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Virtual Journal for Biomedical Optics

| EXPLORING THE INTERFACE OF LIGHT AND BIOMEDICINE

  • Editors: Andrew Dunn and Anthony Durkin
  • Vol. 7, Iss. 6 — May. 25, 2012
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Automated statistical quantification of three-dimensional morphology and mean corpuscular hemoglobin of multiple red blood cells

Inkyu Moon, Bahram Javidi, Faliu Yi, Daniel Boss, and Pierre Marquet  »View Author Affiliations


Optics Express, Vol. 20, Issue 9, pp. 10295-10309 (2012)
http://dx.doi.org/10.1364/OE.20.010295


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Abstract

In this paper, we present an automated approach to quantify information about three-dimensional (3D) morphology, hemoglobin content and density of mature red blood cells (RBCs) using off-axis digital holographic microscopy (DHM) and statistical algorithms. The digital hologram of RBCs is recorded by a CCD camera using an off-axis interferometry setup and quantitative phase images of RBCs are obtained by a numerical reconstruction algorithm. In order to remove unnecessary parts and obtain clear targets in the reconstructed phase image with many RBCs, the marker-controlled watershed segmentation algorithm is applied to the phase image. Each RBC in the segmented phase image is three-dimensionally investigated. Characteristic properties such as projected cell surface, average phase, sphericity coefficient, mean corpuscular hemoglobin (MCH) and MCH surface density of each RBC is quantitatively measured. We experimentally demonstrate that joint statistical distributions of the characteristic parameters of RBCs can be obtained by our algorithm and efficiently used as a feature pattern to discriminate between RBC populations that differ in shape and hemoglobin content. Our study opens the possibility of automated RBC quantitative analysis suitable for the rapid classification of a large number of RBCs from an individual blood specimen, which is a fundamental step to develop a diagnostic approach based on DHM.

© 2012 OSA

1. Introduction

Three-dimensional (3D) optical sensing/imaging systems have been investigated for achieving reliable and non-invasive recognition along with identifying biological micro/nano organisms [1

1. B. Javidi, I. Moon, S. Yeom, and E. Carapezza, “Three-dimensional imaging and recognition of microorganism using single-exposure on-line (SEOL) digital holography,” Opt. Express 13(12), 4492–4506 (2005). [CrossRef] [PubMed]

3

3. I. Moon and B. Javidi, “Three-dimensional identification of stem cells by computational holographic imaging,” J. R. Soc. Interface 4, 305–313 (2007). [CrossRef] [PubMed]

]. The biological microorganism recognition system based on 3D holographic imaging has a large number of biological applications in the areas of medical diagnosis, food safety, environmental monitoring, defense, and security.

Indeed, the RBC, which under normal physiological conditions is a biconcave shape (discocyte), can undergo various shape transitions. The most common types are the cup-shaped RBCs (stomatocyte) and the spiculated RBCs (echynocyte). Theoretical considerations can provide explanations for the stomatocyte-discocyte-echynocyte shape transitions of RBCs based on mechanical properties of the cell membrane [6

6. H. W. G. Lim, M. Wortis, and R. Mukhopadhyay, “Stomatocyte-discocyte-echinocyte sequence of the human red blood cell: evidence for the bilayer- couple hypothesis from membrane mechanics,” Proc. Natl. Acad. Sci. U.S.A. 99(26), 16766–16769 (2002). [CrossRef] [PubMed]

]. However, the chemical and molecular processes in the cell membrane leading to mechanical alterations in blood diseases are still poorly understood.

Digital holography is a useful technique for recording and imaging 3D objects or cells [7

7. J. W. Goodman and R. W. Lawrence, “Digital image formation from electronically detected holograms,” Appl. Phys. Lett. 11(3), 77–79 (1967). [CrossRef]

24

24. M. Mihailescu, M. Scarlat, A. Gheorghiu, J. Costescu, M. Kusko, I. A. Paun, and E. Scarlat, “Automated imaging, identification, and counting of similar cells from digital hologram reconstructions,” Appl. Opt. 50(20), 3589–3597 (2011). [CrossRef] [PubMed]

]. Since the hologram of the 3D object is digitized, numerical techniques can be directly applied. Recently, digital holography has successfully been combined with microscopy, which provides high resolution and noninvasive examination to identify biological specimens [1

1. B. Javidi, I. Moon, S. Yeom, and E. Carapezza, “Three-dimensional imaging and recognition of microorganism using single-exposure on-line (SEOL) digital holography,” Opt. Express 13(12), 4492–4506 (2005). [CrossRef] [PubMed]

3

3. I. Moon and B. Javidi, “Three-dimensional identification of stem cells by computational holographic imaging,” J. R. Soc. Interface 4, 305–313 (2007). [CrossRef] [PubMed]

]. With this technique, results have been reported in microscopic imaging, measurement and recognition of biological microorganisms. Here, we apply off-axis digital holographic microscopy [25

25. P. Marquet, B. Rappaz, E. Cuche, T. Colomb, Y. Emery, C. Depeursinge, and P. Magistretti, “Digital holographic microscopy: a noninvasive contrast imaging technique allowing quantitative visualization of living cells with subwavelength axial accuracy,” Opt. Lett. 30, 468–470 (2005). [CrossRef] [PubMed]

] to three-dimensionally sense the RBCs and reconstruct their original phase image using numerical algorithms [26

26. E. Cuche, P. Marquet, and C. Depeursinge, “Simultaneous amplitude and quantitative phase contrast microscopy by numerical reconstruction of Fresnel off-axis holograms,” Appl. Opt. 38(34), 6994–7001 (1999). [CrossRef] [PubMed]

, 27

27. T. Colomb, E. Cuche, F. Charrière, J. Kühn, N. Aspert, F. Montfort, P. Marquet, and C. Depeursinge, “Automatic procedure for aberration compensation in digital holographic microscopy and applications to specimen shape compensation,” Appl. Opt. 45(5), 851–863 (2006). [CrossRef] [PubMed]

