Anisotropic light scattering of individual
sickle red blood cells
John M. Higgins
Ramachandra R. Dasari
Anisotropic light scattering
of individual sickle red
Youngchan Kim,aJohn M. Higgins,bRamachandra R.
Dasari,cSubra Suresh,dand YongKeun Parka
aKorea Advanced Institute of Science and Technology, Department
of Physics, Daejeon 305-701, Republic of Korea
bCenter for Systems Biology and Department of Pathology,
Massachusetts General Hospital, Boston, Massachusetts 02114, and
Department of Systems Biology, Harvard Medical School, Boston,
cMassachusetts Institute of Technology, George R. Harrison
Spectroscopy Laboratory, Cambridge, Massachusetts 02139
dMassachusetts Institute of Technology, Department of Materials
Science and Engineering, Cambridge, Massachusetts 02139
Abstract. We present the anisotropic light scattering of indi-
vidual red blood cells (RBCs) from a patient with sickle cell
disease (SCD). To measure light scattering spectra along two
independent axes of elongated-shaped sickle RBCs with
arbitrary orientation, we introduce the anisotropic Fourier
transform light scattering (aFTLS) technique and measured
both the static and dynamic anisotropic light scattering.
We observed strong anisotropy in light scattering patterns
of elongated-shaped sickle RBCs along its major axes
using static aFTLS. Dynamic aFTLS analysis reveals the sig-
nificantly altered biophysical properties in individual sickle
RBCs. These results provide evidence that effective viscosity
and elasticity of sickle RBCs are significantly different from
those of the healthy RBCs. © 2012 Society of Photo-Optical Instrumen-
tation Engineers (SPIE). [DOI: 10.1117/1.JBO.17.4.040501]
Keywords: red blood cell; sickle cell disease; light scattering; quantita-
tive phase microscopy.
Paper 11736L received Dec. 12, 2011; revised manuscript received
Jan. 25, 2012; accepted for publication Feb. 8, 2012; published online
Apr. 5, 2012.
Sickle cell disease (SCD) is an inherited blood disorder
where a point mutation in the β-globin gene results into produc-
tion of sickle hemoglobin (HbS) instead of hemoglobin (HbA).1
Under deoxygenated condition, HbS self-assembles inside the
red blood cell (RBC) and dramatically damages the RBC mem-
brane structure, often resulting into a sickle-shaped RBC. This
sickle RBC has a considerably reduced deformability, causing
abnormal rheological properties of sickle blood and eventually
vaso-occlusion and organ damage.
Characterizing sickle cell properties, especially at the single-
cell level, plays crucially important roles in understanding the
pathophysiology of SCD.2However, the characterization of
individual sickle RBCs is complex and not fully addressed. It
is presumably because of the limitations of the measurement
techniques.2Here, we report both static and dynamic light
scattering results from individual sickle RBCs that are enabled
by introducing anisotropic Fourier transform light scattering
Light scattering techniques have been extensively used for
characterizing biological molecules, cells, and tissues.3Static
light scattering can also measure the volume and cytoplasmic
hemoglobin concentration of the RBCs.4Temporal fluctuation
of scattering signals with respect to a specific scattering angle
provides information about motion—a diffusion coefficient of
the scattering object.
