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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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A STRUCTURE-MOTIVATED MODEL OF THE PASSIVE MECHANICAL RESPONSE OF THE PRIMARY PORCINE RENAL ARTERY
Zhou, B., Wolf, L. M., Rachev, A., et al. (2013) · Journal of Mechanics in Medicine and Biology · doi:10.1142/s021951941450033x · Cited by 21
Reduction of coronary flow reserve in patients with increased aortic stiffness
Nemes, A., Forster, T., & Csanády, M. (2007) · Canadian Journal of Physiology and Pharmacology · doi:10.1139/y07-075 · Cited by 21
“Ep was calculated by using the following formula: Ep = (SBP–DBP)/ [(Ds–Dd)/Dd], where SBP is the systolic blood pressure and DBP is the diastolic blood pressure (Peterson et al. 1960).”
MethodA Novel Integrated Rotor of Axial Blood Flow Pump Designed With Computational Fluid Dynamics
Zhang, Y., Xue, S., Gui, X., et al. (2007) · Artificial Organs · doi:10.1111/j.1525-1594.2007.00425.x · Cited by 21
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“Assuming a second-order differential equation to characterize wall dynamics, the frequency response of (5) would be [26]:”
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Control of Vascular Contractility by the Cardiac Pacemaker
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“: M01 This definition of cyclic circumferential strain assumes the diameter at end diastole is the unloaded reference dimension. It also characterizes deformations independent of rigid body motion and takes into account the nonlinear terms that are ignored when using a small deformation assumption. Aortic circumferent…”
BackgroundBiomechanics of Blood Vessels: Structure, Mechanics, and Adaptation
MATSUMOTΟ, T., Sugita, S., & Yaguchi, T. (2015) · Springer series in biomaterials science and engineering · doi:10.1007/978-3-662-46836-4_4 · Cited by 20
“The pressure strain elastic modulus, Ep, presenting stiffness of blood vessel can be expressed by the following equation [18]:”
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“Such a decrease in arterial stiffness can be separated in a geometry-dependent and –independent component (30).”
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Papageorgiou, G. L., & Jones, N. B. (1988) · Journal of Biomedical Engineering · doi:10.1016/0141-5425(88)90031-3 · Cited by 19
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A model for the dynamic mechanical properties of arteries
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Influence of fibrillin-1 genotype on the aortic stiffness in men
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Relation between the elastic properties and intima‐media thickness of the common carotid artery
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“…properties of the common carotid artery wall were estimated by calculating the pressure strain elastic modulus (Ep) and stiffness (b) according to Peterson et al. (1960) and Kawasaki et al. (1987): Ep ¼ KDdiastðPsyst PdiastÞðDsyst DdiastÞ 1 ð1Þ Stiffness ðbÞ ¼ Ddiastðln Psyst ln PdiastÞðDsyst…”
Conformational stress and anastomotic hyperplasia.
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Das Verhalten peripherer Blutgefäße in vivo bei passiven und aktiven Weitenänderungen
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A Soft Sensorized Microfluidic Tubular Actuating Gripper
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RetractedArtery Wall Viscoelasticity: Measurement, Assessment, and Clinical Implications
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“Peterson et al.”
MethodInfluentialAuricchio, F., Conti, M., Ferrara, A., & Lanzarone, E. (2015) · IEEE Transactions on Biomedical Engineering · doi:10.1109/tbme.2014.2343673 · Cited by 16
“The so-called Peterson modulus [29] and Young modulus [30] are the two stiffness indexes considered in this study.”
BackgroundEvaluation of an algorithm for arterial lumen diameter measurements by means of ultrasound
Cinthio, M., Jansson, T. T., Eriksson, A., Ahlgren, Å. R., Persson, H. W., & Lindström, K. (2010) · Medical & Biological Engineering & Computing · doi:10.1007/s11517-010-0660-8 · Cited by 18
“Examples of methods where these methods are crucial include arterial characterization using calculation of arterial stiffness [1, 2, 15, 19 ], as well as volume flow measurements using Doppler techniques [27].”
MethodKatsuda, S.-I., Takazawa, K., Miyake, M., et al. (2014) · Hypertension Research · doi:10.1038/hr.2014.96 · Cited by 18
Noninvasive measurement of aortic pressure waveform by ultrasound
Watanabe, H., Kawai, M., Sibata, T., Hara, M., Furuhata, H., & Mochizuki, S. (1998) · Heart and Vessels · doi:10.1007/bf01744590 · Cited by 18
“In the 1960s, it was discovered that vascular diameter pulse waveforms agreed well with the intravascular pressure waveforms in animal invasive experiments [16].”
