Abstract

As compared with its radial wall displacement, axial wall displacement at the common carotid artery (CCA) carries independent clinical values, but its physical mechanisms are unclear. This study aims to investigate whether axial wall displacement at the CCA is solely from Young waves. A pulse wave propagation theory is utilized to identify two types of waves, Young waves, and Lamb waves, in an artery, and identifies two sources for axial wall displacement, wall shear stress and radial wall displacement gradient with a factor of the difference between axial and circumferential initial tension, which reveals the influence of axial initial tension on the waveform of axial wall displacement. Theoretical expressions are derived for calculating the waveforms of axial wall displacement and its two sources in the Young waves. With the measured pulsatile pressure and blood velocity at the CA of three healthy adults as the inputs, the waveforms of axial wall displacement in the Young waves are calculated at different values of axial initial tension and are found to greatly differ from their measured counterparts. As such, the Lamb waves may contribute to axial wall displacement at the CCA and the associated physical and physiological implications are discussed. Given the clinical values of axial wall displacement at the CCA, the Lamb waves may play a non-negligible role in determining arterial health and needs to be further studied for a comprehensive assessment of arterial wall mechanics.

References

1.
Smith
,
S. M.
,
Marin
,
J.
,
Adams
,
A.
,
West
,
K.
, and
Hao
,
Z.
,
2022
, “
Radial and Axial Motion of the Initially Tensioned Orthotropic Arterial Wall in Arterial Pulse Wave Propagation
,”
ASME J. Med. Diag.
,
5
(
2
), p.
021004
.10.1115/1.4053863
2.
Hao
,
Z.
,
2022
, “
Radial and Axial Displacement of the Initially-Tensioned Orthotropic Arterial Wall Under the Influence of Harmonics and Wave Reflection
,”
ASME J. Med. Diag.
,
5
(
4
), p.
041007
.10.1115/1.4054883
3.
Womersley
,
J. R.
,
1955
, “
XXIV. Oscillatory Motion of a Viscous Liquid in a Thin-Walled Elastic Tube—I: The Linear Approximation for Long Waves
,”
Lond. Edinb. Dublin Philos. Mag. J. Sci.
,
46
(
373
), pp.
199
221
.10.1080/14786440208520564
4.
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
5.
Mirsky
,
I.
,
1967
, “
Wave Propagation in a Viscous Fluid Contained in an Orthotropic Elastic Tube
,”
Biophys. J.
,
7
(
2
), pp.
165
186
.10.1016/S0006-3495(67)86582-2
6.
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. Matter Phys.
,
76
(
6
), p.
066304
.10.1103/PhysRevE.76.066304
7.
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
8.
Mitchell
,
G. F.
,
Hwang
,
S. J.
,
Vasan
,
R. S.
,
Larson
,
M. G.
,
Pencina
,
M. J.
,
Hamburg
,
N. M.
,
Vita
,
J. A.
,
Levy
,
D.
, and
Benjamin
,
E. J.
,
2010
, “
Arterial Stiffness and Cardiovascular Events: The Framingham Heart Study
,”
Circulation
,
121
(
4
), pp.
505
511
.10.1161/CIRCULATIONAHA.109.886655
9.
Willum-Hansen
,
T.
,
Staessen
,
J. A.
,
Torp-Pedersen
,
C.
,
Rasmussen
,
S.
,
Thijs
,
L.
,
Ibsen
,
H.
, and
Jeppesen
,
J.
,
2006
, “
Prognostic Value of Aortic Pulse Wave Velocity as Index of Arterial Stiffness in the General Population
,”
Circulation
,
113
(
5
), pp.
664
670
.10.1161/CIRCULATIONAHA.105.579342
10.
Sutton-Tyrrell
,
K.
,
Najjar
,
S. S.
,
Boudreau
,
R. M.
,
Venkitachalam
,
L.
,
Kupelian
,
V.
,
Simonsick
,
E. M.
,
Havlik
,
R.
, et al.,
2005
, “
Elevated Aortic Pulse Wave Velocity, a Marker of Arterial Stiffness, Predicts Cardiovascular Events in Well-Functioning Older Adults
,”
Circulation
,
111
(
25
), pp.
3384
3390
.10.1161/CIRCULATIONAHA.104.483628
11.
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. Imag.
,
36
(
5
), pp.
376
388
.10.1111/cpf.12240
12.
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
13.
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
14.
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
15.
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. Imag.
,
37
(
3
), pp.
305
313
.10.1111/cpf.12305
16.
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
17.
Ahlgren
,
Å. R.
,
Cinthio
,
M.
,
Steen
,
S.
,
Nilsson
,
T.
,
Sjöberg
,
T.
,
Persson
,
H. W.
, and
Lindström
,
K.
,
2012
, “
Longitudinal Displacement and Intramural Shear Strain of the Porcine Carotid Artery Undergo Profound Changes in Response to Catecholamines
