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 incompressible, so internal pressure changes translate to vessel wall dilation while total wall volume is conserved.
“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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“where Ep(stat) and E*Ut are, respectively, the pressure-strain elastic modulus (Peterson et al., 1960) and incremental isotropic elastic modulus previously defined (Bergel, 1961a; Gow and Taylor, 1968), VAP/AV(stat) VAP/AV(dyn) is the volume elasticity modulus (Gow, 1972) and y the ratio of vessel wall thickness to ou…”
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“, 1976; Alexander, 1954; Vatner and Braunwald, 1975), or in anesthetized animals (Bergel, 1972; McDonald, 1974; Pieper and Paul, 1969; Aars, 1971; Nicolosi and Pieper, 1971; Pagani et al., 1975; Patel and Vaishnav, 1972; Gow, 1972; Gow and Taylor, 1968; Cox, 1975; Gow, 1970; Alexander, 1954; Wiggers and Wegria, 1938;…”
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“-(23) We used the pulsatile change in the aortic luminal area instead of change in the diameter to calculate aortic strain, and therefore our data represent the volume elastic modulus per unit length of the aorta.(14) It is worth noting that although the pressurevolume and pressure-diameter relations reflect arterial…”
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Architecture of Small Arteries during Vasoconstriction
Citters, R. L. V., Wagner, B. M., & Rushmer, R. F. (1962) · Circulation Research · doi:10.1161/01.res.10.4.668 · Cited by 97 · see citing works
Kim, J., & Baek, S. (2011) · Journal of Biomechanics · doi:10.1016/j.jbiomech.2011.04.022 · Cited by 95 · see citing works
“Recent biomedical imaging studies, however, reported that the circumferential deformation and wall distension of the aorta during the cardiac cycle were non-uniform (Draney et al., 2002, 2004; van Prehn et al., 2009).”
Multi-layer approaches to scaffold-based small diameter vessel engineering: A review
Goins, A., Webb, A. R., & Allen, J. B. (2018) · Materials Science and Engineering C · doi:10.1016/j.msec.2018.12.067 · Cited by 95 · see citing works
Morphology and diameter of infrarenal aortic aneurysms: a prospective autopsy study
da Silva, E. S. (2000) · Cardiovascular Surgery · doi:10.1016/s0967-2109(00)00060-0 · Cited by 94 · see citing works
Segers, P., Fostier, G., Neckebroeck, J., & Verdonck, P. (1999) · Catheterization and Cardiovascular Interventions · doi:10.1002/(sici)1522-726x(199903)46:3 · Cited by 17 · see citing works
Arterial Elastic Properties and Cardiovascular Risk/Event
Cheng, K., Baker, C., Hamilton, G., et al. (2002) · European Journal of Vascular and Endovascular Surgery · doi:10.1053/ejvs.2002.1756 · Cited by 93 · see citing works
Biaxial anisotropy of dog carotid artery: Estimation of circumferential elastic modulus
Dobrin, P. B. (1986) · Journal of Biomechanics · doi:10.1016/0021-9290(86)90011-4 · Cited by 92 · see citing works
Barletta, G., Feo, M. L. D., Bene, R. D., Lazzeri, C., Vecchiarino, S., Villa, G. L., Brandi, M. L., & Franchi, F. (2000) · The Journal of Clinical Endocrinology & Metabolism · doi:10.1210/jcem.85.5.6514 · Cited by 96 · see citing works
“Arterial pressure was used to calculate: 1) the arterial elastic modulus (EM): EM 5 {[(SBP-DBP)/(sD-dD)]zdD}, ( 22 ); and 2) the index of arterial stiffness (SI): SI 5 ln (SBP/DBP) * (sD-dD)/dD (23), where SBP and DBP are systolic and diastolic blood pressure, respectively.”
MethodOoi, C. Y., Wang, Z., Tabima, D. M., et al. (2010) · American Journal of Physiology-Heart and Circulatory Physiology · doi:10.1152/ajpheart.00493.2009 · Cited by 91 · see citing works
“The arteries were assumed to be at a fixed length, homogeneous, and incompressible (20, 21, 36).”
BackgroundGeorgakopoulos, D., Little, W. C., Abraham, W. T., Weaver, F. A., & Zile, M. R. (2010) · Journal of Cardiac Failure · doi:10.1016/j.cardfail.2010.09.004 · Cited by 90 · see citing works
Vascular Stiffening in Pulmonary Hypertension: Cause or Consequence? (2013 Grover Conference Series)
Tan, W., Madhavan, K. P. C., Hunter, K. S., Park, D., & Stenmark, K. R. (2014) · Pulmonary Circulation · doi:10.1086/677370 · Cited by 89 · see citing works
Giltay, E. J., Lambert, J., Elbers, J. M. H., Gooren, L. J., Asscheman, H., & Stehouwer, C. D. A. (1999) · Diabetologia · doi:10.1007/s001250051141 · Cited by 89 · see citing works
“The DC and the CC were calculated from the arterial diameter (D), the change in arterial diameter during the heart cycle (dD) and pulse pressure (dP) as follows: DC = (2*dD)/ (D*dP) and CC = (p*dD*D)/(2*dP) [29, 31, 32].”
MethodDynamic Anisotropic Viscoelastic Properties of the Aorta in Living Dogs
PATEL, D. J., Janicki, J. S., Vaishnav, R. N., et al. (1973) · Circulation Research · doi:10.1161/01.res.32.1.93 · Cited by 88 · see citing works
Peluso, G., Petillo, O., Anderson, J. M., Ambrosio, L., Nicolais, L., Melone, M. A. B., Eschbach, F. O., & Huang, S. J. (1997) · Journal of Biomedical Materials Research · doi:10.1002/(sici)1097-4636(19970305)34:3 · Cited by 53 · see citing works
- 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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