We review recent advances in multiscale modeling of the biomechanical characteristics of red blood cells (RBCs) in hematological diseases, and their relevance to the structure and dynamics of defective RBCs. We highlight examples of successful simulations of blood disorders including malaria and other hereditary disorders, such as sickle-cell anemia, spherocytosis, and elliptocytosis.

References

References
1.
Popel
,
A. S.
, and
Johnson
,
P. C.
,
2005
, “
Microcirculation and Hemorheology
,”
Ann. Rev. Fluid Mech.
,
37
(
1
), pp.
43
69
.
2.
McLaren
,
C. E.
,
Brittenham
,
G. M.
, and
Hasselblad
,
V.
,
1987
, “
Statistical and Graphical Evaluation of Erythrocyte Volume Distributions
,”
Am. J. Physiol. Heart Circ. Physiol.
,
252
(
5
), pp.
H857
H866
.http://ajpheart.physiology.org/content/252/4/H857
3.
Chasis
,
J. A.
, and
Shohet
,
S. B.
,
1987
, “
Red Cell Biochemical Anatomy and Membrane Properties
,”
Ann. Rev. Physiol.
,
49
(
1
), pp.
237
248
.
4.
McCaughan
,
L.
, and
Krimm
,
S.
,
1980
, “
X-Ray and Neutron Scattering Density Profiles of the Intact Human Red Blood Cell Membrane
,”
Science
,
207
(
4438
), pp.
1481
1483
.
5.
Hochmuth
,
R.
,
Evans
,
C.
,
Wiles
,
H.
, and
McCown
,
J.
,
1983
, “
Mechanical Measurement of Red Cell Membrane Thickness
,”
Science
,
220
(
4592
), pp.
101
102
.
6.
Nguyen
,
Q. D.
, and
Boger
,
D. V.
,
1987
, “
Characterization of Yield Stress Fluids With Concentric Cylinder Viscometers
,”
Rheol. Acta
,
26
(
6
), pp.
508
515
.
7.
Drochon
,
A. A.
,
Barthes-Biesel
,
D. D.
,
Lacombe
,
C. C.
, and
Lelievre
,
J. C.
,
1990
, “
Determination of the Red Blood Cell Apparent Membrane Elastic Modulus From Viscometric Measurements
,”
ASME J. Biomech. Eng.
,
112
(
3
), pp.
241
249
.
8.
Baskurt
,
O. K.
,
Hardeman
,
M. R.
,
Uyuklu
,
M.
,
Ulker
,
P.
,
Cengiz
,
M.
,
Nemeth
,
N.
,
Shin
,
S.
,
Alexy
,
T.
, and
Meiselman
,
H. J.
,
2009
, “
Comparison of Three Commercially Available Ektacytometers With Different Shearing Geometries
,”
Biorheology
,
46
(
3
), pp.
251
264
.
9.
Jandl
,
J. H.
,
Simmons
,
R. L.
, and
Castle
,
W. B.
,
1961
, “
Red Cell Filtration and the Pathogenesis of Certain Hemolytic Anemias
,”
Blood
,
18
(
2
), pp.
133
148
.http://www.bloodjournal.org/content/18/2/133
10.
Artmann
,
G. M.
,
1995
, “
Microscopic Photometric Quantification of Stiffness and Relaxation Time of Red Blood Cells in a Flow Chamber
,”
Biorheology
,
32
(
5
), pp.
553
570
.
11.
Binnig
,
G.
,
Quate
,
C.
, and
Gerber
,
C.
,
1986
, “
Atomic Force Microscope
,”
Phys. Rev. Lett.
,
56
(
9
), pp.
930
933
.
12.
Popescu
,
G.
,
Ikeda
,
T.
,
Dasari
,
R. R.
, and
Feld
,
M. S.
,
2006
, “
Diffraction Phase Microscopy for Quantifying Cell Structure and Dynamics
,”
Opt. Lett.
,
31
(
6
), pp.
775
777
.
13.
Laurent
,
V. M.
,
Hénon
,
S.
,
Planus
,
E.
,
Fodil
,
R.
,
Balland
,
M.
,
Isabey
,
D.
, and
Gallet
,
F.
,
2002
, “
Assessment of Mechanical Properties of Adherent Living Cells by Bead Micromanipulation: Comparison of Magnetic Twisting Cytometry vs Optical Tweezers
,”
ASME J. Biomech. Eng.
,
124
(
4
), pp.
408
421
.
14.
Puig-de Morales-Marinkovic
,
M.
,
Turner
,
K. T.
,
Butler
,
J. P.
,
Fredberg
,
J. J.
, and
Suresh
,
S.
,
2007
, “
Viscoelasticity of the Human Red Blood Cell
,”
Am. J. Physiol. Cell Physiol.
,
293
(
2
), pp.
C597
C605
.
15.
Evans
,
E.
, and
La Celle
,
P.
,
1975
, “
Intrinsic Material Properties of the Erythrocyte Membrane Indicated by Mechanical Analysis of Deformation
,”
Blood
,
45
(
1
), pp.
29
43
.http://www.bloodjournal.org/content/45/1/29
16.
Henon
,
S.
,
Lenormand
,
G.
,
Richert
,
A.
, and
Gallet
,
F.
,
1999
, “
A New Determination of the Shear Modulus of the Human Erythrocyte Membrane Using Optical Tweezers
,”
Biophys. J.
,
76
(
2
), pp.
1145
1151
.
17.
Dao
,
M.
,
Lim
,
C.
, and
Suresh
,
S.
,
2003
, “
Mechanics of the Human Red Blood Cell Deformed by Optical Tweezers
,”
J. Mech. Phys. Solids
,
51
(11–12), pp.
2259
2280
.
18.
Boynard
,
M.
,
Lelievre
,
J. C.
, and
Guillet
,
R.
,
1987
, “
Aggregation of Red Blood Cells Studied by Ultrasound Backscattering
,”
Biorheology
,
24
(
5
), pp.
451
461
.https://www.ncbi.nlm.nih.gov/pubmed/3446295
19.
Franceschini
,
E.
,
Yu
,
F. T. H.
,
Destrempes
,
F.
, and
Cloutier
,
G.
,
2010
, “
Ultrasound Characterization of Red Blood Cell Aggregation With Intervening Attenuating Tissue-Mimicking Phantoms
,”
J. Acoust. Soc. Am.
,
127
(
2
), pp.
1104
1115
.
20.
Dulinska
,
I.
,
Targosz
,
M.
,
Strojny
,
W.
,
Lekka
,
M.
,
Czuba
,
P.
,
Balwierz
,
W.
, and
Szymonski
,
M.
,
2006
, “
Stiffness of Normal and Pathological Erythrocytes Studied by Means of Atomic Force Microscopy
,”
J. Biochem. Biophys. Methods.
,
66
(1–3), pp.
1
11
.
21.
Maciaszek
,
J. L.
, and
Lykotrafitis
,
G.
,
2011
, “
Sickle Cell Trait Human Erythrocytes are Significantly Stiffer Than Normal
,”
J. Biomech.
,
44
(
4
), pp.
657
661
.
22.
Maciaszek
,
J. L.
,
Andemariam
,
B.
, and
Lykotrafitis
,
G.
,
2011
, “
Sickle Cell Trait Human Erythrocytes are Significantly Stiffer Than Normal
,”
J. Biomech.
,
46
(
4
), pp.
368
379
.
23.
Waugh
,
R.
, and
Evans
,
E.
,
1979
, “
Thermoelasticity of Red Blood Cell Membrane
,”
Biophys. J.
,
26
(
1
), pp.
115
131
.
24.
Park
,
Y.
,
Best
,
C. A.
,
Auth
,
T.
,
Gov
,
N. S.
,
Safran
,
S. A.
,
Popescu
,
G.
