A new separation technique has been developed to determine the forward and backward running arterial pressure wave components. It takes into account friction as well as nonlinear effects due to convective acceleration and to the pressure dependence of the arterial compliance. The new method is a combination of two methods treating friction and nonlinearities separately. The method requires the measurements of pressure and flow at one location as well as the knowledge of the area-pressure relationship. The validity of the method was tested by a simulation experiment in which the forward and backward waves were known a priori. It was shown that the new method is significantly more accurate in the predictions of the forward and backward waves when compared to the classical method assuming linearity and no dissipation. The new wave separation method was also applied to simulated aortic waves for (a) a healthy subject and (b) a subject with decreased compliance. Comparison with the classical linear method showed that neglecting nonlinearities leads to an overestimation of the forward and backward pressure wave amplitudes. The errors, however, were in the order of 5 to 10 percent. We concluded that, for most clinical purposes, the improvement using the nonlinear method is of the same magnitude as experimental errors, and thus the linear method would suffice.

1.
Anliker
M.
,
Rockwell
R. L.
, and
Ogden
E.
,
1971
, “
Nonlinear Analysis of Flow Pulses and Shock Waves in Arteries
,”
Z. Angew. Math Phys.
, Vol.
22
, pp.
217
246
.
2.
Courant, R., and Hilbert, D., 1989, Methods of Mathematical Physics, Vol. II, John Wiley and Sons, New York.
3.
Gevers, M., van der Mooren, K., Stergiopulos, N., van Genderingen, H. R., Lafeber, H. N., Hack, W., and Westerhof, N. “Bisferiens Peaks in the Radial Artery Pressure Wave During Patent Ductus Arteriosus in Newborn Infants: Relationship With Ascending Aortic Flow Waveforms,” Ped. Res., in press.
4.
Holenstein
R. O.
,
1981
, “
A Viscoelastic Model for Use in Predicting Arterial Pulse Waves
,”
ASME JOURNAL OF BIOMECHANICAL ENGINEERING
, Vol.
102
, p.
318
318
.
5.
Jones
C. J. H.
,
Parker
K. H.
,
Hughes
R.
, and
Sheridan
D. J.
,
1992
, “
Nonlinearity of Human Arterial Pulse Wave Transmission
,”
ASME JOURNAL OF BIOMECHANICAL ENGINEERING
, Vol.
114
, pp.
10
14
.
6.
Kubo, Ryogo, 1968, Thermodynamics, North-Holland, New York.
7.
Landau, L. D., and Lifchitz, E. M., 1959, Fluid Mechanics, Vol. 6, Course of Theoretical Physics, Pergamon Press, London.
8.
Langewouters
O. J.
,
Wesseling
K. H.
, and
Goedhard
W. J. A.
,
1984
, “
The Static Elastic Properties of 45 Human Thoracic and 20 Abdominal Aortas in Vitro and the Parameters of a New Model
,”
J. Biomechanics
, Vol.
17
(
6
), pp.
425
435
.
9.
Li
J. K.-J.
,
1986
, “
Time Domain Resolution of Forward and Reflected Waves in the Aorta
,”
IEEE Trans. Biomed. Eng.
, Vol.
33
(
8
), pp.
783
785
.
10.
Ling
S. C.
, and
Atabek
H. B.
,
1972
, “
A Nonlinear Analysis of Pulsatile Flow in Arteries
,”
J. Fluid Mechanics
, Vol.
55
(
3
), pp.
493
511
.
11.
Milnor, W. R., 1989, Hemodynamics, Williams and Wilkins (2nd ed.), Baltimore.
12.
Murgo
J. P.
,
Westerhof
N.
,
Giolma
J. P.
, and
Altobelli
S. A.
,
1981
, “
Manipulation of Ascending Aortic Pressure and Flow Wave Reflections with the Valsalva Maneuver: Relationship to Input Impedance
,”
Circulation
, Vol.
63
(
1
), pp.
122
132
.
13.