BackgroundOn the elastic properties of arteries
Stephanis, C. G., Mourmouras, D. E., & Tsagadopoulos, D. G. (2003) · Journal of Biomechanics · doi:10.1016/s0021-9290(03)00188-x · Cited by 18
“The error from measurements in vivo can be as high as 100% (Peterson et al., 1960; Rutherford, 1995), a fact that causes propagation of the error in the calculation of E: This is the reason why many researchers use simpler equations that do not employ thickness h (Burton, 1951).”
Forearm arterial pressure-volume relationships in man
Gizdulich, P., & Wesseling, K. H. (1988) · Clinical Physics and Physiological Measurement · doi:10.1088/0143-0815/9/2/004 · Cited by 18
Gade, J.-L., Stålhand, J., & Thore, C. (2019) · Computer Methods in Biomechanics & Biomedical Engineering · doi:10.1080/10255842.2018.1561878 · Cited by 17
“…the medical community and different measures have been introduced to determine mechanical properties of arteries in vivo, e.g. the pressurestrain elastic modulus (Ep) (Peterson et al. 1960), the stiffness index (b) (Kawasaki et al. 1987) and the pulse wave velocity (PWV) (Bramwell and Hill 1922).”
BackgroundArterial viscoelasticity: a fractional derivative model
Craiem, D. O., & Armentano, R. L. (2006) · Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC) · doi:10.1109/iembs.2006.259709 · Cited by 18
“The phase response attaining 0.3 rad for higher frequencies resulted similar to some measurements [ 3 ] although a little higher from others [19].”
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Relative Contributions of Age and Atherosclerosis to Vascular Stiffness
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A photoelectric diameter gauge utilizing the image sensor
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Experimental system forex vivomeasurement of murine aortic stiffness
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Hysteretic behavior of soft living animal tissue
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Predicting the compliance of small diameter vascular grafts from uniaxial tensile tests
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Expiratory flow rates, driving pressures and time-dependent factors. Simulation by means of a model
Clément, J., Pardaens, J., & de Woestijne, K. P. V. (1974) · Respiration Physiology · doi:10.1016/0034-5687(74)90032-2 · Cited by 16
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“The pressurestrain moduli (EP) (2, 12) were also calculated at 100 mm Hg for both series A and B; the mean static moduli were 5.”
BackgroundMethodResultWang, Y. L., Sze, W. K., Lin, C.-C., et al. (2015) · Journal of Biomechanics · doi:10.1016/j.jbiomech.2015.02.026 · Cited by 15
“Latex tubes (Qualatex, Australia) with a Peterson's modulus EP ¼ Rð∂P=∂RÞ (Peterson et al., 1960) value of 0.6 105 Nm–2, an inner diameter of 11.38 mm, wall Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/jbiomech www.JBiomech.com Journal of Biomechanics http://dx.doi.org/10.1016/j.…”
BackgroundInfluentialCui, M., Dong, X., Zhuang, Y., et al. (2024) · Bioengineering · doi:10.3390/bioengineering11040306 · Cited by 15
Subclinical arterial stiffness in young children after Kawasaki disease
Oguri, M., Nakamura, T., Tamanuki, K., Akita, C., 北岡, 千., Saikawa, Y., & Takahashi, M. (2013) · Cardiology in the Young · doi:10.1017/s1047951112002302 · Cited by 15
“This may indicate a similarity to the pressure-elastic modulus, which also reflects a change in the vessel diameter relative to blood pressure.(11) With regard to the peak systolic strain and late systolic strain rate, we found significant differences in the degree of arteriosclerosis between the Kawasaki disease and…”
ResultFatigue and endurance of coronary stents
Weiß, S., Szymczak, H., & Meißner, A. (2009) · Materialwissenschaft und Werkstofftechnik · doi:10.1002/mawe.200800409 · Cited by 15
A study of solitary waves in a tapered aorta by using the theory of solitons
Misra, J. C., & Patra, M. K. (2007) · Computers & Mathematics with Applications · doi:10.1016/j.camwa.2006.12.025 · Cited by 15
Ahlgren, Å. R., Sundkvist, G., Sandgren, T., et al. (2002) · Clinical Physiology and Functional Imaging · doi:10.1046/j.1475-097x.2002.00451.x · Cited by 15
“We also calculated Ep, defined according to Peterson et al. (1960) as: Ep ¼ K Psystolic PdiastolicðDsystolic DdiastolicÞ=Ddiastolic Ep is measured in N m)2.”