,
Suresh
,
S.
, and
Feld
,
M. S.
,
2010
, “
Metabolic Remodeling of the Human Red Blood Cell Membrane
,”
Proc. Natl. Acad. Sci. U.S.A.
,
107
(
4
), pp.
1289
1294
.
25.
Evans
,
E.
,
1973
, “
New Membrane Concept Applied to the Analysis of Fluid Shear- and Micropipette-Deformed Red Blood Cells
,”
Biophys. J.
,
13
(
9
), pp.
941
954
.
26.
Betz
,
T.
,
Lenz
,
M.
,
Joanny
,
J.-F.
, and
Sykes
,
C.
,
2009
, “
ATP-Dependent Mechanics of Red Blood Cells
,”
Proc. Natl. Acad. Sci. U.S.A.
,
106
(
36
), pp.
15320
15325
.
27.
Miller
,
L. H.
,
Baruch
,
D. I.
,
Marsh
,
K.
, and
Doumbo
,
O. K.
,
2002
, “
The Pathogenic Basis of Malaria
,”
Nature
,
415
(
6872
), pp.
673
679
.
28.
Suresh
,
S.
,
Spatz
,
J.
,
Mills
,
J. P.
,
Micoulet
,
A.
,
Dao
,
M.
,
Lim
,
C. T.
,
Beil
,
M.
, and
Seufferlein
,
T.
,
2005
, “
Connections Between Single-Cell Biomechanics and Human Disease States: Gastrointestinal Cancer and Malaria
,”
Acta Biomater.
,
1
(
1
), pp.
15
30
.
29.
Pauling
,
L.
,
Itano
,
H. A.
,
Singer
,
S. J.
, and
Wells
,
I. C.
,
1949
, “
Sickle Cell Anemia, a Molecular Disease
,”
Science
,
110
(
2865
), pp.
543
548
.
30.
Barabino
,
G. A.
,
Platt
,
M. O.
, and
Kaul
,
D. K.
,
2010
, “
Sickle Cell Biomechanics
,”
Ann. Rev. Biomed. Eng.
,
12
(
1
), pp.
345
367
.
31.
Perrotta
,
S.
,
Gallagher
,
P. G.
, and
Mohandas
,
N.
,
2008
, “
Hereditary Spherocytosis
,”
Lancet
,
372
(
9647
), pp.
1411
1426
.
32.
Bannerman
,
R.
, and
Renwick
,
J.
,
1962
, “
The Hereditary Elliptocytoses: Clinical and Linkage Data
,”
Ann. Hum. Genet.
,
26
(
1
), pp.
23
38
.
33.
McMillan
,
D. E.
,
Utterback
,
N. G.
, and
La Puma
,
J.
,
1978
, “
Reduced Erythrocyte Deformability in Diabetes
,”
Diabetes
,
27
(
9
), pp.
895
901
.
34.
Schwartz
,
R. S.
,
Madsen
,
J. W.
,
Rybicki
,
A. C.
, and
Nagel
,
R. L.
,
1991
, “
Oxidation of Spectrin and Deformability Defects in Diabetic Erythrocytes
,”
Diabetes
,
40
(
6
), pp.
701
708
.
35.
Mohandas
,
N.
,
Clark
,
M. R.
,
Jacobs
,
M. S.
, and
Shohet
,
S. B.
,
1980
, “
Analysis of Factors Regulating Erythrocyte Deformability
,”
J. Clin. Invest.
,
66
(
3
), pp.
563
573
.
36.
Delaunay
,
J.
,
Alloisio
,
N.
,
Morle
,
L.
,
Baklouti
,
F.
,
DallaVenezia
,
N.
,
Maillet
,
P.
, and
Wilmotte
,
R.
,
1996
, “
Molecular Genetics of Hereditary Elliptocytosis and Hereditary Spherocytosis
,”
Ann. Genet.
,
39
(
4
), pp.
209
221
.https://www.ncbi.nlm.nih.gov/pubmed/9037349
37.
Wan
,
J.
,
Ristenpart
,
W. D.
, and
Stone
,
H. A.
,
2008
, “
Dynamics of Shear-Induced ATP Release From Red Blood Cells
,”
Proc. Natl. Acad. Sci. U.S.A.
,
105
(
43
), pp.
16432
16437
.
38.
Arciero
,
J. C.
,
Carlson
,
B. E.
, and
Secomb
,
T. W.
,
2008
, “
Theoretical Model of Metabolic Blood Flow Regulation: Roles of ATP Release by Red Blood Cells and Conducted Responses
,”
Am. J. Physiol. Heart Circ. Physiol.
,
295
(
4
), pp.
H1562
H1571
.
39.
Forsyth
,
A. M.
,
Wan
,
J.
,
Owrutsky
,
P. D.
,
Abkarian
,
M.
, and
Stone
,
H. A.
,
2011
, “
Multiscale Approach to Link Red Blood Cell Dynamics, Shear Viscosity, and ATP Release
,”
Proc. Natl. Acad. Sci. U.S.A.
,
108
(
27
), pp.
10986
10991
.
40.
Hines
,
P. C.
,
Zen
,
Q.
,
Burney
,
S. N.
,
Shea
,
D. A.
,
Ataga
,
K. I.
,
Orringer
,
E. P.
,
Telen
,
M. J.
, and
Parise
,
L. V.
,
2003
, “
Novel Epinephrine and Cyclic Amp-Mediated Activation of BCAM/Lu-Dependent Sickle RBC Adhesion
,”
Blood
,
101
(
8
), pp.
3281
3287
.
41.
Telen
,
M. J.
,
2005
, “
Erythrocyte Adhesion Receptors: Blood Group Antigens and Related Molecules
,”
Transfus. Med. Rev.
,
19
(
1
), pp.
32
44
.
42.
Maciaszek
,
J. L.
,
Andemariam
,
B.
,
Abiraman
,
K.
, and
Lykotrafitis
,
G.
,
2014
, “
Akap-Dependent Modulation of BCAM/Lu Adhesion on Normal and Sickle Cell Disease RBCs Revealed by Force Nanoscopy
,”
Biophys. J.
,
106
(
6
), pp.
1258
1267
.
43.
Park
,
Y.
,
Diez-Silva
,
M.
,
Popescu
,
G.
,
Lykotrafitis
,
G.
,
Choi
,
W.
,
Feld
,
M. S.
, and
Suresh
,
S.
,
2008
, “
Refractive Index Maps and Membrane Dynamics of Human Red Blood Cells Parasitized by Plasmodium Falciparum
,”
Proc. Natl. Acad. Sci. U.S.A.
,
105
(
37
), pp.
13730
13735
.
44.
An
,
X.
, and
Mohandas
,
N.
,
2008
, “
Disorders of Red Cell Membrane
,”
Brit. J. Haematol.
,
141
(
3
), pp.
367
375
.
45.
Cristini
,
V.
, and
Kassab
,
G. S.
,
2005
. “
Computer Modeling of Red Blood Cell Rheology in the Microcirculation: A Brief Overview
,”
Ann. Biomed. Eng.
,
33
(
12
), pp.
1724
1727
.
46.
Wan
,
J.
,
Forsyth
,
A. M.
, and
Stone
,
H. A.
,
2011
, “
Red Blood Cell Dynamics: From Cell Deformation to ATP Release
,”
Integr. Biol.
,
3
(
10
), pp.
972
981
.
47.
Li
,
X. J.
,
Vlahovska
,
P. V.
, and
Karniadakis
,
G. E.
,
2013
, “
Continuum- and Particle-Based Modeling of Shapes and Dynamics of Red Blood Cells in Health and Disease
,”
Soft Matter
,
9
(
1
), pp.
28
37
.
48.