]. Before feeding the reconstructed RBCs phase images into the RBCs 3D shape or structures analysis module, it is important to filter out the background from the reconstructed phase image and find regions of interest in the RBCs phase image. After segmenting the RBCs phase image, each red blood cell is extracted according to automated procedures. Then, the joint statistical distributions of properties such as projected cell surface, average phase, MCH and MCHSD of each single RBC are automatically measured. The parametric statistical inference algorithm and the nearest neighbor classification technique are applied to these parameters to evaluate the classification performance of RBCs with different types of shapes. This paper focuses on a preliminary study of showing how the different type of RBCs obtained by digital holography can be quantified and classified using our automated procedures. The experimental results illustrate that the proposed automated algorithm has potential for achieving quantitative analysis and classification of 3D morphology, MCH and MCHSD in RBCs with different shapes.

2. Off-axis digital holographic microscopy

Figure 1
Fig. 1 Schematic of the off-axis digital holographic microscopy used in the experiments
shows the schematic of off-axis digital holographic microscopy. We use the off-axis digital holographic imaging system that has been described in [25

25. P. Marquet, B. Rappaz, E. Cuche, T. Colomb, Y. Emery, C. Depeursinge, and P. Magistretti, “Digital holographic microscopy: a noninvasive contrast imaging technique allowing quantitative visualization of living cells with subwavelength axial accuracy,” Opt. Lett. 30, 468–470 (2005). [CrossRef] [PubMed]

]. Holograms are acquired with a transmission digital holographic microscopy (DHM) setup as shown in Fig. 1. The experimental setup is a modified Mach-Zehnder configuration with a laser diode source (λ=682 nm). The laser beam is divided into a reference wave and an object wave. The object wave is diffracted by the RBC samples, magnified by a 40 × /0.75NA microscope objective and interferes, in the off-axis geometry, with the reference wave to produce the hologram recorded via the CCD camera. The reconstruction and aberration compensation of the RBC wavefront is obtained by using the numerical algorithm described in [26

26. E. Cuche, P. Marquet, and C. Depeursinge, “Simultaneous amplitude and quantitative phase contrast microscopy by numerical reconstruction of Fresnel off-axis holograms,” Appl. Opt. 38(34), 6994–7001 (1999). [CrossRef] [PubMed]

, 27

27. T. Colomb, E. Cuche, F. Charrière, J. Kühn, N. Aspert, F. Montfort, P. Marquet, and C. Depeursinge, “Automatic procedure for aberration compensation in digital holographic microscopy and applications to specimen shape compensation,” Appl. Opt. 45(5), 851–863 (2006). [CrossRef] [PubMed]

].

3. Automated statistical quantification of multiple RBCs

RBC phase images are reconstructed from digital holographic data according to the procedure described in Section 2. The maker-controlled watershed segmentation algorithm [28

28. R. C. Gonzalez and R. E. Woods, Digital Imaging Processing (Prentice Hall, 2002).

] is applied to the reconstructed RBC phase images for analyzing RBCs. After the segmentation, each RBC is extracted and analyzed. For investigating the characteristic properties such as 3D morphology and mean corpuscular hemoglobin (MCH) of RBCs, the projected surface area and mean of phase values of each RBC extracted from the segmented RBC phase image is automatically measured. The projected surface area and mean of phase values are calculated by using the following equations, respectively:
S=Np2M2,φ¯=1Ni=1Nxi,
(1)
where N is the total number of pixels within single RBC, p denotes the pixel size, M the magnification of digital holography microscopy and xi is the phase value at the ith pixel within the single cell representing the phase shift induced by the corresponding RBC as far as the phase value of the background is set to zero.

The sphericity coefficient, k [29

29. T. Tishko, T. Dmitry, and T. Vladimir, Holographic Microscopy of Phase Microscopic Objects (World Scientific, 2011).

], is also measured to characterize 3D morphology of RBCs. and is defined as a ratio of thickness at the center of the RBC to the thickness at a quarter of its diameter [see Fig. 2
Fig. 2 The sphericity coefficient k is defined as a ratio of two quantities (phc, phd) in the RBC. The phc and phd are phase values at the center of RBC and quarter of its diameter, respectively. d is the diameter of RBC.
]. Since the thickness of a RBC is reflected by the phase value, the sphericity coefficient can be alternatively calculated by the phase value at the center of RBC and at a quarter of its diameter. While the projected surface of RBCs is viewed as circular form, the phase value in the center point and at a quarter of the diameter can be approximately measured by the average value within a 5 × 5 window over the RBC. The sphericity coefficient, k as a morphological measurement is expressed as follows:
k=phcphd,
(2)
where phc and phd are phase values at the center of RBC and at a quarter of its diameter, respectively.

MCHSD=MCHS.
(4)

These characteristic parameters are automatically calculated for each RBC and the joint statistical distributions of the parameters for RBC are then obtained for the statistical quantification of 3D morphology, MCH, and MCHSD of multiple RBCs.

4. Automated statistical classification of multiple RBCs

For the purpose of classification of RBCs with different types of shapes, two statistical classification methods (parametric statistical inference algorithm [31

31. C. Rencher, Multivariate Statistical Inference and Application (Wiley, 1998).

] and nearest neighbor classification technique [32

32. E. Gose, R. Johnsonbaugh, and S. Jost, Pattern Recognition and Image Analysis (Prentice Hall, 1996).

]) are employed to the observed joint statistical distributions of the parameters (projected cell surface, average phase, mean corpuscular hemoglobin (MCH) and MCH surface density) in RBC.

