quantifying morphological alteration of rbc 1 population from light scattering data

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Clinical Hemorheology and Microcirculation xx (20xx) x–xxDOI:10.3233/CH-131726IOS Press

1

Quantifying morphological alteration of RBC1

population from light scattering data2

Raghwendra Mishraa,b, Debasish Sarkarc, Sourav Bhattacharyaa, Sanjaya Mallickd,e,Mousumi Chakrabortya, Debarati Mukherjeea,b, Manoj Karb and Roshnara Mishraa,∗

3

4

aDepartment of Physiology, University of Calcutta, Kolkata, India5

bDepartment of Biochemistry, NRS Medical College, Kolkata, India6

cDepartment of Chemical Engineering, University of Calcutta, Kolkata, India7

dCU BD Centre of Excellence for Nanobiotechnology, University of Calcutta, Kolkata, India8

eBD Biosciences, India9

Abstract. Studies of RBC morphological alterations, despite their potential clinical and experimental application, are com-10

promised due to lack of simple and rapid techniques. As a complementary approach toward quantitative microscopy, we have11

reconstituted morphological information from light scattering data obtained from flow cytometer. Normal and poikilocytic agent12

treated samples were analyzed by microscopy and respective morphological index (MI) was calculated from the morphology13

based scores assigned to RBC. The samples were simultaneously analyzed by flowcytometer and the scatter data were obtained.14

Accordingly, the best correlated parameters of both forward scatter and side scatter were chosen to formulate a suitable regression15

model with MI as response. Flow cytometry data was also verified with another instrument (BD FACS Verse) and the equation16

obtained was validated with separate set of samples. The multivariate regression analysis yields a quadratic model with MI as17

response (R2 = 0.96, p < 0.001). The flow cytometric data from both instruments were in good agreement (Intra class correla-18

tion 0.9, p < 0.001). The model was found to simulate the sample MI with high accuracy (R2 = 0.97, p < 0.001). This proposed19

method was verified to be simple, rapid, quantitative and cost effective for the measurement of morphological alteration of RBC.20

Keywords: Red blood cell, morphological alteration, morphological index, light scattering, flow cytometry21

Abbreviations21

RBC red blood cellMI morphological indexMS morphological scoreFSC forward scatterSSC Side scatterE5M eosin-5-maleimiderCV robust co-efficient of variance%CV co-efficient of variance

∗Corresponding author: Roshnara Mishra, Assistant Professor, Department of Physiology, University of Calcutta, 92, A.P.C.Road, Kolkata-700009, India. Tel.: +91 33 23508386/6387/6396/1397 (Extn: 226); Fax: +91 33 2351 9755/2241 3288; E-mail:[email protected].

1386-0291/13/$27.50 © 2013 – IOS Press and the authors. All rights reserved

mailto:[email protected]

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2 R. Mishra et al. / Quantifying morphological alteration of RBC

Radj adjusted RICC Intraclass correlationAFM atomic force microscopy.

1. Introduction22

Red blood cell (RBC) also referred sometime as discocyte for its discoid shape, are the most populous23

cell species of blood. RBC morphology and its alteration, under physiological, pathological or experi-24

mental condition are fascinatingly different from any other cell types and thus a challenge on its own.25

In physiological condition it assumes a biconcave disc structure, the discocyte, which in pathological or26

experimental conditions can transform to spherocyte through a series of poikilocyte conversions. Poik-27

ilocytosis is a major deviation from the normal shape of erythrocytes that is associated with an increased28

rate of erythrocyte destruction [7, 9, 29, 35]. Morphological alteration of RBC, unlike other RBC indices,29

may be regarded as a pathological index of several diseases viz. hemoglobinopathies, membranopathies,30

and infectious, inflammatory and congenital diseases, as well as in neonatology, cytoskeletal and mem-31

brane composition studies, in drug interactions studies for research, clinical and screening purpose, RBC32

morphology study is unavoidable [1, 31]. Poikilocytosis is also associated with a certain decrease in33

deformability of the cells (e.g. in sickled cells, echinocytosis) [7, 21, 27], which may lead to a decrease34

in capillary perfusion (microcirculatory disorder) [16, 33]. Recent articles vouch for the need of the35

morphological studies of RBC in routine clinical analysis and awareness about importance of presence of36

poikilocytes in clinical samples [12]. One of the major obstacles in this path is dependence on time and37