,”
Am. J. Physiol. Heart Circ. Physiol.
,
302
(
5
), pp.
H1102
H1115
.10.1152/ajpheart.00470.2011
18.
Ahlgren
,
Å. R.
,
Steen
,
S.
,
Segstedt
,
S.
,
Erlöv
,
T.
,
Lindström
,
K.
,
Sjöberg
,
T.
,
Persson
,
H. W.
,
Ricci
,
S.
,
Tortoli
,
P.
, and
Cinthio
,
M.
,
2015
, “
Profound Increase in Longitudinal Displacements of the Porcine Carotid Artery Wall Can Take Place Independently of Wall Shear Stress: A Continuation Report
,”
Ultrasound Med. Biol.
,
41
(
5
), pp.
1342
1353
.10.1016/j.ultrasmedbio.2015.01.005
19.
Athaide
,
C. E.
,
Spronck
,
B.
, and
Au
,
J. S.
,
2022
, “
Physiological Basis for Longitudinal Motion of the Arterial Wall
,”
Am. J. Physiol. Heart Circ. Physiol.
,
322
(
5
), pp.
H689
H701
.10.1152/ajpheart.00567.2021
20.
Au
,
J. S.
,
Valentino
,
S. E.
,
McPhee
,
P. G.
, and
MacDonald
,
M. J.
,
2017
, “
Diastolic Carotid Artery Longitudinal Wall Motion is Sensitive to Both Aging and Coronary Artery Disease Status Independent of Arterial Stiffness
,”
Ultrasound Med. Biol.
,
43
(
9
), pp.
1906
1918
.10.1016/j.ultrasmedbio.2017.04.026
21.
Zahnd
,
G.
,
Vray
,
D.
,
Sérusclat
,
A.
,
Alibay
,
D.
,
Bartold
,
M.
,
Brown
,
A.
,
Durand
,
M.
,
Jamieson
,
L. M.
,
Kapellas
,
K.
,
Maple-Brown
,
L. J.
,
O'Dea
,
K.
,
Moulin
,
P.
,
Celermajer
,
D. S.
, and
Skilton
,
M. R.
,
2012
, “
Longitudinal Displacement of the Carotid Wall and Cardiovascular Risk Factors: Associations With Aging, Adiposity, Blood Pressure and Periodontal Disease Independent of Cross-Sectional Distensibility and Intima-Media Thickness
,”
Ultrasound Med. Biol.
,
38
(
10
), pp.
1705
1715
.10.1016/j.ultrasmedbio.2012.05.004
22.
Hao
,
Z.
,
2023
, “
Relations of Radial Vibration of the Arterial Wall to Pulsatile Parameters in Blood Flow for Extraction of Arterial Indices
,”
ASME J. Med. Diag.
,
6
(
1
), p.
011002
.10.1115/1.4055390
23.
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
24.
Hao
,
Z.
,
2022
, “
Transmission Characteristics of Pulsatile Parameters in an Initially-Tensioned Orthotropic Artery
,” Paper No. 95078.
25.
Lucas
,
C. L.
,
Wilcox
,
B. R.
,
Ha
,
B.
, and
Henry
,
G. W.
,
1988
, “
Comparison of Time Domain Algorithms for Estimating Aortic Characteristic Impedance in Humans
,”
IEEE Trans. Biomed. Eng.
,
35
(
1
), pp.
62
68
.10.1109/10.1337
26.
Tat
,
J.
,
Au
,
J. S.
,
Keir
,
P. J.
, and
MacDonald
,
M. J.
,
2017
, “
Reduced Common Carotid Artery Longitudinal Wall Motion and Intramural Shear Strain in Individuals With Elevated Cardiovascular Disease Risk Using Speckle Tracking
,”
Clin. Physiol. Funct. Imag.
,
37
(
2
), pp.
106
116
.10.1111/cpf.12270
27.
Zambanini
,
A.
,
Cunningham
,
S. L.
,
Parker
,
K. H.
,
Khir
,
A. W.
,
McG Thom
,
S. A.
, and
Hughes
,
A. D.
,
2005
, “
Wave-Energy Patterns in Carotid, Brachial, and Radial Arteries: A Noninvasive Approach Using Wave-Intensity Analysis
,”
Am. J. Physiol. Heart Circ. Physiol.
,
289
(
1
), pp.
H270
H276
.10.1152/ajpheart.00636.2003
28.
Samijo
,
S. K.
,
Willigers
,
J. M.
,
Barkhuysen
,
R.
,
Kitslaar
,
P. J. E. H. M.
,
Reneman
,
R. S.
,
Brands
,
P. J.
, and
Hoeks
,
A. P. G.
,
1998
, “
Wall Shear Stress in the Human Common Carotid Artery as Function of Age and Gender
,”
Cardiovasc. Res.
,
39
(
2
), pp.
515
522
.10.1016/S0008-6363(98)00074-1
29.
Friis
,
L.
, and
Ohlrich
,
M.
,
2005
, “
Coupled Flexural-Longitudinal Wave Motion in a Finite Periodic Structure With Asymmetrically Arranged Transverse Beams
,”
J. Acoust. Soc. Am.
,
118
(
6
), pp.
3607
3618
.10.1121/1.2126928
30.
Yun
,
Y.
, and
Mak
,
C. M.
,
2009
, “
A Study of Coupled Flexural-Longitudinal Wave Motion in a Periodic Dual-Beam Structure With Transverse Connection
,”
J. Acoust. Soc. Am.
,
126
(
1
), pp.
114
121
.10.1121/1.3132706
31.
Wang
,
X.
, and
Mak
,
C.-M.
,
2012
, “
Wave Propagation in a Duct With a Periodic Helmholtz Resonators Array
,”
J. Acoust. Soc. Am.
,
131
(
2
), pp.
1172
1182
.10.1121/1.3672692
32.
Wang
,
D.
,
Vahala
,
L.
, and
Hao
,
Z.
,
2018
, “
Radial and Longitudinal Motion of the Arterial Wall: Their Relation to Pulsatile Pressure and Flow in the Artery
,”
Phys. Rev.
,
98
(
3
), p.
032402
.10.1103/PhysRevE.98.032402
33.
Humphrey
,
J. D.
,
2009
, “
Vascular Mechanics, Mechanobiology, and Remodeling
,”
J. Mech. Med. Biol.
,
9
(
2
), pp.
243
257
.10.1142/S021951940900295X
34.
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
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