distance transform did not separate some adjacent cells, we proposed a scheme based on the nonlinear functions applied at threshold intervals for contrast enhancement and Gaussian filter convolution. As a result, our MATLAB code recognizes each centroid, identifies cell type, counts IRBCs and MRBCs from at least six images (over 1000 cells), and builds the corresponding histograms automatically. White blood cells are separated for their greater radii. Our measurements are in good agreement with those obtained in bright-field microscopy or using the impedance counter.

The developed code can also exhibit histograms after radius, projection area, projection eccentricity, or other morphological parameters, using the values given by the “regionprops” MATLAB operator. The eccentricity parameter is important because a high value indicates that the cells have abnormal shapes— a known signal for many diseases. The eccentricity is greater than 0.7 for oval RBCs and even greater than 1 for pear-shaped, comma-shaped or sickle cells. For the latter types, careful observations are necessary.

Our results prove that DHM combined with image processing is a suitable instrument for simultaneously performing noncontact, label-free individual RBC morphological investigation and real time imaging, identification, and counting. Important in our studies is the fact that the measurements were performed on different slides prepared in hospital conditions with many tangential cells and the procedure separates IRBCs from MRBCs.

The research presented in this paper is supported by the Sectorial Operational Program for Human Resource Development financed by the European Social Fund and by the Romanian Government under contract POSDRU/89/1.5/S/63700. The equipment used in these experiments were acquired using funds from the Romanian contract 4/CP/I/2007-2009 Capacities.

 

Fig. 1 (a) Classical bright-field microscopy on a slide using chromatographic substances to differentiate the cells; (b) hologram of the same slide in the region of interest recorded using off-axis DHM setup; (c) 3D image in false colors of the reconstructed cells from the previous hologram. The IRBCs are highlighted in all images.

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Fig. 2 IRBCs and MRBCs observed in classical DIC microscopy without chromatographic substances. (a) Sample 3, (c) Sample 13; and in DHM (b) Sample 3, (d) Sample 13. The IRBCs are highlighted in all images.

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Fig. 3 Holograms from regions with at least one IRBC recorded at different distances between the microscope objective and sample: (a) Sample 27 at $z_1$, (b) Sample 27 at $z_2$, (c) Sample 19 at $z_3$, (d) Sample 19 at $z_4$. The IRBCs are highlighted in all images.

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Fig. 4 Diffraction pattern (with reference beam obstructed in DHM setup) from an MRBC (top) and an IRBC (bottom) recorded at different distances between the microscope objective and Sample 27 in the same region as in Fig. 3 at (a) $z=9\mathrm{\mu m}$, (b) $z=6\mathrm{\mu m}$, (c) $z=3\mathrm{\mu m}$, (d) $z=0\mathrm{\mu m}$, (e) $z=-6\mathrm{\mu m}$.

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Fig. 5 Simulated diffraction pattern from MRBC (top) and IRBC (bottom) at the same distances between sample and objective as in Fig. 4.

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Fig. 6 Central intensity dependence on (a) equatorial radius at $z_i$, (b) equatorial radius at $z_{i+1}$, (c) polar radius at $z_i$, (d) polar radius at $z_{i+1}$.

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Fig. 7 (a) Initial 3D phase reconstruction, (b) background correction, (c) 3D phase reconstruction with tilt adjustment.

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Fig. 8 Phase shift profiles for (a) MRBC, (b) IRBC.

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Fig. 9 Distance transform applied on the images obtained from the hologram reconstruction of (a) Sample 3, (b) Sample 5.

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Fig. 10 (a) Initial image. (b) Same image with contrast enhancement using nonlinear functions. (c) Convolution of the previous image with a Gaussian filter.

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Fig. 11 Distance transform applied on the image for (a) Sample 3 and (b) Sample 5.

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Fig. 12 Histograms built after volume for (a) healthy person and (b) suspected patient.

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