Microchannel bioreactors have been used in many studies to manipulate and investigate the fluid microenvironment around cells. In this study, substrate concentrations and shear stresses at the base were computed from a three-dimensional numerical flow-model incorporating mass transport. Combined dimensionless parameters were developed from a simplified analysis. The numerical results of substrate concentration were well correlated by the combined parameters. The generalized results may find applications in design analysis of microchannel bioreactors. The mass transport and shear stress were related in a generalized result. Based on the generalized results and the condition of dynamic similarity, various means to isolate their respective effects on cells were considered.

1.
Folch
,
A.
, and
Toner
,
M.
, 2000, “
Microengineering of Cellular Interactions
,”
Annu. Rev. Biomed. Eng.
1523-9829,
2
, pp.
227
256
.
2.
Levesque
,
M. J.
, and
Nerem
,
R. M.
, 1985, “
The Elongation and Orientation of Cultured Endothelial Cells in Response to Shear Stress
,”
ASME J. Biomech. Eng.
0148-0731,
107
, pp.
341
347
.
3.
Bonnie
,
L. G.
,
Deborah
,
K. L.
,
Scott
,
D. C.
,
Rosemary
,
L. S.
, and
Abdul
,
I. B.
, 2002, “
Microchannel Platform for the Study of Endothelial Cell Shape and Function
,”
Biomed. Microdevices
1387-2176,
4
(
1
), pp.
9
16
.
4.
Tilles
,
A. W.
,
Baskaran
,
H.
,
Roy
,
P.
,
Yarmush
,
M. L.
, and
Toner
,
M.
, 2001, “
Effects of Oxygenation and Flow on the Viability and Function of Rat Hepatocytes Co-cultured in a Microchannel Flat-plate Bioreactor
,”
Biotechnol. Bioeng.
0006-3592,
73
, pp.
379
389
.
5.
Roy
,
P.
,
Baskaran
,
H.
,
Tilles
,
A. W.
,
Yarmush
,
M. L.
, and
Toner
,
M.
, 2001, “
Analysis of Oxygen Transport to Hepatocytes in a Flat-Bed Microchannel Bioreactor
,”
Ann. Biomed. Eng.
0090-6964,
29
, pp.
947
955
.
6.
Beebe
,
D. J.
,
Mensing
,
G. A.
, and
Walker
,
G. M.
, 2002, “
Physics and Applications of Microfluidics in Biology
,”
Annu. Rev. Biomed. Eng.
1523-9829,
4
, pp.
261
286
.
7.
Ledezma
,
G. A.
,
Folch
,
A.
,
Bhatia
,
S. N.
,
Balis
,
U. J.
,
Yarmush
,
M. L.
, and
Toner
,
M.
, 1999, “
Numerical Model of Fluid Flow and Oxygen Transport in a Radial-Flow Microchannel containing Hepatocytes
,”
ASME J. Biomech. Eng.
0148-0731,
121
, pp.
58
64
.
8.
Balis
,
U. J.
,
Behnia
,
K.
,
Dwarakanath
,
B.
,
Bhatia
,
S. N.
,
Sullivan
,
S. J.
,
Yarmush
,
M. L.
, and
Toner
,
M.
, 1999, “
Oxygen Consumption Characteristics of Porcine Hepatocytes
,”
Metab. Eng.
1096-7176,
1
, pp.
49
62
.
9.
Foy
,
B. D.
,
Rotem
,
A.
,
Toner
,
M.
,
Tompkins
,
R. G.
, and
Yarmush
,
M. L.
, 1994, “
A Device to Measure the Oxygen Uptake Rate of Attached Cells: Importance in Bioartificial Organ Design
,”
Cell Transplant
0963-6897,
3
, pp.
515
527
.
10.
Michael
,
L. S.
, and
Fikret
,
K.
, 1992,
Bioprocess Engineering: Basic Concepts
,
Prentice-Hall
, Englewood Cliffs, NJ.
11.
Spiga
,
M.
, and
Morini
,
G. L.
, 1994, “
A Symmetric Solution for Velocity Profile in Laminar Flow through Rectangular Ducts
,”
Int. Commun. Heat Mass Transfer
0735-1933,
21
, pp.
469
475
.
12.
du Toit
,
C. G.
, 2002, “
Calculation of Friction Factors and Nusselt Numbers for Laminar Flow in Rectangular Ducts using Finite Elements
,”
Numer. Heat Transfer, Part B
1040-7790,
41
, pp.
397
407
.
13.
Nollert
,
M. U.
,
Diamond
,
S. L.
, and
Mclntire
,
L. V.
, 1991, “
Hydrodynamic Shear Stress and Mass Transport Modulation of Endothelial Cell Metabolism
,”
Biotechnol. Bioeng.
0006-3592,
38
, pp.
588
602
.
14.
Nollert
,
M. U.
, and
Mclntire
,
L. V.
, 1992, “
Convective Mass Transfer Effects on the Intracellular Calcium Response of Endothelial Cells
,”
ASME J. Biomech. Eng.
0148-0731,
114
, pp.
321
326
.
15.