labour intensive microscopic studies. Morphological Index (MI), a number fraction weighted average38

of morphological score (MS) (MI = ∑xi.MSi, where xi be the number fraction of ith derivative), is a39

quantitative approach to assess morphological alteration of RBC microscopically [4], which is laborious40

and affected by observer’s personalized bias, and thus the quantitative deviation of the calculated MI41

from its true value is always probable. This has limited the clinical and experimental significance of RBC42

morphological information. Need for automation has taken up the indirect approach to RBC morphol-43

ogy by quantifying size or rheological characters in automated cell counters or laser diffractometers,44

ektacytometer, Rayligh scattering, and other methods [6, 8, 14, 28, 32].45

Light scattering of particles is a standard technique to extract information regarding their shape and46

size. Flow cytometry has become a powerful quantitative alternative of microscopy for large scale, high47

throughput analysis of cell populations. Generally, the size dependent small angle or forward scatter (FSC)48

and the shape and surface granularity dependent orthogonal or side scatter (SSC) data readily obtainable49

from a flow cytometer are largely centered on particles spherical in nature and sphere perturbed derivative50

shapes of a model RBC [19], which may be regarded as an oversimplified version of the actual topology.51

Study of nonspherical cells or particles by flow cytometry has staged difficulties in interpreting the findings52

and to monitor the cellular size/shape etc. The major concern around such sort of effort is the difference53

in orientation of the nonspherical cells/particles with respect to the angle of incident light and the angle of54

signal collection. Most of the cytometric investigations with non-spherical particles, reported so far deal55

with RBC and sperm cells. A comparison indicates that the former presents wide spectrum morphological56

variations and hence is largely unattended from a quantitative point of view. Due to its discoid shape57

and presence of central pallor, scattering from RBC varies largely and is hard to interpret. Under shear58

flow RBC elongates and assumes a variety of orientation, each differing from other in some aspect [2].59

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R. Mishra et al. / Quantifying morphological alteration of RBC 3

Both elongation and orientation property of RBC in shear flow contributes to the greater variability in60

the scattering pattern. Moreover, the biconcave disc structure, discocyte, can transform to spherocyte61

through budding off of membrane either externally or internally from spike containing echinocytes or62

invaginated stomatocytes respectively in pathological and experimental conditions [1, 34].63

While RBC shape has been rigorously modeled mathematically for its atypical shape and scattering64

properties [10, 22], morphology study by scattering shows uncertainty in selecting parameters to represent65

the changes. Though the observations based studies by Piagnerelli et al. [28] and Bratosin et al. [6]66

showed uncertainty in selecting flowcytometric parameters as a function of morphology, these attempts67

had clearly depicted association between the corresponding parameters and morphology. The present68

investigation has been undertaken in an attempt to develop a functional relation between scattering data69

of flowcytometry and the MI of a RBC population.70

2. Materials and methods71

2.1. Sample preparation72

We have generated mixed populations of poikilocytic and normal cells by treating whole blood73

sample from normal healthy volunteers (Male-6, female-4; Age-28.9 ± 2.73 years; body weight-74

68.8 ± 11.68 Kg; resting heart rate- 74.6 ± 4.45 beats/minute; Systolic pressure- 125.8 ± 4.57 mmHg75

and diastolic pressure- 84.2 ± 3.33 mmHg; data represented as mean ± standard deviation) with differ-76

ent poikilocytic agents in different doses randomly (n = 30). Blood was collected from antecubital vein77

after overnight fasting and appropriate rest between 9–10 am in a quiet environment and ambient room78

temperature (25 ± 0.5◦C) following the new guidelines for hemorheological laboratory techniques [3] in79

a heparinised vial (15 U/ml). Eosin-5-maelimide [13] (E5M; 1–3 �g/�l packed cell) and Naja kaouthia80

snake venom [36] (0.5–2 �g/ml whole blood) were used to induce echinocytosis and stomatocytosis81

respectively. The samples were analyzed by flow cytometry and microscopy simultaneously. To avoid82

observers’ bias the experiments were double blinded with respect to both microscopy and flowcytometry83

analysis. Additionally a different set, including both control and patient and poikilocyte agent treated84

samples were prepared for model validation (n = 10).85

2.2. Flow cytometry86

Flow cytometry data were generated using a BD FACS Aria III with a 488 nm blue laser and a total of87