MethodIn Situ Mechanical Characterization of Multilayer Soft Tissue Using Ultrasound Imaging
Dargar, S., Akyildiz, A. C., & De, S. (2016) · IEEE Transactions on Biomedical Engineering · doi:10.1109/tbme.2016.2644651 · Cited by 15
“mogenous material have also been performed on the intestines [14]–[16], skin [17]–[21], and arteries [22]–[26].”
BackgroundChanges in pulse wave velocity with age in man: a longitudinal series over 20 years
Monnier, M. (1987) · Cellular and Molecular Life Sciences · doi:10.1007/bf01940417 · Cited by 15
Brodszki, J., Länne, T., Stale, H., et al. (2002) · BJOG An International Journal of Obstetrics & Gynaecology · doi:10.1111/j.1471-0528.2002.01315.x · Cited by 15
“Age (years) 32 [4] 29 [3] 0.02 Height (cm) 166.7 [3.3] 167.2 [5.7] SBP (mmHg)* 111 [ 13 ] 107 [10] DBP (mmHg)* 68 [6] 59 [6] 0.003 Mean arterial pressure (mmHg) 82 [10] 75 [5] 0.01”
InfluentialSystems Behavior, Feed-back Loops, and High Blood Pressure Research
Peterson, L. H. (1963) · Circulation Research · doi:10.1161/01.res.12.5.585 · Cited by 15
Self-citationAbnormal Wall Strain at Distal End-to-Side Anastomoses
Pevec, W. C., L'Italien, G. J., Megerman, J. J., et al. (1993) · Annals of Vascular Surgery · doi:10.1007/bf02042654 · Cited by 15
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Lydrup, M., & Fernö, M. (2003) · Acta Obstetricia Et Gynecologica Scandinavica · doi:10.1034/j.1600-0412.2003.00209.x · Cited by 15
“cantly higher distensibility of the thoracic aorta than of the abdominal aorta in vivo (25).”
BackgroundConformational stress and anastomotic hyperplasia
Pomposelli, F. B., Schoen, F. J., Cohen, R. A., et al. (1984) · Journal of Vascular Surgery · doi:10.1016/0741-5214(84)90038-7 · Cited by 15
Photoelectric device for contact-free recording of the diameters of exposed arteries in situ
Wetterer, E., Busse, R., Bauer, R. D., et al. (1977) · Pflügers Archiv - European Journal of Physiology · doi:10.1007/bf01063468 · Cited by 15
“A variety of methods for the continuous measurement of vascular diameter have been developed but most of the devices involve mechanical contact between the measuring gauge and the wall of the exposed vessel [1,9-13].”
BackgroundRathod, M., Ahn, J., Saha, B., Purwar, P., Lee, Y., Jeon, N. L., & Lee, J. (2018) · ACS Applied Materials & Interfaces · doi:10.1021/acsami.8b12309 · Cited by 14
Computational Simulations for Infrared Laser Sealing and Cutting of Blood Vessels
Giglio, N. C., & Fried, N. M. (2020) · IEEE Journal of Selected Topics in Quantum Electronics · doi:10.1109/jstqe.2020.3045912 · Cited by 14
“inverse Poisson ratio of 2 [33], and a tensile strength of 0.”
