The radial distribution of cells in blood flow inside vessels is highly non-homogeneous. This leads to numerous important properties of blood, yet the mechanisms shaping these distributions are not fully understood. The motion of cells is governed by a variety of hydrodynamic interactions and cell-deformation mechanics. Properties, such as the effective cell diffusivity, are therefore difficult to investigate in flows other than pure shear flows. In this work, several single-cell, cell-pair, and large-scale many-cell simulations are performed using a validated numerical model. Apart from the single-cell mechanical validations, the arising flow profile, cell free layer widths, and cell drift velocities are compared to previous experimental findings. The motion of the cells at various radial positions and under different flow conditions is extracted, and evaluated through a statistical approach. An extended diffusive flux-type model is introduced which describes the cell diffusivities under a wide range of flow conditions and incorporates the effects of cell deformability through a shear dependent description of the cell collision cross sections. This model is applicable for both red blood cells and platelets. Further evaluation of particle trajectories shows that the margination of platelets cannot be the net result of gradients in diffusivity. However, the margination mechanism is strongly linked to the gradient of the hematocrit level. Finally, it shows that platelets marginate only until the edge of the red blood cell distribution and they do not fill the cell free layer.

1.
B.
Davies
and
T.
Morris
, “
Physiological parameters in laboratory animals and humans
,”
Pharm. Res.
10
(
7
),
1093
1095
(
1993
).
2.
D.
Boal
and
D. H.
Boal
,
Mechanics of the Cell
(
Cambridge University Press
,
2012
).
3.
P. C.-H.
Chan
and
L. G.
Leal
, “
The motion of a deformable drop in a second-order fluid
,”
J. Fluid Mech.
92
(
1
),
131
170
(
1979
).
4.
M.
Loewenberg
and
E. J.
Hinch
, “
Collision of two deformable drops in shear flow
,”
J. Fluid Mech.
338
,
299
315
(
1997
).
5.
J. P.
Mills
,
L.
Qie
,
M.
Dao
,
C. T.
Lim
, and
S.
Suresh
, “
Nonlinear elastic and viscoelastic deformation of the human red blood cell with optical tweezers
,”
Mol. Cell. Biomech.
1
(
3
),
169
180
(
2004
).
6.
H.
Zhao
,
A. P.
Spann
, and
E. S. G.
Shaqfeh
, “
The dynamics of a vesicle in a wall-bound shear flow
,”
Phys. Fluids
23
(
12
),
121901
(
2011
).
7.
K.
Klapcsik
and
F.
Hegedűs
, “
The effect of high viscosity on the evolution of the bifurcation set of a periodically excited gas bubble
,”
Chaos, Solitons Fractals
104
,
198
208
(
2017
).
8.
R.
Toy
,
E.
Hayden
,
C.
Shoup
,
H.
Baskaran
, and
E.
Karathanasis
, “
The effects of particle size, density and shape on margination of nanoparticles in microcirculation
,”
Nanotechnology
22
(
11
),
115101
(
2011
).
9.
A.
Kumar
and
M. D.
Graham
, “
Segregation by membrane rigidity in flowing binary suspensions of elastic capsules
,”
Phys. Rev. E
84
(
6
),
066316
(
2011
).
10.
A.
Kumar
,
R. G.
Henríquez Rivera
, and
M. D.
Graham
, “
Flow-induced segregation in confined multicomponent suspensions: Effects of particle size and rigidity
,”
J. Fluid Mech.
738
,
423
462
(
2014
).
11.
M.
de Haan
,
G.
Zavodszky
,
V.
Azizi
, and
A.
Hoekstra
, “
Numerical investigation of the effects of red blood cell cytoplasmic viscosity contrasts on single cell and bulk transport behaviour
,”
Appl. Sci.
8
(
9
),
1616
(
2018
).
12.
M.
Abkarian
and
A.
Viallat
, “
Vesicles and red blood cells in shear flow
,”
Soft Matter
4
(
4
),
653
657
(
2008
).
13.
X.
Grandchamp
,
G.
Coupier
,
A.
Srivastav
,
C.
Minetti
, and
T.
Podgorski
, “
Lift and down-gradient shear-induced diffusion in red blood cell suspensions
,”
Phys. Rev. Lett.
