Wave intensity analysis (WIA) is a powerful technique to study pressure and flow velocity waves in the time domain in vascular networks. The method is based on the analysis of energy transported by the wave through computation of the wave intensity dI=dPdU, where dP and dU denote pressure and flow velocity changes per time interval, respectively. In this study we propose an analytical modification to the WIA so that it can be used to study waves in conditions of time varying elastic properties, such as the left ventricle (LV) during diastole. The approach is first analytically elaborated for a one-dimensional elastic tube-model of the left ventricle with a time-dependent pressure-area relationship. Data obtained with a validated quasi-three dimensional axisymmetrical model of the left ventricle are employed to demonstrate this new approach. Along the base-apex axis close to the base wave intensity curves are obtained, both using the standard method and the newly proposed modified method. The main difference between the standard and modified wave intensity pattern occurs immediately after the opening of the mitral valve. Where the standard WIA shows a backward expansion wave, the modified analysis shows a forward compression wave. The proposed modification needs to be taken into account when studying left ventricular relaxation, as it affects the wave type.

1.
Nichols
,
W. W.
, and
O’Rourke
,
M. F.
, 1990,
McDonald’s Blood Flow in Arteries: Theoretical, Experimental and Clinical Principles
,
3rd ed.
,
Edward Arnold
, Kent, Chap. 8.
2.
Westerhof
,
N.
,
Stergiopulos
,
N.
, and
Noble
,
M. I.
, 2004,
Snapshots of Hemodynamics: An Aid for Clinical Research and Graduate Education
,
Springer Science+Business Media
, New York, Chap. 21.
3.
Weber
,
T.
,
Auer
,
J.
,
O’Rourke
,
M. F.
,
Kvas
,
E.
,
Lassnig
,
E.
,
Berent
,
R.
, and
Eber
,
B.
, 2004, “
Arterial Stiffness, Wave Reflections, and the Risk of Coronary Artery Disease
,”
Circulation
0009-7322,
109
, pp.
184
189
.
4.
Westerhof
,
N.
, and
O’Rourke
,
M. F.
, 1995, “
Haemodynamic Basis for the Development of Left Ventricular Failure in Systolic Hypertension and for its Logical Therapy
,”
J. Hypertens.
0263-6352,
13
, pp.
943
952
.
5.
O’Rourke
,
M. F.
, 1999, “
Mechanical Principles. Arterial Stiffness and Wave Reflection
,”
Pathol. Biol. (Paris)
0369-8114,
47
, pp.
623
633
.
6.
Parker
,
K. H.
, and
Jones
,
C. J. H.
, 1990, “
Forward and Backward Running Waves in the Arteries: Analysis Using the Method of Characteristics
,”
ASME J. Biomech. Eng.
0148-0731,
112
, pp.
322
326
.
7.
Wang
,
J. J.
, and
Parker
,
K. H.
, 2004, “
Wave Propagation in a Model of the Arterial Circulation
,”
J. Biomech.
0021-9290,
37
, pp.
457
470
.
8.
Jones
,
C. J. H.
, and
Sugawara
,
M.
, 1993, “
Wavefronts in the Aorta—Implications for the Mechanisms of the Left Ventricular Ejection and Aortic Valve Closure
,”
Cardiovasc. Res.
0008-6363,
27
, pp.
1902
1905
.
9.
Khir
,
A. W.
, and
Parker
,
K. H.
, 2002, “
Measurements of Wave Speed and Reflected Waves in Elastic Tubes and Bifurcations
,”
J. Biomech.
0021-9290,
35
, pp.
775
783
.
10.
Sun
,
Y.
,
Anderson
,
T. J.
,
Parker
,
K. H.
, and
Tyberg
,
J. V.
, 2000, “
Wave-Intensity Analysis: a New Approach to Coronary Hemodynamics
,”
J. Appl. Physiol.
8750-7587,
89
, pp.
1636
1644
.
11.
Blaesdale
,
R. A.
,
Parker
,
K. H.
, and
Jones
,
J. H.
, 2003, “
Chasing the Wave. Unfashionable but Important new Concepts in Arterial Wave Travel
,”
Am. J. Physiol. Heart Circ. Physiol.
0363-6135,
284
, pp.
1879
1885
.