Fedosov
,
D. A.
,
Dao
,
M.
,
Karniadakis
,
G. E.
, and
Suresh
,
S.
,
2014
, “
Computational Biorheology of Human Blood Flow in Health and Disease
,”
Ann. Biomed. Eng.
,
42
(
2
), pp.
368
387
.
49.
Freund
,
J. B.
,
2014
, “
Numerical Simulation of Flowing Blood Cells
,”
Ann. Rev. Fluid Mech.
,
46
(
1
), pp.
67
95
.
50.
Yazdani
,
A.
,
Li
,
X. J.
, and
Karniadakis
,
G. E.
,
2016
, “
Dynamic and Rheological Properties of Soft Biological Cell Suspensions
,”
Rheol. Acta
,
55
(
6
), pp.
433
447
.
51.
Gompper
,
G.
, and
Fedosov
,
D. A.
,
2016
, “
Modeling Microcirculatory Blood Flow: Current State and Future Perspectives
,”
Wiley Interdiscip. Rev. Syst. Biol. Med.
,
8
(
2
), pp.
157
168
.
52.
Peskin
,
C. S.
,
2002
, “
The Immersed Boundary Method
,”
Acta Numer.
,
11
, pp.
479
517
.
53.
Doddi
,
S. K.
, and
Bagchi
,
P.
,
2009
, “
Three-Dimensional Computational Modeling of Multiple Deformable Cells Flowing in Microvessels
,”
Phys. Rev. E
,
79
(
4
), p.
046318
.
54.
Zhao
,
H.
,
Isfahani
,
A. H.
,
Olson
,
L. N.
, and
Freund
,
J. B.
,
2010
, “
A Spectral Boundary Integral Method for Flowing Blood Cells
,”
J. Comput. Phys.
,
229
(
10
), pp.
3726
3744
.
55.
Veerapaneni
,
S. K.
,
Rahimian
,
A.
,
Biros
,
G.
, and
Zorin
,
D.
,
2011
, “
A Fast Algorithm for Simulating Vesicle Flows in Three Dimensions
,”
J. Comput. Phys.
,
230
(
14
), pp.
5610
5634
.
56.
Kumar
,
A.
, and
Graham
,
M. D.
,
2012
, “
Accelerated Boundary Integral Method for Multiphase Flow in Non-Periodic Geometries
,”
J. Comput. Phys.
,
231
(
20
), pp.
6682
6713
.
57.
Boal
,
D. H.
,
Seifert
,
U.
, and
Zilker
,
A.
,
1992
, “
Dual Network Model for Red Blood Cell Membranes
,”
Phys. Rev. Lett.
,
69
(
23
), pp.
3405
3408
.
58.
Discher
,
D. E.
,
Boal
,
D. H.
, and
Boey
,
S. K.
,
1998
, “
Simulations of the Erythrocyte Cytoskeleton at Large Deformation—II: Micropipette Aspiration
,”
Biophys. J.
,
75
(
3
), pp.
1584
1597
.
59.
Noguchi
,
H.
, and
Gompper
,
G.
,
2005
, “
Shape Transitions of Fluid Vesicles and Red Blood Cells in Capillary Flows
,”
Proc. Natl. Acad. Sci. U.S.A.
,
102
(
40
), pp.
14159
14164
.
60.
Li
,
J.
,
Dao
,
M.
,
Lim
,
C. T.
, and
Suresh
,
S.
,
2005
, “
Spectrin-Level Modeling of the Cytoskeleton and Optical Tweezers Stretching of the Erythrocyte
,”
Biophys. J.
,
88
(
5
), pp.
3707
3719
.
61.
Li
,
J.
,
Lykotrafitis
,
G.
,
Dao
,
M.
, and
Suresh
,
S.
,
2007
, “
Cytoskeletal Dynamics of Human Erythrocyte
,”
Proc. Natl. Acad. Sci. U.S.A.
,
104
(
12
), pp.
4937
4942
.
62.
Pivkin
,
I. V.
, and
Karniadakis
,
G. E.
,
2008
, “
Accurate Coarse-Grained Modeling of Red Blood Cells
,”
Phys. Rev. Lett.
,
101
(
11
), p.
118105
.
63.
Fedosov
,
D. A.
,
Caswell
,
B.
, and
Karniadakis
,
G. E.
,
2010
, “
A Multiscale Red Blood Cell Model With Accurate Mechanics, Rheology, and Dynamics
,”
Biophys. J.
,
98
(
10
), pp.
2215
2225
.
64.
Pan
,
W.
,
Caswell
,
B.
, and
Karniadakis
,
G. E.
,
2010
, “
A Low-Dimensional Model for the Red Blood Cell
,”
Soft Matter
,
6
(
18
), pp.
4366
4376
.
65.
Peng
,
Z.
,
Li
,
X. J.
,
Pivkin
,
I. V.
,
Dao
,
M.
,
Karniadakis
,
G. E.
, and
Suresh
,
S.
,
2013
, “
Lipid–Bilayer and Cytoskeletal Interactions in a Red Blood Cell
,”
Proc. Natl. Acad. Sci. U.S.A.
,
110
(
33
), pp.
13356
13361
.
66.
Tran-Son-Tay
,
R.
,
Sutera
,
S.
, and
Rao
,
P.
,
1984
, “
Determination of Red Blood Cell Membrane Viscosity From Rheoscopic Observations of Tank-Treading Motion
,”
Biophys. J.
,
46
(
1
), pp.
65
72
.
67.
Fischer
,
T. M.
,
2004
, “
Shape Memory of Human Red Blood Cells
,”
Biophys. J.
,
86
(
5
), pp.
3304
3313
.
68.
Fischer
,
T. M.
,
2007
, “
Tank-Tread Frequency of the Red Cell Membrane: Dependence on the Viscosity of the Suspending Medium
,”
Biophys. J.
,
93
(
7
), pp.
2553
2561
.
69.
Abkarian
,
M.
,
Faivre
,
M.
, and
Viallat
,
A.
,
2007
, “
Swinging of Red Blood Cells Under Shear Flow
,”
Phys. Rev. Lett.
,
98
(
18
), p.
188302
.
70.
Skotheim
,
J. M.
, and
Secomb
,
T. W.
,
2007
, “
Red Blood Cells and Other Nonspherical Capsules in Shear Flow: Oscillatory Dynamics and the Tank-Treading-to-Tumbling Transition
,”
Phys. Rev. Lett.
,
98
(
7
), p.
078301
.
71.
Fedosov
,
D. A.
,
Noguchi
,
H.
, and
Gompper
,
G.
,
2014
, “
Multiscale Modeling of Blood Flow: From Single Cells to Blood Rheology
,”
Biomech. Model Mechanobiol.
,
13
(
2
), pp.
239
258
.
72.
Zhang
,
Y.
,
Huang
,
C.
,
Kim
,
S.
,
Golkaram
,
M.
,
Dixon
,
M. W. A.
,
Tilley
,
L.
,
Li
,
J.
,
Zhang
,
S.
, and
Suresh
,
S.
,
2015
, “
Multiple Stiffening Effects of Nanoscale Knobs on Human Red Blood Cells Infected With Plasmodium Falciparum Malaria Parasite
,”
Proc. Natl. Acad. Sci. U.S.A.
,
112
(
19
), pp.
6068
6073
.
73.
Ramanujan
,
S.
, and
Pozrikidis
,
C.
,
1998
, “
Deformation of Liquid Capsules Enclosed by Elastic Membranes in Simple Shear Flow: Large Deformations and the Effect of Fluid Viscosities
,”
J. Fluid Mech.
,
361
, pp.
117
143
.
74.
Lac
,
E.
,
Barthes-Biesel
,
D.
,
Pelekasis
,
N.