110
,
108101
(
2013
).
14.
R.
Fahraeus
and
T.
Lindqvist
, “
The viscosity of the blood in narrow capillary tubes
,”
Am. J. Physiol.-Legacy Content
96
(
3
),
562
568
(
1931
).
15.
R. P.
Axel
,
D.
Neuhaus
, and
P.
Gaehtgens
, “
Blood viscosity in tube flow: Dependence on diameter and hematocrit
,”
Am. J. Physiol.
263
(
6
),
H1770
H1778
(
1992
).
16.
T. W.
Secomb
, “
Blood flow in the microcirculation
,”
Annu. Rev. Fluid Mech.
49
,
443
461
(
2017
).
17.
E. C.
Eckstein
,
D. G.
Bailey
, and
A. H.
Shapiro
, “
Self-diffusion of particles in shear flow of a suspension
,”
J. Fluid Mech.
79
(
1
),
191
208
(
1977
).
18.
P.
Olla
, “
The lift on a tank-treading ellipsoidal cell in a shear flow
,”
J. Phys. II
7
(
10
),
1533
1540
(
1997
).
19.
P.
AMM Aarts
,
S. A. T.
van den Broek
,
G. W.
Prins
,
G. D. C.
Kuiken
,
J. J.
Sixma
, and
R. M.
Heethaar
, “
Blood platelets are concentrated near the wall and red blood cells, in the center in flowing blood
,”
Arteriosclerosis: Off. J. Am. Heart Assoc., Inc.
8
(
6
),
819
824
(
1988
).
20.
H. L.
Goldsmith
,
G. R.
Cokelet
, and
P.
Gaehtgens
, “
Robin fahraeus: Evolution of his concepts in cardiovascular physiology
,”
Am. J. Physiol. Heart Circ. Physiol.
257
(
3
),
H1005
H1015
(
1989
).
21.
P.
Pranay
,
R. G.
Henríquez-Rivera
, and
M. D.
Graham
, “
Depletion layer formation in suspensions of elastic capsules in Newtonian and viscoelastic fluids
,”
Phys. Fluids
24
(
6
),
061902
(
2012
).
22.
P.
Balogh
and
P.
Bagchi
, “
Analysis of red blood cell partitioning at bifurcations in simulated microvascular networks
,”
Phys. Fluids
30
(
5
),
051902
(
2018
).
23.
E.
Kaliviotis
,
J. M.
Sherwood
, and
S.
Balabani
, “
Local viscosity distribution in bifurcating microfluidic blood flows
,”
Phys. Fluids
30
(
3
),
030706
(
2018
).
24.
K.
Müller
,
D. A.
Fedosov
, and
G.
Gompper
, “
Margination of micro-and nano-particles in blood flow and its effect on drug delivery
,”
Sci. Rep.
4
,
4871
(
2014
).
25.
T.
Krüger
, “
Effect of tube diameter and capillary number on platelet margination and near-wall dynamics
,”
Rheol. Acta
55
(
6
),
511
526
(
2016
).
26.
J.
Tan
,
T. R.
Sinno
, and
S. L.
Diamond
, “
A parallel fluid–solid coupling model using lammps and palabos based on the immersed boundary method
,”
J. Comput. Sci.
25
,
89
100
(
2018
).
27.
D.
Leighton
and
A.
Acrivos
, “
The shear-induced migration of particles in concentrated suspensions
,”
J. Fluid Mech.
181
,
415
439
(
1987
).
28.
H. C.
Berg
,
Random Walks in Biology
(
Princeton University Press
,
1993
).
29.
J. M.
Higgins
,
D. T.
Eddington
,
S. N.
Bhatia
, and
L.
Mahadevan
, “
Statistical dynamics of flowing red blood cells by morphological image processing
,”
PLoS Comput. Biol.
5
(
2
),
e1000288
(
2009
).
30.
F. R.
Da Cunha
and
E. J.
Hinch
, “
Shear-induced dispersion in a dilute suspension of rough spheres
,”
J. Fluid Mech.
309
,
211
223
(
1996
).
31.