4.1 Parametric statistical method for classification of RBCs

Let the characteristic properties (projected cell surface, average phase, MCH and MCHSD) for the single RBC is an n-variate random variable. An n-dimensional random vector can be expressed as an 1 × n matrix,X=[X1,Xn].For comparing the n-dimensional location vector [X¯1,X¯n]of the joint statistical sampling distribution, it is assumed that two independent random sample vectors Xr and Xi are drawn from Nr(μXr,kXr) and Ni(μXi,kXi)which n-variate normal distributions of reference and input RBCs, respectively. For the n-variate hypothesis testing to check the equality of the n-dimensional mean vectors between reference and input RBCs populations, the following likelihood ratio is applied [31

31. C. Rencher, Multivariate Statistical Inference and Application (Wiley, 1998).

]:
LR=1/[1+c(E[Xr]E[Xi])Spl1(E[Xr]E[Xi])(Nr+Ni2)](Nr+Ni)2=[11+T2/(Nr+Ni2)](Nr+Ni)2,
(5)
where c=NrNiNr+Ni, Spl is a pooled estimator of the covariance matrix, and the variable T2 has the Hotelling’s distribution. For the statistical decision about whether the observed two n-variate sampling distributions differ significantly, statistical hypothesis testing [31

31. C. Rencher, Multivariate Statistical Inference and Application (Wiley, 1998).

] is performed and then statistical p-value is calculated by using the test statistic T2 value for the statistical decision. It is noted that the null hypothesis (H0:μXr=μXi=μ) can be rejected if the threshold value for the test statistic value is set to classify RBCs with different types of shapes and the test statistic T2Tn,Nr+Ni22 with threshold value.

4.2 Nearest neighbor classification technique for classification of RBCs

In the nearest neighbor classification technique, Euclidean distance defined in Eq. (6) can be used to measure the dissimilarity between two RBC populations that differ in cell morphology.
d(x¯,y¯)=i=1n(x¯iy¯i)2,
(6)
where x¯=(x¯1,x¯2,...,x¯n) and y¯=(y¯1,y¯2,...,y¯n) are two mean feature vectors, n represents the number of features and x¯i, y¯i are the mean value obtained from all the samples in ith feature of corresponding types of RBCs. Since the Euclidean distance refers to the sum of the dissimilarity of individual features, a normalization of each feature must be carried out so that an arbitrary change of one feature will not affect the decision. Usually, this normalization process is done by replacing sample point in each feature, for example, sample point xiin featurexi, with (xiμi)/σi whereμi,σiare a mean and standard deviation of sample points from all of the RBCs types in feature xi. Thus, the automatically extracted six features (projected cell surface and average phase, MCH and MCHSD) are viewed as feature vectors. We obtain the mean feature vectors x¯ and y¯ for the stomatocyte and discocyte shape RBCs, respectively.

5. Experimental results

5.1 Sample preparation

Red blood cells of healthy laboratory personnel were obtained from the Laboratoire Suisse d’Analyse Du Dopage, CHUV. The RBCs were stored at 4°C and DHM measurements were conducted on several days after the blood was drawn from the laboratory personnel. 100-150μl of RBC stock solution were suspended in HEPA buffer (15mM HEPES pH 7.4, 130 mM NaCl, 5.4 mM KCl, 10 mM glucose, 1 mM CaCl2, 0.5 mM MgCl2 and 1 mg/ml bovine serum albumin) at 0.2% hematocrit. 4 μl of the erythrocyte suspension were diluted to 150 μl of HEPA buffer and introduced into the experimental chamber, consisting of two cover slips separated by spacers 1.2 mm thick. Cells were incubated for 30 min at a temperature of 37°C before mounting the chamber on the DHM stage. All experiments were conducted at room temperature (22°C).

5.2 3D sensing, imaging and segmentation of red blood cell (RBC)

The RBCs phase images were reconstructed from the recorded digital holograms with 1024 × 1024 pixels. In Ref [4

4. B. Rappaz, A. Barbul, Y. Emery, R. Korenstein, C. Depeursinge, P. J. Magistretti, and P. Marquet, “Comparative study of human erythrocytes by digital holographic microscopy, confocal microscopy, and impedance volume analyzer,” Cytometry A 73A(10), 895–903 (2008). [CrossRef] [PubMed]

], Rappaz has reported the method of quality control of the DHM data for biological cell imaging.

Figure 3
Fig. 3 The reconstructed red blood cells phase images: (a) The red blood cells (RBCs) on day 14 with predominantly stomatocyte shape. (b) The RBCs on day 38 with predominantly discocyte shape.
shows the phase images of RBCs obtained by using off-axis digital holographic microscopy. The phase images of the RBCs acquired on day 14 and 38 of the blood storage period showed two distinct types of shapes (stomatocyte shape and discocyte one) and were used for the automated quantification of 3D morphology, mean corpuscular hemoglobin (MCH) and MCH surface density (MCHSD) of RBCs. Figure 3(a) shows the RBCs with a predominantly stomatocyte shape (cup-shaped), and Fig. 3(b) shows the RBCs having a predominantly discocyte shape. To adequately calculate the characteristic RBC parameters mentioned above, the background in the reconstructed phase image has been removed by applying a maker-controlled watershed segmentation algorithm. Since the maker-controlled watershed algorithm has the advantage of separating each object when internal and external markers are appropriately identified, the binary image (mask image), in which the white component represents RBCs and black one denotes the background, can be obtained by filling the holes of the csegmented images. Thus, the mask image can be labeled through 8-adjacent connectivity and each different label is viewed as a different RBC. Consequently, each RBC can be extracted by the label of the RBC. Furthermore, the number of pixels for each RBC, which has the same label, can be calculated and the projected surface area of each RBC can be acquired by Eq. (1). After the RBC in the labeled image is selected by indexing label, the mean phase value of each RBC can be obtained with Eq. (1) by multiplying this selected region with the original RBC’s image. However, the background pixels relative to each selected RBC should be excluded for the mean phase value calculation. Figure 4
Fig. 4 The flow chart for automated calculation of projected surface area and mean phase of a single RBC.
shows the flow chart of this process.