, and
Tsamopoulos
,
J.
,
2004
, “
Spherical Capsules in Three-Dimensional Unbounded Stokes Flows: Effect of the Membrane Constitutive Law and Onset of Buckling
,”
J. Fluid Mech.
,
516
, pp.
303
334
.
75.
Yazdani
,
A. Z.
, and
Bagchi
,
P.
,
2011
, “
Phase Diagram and Breathing Dynamics of a Single Red Blood Cell and a Biconcave Capsule in Dilute Shear Flow
,”
Phys, Rev, E
,
84
(
2
), p.
026314
.
76.
Fai
,
T. G.
,
Griffith
,
B. E.
,
Mori
,
Y.
, and
Peskin
,
C. S.
,
2013
, “
Immersed Boundary Method for Variable Viscosity and Variable Density Problems Using Fast Constant-Coefficient Linear Solvers—I: Numerical Method and Results
,”
SIAM J. Sci. Comput.
,
35
(
5
), pp.
B1132
B1161
.
77.
Shi
,
L.
,
Pan
,
T.-W.
, and
Glowinski
,
R.
,
2014
, “
Three-Dimensional Numerical Simulation of Red Blood Cell Motion in Poiseuille Flows
,”
Int. J. Numer. Methods Fluids
,
76
(
7
), pp.
397
415
.
78.
Hao
,
W.
,
Xu
,
Z.
,
Liu
,
C.
, and
Lin
,
G.
,
2015
, “
A Fictitious Domain Method With a Hybrid Cell Model for Simulating Motion of Cells in Fluid Flow
,”
J. Comput. Phys.
,
280
, pp.
345
362
.
79.
Pozrikidis
,
C.
,
1992
,
Boundary Integral and Singularity Methods for Linearized Viscous Flow
,
Cambridge University Press
,
Cambridge, UK
.
80.
Sui
,
Y.
,
Low
,
H.
,
Chew
,
Y.
, and
Roy
,
P.
,
2008
, “
Tank-Treading, Swinging, and Tumbling of Liquid-Filled Elastic Capsules in Shear Flow
,”
Phys. Rev. E
,
77
(
1
), p.
016310
.
81.
Clausen
,
J. R.
,
Reasor
,
D. A.
, and
Aidun
,
C. K.
,
2011
, “
The Rheology and Microstructure of Concentrated Non-Colloidal Suspensions of Deformable Capsules
,”
J. Fluid Mech.
,
685
, pp.
202
234
.
82.
Zhang
,
J.
,
Johnson
,
P. C.
, and
Popel
,
A. S.
,
2007
, “
An Immersed Boundary-Lattice Boltzmann Approach to Simulate Deformable Liquid Capsules and Its Application to Microscopic Blood Flows
,”
Phys. Biol.
,
4
(
4
), pp.
285
295
.
83.
Zhang
,
J.
,
Johnson
,
P. C.
, and
Popel
,
A. S.
,
2008
, “
Red Blood Cell Aggregation and Dissociation in Shear Flows Simulated by Lattice Boltzmann Method
,”
J. Biomech.
,
41
(
1
), pp.
47
55
.
84.
Krüger
,
T.
,
Varnik
,
F.
, and
Raabe
,
D.
,
2011
, “
Efficient and Accurate Simulations of Deformable Particles Immersed in a Fluid Using a Combined Immersed Boundary Lattice Boltzmann Finite Element Method
,”
Comput. Math. Appl.
,
61
(
12
), pp.
3485
3505
.
85.
Reasor
,
D. A.
,
Clausen
,
J. R.
, and
Aidun
,
C. K.
,
2012
, “
Coupling the Lattice-Boltzmann and Spectrin-Link Methods for the Direct Numerical Simulation of Cellular Blood Flow
,”
Int. J. Numer. Methods Fluids
,
68
(
6
), pp.
767
781
.
86.
Reasor
,
D. A.
,
Clausen
,
J. R.
, and
Aidun
,
C. K.
,
2013
, “
Rheological Characterization of Cellular Blood in Shear
,”
J. Fluid Mech.
,
726
, pp.
497
516
.
87.
Li
,
H.
, and
Lykotrafitis
,
G.
,
2012
, “
Two-Component Coarse-Grained Molecular-Dynamics Model for the Human Erythrocyte Membrane
,”
Biophys. J.
,
102
(
1
), pp.
75
84
.
88.
Li
,
H.
, and
Lykotrafitis
,
G.
,
2014
, “
Erythrocyte Membrane Model With Explicit Description of the Lipid Bilayer and the Spectrin Network
,”
Biophys. J.
,
107
(
3
), pp.
642
653
.
89.
Fedosov
,
D. A.
,
Peltomäki
,
M.
, and
Gompper
,
G.
,
2014
, “
Deformation and Dynamics of Red Blood Cells in Flow Through Cylindrical Microchannels
,”
Soft Matter
,
10
(
24
), pp.
4258
4267
.
90.
Hosseini
,
S. M.
, and
Feng
,
J. J.
,
2012
, “
How Malaria Parasites Reduce the Deformability of Infected Red Blood Cells
,”
Biophys. J.
,
103
(
1
), pp.
1
10
.
91.
Wu
,
T. H.
, and
Feng
,
J. J.
,
2013
, “
Simulation of Malaria-Infected Red Blood Cells in Microfluidic Channels: Passage and Blockage
,”
Biomicrofluidics
,
7
(
4
), p.
044115
.
92.
McWhirter
,
J. L.
,
Noguchi
,
H.
, and
Gompper
,
G.
,
2009
, “
Flow-Induced Clustering and Alignment of Vesicles and Red Blood Cells in Microcapillaries
,”
Proc. Natl. Acad. Sci. U.S.A.
,
106
(
15
), pp.
6039
6043
.
93.
Fedosov
,
D. A.
,
Caswell
,
B.
,
Suresh
,
S.
, and
Karniadakis
,
G. E.
,
2011
, “
Quantifying the Biophysical Characteristics of Plasmodium-Falciparum-Parasitized Red Blood Cells in Microcirculation
,”
Proc. Natl. Acad. Sci. U.S.A.
,
108
(
1
), pp.
35
39
.
94.
Li
,
X. J.
,
Popel
,
A. S.
, and
Karniadakis
,
G. E.
,
2012
, “
Blood-Plasma Separation in Y-Shaped Bifurcating Microfluidic Channels: A Dissipative Particle Dynamics Simulation Study
,”
Phys. Biol.
,
9
(
2
), p.
026010
.
95.
Lei
,
H.
, and
Karniadakis
,
G. E.
,
2013
, “
Probing Vasoocclusion Phenomena in Sickle Cell Anemia Via Mesoscopic Simulations
,”
Proc. Natl. Acad. Sci. U.S.A.
,
110
(
28
), pp.
11326
11330
.
96.
Lykov
,
K.
,
Li
,
X. J.
,
Pivkin
,
I. V.
, and
Karniadakis
,
G. E.
,
2015
, “
Inflow/Outflow Boundary Conditions for Particle-Based Blood Flow Simulations: Application to Arterial Bifurcations and Trees
,”
PLOS Comput. Biol.
,
11
(
8
), p.
e1004410
.
97.
Yazdani
,
A.
, and
Karniadakis
,
G. E.
,
2016
, “
Sub-Cellular Modeling of Platelet Transport in Blood Flow Through Microchannels With Constriction
,”
Soft Matter
,
12
(
19
), pp.
4339
4351
.
98.
Li
,
H.
,
Zhang
,
Y. H.
,
Ha
,
V.
, and
Lykotrafitis
,
G.
,
2016
, “
Modeling of Band-3 Protein Diffusion in the Normal and Defective Red Blood Cell Membrane
,”
Soft Matter
,
12
(
15
), pp.