S. D.
Hudson
, “
Wall migration and shear-induced diffusion of fluid droplets in emulsions
,”
Phys. Fluids
15
(
5
),
1106
1113
(
2003
).
32.
H. L.
Goldsmith
and
S.
Spain
, “
Margination of leukocytes in blood flow through small tubes
,”
Microvasc. Res.
27
(
2
),
204
222
(
1984
).
33.
S.
Fitzgibbon
,
A. P.
Spann
,
Q. M.
Qi
, and
E. S. G.
Shaqfeh
, “
In vitro measurement of particle margination in the microchannel flow: Effect of varying hematocrit
,”
Biophys. J.
108
(
10
),
2601
2608
(
2015
).
34.
M. E.
Fay
,
D. R.
Myers
,
A.
Kumar
,
C. T.
Turbyfield
,
R.
Byler
,
K.
Crawford
,
R. G.
Mannino
,
A.
Laohapant
,
E. A.
Tyburski
,
Y.
Sakurai
 et al, “
Cellular softening mediates leukocyte demargination and trafficking, thereby increasing clinical blood counts
,”
Proc. Natl. Acad. Sci. U. S. A.
113
(
8
),
1987
1992
(
2016
).
35.
A. L.
Zydney
and
C. K.
Colton
, “
Augmented solute transport in the shear flow of a concentrated suspension
,”
PhysicoChem. Hydrodyn.
10
(
1
),
77
96
(
1988
).
36.
E. C.
Eckstein
and
F.
Belgacem
, “
Model of platelet transport in flowing blood with drift and diffusion terms
,”
Biophys. J.
60
(
1
),
53
(
1991
).
37.
L.
Crowl
and
A. L.
Fogelson
, “
Analysis of mechanisms for platelet near-wall excess under arterial blood flow conditions
,”
J. Fluid Mech.
676
,
348
375
(
2011
).
38.
T.
Krüger
,
F.
Varnik
, and
D.
Raabe
, “
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
),
3485
3505
(
2011
).
39.
K.
Vahidkhah
and
P.
Bagchi
, “
Microparticle shape effects on margination, near-wall dynamics and adhesion in a three-dimensional simulation of red blood cell suspension
,”
Soft Matter
11
(
11
),
2097
2109
(
2015
).
40.
G.
Závodszky
,
B.
van Rooij
,
V.
Azizi
, and
A. G.
Hoekstra
, “
Cellular level in-silico modeling of blood rheology with an improved material model for red blood cells
,”
Front. Physiol.
8
,
1
14
(
2017
).
41.
H.
Zhao
,
E. S. G.
Shaqfeh
, and
V.
Narsimhan
, “
Shear-induced particle migration and margination in a cellular suspension
,”
Phys. Fluids
24
(
1
),
011902
(
2012
).
42.
A.
Kumar
and
M. D.
Graham
, “
Margination and segregation in confined flows of blood and other multicomponent suspensions
,”
Soft Matter
8
(
41
),
10536
10548
(
2012
).
43.
I. V.
Pivkin
and
G. E.
Karniadakis
, “
A new method to impose no-slip boundary conditions in dissipative particle dynamics
,”
J. Comput. Phys.
207
(
1
),
114
128
(
2005
).
44.
D. A.
Fedosov
,
B.
Caswell
, and
G. E.
Karniadakis
, “
Systematic coarse-graining of spectrin-level red blood cell models
,”
Comput. Methods Appl. Mech. Eng.
199
(
29-32
),
1937
1948
(
2010
).
45.
R. J.
Phillips
,
R. C.
Armstrong
,
R. A.
Brown
,
A. L.
Graham
, and
J. R.
Abbott
, “
A constitutive equation for concentrated suspensions that accounts for shear-induced particle migration
,”
Phys. Fluids A
4
(
1
),
30
40
(
1992
).
46.
P.
Kanehl
and
H.
Stark
, “
Hydrodynamic segregation in a bidisperse colloidal suspension in microchannel flow: A theoretical study
,”
J. Chem. Phys.
142
(
21
),
214901
(
2015
).
47.
P. R.
Nott
and
J. F.
Brady
, “
Pressure-driven flow of suspensions: Simulation and theory
,”
J. Fluid Mech.
275
,
157
199
(
1994
).
48.