Figure 5
Fig. 5 The segmented red blood cells phase images. (a) Segmented RBCs having a stomatocyte shape, and (b) Segmented RBCs having a discocyte shape.
shows the segmented phase images of RBCs having a stomatocyte shape and a discocyte shape, respectively. Since most RBCs appear to have two types of regions as shown in Fig. 5, it is better to separate the different parts for each shape to achieve comprehensive and detailed analysis of the RBCs 3D shape or structure. Here, different regions of RBCs are defined in Fig. 6
Fig. 6 The schematic chart of different parts in the red blood cells (RBCs).
. The B part, which is located on the interior of the A part (single RBC), is the region of central pallor. Note that the mean phase value of the B part is relatively lower than that in the A part resulting from the biconcave RBC shape.

In order to obtain different 3D regions in RBCs, we first use the marker-controlled watershed algorithm to obtain the A part. Then, the A part is taken as a source image, and the B part can be found by applying the marker-controlled watershed. Figure 7
Fig. 7 The segmented phase images of the B parts (area of central pallor) [see Fig. 6] in RBCs. (a) Segmented phase image of the B part in the RBCs having a stomatocyte shape. (b) Segmented phase image of the B part in the RBCs having a discocyte shape.
shows the segmented phase images of the B part in the RBCs with the different shapes, respectively.

5.3 Automatic statistical quantification and classification of red blood cells (RBCs)

For the quantitative investigation of 3D morphology, MCH and MCH surface density of RBCs with two different types of shapes, the characteristic properties of the projected surface area and the mean of the phase value in the A and B parts [see Fig. 6] of single RBC are calculated using Eq. (1), respectively.

Figure 8
Fig. 8 (a) Two statistical distributions for the cell area in part A [see Fig. 6] of RBCs. (b) Two statistical distributions of the mean of phase value in part A of RBCs. Solid line is for the RBCs having a stomatocyte shape. Dotted line is for the RBCs having a discocyte shape.
shows the statistical distributions of the properties projected surface area, X1, and the mean of the phase value, X2, in the A part of a single RBC; Note that each property is considered a random variables. As shown in Fig. 8, the mean and standard deviation of RBCs with a stomatocyte shape for X1 are as 34μm2 and 5μm2, respectively and are 97° and 9° for X2, respectively. For RBCs with a discocyte shape, the mean and standard deviation of variable X1 are 42μm2 and 8μm2, respectively, and are 74° and 15° for variable X2, respectively. The standard deviations of random variable X1 and X2 in RBCs with a stomatocyte shape are smaller than those of RBCs with a discocyte shape. It is noted that the RBC with a stomatocyte shape tends to be more similar to each other than RBCs with a discocyte shape since stomatocytes are inclined to be much closer to the mean value. In addition, the mean of the phase value in the A part of the RBCs with a stomatocyte shape is larger than the RBCs with a discocyte shape while the mean of the projected surface area in the A part of RBCs with a stomatocyte shape is smaller than RBCs with a discocyte shape. It is noted that there was a difference of approximately 23° between the average phase values in the A part of the RBCs with the different types of shapes. Also, there was a difference of approximately 8μm2 between the average projected surface area values in the A part of the RBCs with the different shapes. In addition, the overlapped area between two statistical distributions of the phase value is smaller than that of the projected surface area.

For checking the equality of the location parameters between two projected surface area distributions or mean phase value of the different type of RBCs, the statistical hypothesis testing (t-test) was conducted. The computed statistical p-values were approximately 3.43×10−13 and 1.36×10−19 for the projected surface area (X1), and mean phase value (X2), respectively. This indicates that there is more separation between two statistical distributions of the mean phase value (X2) than those of the projected surface area (X1).

Similarly, the projected surface area, as random variable X3, and the mean phase value, random variable X4, for a single RBC in the B part are used to analyze the distribution of the properties in RBCs having different shapes. The mean and standard deviation of variable X3 are calculated to be 10μm2 and 5μm2 respectively, and those of X4 are 81° and 12°, respectively, in RBCs with a stomatocyte shape. For RBCs with a discocyte shape in B part, the mean and standard deviation of random variable X3 are 18μm2 and 5μm2 respectively, and those for X4 are 60° and 11°, respectively. The mean projected surface area in the B part of the RBCs with a stomatocyte shape is about 8μm2 smaller than that of RBCs with a discocyte shape while the standard deviation is very similar. Figure 9
Fig. 9 A scatter plot of the relationship between the projected surface area and the mean of the phase value in (a) A part and (b) B part [see Fig. 6] of a single RBC.
shows a scatter plot of the relationship between the projected surface area and the mean of the phase value in A and B parts [see Fig. 6] in the RBC, respectively, where all single RBCs from the phase images of RBCs having the different shapes were investigated. As shown in Fig. 9, the projected surface area of the A or B parts of a single RBC is inversely proportional to the mean of the phase value in the A or B parts of both types of single RBCs. Furthermore, there is a strong correlation between the projected surface area and mean of the phase value in the A or B parts of both types of single RBCs. Also, Fig. 9 shows that there is a considerable separation between bivariate distributions or 3D morphology of the different types of RBCs.

