Abstract

With the arterial wall modeled as an initially tensioned thin-walled orthotropic tube, this study aims to analyze radial and axial motion of the arterial wall and thereby reveal the role of axial motion and two initial tensions of the arterial wall in arterial pulse wave propagation. By incorporating related clinical findings into the pulse wave theory in the literature, a theoretical study is conducted on arterial pulse wave propagation with radial and axial wall motion. Since the Young wave is excited by pulsatile pressure and is examined in clinical studies, commonly measured pulsatile parameters in the Young wave are expressed in terms of pulsatile pressure and their values are calculated with the well-established values of circumferential elasticity (Eθ) and initial tension (Tθ0) and assumed values of axial elasticity (Ex) and initial tension (Tx0) at the ascending aorta and the carotid artery. The corresponding values with the exclusion of axial wall motion are also calculated. Comparison of the calculated results between inclusion and exclusion of axial wall motion indicates that (1) axial wall motion does not affect radial wall motion and other commonly measured pulsatile parameters, except wall shear stress; (2) axial wall motion is caused by wall shear stress and radial wall displacement gradient with a factor of (Tx0−Tθ0), and enables axial power transmission through the arterial wall; and (3) while radial wall motion reflects Eθ and Tθ0, axial wall motion reflects Ex and (Tx0−Tθ0).