30,000 events were recorded for each sample. The FSC data were collected on a linear scale, whereas for88

SSC data log scale was used. The height, width and area parameter of the voltage pulse of both FSC and89

SSC were recorded. On the BD FACS Aria III a 70 �m nozzle was used and the custom sheath pressure90

was set at 15 psi with a minimum sample flow rate of 1. Additionally, we have also used BD FACS Verse91

in order to check the instrumental bias of the generated data using both the standard mode (low flow rate)92

and high sensitivity mode of the instrument. Intraclass correlation coefficients (ICC) were calculated for93

these two data sets with the respective FACS Aria III data.94

2.3. Fluorescence labelling of RBC samples95

Washed RBC samples including treated, untreated and patients’ blood, were labelled with E5M dye,96

which reacts covalently with lysine-430 on the extracellular domain of band 3 protein of RBC membrane97

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according to the method of king et al. [18]. Briefly, 25 �l of packed RBC, after washing with 10 mM98

phosphate buffer saline (PBS) (pH = 7.4), from healthy control were incubated with graded dose of E5M99

(5 �l, 10 �l and 15 �l of 5 mg/ml solution of E5M) for 1 hour in dark at room temperature. After incubation100

the sample was washed with 10 mM PBS containing 0.5% BSA thrice to remove the unbound dye and101

then diluted to appropriate number in 10 mM PBS and used for microscopic study.102

2.4. Microscopy imaging103

For imaging BD Pathway 855 instrument was used. The RBCs (both E5M labeled and unlabeled) were104

seeded into a 96 well bioimaging plate and incubated on the stage for 15 min to allow the cells to settle105

and Nipkow spinning disc based confocal images were captured by a CCD Camera in transmission mode106

as well as using excitation and emission filter for FITC (for fluorescence imaging of E5M labeled RBC).107

A 3 × 3 confocal stacked montage image was captured for each well and as mentioned MI was evaluated108

by manual counting all cells in the field. Based on the classification and scoring system of Besis [4]109

we have chosen the MS range to be [−1, +1], with MS = 0 for discocyte, MS = +1 for spherocyte via110

echinocytic pathway, MS = −1 for spherocyte via stomatocytic pathway, as both pathways are mutually111

exclusive. To reduce the complexity in gathered information from the transitional RBC morphological112

species, intermediate population in both pathways were assigned with MS = ±0.5.113

2.5. Atomic force microscopy114

Immediately after treatment a thin layer of heparinized blood was drawn on a glass cover slide to prepare115

a film. Then the films were air dried and were ready for AFM analysis. AFM study was performed with116

VEECO Multimode system having Nanoscope IIIa controller. All the images were taken using taping117

mode in air (at room temperature, 75% humidity) with RTESP tip silicon probes at resonant frequency118

302.87 kHz. 200 �m J scanner was used. The cover slip carrying the blood sample was mounted on XY119

stage of Scanner. The images obtained were analyzed by Nanoscope Software version 5.12 in offline120

mode.121

2.6. Statistical analysis122

Flow cytometry data, in term of (i) area, (ii) height and (iii) width distribution of both FSC and SSC123

were extracted from the raw experimental data of all events with the help of FlowDiva software (version124

6.1.3). Software output also includes basic statistics (mean, median, standard deviation, coefficient of125

variance, etc.) of the respective distribution. The analysis of the obtained statistics was done with statistical126

program packages SPSS (SPSS Version 16 for Windows; SPSS Inc., Chicago, USA). In order to pick the127

best correlated parameters of all the six distributions with the corresponding MI, the univariate curve fit128

estimation was carried out. Accordingly, the best correlated parameters of both FSC and SSC were chosen129

to formulate a suitable regression model with MI as response using the standard Design-Expert (Version130

8.0) package. Internal validation of the model was carried out using residual analysis and appropriate131

statistics. The model was further validated using a new experimental data set, exclusive to the same used132

in model formulation.133

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3. Results134

3.1. Microscopic imaging of RBC morphology135

E5M labeled and unlabeled samples of both control and poikilocytic agent treated sample were pho-136

tomicrographed using BD Pathway 855. The unlabeled RBC sample of control sample contains discocyte137

as the major population (>95%), whereas echinocytogenic and stomatocytogenic agent treated samples138

shows prevalence of respective poikilocytes along with spherocytes in varying percentage (Fig. 1 subset139