In order to evaluate there is a significant 3D morphology distinction in RBC populations that differ in shape for the purpose of classification of RBCs, a parametric statistical inference algorithm [31

31. C. Rencher, Multivariate Statistical Inference and Application (Wiley, 1998).

] is employed to the joint statistical distributions of RBCs. For the statistical decision on the equality of the location vector of the joint statistical sampling distribution for joint random variable (X1, X2) or (X3, X4) of the RBCs with two distinct types of shapes (stomatocyte shape and discocyte one), we have measured average statistical p-value by using the table of Hotelling’s distribution in reference [31

31. C. Rencher, Multivariate Statistical Inference and Application (Wiley, 1998).

], where the statistical hypothesis testing of Eq. (5) was performed. It is noted that the computed statistical p-values for the two-dimensional random variable (X1, X2) and (X3, X4) are zero (<<10−100), which are the probability that the observed test statistic of Eq. (5) would occur in the same population (3D shape profile or 3D morphology for surface area and phase) in the A and B part. Therefore, these experimental results indicate that the joint statistical distributions for the 3D morphology (surface area and phase) of the RBCs can provide a good separation between RBCs having the different shapes.

The MCH of each RBC has been viewed as statistical population. The MCH of a single RBC in RBCs with a stomatocyte shape is denoted as random variable X5, while in RBCs with a discocyte shape it is represented as X6. The mean and standard deviation of random variable X5 are obtained as 31.1pg and 4.0pg, respectively, and those of X6 are 28.9pg and 4.0pg, respectively. It is noted that the averaged MCH values for both types of RBCs are approximately within the typical range of [27

27. T. Colomb, E. Cuche, F. Charrière, J. Kühn, N. Aspert, F. Montfort, P. Marquet, and C. Depeursinge, “Automatic procedure for aberration compensation in digital holographic microscopy and applications to specimen shape compensation,” Appl. Opt. 45(5), 851–863 (2006). [CrossRef] [PubMed]

, 31

31. C. Rencher, Multivariate Statistical Inference and Application (Wiley, 1998).

] picogram/cell. Figure 10(a)
Fig. 10 (a) Statistical distributions of the MCH in the A part of RBCs. (b) A scatter plot of the relationship between the MCH and MCH surface density in the A part of a single RBC.
shows the statistical distributions of the MCH in the A part of a single RBC where we have measured the dry mass of RBCs having the different types of shapes. Note there was a difference of approximately 2.2pg between the averaged MCH values in the A part of RBCs with different types of shapes. The MCH of RBCs with a discocyte shape is a little smaller than RBCs with a stomatocyte shape. Moreover, the dispersion of MCH in both types of RBCs is very stable although the mean MCH in RBCs with a stomatocyte shape is a little larger than that in RBCs with a discocyte one.

For the statistical decision on the equality of the location parameter between two dry mass/MCH distributions of the different type of RBCs, the statistical hypothesis testing (t-test) was performed. A statistical p-value was calculated by using the table of Student’s t distribution the computed statistical p-value for checking of the equality of the location parameter is approximately 0.0002, which is the probability that the observed t-test statistic would occur in the same dry mass/MCH population. Therefore, from the above experimental results, we might investigate any distinctions of the hemoglobin concentration in the RBC with different types of shapes.

Figure 10(b) is a scatter plot of the relationship between MCH and MCH surface density, which is the ratio between MCH and projected surface area in the A part as defined in Eq. (4) for the RBCs with the different shapes. The MCH is approximately directly proportional to MCH surface density both in RBCs with a stomatocyte shape and a discocyte one. Also, the average dry mass density of RBCs with a discocyte shape is smaller than RBCs with a stomatocyte shape; This can be explained because the projected surface area growth rate of single RBC is larger than dry mass production rate when the RBCs have a discocyte shape.

The nearest neighbor classification technique was also utilized to demonstrate that the mean feature vectors (x¯: RBCs with stomatocyte shape, y¯: RBCs with discocyte shape), which are obtained by our proposed method, can represent the corresponding types of RBCs appropriately. We generated 30 trial sample vectors from the estimated joint statistical distributions of the stomatocyte and discocyte RBCs as a class I and II, respectively, where the size of trial sample vectors was 100. It is assumed that the joint statistical distribution follows 6-variate normal probability density function. It is noted that the average Euclidean distance between x¯(RBCs with stomatocyte shape) and the trial mean feature vectors of class I (true-class inputs) is 0.18 while it is 2.81 from the trial mean feature vectors of class II (false-class inputs). Moreover, the average Euclidean distance between y¯(RBCs with discocyte shape) and the trial mean feature vectors of class I (false-class inputs) is 2.76 while it is 0.21 from the trial mean feature vectors of class II (true-class inputs). The Euclidean distance between the two different types of RBCs (x¯andy¯) is computed to be 2.82.

Therefore, the experimental results show that these properties can be used as the feature pattern to classify the RBCs with different types of shapes or blood diseases.

Finally, we examined the sphericity coefficient k defined in Eq. (2), which was taken as a random variable while each single RBC can be serviced as sample data. X7 and X8 are used to denote the random variables for the sphericity coefficient in RBCs with a stomatocyte shape and a discocyte one, respectively. The mean and standard deviation for random variable X7 in RBCs with a stomatocyte shape is calculated to be 0.54 and 0.21, respectively, while those values are 0.63 and 0.18, respectively, for X8 in RBCs with a discocyte shape. Figure 11
Fig. 11 Statistical distribution of the sphericity coefficient, k in A part of RBCs. Solid line is for RBCs having a stomatocyte. Dotted line is for RBCs having a discocyte shape.
shows the statistical distribution for sphericity coefficient in RBCs with a stomatocyte shape and a discocyte one by taking the samples’ mean and standard deviation as population’s mean and standard deviation (There are approximately 100 samples for each class of RBCs). It is noted from Fig. 11 that most of the sphericity coefficients in both types of RBCs are smaller than 1.00 and the average sphericity coefficient in RBCs with a discocyte shape is a little bit larger than that in RBCs with a stomatocyte one.