3643
3653
.
99.
Helfrich
,
W.
,
1973
, “
Elastic Properties of Lipid Bilayers: Theory and Possible Experiments
,”
Z. Naturforsch. C
,
28
(11–12), pp.
693
703
.
100.
Seifert
,
U.
,
Berndl
,
K.
, and
Lipowsky
,
R.
,
1991
, “
Shape Transformations of Vesicles: Phase Diagram for Spontaneous- Curvature and Bilayer-Coupling Models
,”
Phys. Rev. A
,
44
(
2
), pp.
1182
1202
.
101.
Svetina
,
S.
, and
Zeks
,
B.
,
1989
, “
Membrane Bending Energy and Shape Determination of Phospholipid Vesicles and Red Blood Cells
,”
Eur. Biophys. J.
,
17
(
2
), pp.
101
111
.
102.
Heinrich
,
V.
,
Svetina
,
S.
, and
Žekš
,
B.
,
1993
, “
Nonaxisymmetric Vesicle Shapes in a Generalized Bilayer-Couple Model and the Transition Between Oblate and Prolate Axisymmetric Shapes
,”
Phys. Rev. E
,
48
(
4
), pp.
3112
3123
.
103.
Miao
,
L.
,
Seifert
,
U.
,
Wortis
,
M.
, and
Dobereiner
,
H. G.
,
1994
, “
Budding Transitions of Fluid-Bilayer Vesicles: The Effect of Area-Difference Elasticity
,”
Phys. Rev. E
,
49
(
6
), pp.
5389
5407
.
104.
Li
,
X. J.
,
Pivkin
,
I. V.
,
Liang
,
H. J.
, and
Karniadakis
,
G. E.
,
2009
, “
Shape Transformations of Membrane Vesicles From Amphiphilic Triblock Copolymers: A Dissipative Particle Dynamics Simulation Study
,”
Macromolecules
,
42
(
8
), pp.
3195
3200
.
105.
Khairy
,
K.
, and
Howard
,
J.
,
2011
, “
Minimum-Energy Vesicle and Cell Shapes Calculated Using Spherical Harmonics Parameterization
,”
Soft Matter
,
7
(
5
), pp.
2138
2143
.
106.
Paessler
,
M.
, and
Hartung
,
H.
,
2015
, “
Dehydrated Hereditary Stomatocytosis Masquerading as MDS
,”
Blood
,
125
(
11
), pp.
1841
1841
.
107.
Bain
,
B. J.
,
2005
, “
Diagnosis From the Blood Smear
,”
N. Engl. J. Med.
,
353
(
5
), pp.
498
507
.
108.
Hernandez
,
J. D. H.
,
Villasenor
,
O. R.
,
Alvarado
,
J. D. R.
,
Lucach
,
R. O.
,
Zarate
,
A.
,
Saucedo
,
R.
, and
Hernandez-Valencia
,
M.
,
2015
, “
Morphological Changes of Red Blood Cells in Peripheral Blood Smear of Patients With Pregnancy-Related Hypertensive Disorders
,”
Arch. Med. Res.
,
46
(
6
), pp.
479
483
.
109.
Young
,
L. E.
,
Izzo
,
M. J.
, and
Platzer
,
R. F.
,
1951
, “
Hereditary Spherocytosis
,”
Blood
,
6
(
11
), pp.
1073
1098
.http://www.bloodjournal.org/content/6/11/1073
110.
Agre
,
P.
,
Casella
,
J. F.
,
Zinkham
,
W. H.
,
McMillan
,
C.
, and
Bennett
,
V.
,
1985
, “
Partial Deficiency of Erythrocyte Spectrin in Hereditary Spherocytosis
,”
Nature
,
314
(
6009
), pp.
380
383
.
111.
Tomaselli
,
M. B.
,
John
,
K. M.
, and
Lux
,
S. E.
,
1981
, “
Elliptical Erythrocyte Membrane Skeletons and Heat-Sensitive Spectrin in Hereditary Elliptocytosis
,”
Proc. Natl. Acad. Sci. U.S.A.
,
78
(
3
), pp.
1911
1915
.
112.
Marchesi
,
S. L.
,
Letsinger
,
J. T.
,
Speicher
,
D. W.
,
Marchesi
,
V. T.
,
Agre
,
P.
,
Hyun
,
B.
, and
Gulati
,
G.
,
1987
, “
Mutant Forms of Spectrin Alpha-Subunits in Hereditary Elliptocytosis
,”
J. Clin. Invest.
,
80
(
1
), pp.
191
198
.
113.
Liu
,
S. C.
,
Palek
,
J.
,
Prchal
,
J.
, and
Castleberry
,
R. P.
,
1981
, “
Altered Spectrin Dimer-Dimer Association and Instability of Erythrocyte Membrane Skeletons in Hereditary Pyropoikilocytosis
,”
J. Clin. Invest.
,
68
(
3
), pp.
597
605
.
114.
Knowles
,
W. J.
,
Morrow
,
J. S.
,
Speicher
,
D. W.
,
Zarkowsky
,
H. S.
,
Mohandas
,
N.
,
Mentzer
,
W. C.
,
Shohet
,
S. B.
, and
Marchesi
,
V. T.
,
1983
, “
Molecular and Functional Changes in Spectrin From Patients With Hereditary Pyropoikilocytosis
,”
J. Clin. Invest.
,
71
(
6
), pp.
1867
1877
.
115.
Hsu
,
R.
,
Kanofsky
,
J.
, and
Yachnin
,
S.
,
1980
, “
The Formation of Echinocytes by the Insertion of Oxygenated Sterol Compounds Into Red Cell Membranes
,”
Blood
,
56
(
1
), pp.
109
117
.http://www.bloodjournal.org/content/56/1/109
116.
Harlan
,
W. R.
,
Shaw
,
W. A.
, and
Zelkowitz
,
M.
,
1976
, “
Echinocytes and Acquired Deficiency of Plasma Lipoproteins in Burned Patients
,”
Arch. Intern. Med.
,
136
(
1
), pp.
71
76
.
117.
Smith
,
J. A.
,
Lonergan
,
E. T.
, and
Sterling
,
K.
,
1964
, “
Spur-Cell Anemia
,”
N. Engl. J. Med.
,
271
(
8
), pp.
396
398
.
118.
McBride
,
J. A.
, and
Jacob
,
H. S.
,
1970
, “
Abnormal Kinetics of Red Cell Membrane Cholesterol in Acanthocytes: Studies in Genetic and Experimental Abetalipoproteinaemia and in Spur Cell Anaemia
,”
Br. J. Haematol.
,
18
(
4
), pp.
383
398
.
119.
Reinhart
,
W.
, and
Chien
,
S.
,
1986
, “
Red Cell Rheology in Stomatocyte-Echinocyte Transformation: Roles of Cell Geometry and Cell Shape
,”
Blood
,
67
(
4
), pp.
1110
1118
.http://www.bloodjournal.org/content/67/4/1110
120.
Fischer
,
T.
,
Haest
,
C. W.
,
Stöhr-Liesen
,
M.
,
Schmid-Schönbein
,
H.
, and
Skalak
,
R.
,
1981
, “
The Stress-Free Shape of the Red Blood Cell Membrane
,”
Biophys. J.
,
34
(
3
), pp.
409
422
.
121.
Bull
,
B. S.
, and
Kuhn
,
I. N.
,
1970
, “
The Production of Schistocytes by Fibrin Strands (A Scanning Electron Microscope Study)
,”
Blood
,
35
(
1
), pp.
104
111
.http://www.bloodjournal.org/content/35/1/104
122.
Heyes
,
H.
,
Köhle
,
W.
, and
Slijepcevic
,
B.