Ia, IIa and IIIa), the figure in the inset are the AFM images of the major population of each respective140

group. E5M treated sample (at all doses) shows prevalence of echinocytes (Fig. 2) thus limited its use141

to identify the different morphological alteration and hence not used for the calculation of MI of control142

and treated samples. The morphological scoring was done with the photomicrograph of samples taken in143

transmission mode in PBS.144

3.2. Morphological index145

Based on the scoring system adopted and customized for the present work, the MI was calculated146

based on the standard formula. The MI of samples ranged from −0.64 to +0.57, where the sign implies147

the presence of stomatocyte and echinocyte respectively and the numerical value indicates the extent148

of damage. The range covers a wide span and comprises of system which either fall in echinocyte or149

stomatocyte group. In order to check the precision of obtained MI related to number of cells counted, we150

have calculated the MI for 50, 100, 200 and >200 cells for each sample (n = 40). It was found that the MI for151

each set does not varies significantly (One way ANOVA, F = 0.057, p = 0.996). The %CV value of 50.93,152

49.83, 50.25 and 49.15 were obtained for calculated MI for 50, 100, 200 and >200 cells respectively.153

3.3. Flow cytometry analysis154

All the three distribution pattern viz. area, height and width of each sample both control and treated155

were acquired and analysed with FlowDiva software (version 6.1.3). The measures of central tendencies156

(mean & median) and dispersion statistics (standard deviation, robust coefficient of variance and Pearson157

coefficient of dissymmetry) of each sample was then calculated. The scatter plots and histrogram of flow158

cytometric data of each group was depicted in Fig. 1 (subset Ib-f, IIb-f & III b-f).159

3.4. Scatter plot analysis160

The scatter plot of FSC versus SSC data of area distribution shows a “sculptured woodpecker” like161

structure with increasing poikilocytosis, with a trend from discocyte to echinocyte to stomatocyte popu-162

lation (Fig. 1: subset Ic, IIc & IIIc). This observation was more or less persistent for both instruments and163

all set ups. This observation could be a qualitative add-on to identify the major route of spherocytosis,164

i.e. whether it is via echinocytic or stomatocytic pathway.165

3.5. Histogram analysis166

Histogram of FSC and SSC distribution of area, height and width pulse were obtained for each group167

of sample (Fig. 1: subset Id-f, IId-f & IIId-f). Like other reports in this field [6, 28], we did not notice168

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Fig. 1. Determination of red blood cell morphology by analyzing flow cytometric scattering. Photomicrograph and flow cyto-metric scatter analysis of normal and poikilocytic agent treated population of RBCs, the name given are the major cell populationin the sample. Ia) Discocytic population IIa) Echinocytic population IIIa) Stomatocytic population. Microscopy was performedby BD Pathway (in PBS, Plan Apochromat objective, 60× magnification, NA = 0.95, transmission mode) and photomicrographwere used for morphological scoring of RBC and calculation of the morphological index of different groups. Topographicalfeatures of different poikilocytes were showed by atomic force microscopy in tapping mode (inset of a subset a). Sample gatingwas done manually using the area versus height data of normal control samples (subset b) for dublet discrimination and same gatewas used to analyse the normal and treated RBC. Flowcytometric analysis of different poikilocytic populations were representedin dot plots (subset c). The FSC area vs SSC area dot plot showed tapering in echinocytic poikilocytes population which becamea sculptured woodpecker like structure in stomatocytic poikilocytes. FSC and SSC histograms of area (subset d-i and ii), height(subset e-i and ii) and width (subset f-i and ii) of FSC and SSC respectively were depicted where the distribution width showedto be decreased with the loss of discocytic populations.

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(Ia) (IIa) (IIIa)

(Ib) (IIb) (IIIb)

Fig. 2. Photomicrograph of E5M stained control RBC showing echinocytosis in a dose dependent manner. Panel (a) representsthe fluorescence image of E5M labeled RBC using excitation and emission filter for FITC and panel (b) represents the pho-tomicrograph in transmission mode of the same field, microscopy was performed by BD Pathway (in PBS, Plan Apochromatobjective, 60× magnification, NA = 0.95). Subset I: 1 �g E5M/ �l packed RBC, subset II: 2 �g E5M/ �l packed RBC and subsetIII: 3 �g E5M/ �l packed RBC.

