The adhesion of leukocytes to substrates is an important biomedical problem and has drawn extensive research. In this study, employing both single and compound drop models, we investigate how hydrodynamics interacts with an adherent liquid drop in a shear flow. These liquid drop models have recently been used to describe the rheological behavior of leukocytes. Numerical simulation confirms that the drop becomes more elongated when either capillary number or initial contact angle increases. Our results show that there exists a thin region between the drop and the wall as the drop undergoes large stretching, which allows high pressure to build up and provides a lift force. In the literature, existing models regard the leukocyte as a rigid body to calculate the force and torque acting on the drop in order to characterize the binding between cell receptors and endothelial ligands. The present study indicates that such a rigid body model is inadequate and the force magnitude obtained from it is less than half of that obtained using the deformable drop models. Furthermore, because of its much higher viscosity, the cell nucleus introduces a hydrodynamic time scale orders of magnitude slower than the cytoplasm. Hence the single and compound drops experience different dynamics during stretching, but exhibit very comparable steady-state shapes. The present work offers a framework to facilitate the development of a comprehensive dynamic model for blood cells.

1.
Bagge, U., and Braide, M., 1982, “Leukocyte plugging of capillaries in vivo,” in: White Blood Cells: Morphology and Rheology as Related to Function, Bagge, U., Born, G. V. R., and Gaehtgens, P., eds., Martinus Nijhoff, The Hague.
2.
Blixt
A.
, and
Bagge
U.
,
1987
, “
The effect of hypoperfusion on the capillary distribution of leukocyte in cross-striated muscle
,”
Microc. Endo. Lymph.
, Vol.
3
, pp.
383
396
.
3.
Braide
M.
,
Amundson
B.
,
Chien
S.
, and
Hagge
U.
,
1984
, “
Quantitative studies on the influence of the leukocytes on the vascular resistance in a skeletal muscle preparation
,”
Microvasc. Res.
, Vol.
27
, pp.
331
352
.
4.
Brooks
S. B.
, and
To¨zeren
A.
,
1996
, “
Flow past an array of cells that are adherent to the bottom plate of a flow channel
,”
Comp. & Fluids
, Vol.
25
, No.
8
, pp.
741
757
.
5.
Cozens-Roberts
C.
,
Quinn
J. A.
, and
Lauffenburger
D. A.
,
1990
, “
Receptor-mediated adhesion phenomena: model studies with the radial-flow detachment assay
,”
Biophys. J.
, Vol.
58
, pp.
107
125
.
6.
Dembo
M. D.
,
Torney
D. C.
,
Saxman
K.
, and
Hammer
D. A.
,
1988
, “
The reaction-limited kinetics of membrane-to-surface adhesion and detachment
,”
Proc. R. Soc. Lond.
, Vol.
B234
, pp.
55
83
.
7.
Dembo
M. D.
, and
Hammer
D. A.
,
1993
, “
A theoretical analysis for the effect of focal contact formation on cell—substrate attachment strength
,”
Biophys. J.
, Vol.
64
, pp.
936
959
.
8.
Dong
C.
,
Skalak
R.
,
Sung
K.-L. P.
,
Schmid-Schonbein
G. W.
, and
Chien
S.
,
1988
, “
Passive deformation analysis of human leukocytes
,”
ASME JOURNAL OF BIOMECHANICAL ENGINEERING
, Vol.
110
, pp.
27
36
.
9.
Dong
C.
,
Skalak
R.
, and
Sung
K.-L. P.
,
1991
, “
Cytoplasmic rheology of passive neutrophils
,”
Biorheology
, Vol.
28
, pp.
557
567
.
10.
Dutrochet, M., 1824, Recherches Anatomiques et physiologiques sur la structure intime des animaux et des vegetaux et sur leur Motilite, Bailliere et fils, Paris.
11.
Evans
E. A.
, and
Kukan
B.
,
1984
, “
Passive material behavior of granulocytes based on large deformation and recovery after deformation tests
,”
Blood J.
, Vol.
64
, pp.
1028
1035
.