References

1.
Au
,
J. S.
,
Ditor
,
D. S.
,
MacDonald
,
M. J.
, and
Stöhr
,
E. J.
,
2016
, “
Carotid Artery Longitudinal Wall Motion is Associated With Local Blood Velocity and Left Ventricular Rotational, but Not Longitudinal, Mechanics
,”
Physiol. Rep.
,
4
(
14
), p.
e12872
.10.14814/phy2.12872
2.
Au
,
J. S.
,
Bochnak
,
P. A.
,
Valentino
,
S. E.
,
Cheng
,
J. L.
,
Stöhr
,
E. J.
, and
MacDonald
,
M. J.
,
2018
, “
Cardiac and Haemodynamic Influence on Carotid Artery Longitudinal Wall Motion
,”
Exp. Physiol.
,
103
(
1
), pp.
141
152
.10.1113/EP086621
3.
Taivainen
,
S. H.
,
Yli-Ollila
,
H.
,
Juonala
,
M.
,
Kähönen
,
M.
,
Raitakari
,
O. T.
,
Laitinen
,
T. M.
, and
Laitinen
,
T. P.
,
2018
, “
Influence of Cardiovascular Risk Factors on Longitudinal Motion of the Common Carotid Artery Wall
,”
Atherosclerosis
,
272
, pp.
54
59
.10.1016/j.atherosclerosis.2018.02.037
4.
Cinthio
,
M.
,
Ahlgren
,
A. R.
,
Bergkvist
,
J.
,
Jansson
,
T.
,
Persson
,
H. W.
, and
Lindström
,
K.
,
2006
, “
Longitudinal Movements and Resulting Shear Strain of the Arterial Wall
,”
Am. J. Physiol. Heart Circ. Physiol.
,
291
(
1
), pp.
H394
H402
.10.1152/ajpheart.00988.2005
5.
Taivainen
,
S. H.
,
Yli-Ollila
,
H.
,
Juonala
,
M.
,
Kähönen
,
M.
,
Raitakari
,
O. T.
,
Laitinen
,
T. M.
, and
Laitinen
,
T. P.
,
2017
, “
Interrelationships Between Indices of Longitudinal Movement of the Common Carotid Artery Wall and the Conventional Measures of Subclinical Arteriosclerosis
,”
Clin. Physiol. Funct. Imaging
,
37
(
3
), pp.
305
313
.10.1111/cpf.12305
6.
Yli-Ollila
,
H.
,
Laitinen
,
T.
,
Weckström
,
M.
, and
Laitinen
,
T. M.
,
2016
, “
New Indices of Arterial Stiffness Measured From Longitudinal Motion of Common Carotid Artery in Relation to Reference Methods, a Pilot Study
,”
Clin. Physiol. Funct. Imaging
,
36
(
5
), pp.
376
388
.10.1111/cpf.12240
7.
Cardamone
,
L.
,
Valentín
,
A.
,
Eberth
,
J. F.
, and
Humphrey
,
J. D.
,
2009
, “
Origin of Axial Prestretch and Residual Stress in Arteries
,”
Biomech. Model. Mechanobiol.
,
8
(
6
), pp.
431
446
.10.1007/s10237-008-0146-x
8.
Humphrey
,
J. D.
,
Eberth
,
J. F.
,
Dye
,
W. W.
, and
Gleason
,
R. L.
,
2009
, “
Fundamental Role of Axial Stress in Compensatory Adaptations by Arteries
,”
J. Biomech.
,
42
(
1
), pp.
1
8
.10.1016/j.jbiomech.2008.11.011
9.
Nürnberger
,
J.
,
Dammer
,
S.
,
Opazo Saez
,
A.
,
Philipp
,
T.
, and
Schäfers
,
R. F.
,
2003
, “
Diastolic Blood Pressure is an Important Determinant of Augmentation Index and Pulse Wave Velocity in Young, Healthy Males
,”
J. Hum. Hypertens.
,
17
(
3
), pp.
153
158
.10.1038/sj.jhh.1001526
10.
Willemet
,
M.
, and
Alastruey
,
J.
,
2015
, “
Arterial Pressure and Flow Wave Analysis Using Time-Domain 1-D Hemodynamics
,”
Ann. Biomed. Eng.
,
43
(
1
), pp.
190
206
.10.1007/s10439-014-1087-4
11.
Womersley
,
J. R.
,
1955
, “
XXIV. Oscillatory Motion of a Viscous Liquid in a Thin-Walled Elastic Tube—I: The Linear Approximation for Long Waves
,”
London Edinburgh Dublin Philos. Mag. J. Sci.
,
46
(
373
), pp.
199
221
.10.1080/14786440208520564
12.
Atabek
,
H. B.
,
1968
, “
Wave Propagation Through a Viscous Fluid Contained in a Tethered, Initially Stresses, Orthotropic Elastic Tube
,”
Biophys J.
,
8
(
5
), pp.
626
649
.10.1016/S0006-3495(68)86512-9
13.
Mirsky
,
I.
,
1967
, “
Wave Propagation in a Viscous Fluid Contained in an Orthotropic Elastic Tube
,”
Biophys. J..
7
(
2
), pp.
165
86
.10.1016/S0006-3495(67)86582-2
14.
Cox
,
R. H.
,
1969
, “
Comparison of Linearized Wave Propagation Models for Arterial Blood Flow Analysis
,”
J Biomech.
,
2
(
3
), pp.
251
265
.10.1016/0021-9290(69)90082-7
15.
Klip
,
W.
,
Van Loon
,
P.
, and
Klip
,
D. A.
,
1967
, “
Formulas for Phase Velocity and Damping of Longitudinal Waves in Thick-Walled Viscoelastic Tubes
,”
J. Appl. Phys.
,
38
(
9
), pp.
3745
3755
.10.1063/1.1710205
16.
Holzapfel
,
G. A.
, and
Ogden
,
R. W.
,
2010
, “
Constitutive Modelling of Arteries
,”
Proc. R. Soc. A.
,
466
(
2118
), pp.
1551
1597
.10.1098/rspa.2010.0058
17.
Humphrey
,
J. D.
,
2009
, “
Vascular Mechanics, Mechanobiology, and Remodeling
,”
J. Mech. Med. Biol.
,
09
(
02
), pp.
243
257
.10.1142/S021951940900295X
18.
Pinnington
,
R. J.
, and
Briscoe
,
A. R.
,
1994
, “
Externally Applied Sensor for Axisymmetric Waves in a Fluid Filled Pipe
,”
J. Sound Vib.
,
173
(
4
), pp.
503
516
.10.1006/jsvi.1994.1243
19.
Carew
,
T. E.
,
Vaishnav
,
R. N.
, and
Patel
,
D. J.
,
1968
, “
Compressibility of the Arterial Wall
,”
Circ. Res.
,
23
(
1
), pp.
61
68
.10.1161/01.RES.23.1.61
20.
Anliker
,
M.
,
Moritz
,
W. E.
, and
Ogden
,
E.
,
1968
, “
Transmission Characteristics of Axial Waves in Blood Vessels
,”
J. Biomech.
,
1
(
4
), pp.
235
246
.10.1016/0021-9290(68)90019-5
21.
Jagielska
,
K.
,
Trzupek
,
D.
,
Lepers
,
M.
,
Pelc
,
A.
, and
Zieliński
,
P.
,
2007
, “
Effect of Surrounding Tissue on Propagation of Axisymmetric Waves in Arteries
,”
Phys. Rev. E Stat. Nonlinear Soft Matter Phys.
,
76
(
6 Pt 2
), p.
066304
.10.1103/PhysRevE.76.066304
22.
Riley
,
W. A.
,
Barnes
,
R. W.
,
Evans
,
G. W.
, and
Burke
,
G. L.
,
1992
, “
Ultrasonic Measurement of the Elastic Modulus of the Common Carotid Artery
,” Atheroscler. Risk Commun. (
ARIC
) Study. Stroke,
23
(
7
), pp.
952
956
.10.1161/01.str.23.7.952
23.
Dobrin
,
P. B.
,
1978
, “
Mechanical Properties of Arteries
,”
Physiol. Rev.
,
58
(
2
), pp.
397
460
.10.1152/physrev.1978.58.2.397
24.
Patel
,
D. J.
,
Janicki
,
J. S.
,
Vaishnav
,
R. N.
, and
Young
,
J. T.
,
1973
, “
Dynamic Anisotropic Viscoelastic Properties of the Aorta in Living Dogs
,”
Circ. Res.
,
32
(
1
), pp.
93
107
.10.1161/01.RES.32.1.93
25.
Al-Jumaily
,
A.
, and
Lowe
,
A.
,
2013
, “
Accuracy of the Wave Equation in Predicting Arterial Pulse Propagation
,”
Math. Comput. Modell.
,
57
(
3–4
), pp.
460
468
.10.1016/j.mcm.2012.06.023
26.
Yu
,
X.
,
Wang
,
Y.
, and
Zhang
,
Y.
,
2018
, “
Transmural Variation in Elastin Fiber Orientation Distribution in the Arterial Wall
,”
J. Mech. Behav. Biomed. Mater.
,
77
, pp.
745
753
.10.1016/j.jmbbm.2017.08.002
27.
Li
,
D.
, and
Robertson
,
A. M.
,
2009
, “
A Structural Multi-Mechanism Constitutive Equation for Cerebral Arterial Tissue
,”
Int. J. Solids Struct.
,
46
(
14–15
), pp.
2920
2928
.10.1016/j.ijsolstr.2009.03.017
28.
Qureshi
,
M. U.
,
Colebank
,
M. J.
,
Schreier
,
D. A.
,
Tabima
,
D. M.
,
Haider
,
M. A.
,
Chesler
,
N. C.
, and
Olufsen
,
M. S.
,
2018
, “
Characteristic Impedance: Frequency or Time Domain Approach?
,”
Physiol. Meas.
,
39
(
1
), p.
014004
.10.1088/1361-6579/aa9d60
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