a prominent bimodal distribution even for the discocyte population, instead a shouldering was noticed169

in FSC area and height histogram on FASCAria III limiting its usability for the prediction of shape170

alteration. The SSC area and height histogram shows somewhat more prominent bimodality in case of171

discocyte population. On the contrary bimodality was noticed in discocyte population when samples are172

run on FACS Verse for validation on both modes. The width distribution in all cases and both instruments173

shows a unimodal distribution. All distribution histogram gradually tappers with poikilocytosis with a174

maximum tapering in stomatocytic population.175

3.6. Regression model using response surface methodology176

At univariate level the statistics of the width pulse distributions shows significant and better correlationwith the MI calculated from microscopy. The distribution of the selected parameters of width pulse wasshown in Fig. 3 as box and whisker plot, which depicts the variation of the representative statistics ofthe scatter data in the control and experimental groups. In the multistep regression we have chosen thebest and optimum subset of regressors obtained from curve fit estimation (the best suited model beingthe quadratic model, p < 0.001), which are Median of FSC width distribution (X1) (Rquadratic = 0.640),Median of SSC width distribution (X2) (Rquadratic = 0.701), Robust coefficient of variance (rCV) ofFSC width distribution (X3) (Rquadratic = 0.917) and Robust coefficient of variance (rCV) of SSC widthdistribution (X4) (Rquadratic = 0.742). The functional form becomes

MI = f (X) , where X =[X1 X2 X3 X4

]T

(1)

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60000.00

FS

CM

edia

n

FS

CrC

V

SS

CrC

VS

SC

Med

ian

Control

(a) (b)

(c) (d)

Echinocyte Stomatocyte

Control Echinocyte Stomatocyte Control Echinocyte Stomatocyte

Control Echinocyte Stomatocyte

12.00

10.0015.00

10.00

5.00

8.00

6.00

4.00

2.00

65000.00

70000.00

75000.00

80000.00

85000.00

90000.00

70000.00

80000.00

90000.00

100000.00

110000.00

Fig. 3. Box and whisker plot showing the distribution pattern of the predictors in each group used to formulate the regressionmodel with MI as response: (a) FSC Median, (b) SSC Median, (c) FSC rCV and (d) SSC rCV.

As {Xi}i=1, 4 cannot be precisely adjusted by changing the dose of the poikilocytic agent, the set of177

data used in the study may be regarded as random historical data, distributed over a wide spectrum of178

MI ⇒ [−0.64, + 0.57].179

Initially we have tried to fit a linear multivariable regression model of the form

MI = β0 +4∑

i=1

βiXi (2)

where {βi}i=0, 4 are constants parameters. However, the statistical analysis indicates a poor fit as reflectedby the correlation coefficient (both R2 and R2

adj) and % CV. For linear regression model we have foundR2 = 0.87, R2

adj = 0.85 and % CV = 130.24. The parity diagram for the linear model shown in Fig. 4aalso reflects the lack of fit. Because of this insufficiency we have next explored the multivariable quadraticmodel

MI = β0 + Xb + XBXT = β0 +4∑

i=1

βiXi +4∑

i=1

4∑i=1

βijXiXj (3)

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where {βi}i=0, 4 and{βij

}i=0, 4;j=1, 4 are constant model parameters and X =

[X1 X2 X3 X4

]T

, b =180

[β1 β2 β3 β4

]T

and B =

⎡⎢⎢⎢⎢⎢⎣

β11β122

β132

β142

β22β232

β242

β33β342

sym. β44

⎤⎥⎥⎥⎥⎥⎦

T

. For the quadratic model we have found R2 = 0.96,181

R2adj = 0.92 and %CV = 92.12 indicating general usefulness. The model has been also validated by F182

test. F value of 26.26 (p < 0.0001) implies that the model is significant and there is only a 0.01% chance183

that a model F value this large could occur due to noise. The parity diagram of the quadratic regression184

model is shown in Fig. 4b. We have also tested the cubic regression model to fit the experimental data,185

though the cubic model does not significantly improve the test parameters (R2, R2adj and %CV) over186

the quadratic one, at the same time the regression equation became too complicated to use. So the final187