Angular light scattering has traditionally been measured with
goniometer-based instruments and several measurement techni-
ques have been used to study light scattering of objects.5,6
Recently, a significant breakthrough in light scattering detection
sensitivity has been achieved by the development of Fourier
transform light scattering (FTLS) technique.7In FTLS, light
scattering patterns from a sample can be obtained from the
electric field (E-field) of the sample via quantitative phase ima-
ging technique. The E-field Eð~ r;tÞ is then numerically propa-
gated to far-field by 2-D Fourier transform as Ið~ q;tÞ ¼
jR REð~ r;tÞexp½−j~ q · ~ r?j2∕2π, where ~ q is the spatial frequency
of studies using FTLS is indicative of its effectiveness in the
study of various phenomena in biophysics and cell biology.8–11
To measure light scattering from sickle RBCs, we prepared
blood samples extractedfrom apatient with SCD as well as from
a healthy individual under a research protocol approved by the
institutional review board (IRB). The SCD patient was under
treatment with hydroxyurea. The blood was collected in ethy-
lenediaminetetraacetic acid (EDTA) anticoagulant and stored
at 4°C. For measurement, the blood sample was first diluted
with a phosphate-buffered saline. To quantitatively measure
the E-field maps of sickle RBCs, we employed diffraction
phase microscopy.12,13For each sickle RBC, we measured
the E-field Eð~ r;tÞ ¼ Að~ r;tÞexp½jΔϕð~ r;tÞ?, where Að~ r;tÞ and
Δϕð~ r;tÞ are the amplitude and phase delay, respectively. All
the measurements were performed at ambient oxygen concen-
tration (21%) and room temperature (23°C). The time-averaged
cell height maps can be retrieved from the measured phase maps
as hð~ r Þ ¼ hΔϕð~ r;tÞi · λ∕ð2π · ΔnÞ, where λ is the wavelength
of the laser and Δn is the difference in refractive index between
RBC cytoplasm and surrounding medium. The sickle RBCs
are classified in accordance with the morphology: echinocyte
(type II), discocyte (type III), and crescent-shaped irreversibly
sickled cell (type IV; ISC) (Fig. 1). This classification corre-
sponds with sickle RBC fraction II–IV by density separation.14
The measured topographies of the sickle cells are consistent
with a recent study using quantitative phase imaging.15
To retrieve anisotropic light scattering, we introduce aFTLS
analysis (Fig. 2). We first processed the E-field of individual
sickle RBCs such that the horizontal axis of the E-fields is
parallel to the long axis of the cell. Then the angular light-
intensity scattering pattern of the sickle RBC is retrieved by
applying 2D Fourier transformations to the E-field. The spatial
frequency vector and the scattering angle can be related as
j~ qj ¼ 2πn sin θ∕λ, where n is the refractive index of medium.
The light scattering patterns along the long and short axes
are retrieved by selecting the scattering patterns of polar
angle width of 30 deg along the horizontal and vertical axes,
respectively. Then, the light scattering signals along the long
and short axes are retrieved as a function of scattering angle after
vector. The growing scientific interest and increased number
Address all correspondence to: YongKeun Park, Korea Advanced Institute of
Science and Technology, Department of Physics, Daejeon 305-701, Republic
of Korea; E-mail: firstname.lastname@example.org.
0091-3286/2012/$25.00 © 2012 SPIE
Journal of Biomedical Optics040501-1April 2012 • Vol. 17(4)
azimuthal average. The ISC showed significantly different scat-
tering signals along the long and short axes [Fig. 2(d)].
We then retrieved the scattering of sickle RBCs in different
morphological types (Fig. 3). From the blood extracted from a
patient with SCD, we measured 24 cells, 26 cells, and 12 cells of
types II, III, and IV, respectively. For comparison purpose, we
also measured 25 RBCs from a healthy individual. The sickle
RBCs in type IV showed significantly different angular scatter-
ing signals the along long and short axes (p-value < 10−5)
whereas sickle RBCs in types II–III did not show statistically
different light scattering signals long those two axes. These ani-
sotropic scattering signals in type IV sickle RBCs can explained
by the crescent- and elongated-shapes.
To our knowledge, there has been no prior study of light
scattering of individual sickle RBCs in different morphologies.
Attempts to measure the angular light scattering from individual
sickle RBCs with a goniometer-based instruments or ektacyt-
ometers would be extremely challenging because of the follow-
1. it is difficult to classify individual sickle RBCs in
different morphological groups without imaging the
corresponding cell at the microscopic level
2. the scattered power from an individual sickle RBC is
3. even if successful in both classification and detection,
selection of scattering signal along the long and short
axes is difficult without knowing the orientation of the
sickle RBC simultaneously.
To measure the dynamic light scattering of sickle RBCs, we
measured the E-fields of the sickle RBCs for about 2 s at 120
frames per s. For each E-field, we perform aFTLS analysis,
which provide the dynamic light scattering information. We
then calculated normalized temporal autocorrelation of the scat-
tering light intensity fluctuations for each scattering angle,
hIðθ;τÞIðθ;0Þi∕hIðθ;0Þi2. Since the spectrum of dynamic light
scattering can be described approximately as Lorentzian, its
autocorrelation can be expressed as a damped cosine function
with a peak frequency ω0and a line width Γ as GðτÞ ¼ Aþ
B cosðω0τ þ φÞexp½−Γτ − β2τ2?.16The phase term φ was added
to consider the deviation of the spectrum from an exact Lorenzian
function and the β term accounts for instrument deviation.
For sickle RBCs of types II-IV, the intensity autocorrelation
was calculated at each scattering angle, from which ω0and Γ
were retrieved by fitting to the damped cosine function.
Then, ω0and Γ along the long and short axes are averaged
in the range of the specific scattering angle from 0 to 7 deg.
