Red blood cells (RBCs) are the most abundant cellular element suspended in blood. Together with the usual biconcave-shaped RBCs, i.e., discocytes, unusual-shaped RBCs are also observed under physiological and experimental conditions, e.g., stomatocytes and echinocytes. Stomatocytes and echinocytes are formed from discocytes and in addition can revert back to being discocytes; this shape change is known as the stomatocyte–discocyte–echinocyte (SDE) transformation. To-date, limited research has been conducted on the numerical prediction of the full SDE transformation. Spring-particle RBC (SP-RBC) models are commonly used to numerically predict RBC mechanics and rheology. However, these models are incapable of predicting the full SDE transformation because the typically employed bending model always leads to numerical instability with severely deformed shapes. In this work, an enhanced SP-RBC model is proposed in order to extend the capability of this model type and so that the full SDE transformation can be reproduced. This is achieved through the leveraging of an advanced bending model. Transformed vesicle and RBC shapes are predicted for a range of reduced volume and reduced membrane area difference (MAD), and very good agreement is obtained in the comparison of predicted shapes with experimental observations. Through these predictions, vesicle and SDE transformation phase diagrams are developed and, importantly, in the SDE case, shape boundaries are proposed for the first time relating RBC shape categories to RBC reduced volume and reduced MAD.

References

References
1.
Sherwood
,
L.
,
2010
,
Human Physiology: From Cells to Systems
,
Brooks/Cole, Cengage Learning
, Belmont,
Australia
.
2.
Skalak
,
R.
,
Ozkaya
,
N.
, and
Skalak
,
T. C.
,
1989
, “
Biofluid Mechanics
,”
Annu. Rev. Fluid Mech.
,
21
(
1
), pp.
167
204
.
3.
Ruef
,
P.
, and
Linderkamp
,
O.
,
1999
, “
Deformability and Geometry of Neonatal Erythrocytes With Irregular Shapes
,”
Pediatr. Res.
,
45
(
1
), pp.
114
119
.
4.
Wolanskyj
,
A. P.
,
2013
, “
Benign Hematology
,”
Mayo Clinic Internal Medicine Board Review
,
R. D.
Ficalora
, ed.,
Oxford University Press
,
Oxford, UK
, pp.
497
511
.
5.
Chen
,
Y.
,
Cai
,
J.
, and
Zhao
,
J.
,
2002
, “
Diseased Red Blood Cells Studied by Atomic Force Microscopy
,”
Int. J. Nanosci.
,
1
(
5&6
), pp.
683
688
.
6.
Zehnder
,
L.
,
Schulzki
,
T.
,
Goede
,
J. S.
,
Hayes
,
J.
, and
Reinhart
,
W. H.
,
2008
, “
Erythrocyte Storage in Hypertonic (SAGM) or Isotonic (PAGGSM) Conservation Medium: Influence on Cell Properties
,”
Vox Sang.
,
95
(
4
), pp.
280
287
.
7.
Chabanel
,
A.
,
Reinhart
,
W.
, and
Chien
,
S.
,
1987
, “
Increased Resistance to Membrane Deformation of Shape-Transformed Human Red Blood Cells
,”
Blood
,
69
(
3
), pp.
739
743
.
8.
Waugh
,
R. E.
,
1996
, “
Elastic Energy of Curvature-Driven Bump Formation on Red Blood Cell Membrane
,”
Biophys. J.
,
70
(
2
), pp.
1027
1035
.
9.
Gedde
,
M. M.
,
Davis
,
D. K.
, and
Huestis
,
W. H.
,
1997
, “
Cytoplasmic pH and Human Erythrocyte Shape
,”
Biophys. J.
,
72
(
3
), pp.
1234
1246
.
10.
Jan
,
K. M.
, and
Chien
,
S.
,
1973
, “
Role of Surface Electric Charge in Red Blood Cell Interactions
,”
J. Gen. Physiol.
,
61
(
5
), pp.
638
654
.
11.
Hsu
,
R.
,
Kanofsky
,
J. R.
, 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
.
12.
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
.
13.
Skalak
,
R.
,
Tozeren
,
A.
,
Zarda
,
R. P.
, and
Chien
,
S.
,
1973
, “
Strain Energy Function of Red Blood Cell Membranes
,”
Biophys. J.
,
13
(
3
), pp.
245
264
.
14.
Khairy
,
K.
, and
Howard
,
J.
,
2011
, “
Minimum-Energy Vesicle and Cell Shapes Calculated Using Spherical Harmonics Parameterization
,”
Soft Matter
,
7
(
5
), pp.
2138
2143
.
15.
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
.
16.
Dupin
,
M. M.
,
Halliday
,
I.
,
Care
,
C. M.
, and
Munn
,
L. L.
,
2008
, “
Lattice Boltzmann Modelling of Blood Cell Dynamics
,”
Int. J. Comput. Fluid Dyn.
,
22
(
7
), pp.
481
492
.
17.
Imai
,
Y.
,
Nakaaki
,
K.
,
Kondo
,
H.
,
Ishikawa
,
T.
,
Teck Lim
,
C.
, and
Yamaguchi
,
T.
,
2011
, “
Margination of Red Blood Cells Infected by Plasmodium Falciparum in a Microvessel
,”
J. Biomech.
,
44
(
8
), pp.
1553
1558
.
18.
Dao
,
M.
,
Li
,
J.
, and
Suresh
,
S.