working equation of MI as a function of X =[X1 X2 X3 X4

]T

becomes188

MI = 43.70338 + 5.61906 × 10−4X1 − 2.25751 × 10−3X2 + 6.49537X3 − 0.615890X4189

+2.10773 × 10−9X1X2 − 2.64946 × 10−5X1X3 + 1.23169 × 10−5X1X4190

−8.54377 × 10−5X2X3 − 3.16989 × 10−6X2X4 + 0.08X3X4 − 3.80161 × 10−9X21191

+1.71499 × 10−8X22 + 0.12437X2

3 − 0.032371X24 (4)192

Six different contour plots representing the variations of MI as functions of set of two predictors(keeping other two constant) are shown in Fig. 4d–i. Out of the six different contours, four representsaddle, while the rest of the two are centers. Complete characterization of the response surface cannot bedone only with the contour plots; a more formal canonical analysis may be useful. The stationary point(XS) of the response surface can be located as

XS = −1

2B−1b (5)

The stationary point for the present quadratic model was found to be XS =[− 5.7305 × 104

193

5.8632 × 104 3 27]T

. The result indicates that the stationary point is far outside the region of explo-194

ration for fitting the regression model. The nature of the response surface can be further analyzed from the195

signs and magnitudes of the eigenvalues {λi}i=1, 4 of matrix B, which are λ =[− 0.042 0 0 0.134

]T

.196

This indicates that the present response surface is a rising ridge type [26].197

3.7. Validation198

The proposed model was also validated using a new set of experimental data distributed over MI ⇒199

[−0.63, 0.52], exclusive to model formulation. The corresponding parity diagram is shown in Fig. 4c.200

The correlation coefficient of the data set with respect to the 45◦ line was found to be 0.97 (p < 0.001).201

High intraclass correlation (ranging from 0.879–0.990, p < 0.001) among the predictors used on different202

instrument setup for same sample shows instrument independency of current method.203

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(a) (b) (c)

(d)

(g) (h) (i)

(e) (f)

Fig. 4. Residual plot of predicted versus actual MI for (a) linear model and (b) quadratic model. Plot (c) shows the parity diagramfor actual versus predicted MI (equation 4) of patient samples. Six different contour plots representing the variations of MI asfunctions of (d) X1 and X2 (at fixed X3 and X4 (e) X1 and X3 (at fixed X2 and X4) (f) X1 and X4 (at fixed X2 and X3) (g) X2

and X3 (at fixed X1 and X4) (h) X2 and X4 (at fixed X1 and X3) and (i) X3 and X4 (at fixed X1 and X4).

4. Discussion204

RBC morphological alteration in response to physiological, pathological and experimental stimuli is of205

great interest to clinicians, especially hematologists and basic scientists as they generally precedes other206

indicators of hematological alterations, such as hemolysis, etc. The primary source of investigation of207

morphological alteration till date is microscopic analysis which besides being qualitative in nature also has208

other limitations as also stated by Teodori et al. [32] (and references therein). A more quantitative approach209

toward study of morphological alteration was to score individual normal and altered RBC with empirical210

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scoring and thereby to calculate the morphological index of the RBC population. This system, though211

give quantitative information, is a representative of small population consisting of 100–200 RBC [4, 11,212

17, 27] and can be affected by field selection and observers bias to precisely score the individual stage of213

morphological responses. The conventional scoring of morphologically altered RBC was based on light214

microscopy according nomenclature of Bessis [4], later modified by Ferrell et al. [11] and personalized215

[17] for particular works. Discocyte has the score of zero. Species with spiculation has positive values216

ascertained to them, whereas species with invagination has negative values according to deviation from217

normal. The highest scores, positive as well as negative, were assigned to the spherocytic RBC population218

obtained through either via echinocytosis or stomatocytosis respectively. Reported literatures [5, 23] also219

indicates that stomatocytosis and echinocytosis are mutually exclusive because a particular poikilocytic220

agent could induce either spiculation or invagination. This universal “main sequence” of shapes and221

their order of appearance is not influenced by specific echinocytogenic or stomatocytogenic agent though222

shapes outside this sequence can be found as some special cases [23]. Based on this knowledge we chose223

poikilocytic (echinocytogenic or stomatocytogenic) agents at random and generated different population224

of RBC morphological species in whole blood aliquots. Thereafter MI values of control and poikilocytic225

agent treated samples were calculated from Z stacked images from BD Pathway 855 (transmission mode).226

The use of fluorescence dye to label RBC was limited due to two reasons i) the fluorescence dye itself or227

fluorescently labelled agglutinins may themselves alter RBC shape as also suggested by Piagnerelli et al.228