6. Conclusion

In summary, we have presented a methodology to automatically quantify information about the 3D morphology, and hemoglobin content of RBCs using quantitative phase images obtained by off-axis digital holographic microscopy. After reconstructing the RBCs phase images from their digital holograms by using numerical algorithm, we have applied the segmentation algorithm to remove the unnecessary background in the reconstructed phase image. Then, we have automatically calculated the characteristic properties such as projected cell surface, average phase, sphericity coefficient, mean corpuscular hemoglobin (MCH) and MCH surface density (MCHSD) of every single RBC in the segmented phase image. For the statistical quantification of the characteristic properties of RBCs, we have demonstrated that our algorithm can provide joint statistical distributions of the properties of RBC. It has been shown that the joint statistical distributions might be used as a feature pattern to investigate any distinctions of 3D morphology or MCH in RBCs that differ in shape. In addition, advanced statistical pattern analysis [33

33. F. A. Sadjadi and A. Mahalanobis, “Target-adaptive polarimetric synthetic aperture radar target discrimination using maximum average correlation height filters,” Appl. Opt. 45(13), 3063–3070 (2006). [CrossRef] [PubMed]

] can be performed with the joint statistical distribution for identifying the various types of RBCs or studying dynamics of RBCs. The development of these automatic algorithms allows thus to explore large number of cells and to rapidly classify, from parameters measured at a single cell level, RBCs into well-defined subpopulations, opening the way for promoting DHM as a diagnostic method.

Acknowledgment

This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2009-0088195).

References and links

1.

B. Javidi, I. Moon, S. Yeom, and E. Carapezza, “Three-dimensional imaging and recognition of microorganism using single-exposure on-line (SEOL) digital holography,” Opt. Express 13(12), 4492–4506 (2005). [CrossRef] [PubMed]

2.

A. Stern and B. Javidi, “Theoretical analysis of three-dimensional imaging and recognition of micro-organisms with a single-exposure on-line holographic microscope,” J. Opt. Soc. Am. A 24, 163–168 (2007). [CrossRef]

3.

I. Moon and B. Javidi, “Three-dimensional identification of stem cells by computational holographic imaging,” J. R. Soc. Interface 4, 305–313 (2007). [CrossRef] [PubMed]

4.

B. Rappaz, A. Barbul, Y. Emery, R. Korenstein, C. Depeursinge, P. J. Magistretti, and P. Marquet, “Comparative study of human erythrocytes by digital holographic microscopy, confocal microscopy, and impedance volume analyzer,” Cytometry A 73A(10), 895–903 (2008). [CrossRef] [PubMed]

5.

R. Barer, “Interference microscopy and mass determination,” Nature 169(4296), 366–367 (1952). [CrossRef] [PubMed]

6.

H. W. G. Lim, M. Wortis, and R. Mukhopadhyay, “Stomatocyte-discocyte-echinocyte sequence of the human red blood cell: evidence for the bilayer- couple hypothesis from membrane mechanics,” Proc. Natl. Acad. Sci. U.S.A. 99(26), 16766–16769 (2002). [CrossRef] [PubMed]

7.

J. W. Goodman and R. W. Lawrence, “Digital image formation from electronically detected holograms,” Appl. Phys. Lett. 11(3), 77–79 (1967). [CrossRef]

8.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).

9.

U. Schnars and W. Jueptner, Digital Holography: Digital Hologram Recording, Numerical Reconstruction and Related Techniques (Springer, 2005).

10.

U. Schnars and W. P. O. Jueptner, “Digital recording and numerical reconstruction of holograms,” Meas. Sci. Technol. 13(9), R85–R101 (2002). [CrossRef]

11.

T. Kreis, Handbook of Holographic Interferometry (Wiley, 2005).

12.

F. Dubois, L. Joannes, and J.-C. Legros, “Improved three-dimensional imaging with digital holography microscope using a partial spatial coherent source,” Appl. Opt. 38(34), 7085–7094 (1999). [CrossRef] [PubMed]

13.

T. Nomura, S. Murata, E. Nitanai, and T. Numata, “Phase-shifting digital holography with a phase difference between orthogonal polarizations,” Appl. Opt. 45(20), 4873–4877 (2006). [CrossRef] [PubMed]

14.

Y. Frauel, T. J. Naughton, O. Matoba, E. Tajahuerce, and B. Javidi, “Three dimensional imaging and display using computational holographic imaging,” Proc. IEEE 94(3), 636–653 (2006). [CrossRef]

15.

E. Cuche, P. Marquet, and C. Depeursinge, “Spatial filtering for zero-order and twin-image elimination in digital off-axis holography,” Appl. Opt. 39(23), 4070–4075 (2000). [CrossRef] [PubMed]

16.

Y. Zhang, G. Pedrini, W. Osten, and H. J. Tiziani, “Reconstruction of in-line digital holograms from two intensity measurements,” Opt. Lett. 29(15), 1787–1789 (2004). [CrossRef] [PubMed]

17.

P. Ferraro, S. Grilli, D. Alfieri, S. De Nicola, A. Finizio, G. Pierattini, B. Javidi, G. Coppola, and V. Striano, “Extended focused image in microscopy by digital Holography,” Opt. Express 13(18), 6738–6749 (2005). [CrossRef] [PubMed]

18.

V. Micó, J. García, Z. Zalevsky, and B. Javidi, “Phase-shifting Gabor holography,” Opt. Lett. 34(10), 1492–1494 (2009). [CrossRef] [PubMed]

19.

A. Faridian, D. Hopp, G. Pedrini, U. Eigenthaler, M. Hirscher, and W. Osten, “Nanoscale imaging using deep ultraviolet digital holographic microscopy,” Opt. Express 18(13), 14159–14164 (2010). [CrossRef] [PubMed]

20.

B. Javidi and E. Tajahuerce, “Three-dimensional object recognition by use of digital holography,” Opt. Lett. 25(9), 610–612 (2000). [CrossRef] [PubMed]

21.