Holden
,
M. A.
,
Kumar
,
S.
,
Castellana
,
E. T.
,
Beskok
,
A.
, and
Cremer
,
P. S.
, 2003, “
Generating Fixed Concentration Arrays in a Microfluidic Device
,”
Sens. Actuators B
0925-4005,
92
, pp.
199
207
.
16.
Patankar
,
S. V.
, 1980,
Numerical Heat Transfer and Fluid Flow
,
Hemisphere
, New York.
17.
Carslaw
,
H. S.
, and
Jaeger
,
J. C.
, 1959,
Conduction of Heat in Solids
,
Oxford University Press
, London.
18.
Peng
,
C. A.
, and
Palsson
,
B. O.
, 1996, “
Determination of Specific Oxygen Uptake Rates in Human Hematopoietic Cultures and Implication for Bioreactor Design
,”
Annu. Rev. Biomed. Eng.
1523-9829,
24
, pp.
371
381
.
19.
Chisti
,
Y.
, 2001, “
Hydrodynamic Damage to Animal Cells
,”
Crit. Rev. Biotechnol.
0738-8551,
21
(
2
), pp.
67
110
.
20.
Olivier
,
L. A.
, and
Truskey
,
G. A.
, 1993, “
A Numerical Analysis of Forces Exerted by Laminar Flow on Spreading Cells in a Parallel Plate Flow Chamber Assay
,”
Biotechnol. Bioeng.
0006-3592,
42
, pp.
963
973
.
21.
Sirois
,
E.
,
Charara
,
J.
,
Ruel
,
J.
,
Dussault
,
J. C.
,
Gagnon
,
P.
, and
Doillon
,
C. J.
, 1998, “
Endothelial Cells Exposed to Erythrocytes under Shear Stress: an in Vitro Study
,”
Biomaterials
0142-9612,
19
, pp.
1925
1934
.
22.
Roy
,
P.
,
Washizu
,
J.
,
Tilles
,
A. W.
,
Yarmush
,
M. L.
, and
Toner
,
M.
, 2001, “
Effect of Flow on the Detoxification Function of Rat Hepatocytes in a Bioartificial Liver Reactor
,”
Cell Transplant
0963-6897,
10
, pp.
609
614
.
23.
Aunins
,
J. G.
, and
Henzler
,
H. J.
, 1993, “
Aeration in Cell Culture Bioreactors
,” in
H. J.
Rehm
, and
G.
Reed
(eds.),
Biotechnology
,
2nd ed
,
VCH
, Weinheim, Vol.
3
, pp.
219
281
.
24.
Beek
,
W. J.
,
Muttzall
,
K. M. K.
, and
Van Heuven
,
J. W.
, 1999,
Transport Phenomena
,
John Wiley and Sons
, New York.
25.
Schlichting
,
H.
, 1968,
Boundary-Layer Theory
,
McGraw-Hill Book Company
, New York.
26.
Fournier
,
R. L.
, 1999,
Basic Transport Phenomena in Biomedical Engineering
,
Taylor & Francis
, Philadelphia, PA.
27.
Patil
,
V. R.
,
Campbell
,
C. J.
,
Yun
,
Y. H.
,
Slack
,
S. M.
, and
Goetz
,
D. J.
, 2001, “
Particle Diameter Influences Adhesion under Flow
,”
Biophys. J.
0006-3495,
80
, pp.
1733
1743
.
28.
Satcher
,
R. L.
, Jr.
,
Bussolari
,
S. R.
,
Gimbrone
,
M. A.
, Jr.
, and
Dewey
,
C. F.
, Jr.
, 1992, “
The Distribution of Fluid Forces on Model Arterial Endothelium Using Computational Fluid Dynamics
,”
ASME J. Biomech. Eng.
0148-0731,
114
, pp.
309
316
.
29.
Yamaguchi
,
T.
,
Hoshial
,
K.
,
Okino
,
H.
,
Sakurai
,
A.
,
Hanai
,
S.
,
Masuda
,
M.
, and
Fujiwara
,
K.
, 1993, “
Shear Stress Distribution over Confluently Cultured Endothelial Cells Studied by Computational Fluid Mechanics
,”
Adv. Bioeng.
0360-9960,
20
, pp.
167
170
.
30.
Gaver
,
D. P.
, III
, and
Kute
,
S. M.
, 1998, “
A Theoretical Model Study of the Influence of Fluid Stresses on a Cell Adhering to a Microchannel Wall
,”
Biophys. J.
0006-3495,
75
, pp.
721
733
.
31.
Hu
,
Y. D.
,
Werner
,
C.
, and
Li
,
D. Q.
, 2003, “
Electrokinetic Transport through Rough Microchannels
,”
Anal. Chem.
0003-2700,
75
, pp.
5747
5758
.
32.
Zeng
,
Y.
,
Lee
,
T. S.
,
Yu
,
P.
, and
Low
,
H. T.
, 2005, “
Effect of Surface Roughness on Mass Transfer in a Flat-Plate Microchannel Bioreactor
,”
Proceedings of the International Symposium on Physics of Fluids
,
Huangshan
, China.
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