R. M.
Miller
and
J. F.
Morris
, “
Normal stress-driven migration and axial development in pressure-driven flow of concentrated suspensions
,”
J. Non-Newtonian Fluid Mech.
135
(
2-3
),
149
165
(
2006
).
49.
See https://www.hemocell.eu for Hemocell–A high-performance framework for dense cellular suspension flows; accessed
10 January 2018
.
50.
G.
Závodszky
and
G.
Paál
, “
Validation of a lattice Boltzmann method implementation for a 3D transient fluid flow in an intracranial aneurysm geometry
,”
Int. J. Heat Fluid Flow
44
,
276
283
(
2013
).
51.
V. W. A.
Tarksalooyeh
,
G.
Závodszky
,
B. J. M.
van Rooij
, and
A. G.
Hoekstra
, “
Inflow and outflow boundary conditions for 2D suspension simulations with the immersed boundary lattice Boltzmann method
,”
Comput. Fluids
172
,
312
317
(
2018
).
52.
G.
Závodszky
,
G.
Károlyi
, and
G.
Paál
, “
Emerging fractal patterns in a real 3D cerebral aneurysm
,”
J. Theor. Biol.
368
,
95
101
(
2015
).
53.
B.
Czaja
,
G.
Závodszky
,
V. A.
Tarksalooyeh
, and
A. G.
Hoekstra
, “
Cell-resolved blood flow simulations of saccular aneurysms: Effects of pulsatility and aspect ratio
,”
J. R. Soc., Interface
15
(
146
),
20180485
(
2018
).
54.
L.
Mountrakis
,
E.
Lorenz
,
O.
Malaspinas
,
S.
Alowayyed
,
B.
Chopard
, and
A. G.
Hoekstra
, “
Parallel performance of an IB-LBM suspension simulation framework
,”
J. Comput. Sci.
9
,
45
50
(
2015
).
55.
S.
Alowayyed
,
G.
Závodszky
,
V.
Azizi
, and
A. G.
Hoekstra
, “
Load balancing of parallel cell-based blood flow simulations
,”
J. Comput. Sci.
24
,
1
7
(
2018
).
56.
R.
Skalak
,
A.
Tozeren
,
R. P.
Zarda
, and
S.
Chien
, “
Strain energy function of red blood cell membranes
,”
Biophys. J.
13
(
3
),
245
264
(
1973
).
57.
M.
Dao
,
J.
Li
, and
S.
Suresh
, “
Molecularly based analysis of deformation of spectrin network and human erythrocyte
,”
Mater. Sci. Eng.: C
26
(
8
),
1232
1244
(
2006
).
58.
E. J.
Carboni
,
B. H.
Bognet
,
G. M.
Bouchillon
,
A. L.
Kadilak
,
L. M.
Shor
,
M. D.
Ward
, and
A. W. K.
Ma
, “
Direct tracking of particles and quantification of margination in blood flow
,”
Biophys. J.
111
(
7
),
1487
1495
(
2016
).
59.
V.
Breedveld
,
D.
Van Den Ende
,
M.
Bosscher
,
R. J. J.
Jongschaap
, and
J.
Mellema
, “
Measurement of the full shear-induced self-diffusion tensor of noncolloidal suspensions
,”
J. Chem. Phys.
116
(
23
),
10529
10535
(
2002
).
60.
H. L.
Goldsmith
,
J.
Marlow
, and
F. C.
MacIntosh
, “
Flow behaviour of erythrocytes-i. Rotation and deformation in dilute suspensions
,”
Proc. R. Soc. London, Ser. B
182
(
1068
),
351
384
(
1972
).
61.
M. E.
Rosti
,
L.
Brandt
, and
D.
Mitra
, “
Rheology of suspensions of viscoelastic spheres: Deformability as an effective volume fraction
,”
Phys. Rev. Fluids
3
(
1
),
012301
(
2018
).
62.
W.
Yao
,
Z.
Wen
,
Z.
Yan
,
D.
Sun
,
K.
Weibo
,
L.
Xie
, and
S.
Chien
, “
Low viscosity Ektacytometry and its validation tested by flow chamber
,”
J. Biomech.
34
(
11
),
1501
1509
(
2001
).
63.