T. Nomura, B. Javidi, S. Murata, E. Nitanai, and T. Numata, “Polarization imaging of a 3D object by use of on-axis phase-shifting digital holography,” Opt. Lett. 32(5), 481–483 (2007). [CrossRef] [PubMed]

22.

L. Martínez-León and B. Javidi, “Synthetic aperture single-exposure on-axis digital holography,” Opt. Express 16(1), 161–169 (2008). [CrossRef] [PubMed]

23.

P. Langehanenberg, L. Ivanova, I. Bernhardt, S. Ketelhut, A. Vollmer, D. Dirksen, G. Georgiev, G. von Bally, and B. Kemper, “Automated three-dimensional tracking of living cells by digital holographic microscopy,” J. Biomed. Opt. 14(1), 014018 (2009). [CrossRef] [PubMed]

24.

M. Mihailescu, M. Scarlat, A. Gheorghiu, J. Costescu, M. Kusko, I. A. Paun, and E. Scarlat, “Automated imaging, identification, and counting of similar cells from digital hologram reconstructions,” Appl. Opt. 50(20), 3589–3597 (2011). [CrossRef] [PubMed]

25.

P. Marquet, B. Rappaz, E. Cuche, T. Colomb, Y. Emery, C. Depeursinge, and P. Magistretti, “Digital holographic microscopy: a noninvasive contrast imaging technique allowing quantitative visualization of living cells with subwavelength axial accuracy,” Opt. Lett. 30, 468–470 (2005). [CrossRef] [PubMed]

26.

E. Cuche, P. Marquet, and C. Depeursinge, “Simultaneous amplitude and quantitative phase contrast microscopy by numerical reconstruction of Fresnel off-axis holograms,” Appl. Opt. 38(34), 6994–7001 (1999). [CrossRef] [PubMed]

27.

T. Colomb, E. Cuche, F. Charrière, J. Kühn, N. Aspert, F. Montfort, P. Marquet, and C. Depeursinge, “Automatic procedure for aberration compensation in digital holographic microscopy and applications to specimen shape compensation,” Appl. Opt. 45(5), 851–863 (2006). [CrossRef] [PubMed]

28.

R. C. Gonzalez and R. E. Woods, Digital Imaging Processing (Prentice Hall, 2002).

29.

T. Tishko, T. Dmitry, and T. Vladimir, Holographic Microscopy of Phase Microscopic Objects (World Scientific, 2011).

30.

B. Rappaz, E. Cano, T. Colomb, J. Kühn, C. Depeursinge, V. Simanis, P. J. Magistretti, and P. Marquet, “Noninvasive characterization of the fission yeast cell cycle by monitoring dry mass with digital holographic microscopy,” J. Biomed. Opt. 14(3), 034049 (2009). [CrossRef] [PubMed]

31.

C. Rencher, Multivariate Statistical Inference and Application (Wiley, 1998).

32.

E. Gose, R. Johnsonbaugh, and S. Jost, Pattern Recognition and Image Analysis (Prentice Hall, 1996).

33.

F. A. Sadjadi and A. Mahalanobis, “Target-adaptive polarimetric synthetic aperture radar target discrimination using maximum average correlation height filters,” Appl. Opt. 45(13), 3063–3070 (2006). [CrossRef] [PubMed]

OCIS Codes
(100.6890) Image processing : Three-dimensional image processing
(170.1530) Medical optics and biotechnology : Cell analysis
(170.3880) Medical optics and biotechnology : Medical and biological imaging
(090.1995) Holography : Digital holography

ToC Category:
Medical Optics and Biotechnology

History
Original Manuscript: January 24, 2012
Revised Manuscript: April 2, 2012
Manuscript Accepted: April 3, 2012
Published: April 19, 2012

Virtual Issues
Vol. 7, Iss. 6 Virtual Journal for Biomedical Optics

Citation
Inkyu Moon, Bahram Javidi, Faliu Yi, Daniel Boss, and Pierre Marquet, "Automated statistical quantification of three-dimensional morphology and mean corpuscular hemoglobin of multiple red blood cells," Opt. Express 20, 10295-10309 (2012)
http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=oe-20-9-10295