The values of ω0for all types of sickle RBCs are approximately
(p-value < 10−4) [Fig. 4(a)]. Between different types in sickle
RBCs, ω0is not statistically different. The Γ values of sickle
RBCs of types II and III are not significantly different from
those of the healthy RBCs. However, Γ values of type IV sickle
RBCs are significantly smaller than those of the healthy RBCs
(p-value < 0.05; long axis) [Fig. 4(b)]. The values for ω0and Γ
did not show statistical difference between the long and short
axes; this result implies that the biomechanical properties of
the sickle cells do not exhibit anisotropic behavior.
The dynamic light scattering from membrane fluctuations
can provide biomechanical properties of the membrane. For a
simple flat lipid bilayer, the values for ω0and Γ can be directly
related to membrane tension and medium viscosity, respec-
tively.16However, the human RBC membrane has a complex
biconcave shape, and there does not exist a theoretical model
relating dynamic light scattering to the mechanical properties
of the RBC membrane. Nevertheless, the effective elasticity
and effective viscosity of the RBC membrane can be inferred
from a peak frequency ω0and a line width Γ, respectively.10
The increase of ω0in all types of sickle RBCs indicates the
loss of deformability [Fig. 4(a)], which is consistent with pre-
vious reports based on measurements using micropipette aspira-
tion and an ektacytometer.17,18This loss of deformability in
the sickle RBCs can be explained by alterations in RBC meta-
bolism and membrane structure including loss of membrane
(type III), and (c) crescent-shaped ISC (type IV).
Fig. 2 (a) Phase image of a typical sickle RBC. (b) The long axis is
rotated to be aligned with the horizontal axis and the center of mass
of the sickle RBCis movedto the center. (c) The retrieved light scattering
pattern with the denoted angle ranges for the long and short axes.
(d) Light intensity-scattering patterns with respect to the long and
short axes of the RBC.
Fig. 3 The static light-intensity scattering patterns associated with indi-
vidual sickle RBCs of (a) type II, (b) type III, and (c) type IV. Thin lines are
from individual sickle RBCs; thick line represents the averaged scatter-
ing pattern. The scattering patterns along the long axis are offset up for
clarity. (inset) the averaged scattering patterns along short and long axes
Journal of Biomedical Optics040501-2April 2012 • Vol. 17(4)
phospholipid symmetry,19uncoupling of the lipid bilayer from Download full-text
the sub-membrane structure,20and abnormal membrane phos-
phorylation.21Abnormal membrane phosphorylation may ser-
iously affect the enhanced membrane fluctuations in the
presence of ATP.9,22The self-assembly of HbS may also
decrease the deformability in the sickle RBCs; polymerization
of HbS could transform the viscous Hb solution in the sickle
RBC cytoplasm into viscoelastic material.
Whereas elasticity characterizes resistance to deformation,
viscosity characterizes resistance to a rate of deformation.
For the RBC, the effectiveviscosity is associated with the recov-
ery time after large deformation tc,and it is primarily determined
by the shear modulus of the spectrin network μ and the mem-
brane surface viscosity ηm as tc¼ ηm∕μ.23The significant
decrease in effective viscosity of ISCs, implying a decrease
in recovery time, suggests a decrease in ηmor an increase in
μ, or both. The increase in ηmmay be explained by alterations
in the composition or structures of the RBC lipid bilayers or
decreased binding of glyceraldehyde phosphate dehydrogenase
to the membrane.24These altered viscoelastic properties of the
sickle cell can explain the significantly decreased dynamic fluc-
tuations in the sickle cell membrane.15
In conclusion, we present anisotropic light scattering of
sickle RBCs. The aFTLS technique, a variation of FTLS, pre-
cisely and systematically measures anisotropic light scattering
of asymmetric small objects. Using aFTLS, we study the
light scattering from sickle RBCs and demonstrate anisotropic
static light scattering patterns with respect to the elongated
shape of sickle RBCs. The dynamic light scattering analysis
reveals alterations in mechanical properties depending on the
morphological type of sickle RBCs. In the future, the aFTLS
technique could be used in combination with other existing opti-
cal imaging techniques to better study other RBC related
diseases, for example, to understand the protective mechanism
of sickle RBCs against infection of malaria parasite.25
This work was supported by KAIST (N10110038, N10110048,
G04100075), the Korean Ministry of Education, Science
and Technology (MEST) Grant No. 2009-0087691 (BRL),
National Research Foundation (NRF-2011-355-c00039), and
R01HL094270, and DK083242). YKP acknowledges support
from POSCO TJ Park Fellowship.
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