12.
Evans
E.
, and
Yeung
A.
,
1989
, “
Apparent viscosity and cortical tension of blood granulocytes determined by micropipet aspiration
,”
Biophys. J.
, Vol.
56
, pp.
151
160
.
13.
Fauci
L. J.
, and
Peskin
C. S.
,
1988
, “
A computational model of aquatic animal motion
,”
J. Comp. Phys.
, Vol.
77
, pp.
85
108
.
14.
Firell
J. C.
, and
Lipowsky
H. H.
,
1989
, “
Leukocyte margination and deformation in mesenteric venules of rat
,”
Am. J. Physiol.
, Vol.
256
, pp.
H1667–H1674
H1667–H1674
.
15.
Goldsmith
H. L.
, and
Spain
S.
,
1984
, “
Margination of leukocytes in blood flow through small tubes
,”
Microvasc. Res.
, Vol.
27
, pp.
204
222
.
16.
Hammer
D. A.
, and
Apte
S. M.
,
1992
, “
Simulation of cell rolling and adhesion on surface in shear flow: general results and analysis of selectin-mediated neutrophil adhesion
,”
Biophys. J.
, Vol.
63
, pp.
35
57
.
17.
Hochmuth
R. M.
,
Ting-Beall
H. P.
,
Beaty
B. B.
,
Needham
D.
, and
Tran-Son-Tay
R.
,
1993
, “
Viscosity of passive human neutrophils undergoing small deformations
,”
Biophys. J.
, Vol.
64
, pp.
1596
1601
.
18.
House
S. D.
, and
Lipowsky
H. H.
,
1987
, “
Leukocyte—endothelium adhesion: microhemodynamics in mesentery of cat
,”
Microvasc. Res.
, Vol.
34
, pp.
363
379
.
19.
House
S. D.
, and
Lipowsky
H. H.
,
1988
, “
In vivo measurements of the force of leukocyte-endothelium adhesion in the mesentery of the cat
,”
Circ. Res.
, Vol.
63
, pp.
658
668
.
20.
House
S. D.
, and
Lipowsky
H. H.
,
1991
, “
Dynamics of leukocyte-endothelium interactions in the splanchnic microcirculation
,”
Microvasc. Res.
, Vol.
42
, pp.
288
304
.
21.
Jones, D. A., Smith, C. W., and McIntire, L. V., 1995, “Effects of fluid shear stress on leukocyte adhesion to endothelial cells,” in: Physiology and Pathophysiology of Leukocytes Adhesion, Oxford University Press, New York, pp. 148–168.
22.
Kan
H.-C.
,
Udaykumar
H. S.
,
Shyy
W.
, and
Tran-Son-Tay
R.
,
1998
, “
Hydrodynamics of a compound drop with application to leukocyte modeling
,”
Phys. Fluids
, Vol.
10
, pp.
760
774
.
23.
Klotz, I. M., 1997, Ligand—Receptor Energetics, Wiley, New York.
24.
Kuo
S. C.
,
Hammer
D. A.
, and
Lauffenburger
D. A.
,
1997
, “
Simulation of detachment of specifically bound particles from surfaces by shear flow
,”
Biophys. J.
, Vol.
73
, pp.
517
531
.
25.
Lasky
L. A.
,
1997
, “
How integrins are activated
,”
Nature
, Vol.
390
, pp.
15
17
.
26.
Lipowsky, H. H., 1995, “Leukocyte margination and deformation in postcapillary venules,” in: Physiology and Pathophysiology of Leukocytes Adhesion, Oxford University Press, New York, pp. 130–147.
27.
Mayrovitz, H. N., and Wiedeman, M. P., 1977, “Leukocyte adhesiveness as influenced by blood velocity,” in Microcirculation, Grayson, S., and Zingg, G., eds., Plenum Press, New York, pp. 128–130.
28.
Patankar, S. V., 1980, Numerical Heat Transfer and Fluid Flow, Hemisphere Publishing Corp., Washington, DC.
29.
