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Mechanical Properties of Arteries in Vivo
Abstract
Methods have been assembled permitting the simultaneous recording of intra-arterial pressure and arterial diameter with sufficient accuracy so that the mechanical properties of arteries in vivo, under physiologic conditions, can be derived. The analysis necessitates finding the relationships between 5 simultaneous variables; hence the data were recorded on magnetic tape and processed by analog and digital computer technics. Analysis of the data established the fact that the mechanical properties of arteries can be described by a linear, first-order differential equation whose coefficients can be defined as the moduli of elasticity and viscosity. Furthermore, the magnitudes of the coefficients were evaluated. The strain which the arteries undergo as a result of arterial pulse pressure variations is normally between 0.01 and 0.04, i.e., between 1 and 4 per cent change in circumference. The total strain associated with marked constriction and dilation does not usually exceed 10 per cent. Therefore, it is established that the circumferential motion of arteries may be characterized as small strain. The fact that the strain is effectively small is confirmed by analytical consideration, i.e., stress-strain relationships can be linearized under physiologic conditions without introducing significant error. The mass of the artery wall does not play a significant role in determining the mechanical behavior of the arteries and can therefore be neglected in any such considerations. The harmonic content, i.e., the frequency spectrum, comprising the pressure and diameter pulsations associated with the cardiac cycle have been evaluated by Fourier analysis. The magnitudes of the coefficients relating pressure and strain are: elastic (E p ) varies from 1,000 to 6,000 Gm./cm. 2 (with the exception of a value of 500 in the thoracic aorta of a 12-week-old puppy), viscous (R p ) from 10 to 150, and mass (M p ) from 0.0002 to 0.005. The magnitudes of the coefficients vary from individual to individual, from one site to another within the vascular tree and temporally in response to vasoactive factors. The effects of epinephrine, norepinephrine, acetylcholine and autonomic nerve stimulation on the mechanical properties and behavior of arteries are discussed. The differences between the pressure-strain relationships and the wall tension-strain relationships are discussed, since the mechanical properties of the wall material itself is not given directly by the pressure-strain relationships, i.e., radius and wall thickness must be considered. An analytical discussion is developed and mathematical equations are derived which relate pressure, wall tension, radius, strain, elasticity, viscosity and inertia in a tube which has been shown to be a reliable model of the living artery. It is concluded that the concept that the arteries function as a "peripheral heart," i.e., rhythmically contract in synchrony with the heart, is not justified. Probable relationships of these properties to the structure and functions of the arterial system are discussed.
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“The arterial wall is often treated as incompressible44,51, pressure changes applied internally translates to vessel wall dilation, but the total wall volume is conserved.”
From Synthetic photoplethysmography (PPG) of the radial artery through parallelized Monte Carlo and its correlation to body mass index (BMI) (2021) · cites this paper as [44]
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“Since it is very often difficult to obtain correct values for the arterial wall thickness, a pressure-strain elastic modulus, also called Peterson’s elastic modulus, Ep was introduced by Petersen (Peterson et al. 1960), Ep = Dd Ps − Pd Ds − Dd (2) where (Ps −Pd) and (Ds −Dd) are pulse pressure and pulse diameter, resp…”
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“For the purpose of early detection of arteriosclerosis, the method for measuring the elastic modulus of carotid artery by observing the systaltic movement of carotid artery in ultrasonic echo images has been proposed [ 1-5 ].”
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“[15] Indices of structural stiffness are descriptors of the overall stiffness of the wall of an artery, and describe the elastic behavior of the whole arterial wall at the point of measurement, such as the pressure strain elastic modulus (Ep).[16] Indices of material stiffness describe the physical properties of the s…”
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“The Ep was calculated as DP Dd/DD as described by Peterson et al.8 Doppler examination was performed at the same site as the B-flow examination.”
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“…between measurements varying from a few seconds to about 1 min, and the mean pressure strain elastic modulus (Ep) was calculated as described by Peterson et al. (1960): Ep ¼ KDdiastðSAP DAPÞ=ðDsyst DdiastÞ; where Dsyst and Ddiast denote systolic and end-diastolic lumen diameters and K denotes…”
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“Peterson has described the modulus of elasticity or tension per unit of wall thickness as the most important physiological measure (Peterson et al., 1960).”
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Vascular Elasticity from Regional Displacement Estimates
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“In this study, the pressure strain elastic modulus propounded by (Peterson et al., 1960), which is easy to manipulate, is used.”
Methodİnci, S., Nar, G., Erol, M. K., et al. (2014) · Echocardiography · doi:10.1111/echo.12799 · Cited by 3
“Aortic stiffness is a measure of the dilatation ability of the aortic wall against the pulse pressure.(2,3) Impaired endothelial function increases aortic stiffness, which is an independent risk factor for cardiovascular mortality(4,5); therefore, an increase in aortic stiffness was recently acknowledged to be a risk…”
BackgroundThe functional limits of the aneurysmal aortic root. A unique pressure testing apparatus
Surman, T. L., Abrahams, J. M., O’Rourke, D., et al. (2020) · Journal of Cardiothoracic Surgery · doi:10.1186/s13019-020-01288-8 · Cited by 3
Yamakoshi, T., Rolfe, P. J., Kamiya, A., & Yamakoshi, K.-I. (2021) · Medical & Biological Engineering & Computing · doi:10.1007/s11517-021-02391-1 · Cited by 3
Metadata
- Authors
- PETERSON, L. H., JENSEN, R. E., & PARNELL, J.
- Affiliations
- University of Pennsylvania (US)
- Venue
- Circulation Research
- Published
- 1960-05
- Volume
- 8
- Issue
- 3
- Pages
- 622-639
- ISSN
- 0009-7330 (ISSN-L)
- 1524-4571
- OpenAlex
- W2091983820
- Cited by
- 679
- References
- 0
- Citations by year
- 2026: 1 · 2025: 6 · 2024: 5 · 2023: 8 · 2022: 6 · 2021: 12 · 2020: 10 · 2019: 12 · 2018: 9 · 2017: 10 · 2016: 5 · 2015: 11 · 2014: 15 · 2013: 17 · 2012: 18
- FWCI
- 16.92
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Circulation Research (publishedVersion)
- Funders
- University of Pennsylvania
- Topics
- Physical Sciences › Engineering › Biomedical Engineering › Elasticity and Material Modeling
- Health Sciences › Medicine › Cardiology and Cardiovascular Medicine › Cardiovascular Health and Disease Prevention
- Physical Sciences › Engineering › Biomedical Engineering › Non-Invasive Vital Sign Monitoring
- Keywords
- arterial wall mechanics, arterial diameter, pulse pressure, elastic modulus, viscous damping, first-order differential equations, wall tension, epinephrine, norepinephrine, acetylcholine, autonomic nerve stimulation, vasoactive factors, thoracic aorta
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Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
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