[28] and ii) the buffer which was used to wash the unbound dye to reduce the background noise for proper229

fluorescence microscopy generally contains albumin a known stomatocytic agent [24, 34]. We have used230

E5M for fluorescence labelling of RBC in this experiment, which shows echinocytosis at all doses used231

and is in accordance with other studies [13, 20]. PBS-BSA washing does not inhibit or help to recover232

the echinocyte induced due to E5M labeling as reported by Lee et al. [20]. Another problem associated233

with this shape recovery procedure is that the recovered shape may vary from the original shaped RBC234

in membrane property [30] and thus could affect the scattering behavior and also the extent of recovery235

is undetermined. As the glass effect also leads to echinocytosis [24] we have used unlabelled RBCs in236

PBS medium for imaging as it does not induces any shape transition [25].237

With increasing awareness of the clinical and experimental usability of RBC morphological alterations238

in recent time [1, 12], several attempts were taken for the automation and rapid quantification of RBC239

morphological alterations using different instrument and techniques, of which automated cytometric240

analysis has its greater share. The recent trend has its major focus in the use of scattering techniques241

and includes both simulation and wet lab experiments. Use of scattering property to identify the RBC242

morphological alteration could be traced back to Hoffman [14], who has used the variability of the243

Rayleigh scattering of light from a stirred suspension to describe the shape alteration in RBC. He has244

shown that as RBC approaches sphericity, the noise (i.e. the variability) diminishes and the scattering245

becomes somewhat more uniform, but information of individual RBC was lost. Piagnerelli et al. [28]246

and Bratison et al. [6] used a more refined approach regarding scattering property of RBC to describe247

its shape alteration. They have used the FSC height data of flow cytometry, which provides information248

at unit level. Both have shown with shape alteration the bimodality of FSC height data was lost and249

with increasing sphericity uniform scattering pattern was observed with low dispersed data compared to250

discocyte. Piagnerelli et al. [28] also tries to approach the problem in a more quantitative way by defining251

M2:M1 ratio (i.e. is the median value of the two modes) and Pearson dissymmetry coefficient to calculate252

the degree of sphericity. In both the studies SSC scattering data, known to contain information about253

the shape and granularity was completely overlooked, as in scatter based automated cell counters. None254

of the distributions shows a clear bimodality on BD FACSAria III for any sample as reported by others255

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[6, 28] thus limiting its use. In order to generate a more robust method to use the scattering information256

from normal and morphologically altered RBCs, we first identified the better representative scattering257

distribution pattern. Out of the three parameters, width distribution was chosen in order to formulate258

suitable regression model, with MI as response. The reason behind this selection is threefold:259

i. width parameters are independent of many factors that affects light scattering [15]260

ii. unimodality of distribution (which requires only two statistical parameters; one representing central261

tendency whereas another represents dispersion statistics) and262

iii. the width distribution statistics showed highest correlation with MI263

Afterward, the best correlated model and parameters were identified using the curve fit estimate at264

univariate level. Based on these information a quadratic regression model was established using the265

representative of statistics of both FSC and SSC width distribution. The model was validated for other266

instrument and fresh sample indicates the usability of the developed model for the rapid quantification267

of MI.268

5. Conclusion269

It may be concluded that the information about RBC morphology could be reconstructed from FSC270

and SSC distribution statistics. The proposed quadratic model can efficiently predict the MI value of271

a blood sample from the rapidly generable flow cytometric data with reasonable accuracy and avoids272

the microscopic analysis, which is laborious and prone to personalised bias. In a more generalized way273

it could be said that the current method suggests a new approach toward the use of scatter data from274

unadulterated sample to get the qualitative and quantitative information about RBC morphology.275

Acknowledgments276

We are grateful to Centre for Research in Nanoscience and Nanotechnology (CRNN), University of277

Calcutta. This work was funded by Department of Science & Technology, Government of West Bengal278

[Ref No: 371/ST/P/S&T/9G-7/2009].279

Author contributions280

R.M., R.M., and S.B. conceived the project, R.M., S.B., S.M., M.C., and D.M. performed experiments,281

R.M., D.S. and S.M. analysed the data, R.M., R.M., D.S., S.B., and M.K. wrote the manuscript.282

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quantifying morphological alteration of rbc 1 population from light scattering data

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