Automated statistical quantification of three ... - OSA Publishing

Automated statistical quantification of threedimensional morphology and mean corpuscular hemoglobin of multiple red blood cells Inkyu Moon,1,* Bahram Javidi,2 Faliu Yi,1 Daniel Boss,3 and Pierre Marquet3,4 1

School of Computer Engineering, Chosun University, 375 Seosuk-dong, Dong-gu, Gwangju 501-759, Korea Department of Electrical and Computer Engineering, U-2157, University of Connecticut, Storrs, Connecticut 06269-2157, USA 3 LNDC, BMI, Ecole Polytechnique Fédérale de Lausanne, Lausanne, Switzerland 4 Centre de Neurosciences Psychiatriques, Département de psychiatrie DPCHUV, PrillyLausanne, Switzerland *[email protected] 2

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 threedimensionally 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 Optical Society of America OCIS codes: (090.1995) Digital holography; (100.6890) Three-dimensional image processing; (170.3880) Medical and biological imaging; (170.1530) Cell analysis.

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Received 24 Jan 2012; revised 2 Apr 2012; accepted 3 Apr 2012; published 19 Apr 2012

23 April 2012 / Vol. 20, No. 9 / OPTICS EXPRESS 10295

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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 [1–3]. 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. In a previous paper [4], it has been demonstrated that off-axis digital holographic microscopy (DHM) can accurately and quantitatively measure, at the single cell level, important red blood cell (RBC) parameters; these parameters include cell morphology and

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mean corpuscular hemoglobin (MCH) altered in many pathological states such as blood diseases. To promote DHM as a diagnostic method, developments of efficient algorithms allowing an automatic analysis of these RBC parameters are required. Indeed, diagnostic decisions rely upon the analysis of a large number of cells revealing specific subpopulations based on these parameters measured at a single cell level. Consequently, we present an automated approach to quantify information about 3D morphology, MCH and MCH surface density (MCHSD) of mature red blood cells (RBCs) using off-axis digital holographic microscopy to identify various types of RBCs. The (MCH) is considered an important parameter to investigate any modifications or conservation of the hemoglobin content in RBCs since the phase of an optical beam is directly related to the MCH [5]. This paper focuses on the methodological aspects of showing how to discriminate between two RBC populations that differ in cell morphology. Indeed, the RBC, which under normal physiological conditions is a biconcave shape (discocyte), can undergo various shape transitions. The most common types are the cupshaped 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]. 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– 24]. 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 [1–3]. 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] to three-dimensionally sense the RBCs and reconstruct their original phase image using numerical algorithms [26, 27]. 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 shows the schematic of off-axis digital holographic microscopy. We use the off-axis digital holographic imaging system that has been described in [25]. 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, 27].

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Reference Wave Beam Splitter

Mirror

Object Wave

CCD

MO Sample

Mirror Laser

Beam Expander Beam Splitter

Fig. 1. Schematic of the off-axis digital holographic microscopy used in the experiments

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] 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=N

p2 1 ,ϕ = 2 M N

N

∑x , i

(1)

i =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], 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]. 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=

phc , phd

(2)

where phc and phd are phase values at the center of RBC and at a quarter of its diameter, respectively.

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phc

phd d

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.

On the other hand, dry mass (DM) is the weight of the cell when completely dried and is usually considered a reliable measurement of the biomass. Practically, the phase shift induced by a cell is related to its DM by the following equation [30];

Dry Mass ( DM ) =

10λ 2πα

10λ

∫ ϕ ds = 2πα ϕ S , S

(3)

where λ is the wavelength of the light source, α is a constant, known as the specific refraction increment (in m3/kg or dl/g) related to the protein concentration. It is noted that DM is proportional to the projected surface area, S, and the averaged phase value over S, ϕ . According to Ref [4, 5], as far as RBC are concerned, Eq. (3) used with the hemoglobin refraction increment αHb provides specifically the mean corpuscular hemoglobin (MCH). MCH is an important parameter which can be used to investigate any distinctions, alterations or conservation of the hemoglobin content in RBCs. The MCH surface density (MCSD) shows the MCH concentration, which is defined as the ratio of MCH and projected surface area, S as follows:

MCH . (4) S 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. MCHSD =

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] and nearest neighbor classification technique [32]) 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 = [ X 1 ,⋯ X n ] . 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 N r (µ Xr , k Xr ) and

N i (µ Xi , k Xi ) which n-variate normal distributions of reference and input RBCs, respectively.

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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]:

 ( E[ Xr ] − E[ Xi ])′ S pl−1 ( E[ Xr ] − E[ X i ])  LR = 1 / 1 + c  ( N r + N i − 2)   (5)

( N r + Ni ) 2

  1 =  2 1 + T / ( N r + N i − 2) 

( Nr + Ni ) 2

,

N r Ni , S pl is a pooled estimator of the covariance matrix, and the variable T2 N r + Ni has the Hotelling’s distribution. For the statistical decision about whether the observed two nvariate sampling distributions differ significantly, statistical hypothesis testing [31] 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 ( H 0 : µ Xr = µ Xi = µ ) can be rejected if where c =

the threshold value for the test statistic value is set to classify RBCs with different types of shapes and the test statistic T 2 ≥ Tn2, Nr + Ni − 2 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 ) =

n

∑ (x − y ) i

i

2

,

(6)

i =1

where x = ( x1 , x2 ,..., xn ) and y = ( y1 , y2 ,..., yn ) are two mean feature vectors, n represents the number of features and xi , yi 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 xi in feature xi , with ( xi − µi ) / σ i where µi , σ i are 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. 100150µl 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

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

(a)

(b)

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.

Figure 3 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 shows the flow chart of this process.

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Input RBCs image

Segmentation

Mask image

Region labeling

Isolated region extraction

Area calculation

Multiply with original RBCs image

Mean phase calculation

Fig. 4. The flow chart for automated calculation of projected surface area and mean phase of a single RBC.

Figure 5 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. 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.

(a)

(b)

Fig. 5. The segmented red blood cells phase images. (a) Segmented RBCs having a stomatocyte shape, and (b) Segmented RBCs having a discocyte shape.

A part

B part

Fig. 6. The schematic chart of different parts in the red blood cells (RBCs).

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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 shows the segmented phase images of the B part in the RBCs with the different shapes, respectively.

(a)

(b)

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.

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 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.

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Probability Density Function

0.1

0.08

RBCs with a stomatocyte shape RBCs with a discocyte shape

0.06

0.04 0.02

0 10

20

30

40

50

60

70

120

140

Surface Area (µm2)

(a) Probability Density Function

0.05 RBCs with a stomatocyte shape RBCs with a discocyte shape 0.04

0.03

0.02

0.01

0 20

40

60

80

100

Average Phase of Single RBC (Deg.)

(b) 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.

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).

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RBCs with a stomatocyte shape RBCs with a discocyte shape

140 120 100 80 60 40 20

30

40

50

60

Surface Area (µm2)


(a) 140 RBCs with a stomatocyte shape RBCs with a discocyte shape

120 100 80 60 40 20 0

5

10

15

20

25

30

Surface Area (µm2)

(b) 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.

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 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.

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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] 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], where the statistical hypothesis testing of Eq. (5) was performed. It is noted that the computed statistical p-values for the twodimensional random variable (X1, X2) and (X3, X4) are zero (