R. M.
MacMECCAN
,
J. R.
Clausen
,
G. P.
Neitzel
, and
C. K.
Aidun
, “
Simulating deformable particle suspensions using a coupled lattice-Boltzmann and finite-element method
,”
J. Fluid Mech.
618
,
13
39
(
2009
).
64.
M.
Brust
,
C.
Schaefer
,
R.
Doerr
,
L.
Pan
,
M.
Garcia
,
P. E.
Arratia
, and
C.
Wagner
, “
Rheology of human blood plasma: Viscoelastic versus Newtonian behavior
,”
Phys. Rev. Lett.
110
(
7
),
078305
(
2013
).
65.
N. O.
Jaensson
,
M. A.
Hulsen
, and
P. D.
Anderson
, “
Direct numerical simulation of particle alignment in viscoelastic fluids
,”
J. Non-Newtonian Fluid Mech.
235
,
125
142
(
2016
).
66.
H. L.
Goldsmith
and
J. C.
Marlow
, “
Flow behavior of erythrocytes. II. particle motions in concentrated suspensions of ghost cells
,”
J. Colloid Interface Sci.
71
(
2
),
383
407
(
1979
).
67.
H. L.
Goldsmith
and
V. T.
Turitto
, “
Rheological aspects of thrombosis and haemostasis: Basic principles and applications. Icth-report–subcommittee on rheology of the international committee on thrombosis and haemostasis
,”
Thromb. Haemostasis
55
(
3
),
415
(
1986
).
68.
M.
Mehrabadi
,
D. N.
Ku
, and
C. K.
Aidun
, “
A continuum model for platelet transport in flowing blood based on direct numerical simulations of cellular blood flow
,”
Ann. Biomed. Eng.
43
(
6
),
1410
1421
(
2015
).
69.
I. E.
Zarraga
and
D. T.
Leighton
, Jr.
, “
Normal stress and diffusion in a dilute suspension of hard spheres undergoing simple shear
,”
Phys. Fluids
13
(
3
),
565
577
(
2001
).
70.
G.
Drazer
,
J.
Koplik
,
B.
Khusid
, and
A.
Acrivos
, “
Deterministic and stochastic behaviour of non-Brownian spheres in sheared suspensions
,”
J. Fluid Mech.
460
,
307
335
(
2002
).
71.
R.
Rusconi
and
H. A.
Stone
, “
Shear-induced diffusion of platelike particles in microchannels
,”
Phys. Rev. Lett.
101
(
25
),
254502
(
2008
).
72.
M.
Saadatmand
,
T.
Ishikawa
,
N.
Matsuki
,
M. J.
Abdekhodaie
,
Y.
Imai
,
H.
Ueno
, and
T.
Yamaguchi
, “
Fluid particle diffusion through high-hematocrit blood flow within a capillary tube
,”
J. Biomech.
44
(
1
),
170
175
(
2011
).
73.
L.
Mountrakis
,
E.
Lorenz
, and
A. G.
Hoekstra
, “
Scaling of shear-induced diffusion and clustering in a blood-like suspension
,”
Europhys. Lett.
114
(
1
),
14002
(
2016
).
74.
Q. M.
Qi
and
E. S. G.
Shaqfeh
, “
Theory to predict particle migration and margination in the pressure-driven channel flow of blood
,”
Phys. Rev. Fluids
2
(
9
),
093102
(
2017
).
75.
N.
Tateishi
,
Y.
Suzuki
,
M.
Soutani
, and
N.
Maeda
, “
Flow dynamics of erythrocytes in microvessels of isolated rabbit mesentery: Cell-free layer and flow resistance
,”
J. Biomech.
27
(
9
),
1119
1125
(
1994
).
76.
K.
Vahidkhah
,
S. L.
Diamond
, and
P.
Bagchi
, “
Platelet dynamics in three-dimensional simulation of whole blood
,”
Biophys. J.
106
(
11
),
2529
2540
(
2014
).
77.
S.
Varchanis
,
Y.
Dimakopoulos
,
C.
Wagner
, and
J.
Tsamopoulos
, “
How viscoelastic is human blood plasma?
,”
Soft Matter
14
(
21
),
4238
4251
(
2018
).
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