The purpose of this study was to model the transport of oxygen in large arteries, including the physiologically important effects of oxygen transport by hemoglobin, coupling of transport between oxygen in the blood and in wall tissue, and metabolic consumption of oxygen by the wall. Numerical calculations were carried out in an 89 percent area reduction axisymmetric stenosis model for several wall thicknesses. The effects of different boundary conditions, different schemes for linearizing the oxyhemoglobin saturation curve, and different Schmidt numbers were all examined by comparing results against a reference solution obtained from solving the full nonlinear governing equations with physiologic values of Schmidt number. Our results showed that for parameters typical of oxygen mass transfer in the large arteries, oxygen transport was primarily determined by wall-side effects, specifically oxygen consumption by wall tissue and wall-side mass transfer resistance. Hemodynamic factors played a secondary role, producing maximum local variations in intimal oxygen tension on the order of only 5–6 mmHg. For purposes of modeling blood-side oxygen transport only, accurate results were obtained through use of a computationally efficient linearized form of the convection-diffusion equation, so long as blood-side oxygen tensions remained in the physiologic range for large arteries. Neglect of oxygen binding by hemoglobin led to large errors, while arbitrary reduction of the Schmidt number led to more modest errors. We conclude that further studies of oxygen transport in large arteries must couple blood-side oxygen mass transport to transport in the wall, and accurately model local oxygen consumption within the wall.

1.
Crawford
D. W.
and
Blankenhorn
D. H.
, “
Arterial wall oxygenation, oxyradicals, and atherosclerosis
,”
Atherosclerosis
, Vol.
39
,
1991
, pp.
97
108
.
2.
Zemplenyi
T.
,
Crawford
D. W.
, and
Cole
M. A.
, “
Adaptation to arterial wall hypoxia demonstrated in vivo with oxygen microcathodes
,”
Atherosclerosis
, Vol.
76
,
1989
, pp.
173
179
.
3.
Massaldi
H. A.
and
Taquini
A. C.
, “
Haemodynamics and arterial wall metabolism: their possible combined role in atherogenesis
,”
Medical Hypothesis
, Vol.
35
,
1991
, pp.
210
218
.
4.
Hajjar
D. P.
,
Farber
I. C.
, and
Smith
S. C.
, “
Oxygen tension within the arterial wall: relationship to altered bioenergetic metabolism and lipid accumulation
,”
Arc. Biochem. and Biophys.
, Vol.
262
(
1
),
1988
,
375
380
.
5.
Barker
S. G. E.
,
Talbert
A.
,
Cottam
S.
,
Baskerville
P. A.
, and
Martin
J. F.
, “
Arterial intimal hyperplasia after occlusion of the adventitial vasa vasorum in the pig
,”
Arterio. and Thromb.
, Vol.
13
,
1993
, pp.
70
77
.
6.
Buerk
D. G.
and
Goldstick
T. K.
, “
Arterial wall oxygen consumption rate varies spatially
,”
Am. J. Physiol.
, Vol.
243
,
1982
, pp.
H948–H959
H948–H959
.
7.
Back
L. H.
,
Radbill
J. R.
, and
Crawford
D. W.
, “
Analysis of oxygen transport from pulsatile viscous blood flow to diseased coronary arteries of man
,”
J. Biomech.
, Vol.
10
,
1977
, pp.
763
774
.
8.
Schneiderman
G.
and
Goldstick
T. K.
, “
Significance of luminal plasma layer resistance in arterial wall oxygen supply
,”
Atherosclerosis
, Vol.
31
,
1978
, pp.
11
20
.
9.
Schneiderman
G.
,
Ellis
C. G.
, and
Goldstick
T. K.
, “
Mass transport to walls of stenosed arteries: variation with Reynolds number and blood flow separation
,”
J. Biomech.
, Vol.
12
,
1979
, pp.
869
877
.
10.
Rappitsch
M.
and
Perktold
K.
, “
Computer simulation of convective diffusion processes in large arteries
,”
J. Biomech.
, Vol.
29
,
1996
, pp.
207
215
.
11.
E. A. McClelland and D. N. Ku, “An investigation of transient transport phenomena in separated flow,” in: M. S. Hefzy, R. M. Hochmuth, and N. A. Langrana, eds., Proc. Summer Bioengineering Conference, ASME BED-Vol. 29, 1995, pp. 17–18.
12.
C. G. Caro, T. J. Pedley, R. C. Schroter, and W. A. Seed, The Mechanics of the Circulation, Oxford University Press, Oxford, 1978.
13.
Schneiderman
G.
,
Mockros
L. F.
, and
Goldstick
T. K.
, “
Effect of pulsatility on oxygen transport to the human arterial wall
,”
J. Biomech.
, Vol.
15
,
1982
, pp.
849
858
.
14.
Colton
C. K.
and
Drake
R. F.
, “
Effect of boundary conditions on oxygen transport to blood flowing in a tube
,”
Chem. Eng. Symp. Ser, Adv. Bioengng.
, Vol.
67
(
114
),
1971
, pp.
88
95
.
15.
M. L. M. Stoop and P. H. M. Bovendeerd, “The influence of steady fluid flow on solute transfer in a two-dimensional carotid artery bifurcation,” in: R. Vanderby, Jr., ed., 1991 Bioengineering Conference: BED-Vol. 20, 1991, pp. 223–226.
16.
Back
L. H.
, “
Analysis of oxygen transport in the avascular region of arteries
,”
Math Biosci.
, Vol.
31
,
1976
, pp.
285
306
.
17.
W. W. Nichols and M. F. O’Rourke, McDonald’s blood flow in arteries, Lea & Febiger, Philadelphia, 3rd ed., 1990.
18.
Stein
T. R.
,
Martin
J. C.
, and
Keller
K. H.
, “
Steady-state oxygen transport through red blood cell suspensions
,”
J. Applied Physiology
, Vol.
31
,
1971
, pp.
397
402
.
19.
D. A. Steinman and C. R. Ethier, “Code testing with an exact solution to the 3D Navier-Stokes equations,” in: J. J. Gottlieb and C. R. Ethier, eds., Proc. CFD 94, 1994, pp. 115–122.
20.
Fletcher
D. F.
,
Maskill
S. J.
, and
Patrick
M. A.
, “
Heat and mass transfer computations for laminar flow in an aximsymmetric sudden expansion
,”
Computers and Fluids
, Vol.
13
,
1985
, pp.
207
221
.
21.
Ma
P.
,
Li
X.
, and
Ku
D. N.
, “
Heat and mass transfer in a separated flow region for high Prandtl and Schmidt numbers under pulsatile conditions
,”
Int. J. Heat and Mass Transfer
, Vol.
37
,
1994
, pp.
2723
2736
.
22.
Steinman
D. A.
,
Ballyk
P. D.
, and
Ethier
C. R.
, “
Simulation of non-Newtonian blood flow in an end-to-side anastomosis
,”
Biorheology
, Vol.
31
,
1994
, pp.
565
586
.
23.
Deng
X.
,
King
M. W.
, and
Guidon
R.
, “
Localization of atherosclerosis in arterial junctions: Concentration distribution of low density lipoproteins at the lumenal surface in regions of disturbed flow
,”
ASAIO Journal
, Vol.
41
,
1995
, pp.
58
67
.
24.
R. B. Bird, W. E. Stewart, and E. N. Lightfoot, Transport Phenomena, Wiley, New York, 1960.
This content is only available via PDF.
You do not currently have access to this content.