Newman
D. L.
, and
Greenwald
S. E.
,
1980
, “
Analysis of Forward and Backward Pressure Waves by a Total-Occlusion Method
,”
Med. & Biol. Engng & Comp.
, Vol.
18
, pp.
241
245
.
14.
Parker
K. H.
, and
Jones
J. H.
,
1990
, “
Formard and Backward Running Waves in Arteries: Analysis Using the Method of Characteristics
,”
ASME JOURNAL OF BIOMECHANICAL ENGINEERING
, Vol.
112
, pp.
322
326
.
15.
Pythoud, F., Stergiopulos, N., and Meister, J.-J., 1993, “Nonlinear Time-Domain Analysis of Wave Reflections in Elastic Tubes,” Proc. of the 14th ISB Congress, Paris, pp. 1088–1089.
16.
Reuderink
P. J.
,
Hoogstraten
H. W.
,
Sipkema
P.
,
Hillen
B.
, and
Westerhof
N.
,
1989
, “
Linear and Nonlinear One-Dimensional Models of Pulse Wave Transmission at High Womersley Numbers
,”
J. Biomechanics
, Vol.
22
(
8/9
), pp.
819
827
.
17.
Stergiopulos
N.
,
Young
D. F.
, and
Rogge
T. R.
,
1990
, “
Computer Simulations of Arterial Flow with Applications to Arterial and Aortic Stenoses
,”
J. Biomechanics
, Vol.
25
, pp.
1477
1488
.
18.
Stergiopulos
N.
,
Tardy
Y.
, and
Meister
J.-J.
,
1993
, “
Nonlinear Separation of Forward and Backward Running Waves in Elastic Conduits
,”
J. Biomechanics
, Vol.
26
, pp.
201
209
.
19.
Stergiopulos, N., Pythoud, F., and Meister, J.-J., 1994, “Analysis of the Forward and Backward Running Waves in Arteries: The Role of Nonlinear Wall Elasticity,” Proceedings of the 3rd International Symposium in Biofluid Mechanics, pp. 899–902.
20.
Stergiopulos, N., Spiridon, M., Pythoud, F., and Meister, J.-J., 1994, “Modeling of the Wave Transmission and Reflection Properties of Stenoses,” J. Biomechanics, In press.
21.
Schaaf
B. N.
, and
Abbrecht
D. H.
,
1972
, “
Digital Computer Simulation of the Human Systemic Arterial Pulse Wave Transmission: A Nonlinear Model
,”
J. Biomechanics
, Vol.
5
, pp.
345
364
.
22.
Tardy
Y.
,
Meister
J.-J.
,
Perret
F.
,
Brunner
H. R.
, and
Arditi
M.
,
1991
, “
Non-invasive Estimate of the Mechanical Properties of Peripheral Arteries from Ultrasonic and Photoplethysmographic Measurements
,”
Clin. Phys. Physiol. Meas.
, Vol.
12
(
1
), pp.
39
54
.
23.
Van den Bos
G. C.
,
Westerhof
N.
, and
Randall
O. S.
, “
Pulse Wave Reflections: Can it Explain Differences Between Systemic and Pulmonary Pressure and Flow Waves? A Study in Dogs
,”
Circ. Res.
, Vol.
51
, pp.
479
485
.
24.
Westerhof
N.
,
Sipkema
P.
,
Bos
C. G. V.
, and
Elzinga
G.
,
1972
, “
Forward and Backward Waves in the Arterial System
,”
Cardiovasc. Res.
, Vol.
6
, pp.
648
656
.
25.
Westerhof
N.
,
Bosman
F.
,
De Vries
C. J.
, and
Noordergraaf
A.
,
1969
, “
Analog Studies of the Human Systemic Arterial Tree
,”
J. Biomechanics
, Vol.
2
, pp.
121
143
.
26.
Zagzoule
M.
, and
Marc-Verges
J. P.
,
1986
, “
A Global Mathematical Model of the Cerebral Circulation in Man
,”
J. Biomechanics
, Vol.
19
, pp.
1015
1022
.
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