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References

  1. B. Javidi, I. Moon, S. Yeom, and E. Carapezza, “Three-dimensional imaging and recognition of microorganism using single-exposure on-line (SEOL) digital holography,” Opt. Express13(12), 4492–4506 (2005). [CrossRef] [PubMed]
  2. A. Stern and B. Javidi, “Theoretical analysis of three-dimensional imaging and recognition of micro-organisms with a single-exposure on-line holographic microscope,” J. Opt. Soc. Am. A24, 163–168 (2007). [CrossRef]
  3. I. Moon and B. Javidi, “Three-dimensional identification of stem cells by computational holographic imaging,” J. R. Soc. Interface4, 305–313 (2007). [CrossRef] [PubMed]
  4. B. Rappaz, A. Barbul, Y. Emery, R. Korenstein, C. Depeursinge, P. J. Magistretti, and P. Marquet, “Comparative study of human erythrocytes by digital holographic microscopy, confocal microscopy, and impedance volume analyzer,” Cytometry A73A(10), 895–903 (2008). [CrossRef] [PubMed]
  5. R. Barer, “Interference microscopy and mass determination,” Nature169(4296), 366–367 (1952). [CrossRef] [PubMed]
  6. H. W. G. Lim, M. Wortis, and R. Mukhopadhyay, “Stomatocyte-discocyte-echinocyte sequence of the human red blood cell: evidence for the bilayer- couple hypothesis from membrane mechanics,” Proc. Natl. Acad. Sci. U.S.A.99(26), 16766–16769 (2002). [CrossRef] [PubMed]
  7. J. W. Goodman and R. W. Lawrence, “Digital image formation from electronically detected holograms,” Appl. Phys. Lett.11(3), 77–79 (1967). [CrossRef]
  8. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).
  9. U. Schnars and W. Jueptner, Digital Holography: Digital Hologram Recording, Numerical Reconstruction and Related Techniques (Springer, 2005).
  10. U. Schnars and W. P. O. Jueptner, “Digital recording and numerical reconstruction of holograms,” Meas. Sci. Technol.13(9), R85–R101 (2002). [CrossRef]
  11. T. Kreis, Handbook of Holographic Interferometry (Wiley, 2005).
  12. F. Dubois, L. Joannes, and J.-C. Legros, “Improved three-dimensional imaging with digital holography microscope using a partial spatial coherent source,” Appl. Opt.38(34), 7085–7094 (1999). [CrossRef] [PubMed]
  13. T. Nomura, S. Murata, E. Nitanai, and T. Numata, “Phase-shifting digital holography with a phase difference between orthogonal polarizations,” Appl. Opt.45(20), 4873–4877 (2006). [CrossRef] [PubMed]
  14. Y. Frauel, T. J. Naughton, O. Matoba, E. Tajahuerce, and B. Javidi, “Three dimensional imaging and display using computational holographic imaging,” Proc. IEEE94(3), 636–653 (2006). [CrossRef]
  15. E. Cuche, P. Marquet, and C. Depeursinge, “Spatial filtering for zero-order and twin-image elimination in digital off-axis holography,” Appl. Opt.39(23), 4070–4075 (2000). [CrossRef] [PubMed]
  16. Y. Zhang, G. Pedrini, W. Osten, and H. J. Tiziani, “Reconstruction of in-line digital holograms from two intensity measurements,” Opt. Lett.29(15), 1787–1789 (2004). [CrossRef] [PubMed]
  17. P. Ferraro, S. Grilli, D. Alfieri, S. De Nicola, A. Finizio, G. Pierattini, B. Javidi, G. Coppola, and V. Striano, “Extended focused image in microscopy by digital Holography,” Opt. Express13(18), 6738–6749 (2005). [CrossRef] [PubMed]
  18. V. Micó, J. García, Z. Zalevsky, and B. Javidi, “Phase-shifting Gabor holography,” Opt. Lett.34(10), 1492–1494 (2009). [CrossRef] [PubMed]
  19. A. Faridian, D. Hopp, G. Pedrini, U. Eigenthaler, M. Hirscher, and W. Osten, “Nanoscale imaging using deep ultraviolet digital holographic microscopy,” Opt. Express18(13), 14159–14164 (2010). [CrossRef] [PubMed]
  20. B. Javidi and E. Tajahuerce, “Three-dimensional object recognition by use of digital holography,” Opt. Lett.25(9), 610–612 (2000). [CrossRef] [PubMed]
  21. T. Nomura, B. Javidi, S. Murata, E. Nitanai, and T. Numata, “Polarization imaging of a 3D object by use of on-axis phase-shifting digital holography,” Opt. Lett.32(5), 481–483 (2007). [CrossRef] [PubMed]
  22. L. Martínez-León and B. Javidi, “Synthetic aperture single-exposure on-axis digital holography,” Opt. Express16(1), 161–169 (2008). [CrossRef] [PubMed]
  23. P. Langehanenberg, L. Ivanova, I. Bernhardt, S. Ketelhut, A. Vollmer, D. Dirksen, G. Georgiev, G. von Bally, and B. Kemper, “Automated three-dimensional tracking of living cells by digital holographic microscopy,” J. Biomed. Opt.14(1), 014018 (2009). [CrossRef] [PubMed]
  24. M. Mihailescu, M. Scarlat, A. Gheorghiu, J. Costescu, M. Kusko, I. A. Paun, and E. Scarlat, “Automated imaging, identification, and counting of similar cells from digital hologram reconstructions,” Appl. Opt.50(20), 3589–3597 (2011). [CrossRef] [PubMed]
  25. P. Marquet, B. Rappaz, E. Cuche, T. Colomb, Y. Emery, C. Depeursinge, and P. Magistretti, “Digital holographic microscopy: a noninvasive contrast imaging technique allowing quantitative visualization of living cells with subwavelength axial accuracy,” Opt. Lett.30, 468–470 (2005). [CrossRef] [PubMed]
  26. E. Cuche, P. Marquet, and C. Depeursinge, “Simultaneous amplitude and quantitative phase contrast microscopy by numerical reconstruction of Fresnel off-axis holograms,” Appl. Opt.38(34), 6994–7001 (1999). [CrossRef] [PubMed]
  27. T. Colomb, E. Cuche, F. Charrière, J. Kühn, N. Aspert, F. Montfort, P. Marquet, and C. Depeursinge, “Automatic procedure for aberration compensation in digital holographic microscopy and applications to specimen shape compensation,” Appl. Opt.45(5), 851–863 (2006). [CrossRef] [PubMed]
  28. R. C. Gonzalez and R. E. Woods, Digital Imaging Processing (Prentice Hall, 2002).
  29. T. Tishko, T. Dmitry, and T. Vladimir, Holographic Microscopy of Phase Microscopic Objects (World Scientific, 2011).
  30. B. Rappaz, E. Cano, T. Colomb, J. Kühn, C. Depeursinge, V. Simanis, P. J. Magistretti, and P. Marquet, “Noninvasive characterization of the fission yeast cell cycle by monitoring dry mass with digital holographic microscopy,” J. Biomed. Opt.14(3), 034049 (2009). [CrossRef] [PubMed]
  31. C. Rencher, Multivariate Statistical Inference and Application (Wiley, 1998).
  32. E. Gose, R. Johnsonbaugh, and S. Jost, Pattern Recognition and Image Analysis (Prentice Hall, 1996).
  33. F. A. Sadjadi and A. Mahalanobis, “Target-adaptive polarimetric synthetic aperture radar target discrimination using maximum average correlation height filters,” Appl. Opt.45(13), 3063–3070 (2006). [CrossRef] [PubMed]

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