BackgroundBiomechanical Study of the Bile Duct System Outside the Liver
Jian, C., & Wang, G. (1991) · Bio-Medical Materials and Engineering · doi:10.3233/bme-1991-1203 · Cited by 14
Nemes, A., Forster, T., & Csanády, M. (2007) · Heart and Vessels · doi:10.1007/s00380-006-0939-8 · Cited by 14
“The elastic modulus [E(p)] and Young’s circumferential static elastic modulus [E(s)] of thoracic descending aorta can be determined during a routine transesophageal echocardiography (TEE) examination by measuring the aortic parameters and blood pressure data.(1,2) The coronary fl ow velocity reserve (CFVR) measured by…”
BackgroundMethodAnatomical and Physiological Characteristics of Arteries
Wolf, S., & Werthessen, N. T. (1979) · Advances in experimental medicine and biology · doi:10.1007/978-1-4684-7508-1_1 · Cited by 14
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Assessment of Arterial Compliance by Carotid Midwall Strain-Stress Relation in Hypertension
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IN VIVO ESTIMATION OF ELASTIC CHARACTERISTICS OF THE ARTERIES IN THE LOWER EXTREMITIES OF MAN
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Two directional delayed compliance in the canine abdominal aorta
Bagshaw, J., & Attinger, F. M. L. (1972) · Cellular and Molecular Life Sciences · doi:10.1007/bf01923141 · Cited by 14
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Ultrasonography and Tonometry for the Assessment of Human Arterial Stiffness
Graeme, J., Katharine, D., Maureen, J. C., & Neil, D. (2012) · InTech eBooks · doi:10.5772/39193 · Cited by 15
“Peterson’s elastic modulus (Peterson et al., 1960), outlined in equation [4], is different from”
BackgroundTertiary blends of PAMAM/PEG/PEG tissue bioadhesives
Shah, A. H., Djordjevic, I., & Steele, T. W. J. (2019) · Journal of the mechanical behavior of biomedical materials/Journal of mechanical behavior of biomedical materials · doi:10.1016/j.jmbbm.2019.103405 · Cited by 12
A nonlinear multi-scale model for blood circulation in a realistic vascular system
Qohar, U. N. A., Munthe-Kaas, A. Z., Nordbotten, J. M., & Hanson, E. (2021) · Royal Society Open Science · doi:10.1098/rsos.201949 · Cited by 13
“The vessel elasticity parameters were chosen based on the mechanical properties of vessels around those sizes [21,27,28].”
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Noninvasive Ultrasound Techniques for the Assessment of Atherosclerosis in Coronary Artery Disease
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A Reproducibility Study of a TDI-Based Method to Calculate Indices of Arterial Stiffness
Claridge, M., Bate, G. R., Dineley, J., et al. (2007) · Ultrasound in Medicine & Biology · doi:10.1016/j.ultrasmedbio.2007.08.010 · Cited by 13
Mechanical behavior of polyurethane-based small-diameter vascular grafts
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Die Durchmesser-Druck-Beziehung des intakten Gef��gebietes der A. carotis communis von Katzen
Leitz, K. H., & Arndt, J. O. (1968) · Pflügers Archiv - European Journal of Physiology · doi:10.1007/bf00412418 · Cited by 13
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“Even though considerable ex vivo experimental data have accumulated over the years, they only provided biomechanical information of arterial diseases at one time-point, which is very limited for clinical applications for two reasons: (a) ex vivo arterial tissues isolated from the vascular tree might not represent the…”
BackgroundMethodThe Arterial Pulse: Vascular Biology, Vascular Function Testing, and Therapies
Zafari, A. M., Quyyumi, A. A., Halcox, J., & Rajagopalan, S. (2011) · Cardiology Research and Practice · doi:10.4061/2011/151428 · Cited by 12
Pressure-Dependent and Frequency Domain Characteristics of the Systemic Arterial System
Matonick, J. P., & Li, J. K.-J. (2001) · Cardiovascular Engineering An International Journal · doi:10.1023/a:1011535522042 · Cited by 12
Ifuku, H., Taniguchi, K., & Matsumoto, H. (1994) · European Journal of Applied Physiology · doi:10.1007/bf01094796 · Cited by 12
“between P and volume (Peterson et al. 1960), the resultant P changes have been found to have a considerable resemblance to the volume changes in the carotid artery (Robinson 1963).”
ResultComparative Models of Overall Circulatory Mechanics
SAGAWA, K. (1973) · Elsevier eBooks · doi:10.1016/b978-0-12-004903-5.50006-6 · Cited by 12
The acute effect of hyperglycaemia on vessel wall properties
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Increased aortic stiffness in patients with coronary artery ectasia
Koşar, F., Sıncer, İ., Aksoy, Y., Topal, E., & Cehreli, S. (2005) · Coronary Artery Disease · doi:10.1097/00019501-200512000-00008 · Cited by 11
Design and Fabrication of a Mechanically Matched Vascular Graft
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Continuous measurement of aortic radius changein vivo with an intra-aortic ultrasonic catheter
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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.
Statistics and arithmetic are recomputed, not judged.
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