,
1976
, “
The Appearance of Schistocytes in the Peripheral Blood in Correlation to the Degree of Disseminated Intravascular Coagulation
,”
Pathophysiol. Haemostasis Thromb.
,
5
(2), pp.
66
73
.
123.
Kaul
,
D. K.
,
Fabry
,
M. E.
,
Windisch
,
P.
,
Baez
,
S.
, and
Nagel
,
R. L.
,
1983
, “
Erythrocytes in Sickle Cell Anemia are Heterogeneous in Their Rheological and Hemodynamic Characteristics
,”
J. Clin. Invest.
,
72
(
1
), pp.
22
31
.
124.
Evans
,
E.
,
Mohandas
,
N.
, and
Leung
,
A.
,
1984
, “
Static and Dynamics Rigidities of Normal and Sickle Erythrocytes: Major Influence of Cell Hemoglobin Concentration
,”
J. Clin. Invest.
,
73
(
2
), pp.
477
488
.
125.
Gallagher
,
P. G.
,
2005
, “
Red Cell Membrane Disorders
,”
Hematol. Am. Soc. Hematol. Educ. Program
,
2005
(
1
), pp.
13
18
.
126.
Seifert
,
U.
,
1997
, “
Configurations of Fluid Membranes and Vesicles
,”
Adv. Phys.
,
46
(
1
), pp.
13
137
.
127.
Lim
,
H. W. G.
,
Wortis
,
M.
, and
Mukhopadhyay
,
R.
,
2002
, “
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
), pp.
16766
16769
.
128.
Spangler
,
E. J.
,
Harvey
,
C. W.
,
Revalee
,
J. D.
,
Kumar
,
P. B. S.
, and
Laradji
,
M.
,
2011
, “
Computer Simulation of Cytoskeleton-Induced Blebbing in Lipid Membranes
,”
Phys. Rev. E
,
84
(
5
), p.
051906
.
129.
Gov
,
N.
,
Cluitmans
,
J.
,
Sens
,
P.
, and
Bosman
,
G.
,
2009
, “
Cytoskeletal Control of Red Blood Cell Shape: Theory and Practice of Vesicle Formation
,”
Advances in Planar Lipid Bilayers and Liposomes
, Vol.
10
,
Academic Press
,
San Diego, California
, pp.
95
119
.
130.
Li
,
H.
, and
Lykotrafitis
,
G.
,
2015
, “
Vesiculation of Healthy and Defective Red Blood Cells
,”
Phys. Rev. E
,
92
(
1
), p.
012715
.
131.
Sens
,
P.
, and
Gov
,
N.
,
2007
, “
Force Balance and Membrane Shedding at the Red-Blood-Cell Surface
,”
Phys. Rev. Lett.
,
98
(
1
), p.
018102
.
132.
Hess
,
J. R.
,
2014
, “
Measures of Stored Red Blood Cell Quality
,”
Vox Sang.
,
107
(
1
), pp.
1
9
.
133.
Greenwalt
,
T. J.
,
2006
, “
The How and Why of Exocytic Vesicles
,”
Transfusion
,
46
(
1
), pp.
143
152
.
134.
Alaarg
,
A.
,
Schiffelers
,
R.
,
van Solinge
,
W. W.
, and
Van Wijk
,
R.
,
2013
, “
Red Blood Cell Vesiculation in Hereditary Hemolytic Anemia
,”
Front. Physiol.
,
4
, p.
365
.
135.
Lei
,
H.
, and
Karniadakis
,
G. E.
,
2012
, “
Predicting the Morphology of Sickle Red Blood Cells Using Coarse-Grained Models of Intracellular Aligned Hemoglobin Polymers
,”
Soft Matter
,
8
(
16
), pp.
4507
4516
.
136.
Quinn
,
D. J.
,
Pivkin
,
I. V.
,
Wong
,
S. K.
,
Chiam
,
K. H.
,
Dao
,
M.
,
Karniadakis
,
G. E.
, and
Suresh
,
S.
,
2011
, “
Combined Simulation and Experimental Study of Large Deformation of Red Blood Cells in Microfluidic Systems
,”
Ann. Biomed. Eng.
,
39
(
3
), pp.
1041
1050
.
137.
Imai
,
Y.
,
Kondo
,
H.
,
Ishikawa
,
T.
,
Lim
,
C. T.
, and
Yamaguchi
,
T.
,
2010
, “
Modeling of Hemodynamics Arising From Malaria Infection
,”
J. Biomech.
,
43
(
7
), pp.
1386
1393
.
138.
Fedosov
,
D. A.
,
Lei
,
H.
,
Caswell
,
B.
,
Suresh
,
S.
, and
Karniadakis
,
G. E.
,
2011
, “
Multiscale Modeling of Red Blood Cell Mechanics and Blood Flow in Malaria
,”
PLOS Comput. Biol.
,
7
(
12
), p.
e1002270
.
139.
Ye
,
T.
,
Phan-Thien
,
N.
,
Khoo
,
B. C.
, and
Lim
,
C. T.
,
2013
, “
Stretching and Relaxation of Malaria-Infected Red Blood Cells
,”
Biophys. J.
,
105
(
5
), pp.
1103
1109
.
140.
Imai
,
Y.
,
Nakaaki
,
K.
,
Kondo
,
H.
,
Ishikawa
,
T.
,
Lim
,
C. T.
, and
Yamaguchi
,
T.
,
2011
, “
Margination of Red Blood Cells Infected by Plasmodium Falciparum in a Microvessel
,”
J. Biomech.
,
44
(
8
), pp.
1553
1558
.
141.
Aingaran
,
M.
,
Zhang
,
R.
,
Law
,
S. K. Y.
,
Peng
,
Z. L.
,
Undisz
,
A.
,
Meyer
,
E.
,
Diez-Silva
,
M.
,
Burke
,
T. A.
,
Spielmann
,
T.
,
Lim
,
C. T.
,
Suresh
,
S.
,
Dao
,
M.
, and
Marti
,
M.
,
2012
, “
Host Cell Deformability is Linked to Transmission in the Human Malaria Parasite Plasmodium Falciparum
,”
Cell Microbiol.
,
14
(
7
), pp.
983
993
.
142.
Bow
,
H.
,
Pivkin
,
I. V.
,
Diez-Silva
,
M.
,
Goldfless
,
S. J.
,
Dao
,
M.
,
Niles
,
J. C.
,
Suresh
,
S.
, and
Han
,
J.
,
2011
, “
A Microfabricated Deformability-Based Flow Cytometer With Application to Malaria
,”
Lab Chip
,
11
(
6
), pp.
1065
1073
.
143.
Ye
,
T.
,
Phan-Thien
,
N.
,
Khoo
,
B. C.
, and
Lim
,
C. T.
,
2014
, “
Numerical Modelling of a Healthy/Malaria-Infected Erythrocyte in Shear Flow Using Dissipative Particle Dynamics Method
,”
J. Appl. Phys.
,
115
(
22
), p.
224701
.
144.
Fedosov
,
D. A.
,
Caswell
,
B.
, and
Karniadakis
,
G. E.
,
2011
, “
Wall Shear Stress-Based Model for Adhesive Dynamics of Red Blood Cells in Malaria
,”
Biophys. J.
,
100
(
9
), pp.
2084
2093
.
145.
Hou
,
H. W.
,
Bhagat
,
A. A. S.
,
Lee
,
W. C.
,
Huang
,
S.
,
Han
,
J.
, and
Lim
,
C. T.
,
2011
, “
Microfluidic Devices for Blood Fractionation
,”
Micromachines
,
2
(
4
), p.
319
.
146.
Chien
,
S.
,
Usami
,
S.
, and
Bertles
,
J. F.
,
1970
, “
Abnormal Rheology of Oxygenated Blood in Sickle Cell Anemia
,”
J. Clin. Invest.
,
49
(
4
), pp.