,
2006
, “
Molecularly Based Analysis of Deformation of Spectrin Network and Human Erythrocyte
,”
Mater. Sci. Eng. C
,
26
(
8
), pp.
1232
1244
.
19.
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
.
20.
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
.
21.
Fedosov
,
D. A.
,
Caswell
,
B.
, and
Karniadakis
,
G.
,
2010
, “
Dissipative Particle Dynamics Modeling of Red Blood Cells
,”
Computational Hydrodynamics of Capsules and Biological Cells
,
C.
Pozrikidis
, ed.,
CRC Press
,
Boca Raton, FL
, pp.
183
218
.
22.
Li
,
X.
,
Vlahovska
,
P. M.
, 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
.
23.
Pivkin
,
I.
, and
Karniadakis
,
G.
,
2008
, “
Accurate Coarse-Grained Modeling of Red Blood Cells
,”
Phys. Rev. Lett.
,
101
(
11
), pp.
1
4
.
24.
Alizadehrad
,
D.
,
Imai
,
Y.
,
Nakaaki
,
K.
,
Ishikawa
,
T.
, and
Yamaguchi
,
T.
,
2012
, “
Quantification of Red Blood Cell Deformation at High-Hematocrit Blood Flow in Microvessels
,”
J. Biomech.
,
45
(
15
), pp.
2684
2689
.
25.
Lim
,
H. W. G.
,
Wortis
,
M.
, and
Mukhopadhyay
,
R.
,
2008
, “
Red Blood Cell Shapes and Shape Transformations: Newtonian Mechanics of a Composite Membrane
,”
Soft Matter
,
Wiley-VCH Verlag GmbH
,
Weinheim, Germany
, pp.
139
204
.
26.
Evans
,
E. A.
, and
Fung
,
Y.-C.
,
1972
, “
Improved Measurements of the Erythrocyte Geometry
,”
Microvasc. Res.
,
4
(
4
), pp.
335
347
.
27.
Boey
,
S. K.
,
Boal
,
D. H.
, and
Discher
,
D. E.
,
1998
, “
Simulations of the Erythrocyte Cytoskeleton at Large Deformation—I: Microscopic Models.
,”
Biophys. J.
,
75
(
3
), pp.
1573
1583
.
28.
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
.
29.
Gompper
,
G.
, and
Kroll
,
D. M.
,
1996
, “
Random Surface Discretizations and the Renormalization of the Bending Rigidity
,”
J. Phys. I
,
6
(
10
), pp.
1305
1320
.
30.
Chen
,
M.
, and
Boyle
,
F. J.
,
2014
, “
Investigation of Membrane Mechanics Using Spring Networks: Application to Red-Blood-Cell Modelling
,”
Mater. Sci. Eng. C
,
43
, pp.
506
516
.
31.
Boal
,
D.
,
2012
, “
Introduction to the Cell
,”
Mechanics of the Cell
,
Cambridge University Press
,
Cambridge, UK
, pp.
1
24
.
32.
Housner
,
G. W.
, and
Hudson
,
D. E.
,
1980
, “
Dynamics of a Particle
,”
Applied Mechanics Dynamics
,
California Institute of Technology
,
Pasadena, CA
, pp.
26
47
.
33.
Svetina
,
S.
, and
Zeks
,
B.
,
2002
, “
Shape Behavior of Lipid Vesicles as the Basis of Some Cellular Processes
,”
Anat. Rec.
,
268
(
3
), pp.
215
225
.
34.
Käs
,
J.
, and
Sackmann
,
E.
,
1991
, “
Shape Transitions and Shape Stability of Giant Phospholipid Vesicles in Pure Water Induced by Area-to-Volume Changes
,”
Biophys. J.
,
60
(
4
), pp.
825
844
.
35.
Käs
,
J.
,
Sackmann
,
E.
,
Podgornik
,
R.
,
Svetina
,
S.
, and
Žekš
,
B.
,
1993
, “
Thermally Induced Budding of Phospholipid Vesicles—A Discontinuous Process
,”
J. Phys. II
,
3
(
5
), pp.
631
645
.
36.
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
.
37.
Bessis
,
M.
,
1973
, “
Red Cell Shapes: An Illustrated Classification and Its Rationale
,”
Red Cell Shape
,
M.
Bessis
,
R. I.
Weed
, and
P.
Leblond
, eds.,
Springer
,
Berlin
, pp.
1
26
.
38.
Brailsford
,
J. D.
,
Korpman
,
R. A.
, and
Bull
,
B. S.
,
1980
, “
Crenation and Cupping of the Red Cell: A New Theoretical Approach—Part II: Cupping
,”
J. Theor. Biol.
,
86
(
3
), pp.
531
546
.
39.
Jay
,
A. W.
,
1975
, “
Geometry of the Human Erythrocyte—I: Effect of Albumin on Cell Geometry
,”
Biophys. J.
,
15
(
3
), pp.
205
222
.
40.
Pan
,
W.
,
Fedosov
,
D. A.
,
Caswell
,
B.
, and
Karniadakis
,
G. E.
,
2011
, “
Predicting Dynamics and Rheology of Blood Flow: A Comparative Study of Multiscale and Low-Dimensional Models of Red Blood Cells.
,”
Microvasc. Res.
,
82
(
2
), pp.
163
170
.
41.
Helfrich
,
W.
,
1973
, “
Elastic Properties of Lipid Bilayers: Theory and Possible Experiments
,”
Z. Naturforsch. C
,
28
(
11–12
), pp.
693
703
.
You do not currently have access to this content.