12.
MacRae
,
J. M.
,
Sun
,
Y.
,
Isaac
,
D. L.
,
Dobson
,
G. M.
,
Cheng
,
C.
,
Little
,
W. C.
,
Parker
,
K. H.
, and
Tyberg
,
J. V.
, 1997, “
Wave Intensity Analysis: A New Approach to Left Ventricular Filling Dynamics
,”
Heart Vessels
0910-8327,
12
, pp.
53
59
.
13.
Khir
,
A. W.
,
O’Brien
,
A.
,
Gibbs
,
J. S. R.
, and
Parker
,
K. H.
, 2001, “
Determination of Wave Speed and Wave Separation in the Arteries
,”
J. Biomech.
0021-9290,
34
, pp.
1145
1155
.
14.
Shishido
,
T.
,
Sugimachi
,
M.
,
Kawaguchi
,
O.
,
Miyano
,
H.
,
Kawada
,
T.
,
Matsuura
,
W.
,
Ikeda
,
Y.
, and
Sunagawa
,
K.
, 1999, “
Novel Method to Estimate Ventricular Contractility Using Intraventriculear Pulse Wave Velocity
,”
Am. J. Physiol.
0002-9513,
277
(
6
), pp.
2409
2415
.
15.
Wang
,
J. J.
,
Parker
,
K. H.
, and
Tyberg
,
J. V.
, 2001, “
Left Ventricular Wave Speed
,”
J. Appl. Physiol.
8750-7587,
91
, pp.
2531
2536
.
16.
Owen
,
A.
, 1993, “
A Numerical Model of Early Diastolic Filling: Importance of Intraventricular Wave Propagation
,”
Cardiovasc. Res.
0008-6363,
27
(
2
), pp.
255
261
.
17.
Verdonck
,
P.
,
Vierendeels
,
J.
,
Riemslagh
,
K.
, and
Dick
,
E.
, 1999, “
Left Ventricular Pressure Gradients: a Computer Model Simulation
,”
Med. Biol. Eng. Comput.
0140-0118,
37
(
4
), pp.
511
516
.
18.
Vierendeels
,
J. A.
,
Dick
,
E.
, and
Verdonck
,
P. R.
, 2002, “
Hydrodynamics of Color M-mode Doppler Flow Wave Propagation Velocity V(p): a Computer Study
,”
J. Am. Soc. Echocardiogr
0894-7317,
15
(
3
), pp.
219
224
.
19.
Vierendeels
,
J. A.
,
Riemslagh
,
K.
,
Dick
,
E.
, and
Verdonck
,
P. R.
, 2000, “
Computer Simulation of Intraventricular Flow and Pressure Gradients During Diastole
,”
ASME J. Biomech. Eng.
0148-0731,
122
(
6
), pp.
667
674
.
20.
Meisner
,
J.
, 1986, “
Left Atriale Role in Left Ventricular Filling: Dog and Computer-studies
,” Ph.D. thesis, Yeshiva University, NY.
21.
Janz
,
R. F.
, and
Grimm
,
A. F.
, 1973, “
Deformation of the Diastolic Left Ventricle—I. Nonlinear Elastic Effects
,”
Biophys. J.
0006-3495,
13
, pp.
689
704
.
22.
Janz
,
R. F.
,
Kubert
,
B. R.
,
Moriarty
,
T. F.
, and
Grimm
,
A. F.
, 1973, “
Deformation of the Diastolic Left Ventricle—II. Nonlinear Geometric Effects
,”
J. Biomech.
0021-9290,
7
, pp.
509
516
.
23.
Yellin
,
E.
, 1995, “
The Momentum of Mass, the Momentum of Ideas, and Diastolic Function
,” in
N.
Ingels
,
G.
Daughters
,
J.
Baan
,
J.
Covell
,
R.
Reneman
, and
F.
Yin
, editors,
Systolic and Diastolic Function of the Heart
,
IOS Press
, Amsterdam.
24.
Dawson
,
J. R.
, and
Gibson
,
D. G.
, 1989, “
Left Ventricular Filling and Early Diastolic Function at Rest and During Angina in Patients with Coronary Artery Disease
,”
Br. Heart J.
0007-0769,
61
(
3
), pp.
248
257
.
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