623
634
.
147.
Kaul
,
D. K.
, and
Xue
,
H.
,
1991
, “
Rate of Deoxygenation and Rheologic Behavior of Blood in Sickle Cell Anemia
,”
Blood
,
77
(
6
), pp.
1353
1361
.http://www.bloodjournal.org/content/77/6/1353
148.
Ferrone
,
F. A.
,
Hofrichter
,
J.
, and
Eaton
,
W. A.
,
1985
, “
Kinetics of Sickle Hemoglobin Polymerization II: A Double Nucleation Mechanism
,”
J. Mol. Biol.
,
183
(
4
), pp.
611
631
.
149.
Vekilov
,
P. G.
,
2007
, “
Sickle-Cell Haemoglobin Polymerization: Is It the Primary Pathogenic Event of Sickle-Cell Anaemia?
,”
Br. J. Haematol.
,
139
(
2
), pp.
173
184
.
150.
Lu
,
L.
,
Li
,
X. J.
,
Vekilov
,
P. G.
, and
Karniadakis
,
G. E.
,
2016
, “
Probing the Twisted Structure of Sickle Hemoglobin Fibers Via Particle Simulations
,”
Biophys. J.
,
110
(
9
), pp.
2085
2093
.
151.
Li
,
X. J.
,
Caswell
,
B.
, and
Karniadakis
,
G. E.
,
2012
, “
Effect of Chain Chirality on the Self-Assembly of Sickle Hemoglobin
,”
Biophys. J.
,
103
(
6
), pp.
1130
1140
.
152.
Li
,
H.
, and
Lykotrafitis
,
G.
,
2011
, “
A Coarse-Grain Molecular Dynamics Model for Sickle Hemoglobin Fibers
,”
J. Mech. Behav. Biomed. Mater.
,
4
(
2
), pp.
162
173
.
153.
Li
,
H.
,
Ha
,
V.
, and
Lykotrafitis
,
G.
,
2012
, “
Modeling Sickle Hemoglobin Fibers as One Chain of Coarse-Grained Particles
,”
J. Biomech.
,
45
(
11
), pp.
1947
1951
.
154.
Liu
,
S. C.
,
Derick
,
L. H.
,
Zhai
,
S.
, and
Palek
,
J.
,
1991
, “
Uncoupling of the Spectrin-Based Skeleton From the Lipid Bilayer in Sickled Red Cells
,”
Science
,
252
(
5005
), pp.
574
576
.
155.
Odiévre
,
M.-H.
,
Verger
,
E.
,
Silva-Pinto
,
A. C.
, and
Elion
,
J.
,
2011
, “
Pathophysiological Insights in Sickle Cell Disease
,”
Indian J. Med. Res.
,
134
(
4
), pp.
532
537
.http://www.ijmr.org.in/text.asp?2011/134/4/532/89895
156.
Dupin
,
M.
,
Halliday
,
I.
,
Care
,
C. M.
, and
Munn
,
L. L.
,
2008
, “
Lattice Boltzmann Modeling of Blood Cell Dynamics
,”
Int. J. Comput. Fluid Dyn.
,
22
(
7
), pp.
481
492
.
157.
Chang
,
H.-Y.
,
Li
,
X. J.
,
Li
,
H.
, and
Karniadakis
,
G. E.
,
2016
, “
MD/DPD Multiscale Framework for Predicting Morphology and Stresses of Red Blood Cells in Health and Disease
,”
PLOS Comput. Biol.
,
12
(
10
), p.
e1005173
.
158.
Kodippili
,
G. C.
,
Spector
,
J.
,
Sullivan
,
C.
,
Kuypers
,
F. A.
,
Labotka
,
R.
,
Gallagher
,
P. G.
,
Ritchie
,
K.
, and
Low
,
P. S.
,
2009
, “
Imaging of the Diffusion of Single Band 3 Molecules on Normal and Mutant Erythrocytes
,”
Blood
,
113
(
24
), pp.
6237
6245
.
159.
Cho
,
M. R.
,
Eber
,
S. W.
,
Liu
,
S.-C.
,
Lux
,
S. E.
, and
Golan
,
D. E.
,
1998
, “
Regulation of Band 3 Rotational Mobility by Ankyrin in Intact Human Red Cells
,”
Biochemistry
,
37
(
51
), pp.
17828
17835
.
160.
Tsuji
,
A.
, and
Ohnishi
,
S.
,
1986
, “
Restriction of the Lateral Motion of Band 3 in the Erythrocyte Membrane by the Cytoskeletal Network: Dependence on Spectrin Association State
,”
Biochemistry
,
25
(
20
), pp.
6133
6139
.
161.
Schindler
,
M.
,
Koppel
,
D. E.
, and
Sheetz
,
M. P.
,
1980
, “
Modulation of Membrane Protein Lateral Mobility by Polyphosphates and Polyamines
,”
Proc. Natl. Acad. Sci. U.S.A.
,
77
(
3
), pp.
1457
1461
.
162.
Sheetz
,
M. P.
,
Febbroriello
,
P.
, and
Koppel
,
D. E.
,
1982
, “
Triphosphoinositide Increases Glycoprotein Lateral Mobility in Erythrocyte Membranes
,”
Nature
,
296
(
5852
), pp.
91
93
.
163.
Smith
,
D. K.
, and
Palek
,
J.
,
1982
, “
Modulation of Lateral Mobility of Band 3 in the Red Cell Membrane by Oxidative Cross-Linking of Spectrin
,”
Nature
,
297
(
5865
), pp.
424
425
.
164.
Saxton
,
M. J.
,
1995
, “
Single-Particle Tracking: Effects of Corrals
,”
Biophys. J.
,
69
(
2
), pp.
389
398
.
165.
Saxton
,
M. J.
,
1989
, “
The Spectrin Network as a Barrier to Lateral Diffusion in Erythrocytes: A Percolation Analysis
,”
Biophys. J.
,
55
(
1
), pp.
21
28
.
166.
Saxton
,
M. J.
,
1990
, “
The Membrane Skeleton of Erythrocytes: A Percolation Model
,”
Biophys. J.
,
57
(
6
), pp.
1167
1177
.
167.
Saxton
,
M. J.
,
1990
, “
The Membrane Skeleton of Erythrocytes: Models of Its Effect on Lateral Diffusion
,”
Int. J. Biochem. Cell Biol.
,
22
(
8
), pp.
801
809
.
168.
Brown
,
F. L.
,
Leitner
,
D. M.
,
McCammon
,
J. A.
, and
Wilson
,
K. R.
,
2000
, “
Lateral Diffusion of Membrane Proteins in the Presence of Static and Dynamic Corrals: Suggestions for Appropriate Observables
,”
Biophys. J.
,
78
(
5
), pp.
2257
2269
.
169.
Kenkre
,
V. M.
,
Giuggioli
,
L.
, and
Kalay
,
Z.
,
2008
, “
Molecular Motion in Cell Membranes: Analytic Study of Fence-Hindered Random Walks
,”
Phys. Rev. E
,
77
(
5
), p.
051907
.
170.
Auth
,
T.
, and
Gov
,
N. S.
,
2009
, “
Diffusion in a Fluid Membrane With a Flexible Cortical Cytoskeleton
,”
Biophys. J.
,
96
(
3
), pp.
818
830
.
171.
Bouchaud
,
J.-P.
, and
Georges
,
A.
,
1990
, “
Anomalous Diffusion in Disordered Media: Statistical Mechanisms, Models and Physical Applications
,”
Phys. Rep.
,
195
(4–5), pp.
127
293
.
172.
Saxton
,
M. J.
,
2007
, “
A Biological Interpretation of Transient Anomalous Subdiffusion—I: Qualitative Model
,”
Biophys. J.