Peskin
C. S.
,
1977
, “
Numerical analysis of blood flow in the heart
,”
J. Comp. Phys.
, Vol.
25
, pp.
220
252
.
30.
Schmid-Schonbein
G.
,
Usami
S.
,
Skalak
R.
, and
Chien
S.
,
1980
, “
The interaction of leukocytes and erythrocytes in capillary vessels
,”
Microvasc. Res.
, Vol.
19
, pp.
45
70
.
31.
Shyy, W., 1994, Computational Modelling for Fluid Flow and Interfacial Transport, Elsevier, Amsterdam, The Netherlands (corrected printing, 1997).
32.
Shyy, W., Udaykumar, H. S., Rao, M. M., and Smith, R. W., 1996, Computational Fluid Dynamics With Moving Boundaries, Taylor & Francis, Washington, DC (corrected printing, 1997).
33.
Shyy, W., Thakur, S. S., Ouyang, H., Liu, J., and Blosch, E. L. 1997, Computational Techniques for Complex Transport Phenomena, Cambridge University Press, New York.
34.
Skalak
R.
,
Dong
C.
, and
Zhu
C.
,
1990
, “
Passive deformation and active motions of lenkocytes
,”
ASME JOURNAL OF BIOMECHANICAL ENGINEERING
, Vol.
112
, pp.
295
302
.
35.
To¨zeren
A.
, and
Ley
K.
,
1992
, “
How do selectins mediate leukocyte rolling in venules
,”
Biophys. J.
, Vol.
63
, pp.
700
709
.
36.
Tran-Son-Tay
R.
,
Needham
D.
,
Yeung
A.
, and
Hochmuth
R. M.
,
1991
, “
Time-dependent recovery of passive neutrophils after large deformation
,”
Biophys. J.
, Vol.
60
, pp.
856
866
.
37.
Tran-Son-Tay, R., Ting-Beall, H. P., Zhelev, D. V., and Hochmuth, R. M., 1994, “Viscous behavior of leukocytes,” in: Cell Mechanics and Cellular Engineering, Mow, V. C., Guilak, F., Tran-Son-Tay, R., and Hochmuth, R. M., eds., Springer-Verlag, New York, pp. 22–32.
38.
Tran-Son-Tay
R.
,
Kan
H.-C.
,
Udaykumar
H. S.
,
Damay
E.
, and
Shyy
W.
,
1998
, “
Rheological modeling of leukocytes
,”
Medical & Biological Engng. & Comput.
, Vol.
36
, pp.
246
250
.
39.
Udaykumar
H. S.
,
Shyy
W.
, and
Rao
M. M.
,
1996
, “
ELAFINT—A mixed Eulerian Lagrangian method for fluid flows with complex and moving boundaries
,”
Int. J. Numer. Meths. Eluid
, Vol.
22
, No.
8
, pp.
691
712
.
40.
Udaykumar
H. S.
,
Kan
H.-C.
,
Shyy
W.
, and
Tran-Son-Tay
R.
,
1997
, “
Multiphase dynamics in arbitrary geometries on fixed Cartesian grids
,”
J. Comp. Phys.
, Vol.
137
, pp.
366
405
.
41.
Unverdi
S. O.
, and
Tryggvason
G.
,
1992
, “
A front tracking method for viscous, incompressible, multi-fluid flows
,”
J. Comp. Phys.
, Vol.
100
, pp.
25
37
.
42.
Ward
M. D.
, and
Hammer
D. A.
,
1993
, “
A theoretical analysis for the effect of focal contact formation on cell—substrate attachment strength
,”
Biophys. J.
, Vol.
64
, pp.
936
959
.
43.
Yeung
A.
, and
Eyans
E.
,
1989
, “
Cortical shell—liquid core model for passive flow of liquid-like spherical cells into micropipets
,”
Biophys. J.
, Vol.
56
, pp.
139
149
.
44.
Zhao
Y.
,
Chien
S.
, and
Skalak
R.
,
1995
, “
A stochastic model of leukocyte rolling
,”
Biophys. J.
, Vol.
69
, pp.
1309
1320
.
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