,
92
(
4
), pp.
1178
1191
.
173.
Powles
,
J. G.
,
Mallett
,
M. J. D.
,
Rickayzen
,
G.
, and
Evans
,
W. A. B.
,
1992
, “
Exact Analytic Solutions for Diffusion Impeded by an Infinite Array of Partially Permeable Barriers
,”
Proc. R. Soc. London A Math. Phys. Sci.
,
436
(
1897
), pp.
391
403
.
174.
Daumas
,
F.
,
Destainville
,
N.
,
Millot
,
C.
,
Lopez
,
A.
,
Dean
,
D.
, and
Salome
,
L.
,
2003
, “
Confined Diffusion Without Fences of a G-Protein-Coupled Receptor as Revealed by Single Particle Tracking
,”
Biophys. J.
,
84
(
1
), pp.
356
366
.
175.
Brown
,
C. D.
,
Ghali
,
H. S.
,
Zhao
,
Z.
,
Thomas
,
L. L.
, and
Friedman
,
E. A.
,
2005
, “
Association of Reduced Red Blood Cell Deformability and Diabetic Nephropathy
,”
Kidney Int.
,
67
(
1
), pp.
295
300
.
176.
Agrawal
,
R.
,
Smart
,
T.
,
Nobre-Cardoso
,
J.
,
Richards
,
C.
,
Bhatnagar
,
R.
,
Tufail
,
A.
,
Shima
,
D.
,
Jones
,
P. H.
, and
Pavesio
,
C.
,
2016
, “
Assessment of Red Blood Cell Deformability in Type 2 Diabetes Mellitus and Diabetic Retinopathy by Dual Optical Tweezers Stretching Technique
,”
Sci. Rep.
,
6
, p.
15873
.
177.
Shin
,
S.
,
Ku
,
Y.-H.
,
Ho
,
J.-X.
,
Kim
,
Y.-K.
,
Suh
,
J.-S.
, and
Singh
,
M.
,
2007
, “
Progressive Impairment of Erythrocyte Deformability as Indicator of Microangiopathy in Type 2 Diabetes Mellitus
,”
Clin. Hemorheol. Micro.
,
36
(
1
), pp.
253
261
.http://content.iospress.com/articles/clinical-hemorheology-and-microcirculation/ch977
178.
Chien
,
S.
,
1987
, “
Red Cell Deformability and Its Relevance to Blood Flow
,”
Ann. Rev. Physiol.
,
49
(
1
), pp.
177
192
.
179.
Tsukada
,
K.
,
Sekizuka
,
E.
,
Oshio
,
C.
, and
Minamitani
,
H.
,
2001
, “
Direct Measurement of Erythrocyte Deformability in Diabetes Mellitus With a Transparent Microchannel Capillary Model and High-Speed Video Camera System
,”
Microvasc. Res.
,
61
(
3
), pp.
231
239
.
180.
Singh
,
M.
, and
Shin
,
S.
,
2009
, “
Changes in Erythrocyte Aggregation and Deformability in Diabetes Mellitus: A Brief Review
,”
Indian J. Exp. Biol.
,
47
(
1
), pp.
7
15
.http://www.niscair.res.in/sciencecommunication/researchjournals/rejour/ijeb/ijeb2k9/ijeb_jan09.asp#7
181.
Tomaiuolo
,
G.
,
2014
, “
Biomechanical Properties of Red Blood Cells in Health and Disease Towards Microfluidics
,”
Biomicrofluidics
,
8
(
5
), p.
051501
.
182.
Kim
,
J.
,
Lee
,
H.
, and
Shin
,
S.
,
2015
, “
Advances in the Measurement of Red Blood Cell Deformability: A Brief Review
,”
J. Cell. Biotechnol.
,
1
(
1
), pp.
63
79
.
183.
Buys
,
A. V.
,
Van Rooy
,
M.-J.
,
Soma
,
P.
,
Van Papendorp
,
D.
,
Lipinski
,
B.
, and
Pretorius
,
E.
,
2013
, “
Changes in Red Blood Cell Membrane Structure in Type 2 Diabetes: A Scanning Electron and Atomic Force Microscopy Study
,”
Cardiovasc. Diabetol.
,
12
(
1
), p.
25
.
184.
Singh
,
R.
,
Barden
,
A.
,
Mori
,
T.
, and
Beilin
,
L.
,
2001
, “
Advanced Glycation End-Products: A Review
,”
Diabetologia
,
44
(
2
), pp.
129
146
.
185.
Ahmed
,
N.
,
2005
, “
Advanced Glycation Endproducts–Role in Pathology of Diabetic Complications
,”
Diabetes Res. Clin. Pract.
,
67
(
1
), pp.
3
21
.
186.
Takakuwa
,
Y.
, and
Mohandas
,
N.
,
1988
, “
Modulation of Erythrocyte Membrane Material Properties by Ca2+ and Calmodulin: Implications for Their Role in Regulation of Skeletal Protein Interactions
,”
J. Clin. Invest.
,
82
(
2
), p.
394
.
187.
Kunt
,
T.
,
Schneider
,
S.
,
Pfützner
,
A.
,
Goitum
,
K.
,
Engelbach
,
M.
,
Schauf
,
B.
,
Beyer
,
J.
, and
Forst
,
T.
,
1999
, “
The Effect of Human Proinsulin C-Peptide on Erythrocyte Deformability in Patients With Type 1 Diabetes Mellitus
,”
Diabetologia
,
42
(
4
), pp.
465
471
.
188.
Hashemi
,
Z. Z.
,
Rahnama
,
M. M.
, and
Jafari
,
S. S.
,
2016
, “
Lattice Boltzmann Simulation of Healthy and Defective Red Blood Cell Settling in Blood Plasma
,”
ASME J. Biomech. Eng.
,
138
(
5
), p.
051002
.
189.
Schubert
,
C.
,
2011
, “
Single-Cell Analysis: The Deepest Differences
,”
Nature
,
480
(
7375
), pp.
133
137
.
190.
Itoh
,
T.
,
Chien
,
S.
, and
Usami
,
S.
,
1995
, “
Effects of Hemoglobin Concentration on Deformability of Individual Sickle Cells After Deoxygenation
,”
Blood
,
85
(
8
), pp.
2245
2253
.http://www.bloodjournal.org/content/85/8/2245
191.
Kaul
,
D.
,
Chen
,
D.
, and
Zhan
,
J.
,
1994
, “
Adhesion of Sickle Cells to Vascular Endothelium is Critically Dependent on Changes in Density and Shape of the Cells
,”
Blood
,
83
(
10
), pp.
3006
3017
.http://www.bloodjournal.org/content/83/10/3006
192.
Alapan
,
Y.
,
Little
,
J. A.
, and
Gurkan
,
U. A.
,
2014
, “
Heterogeneous Red Blood Cell Adhesion and Deformability in Sickle Cell Disease
,”
Sci. Rep.
,
4
, p.
7173
.
193.
Li
,
X. J.
,
Du
,
E.
,
Lei
,
H.
,
Tang
,
Y.-H.
,
Dao
,
M.
,
Suresh
,
S.
, and
Karniadakis
,
G. E.
,
2016
, “
Patient-Specific Blood Rheology in Sickle-Cell Anaemia
,”
Interface Focus
,
6
(
1
), p.
20150065
.
194.
Padilla
,
F.
,
Bromberg
,
P. A.
, and
Jensen
,
W. N.
,
1973
, “
The Sickle-Unsickle Cycle: A Cause of Cell Fragmentation Leading to Permanently Deformed Cells
,”
Blood
,
41
(
5
), pp.
653
660
.http://www.bloodjournal.org/content/41/5/653
You do not currently have access to this content.