• Nicolaas Westerhof
  • Nikolaos Stergiopulos
  • Mark I. M. Noble
  • Berend E. Westerhof


When the transmural or distending pressure of an organ is increased, the volume increases. For biological organs the relation between transmural pressure and volume is, in general, not straight but convex to the volume axis, implying that, Compliance C = ΔV/ΔP, and Elastance, inverse of compliance, depend on pressure or volume. When organs of different size are to be compared we can normalize both C and E with respect to volume. These normalized descriptions are distensibility, and bulk modulus or volume elasticity, respectively. When cross-sectional area is measured, as is often done in blood vessels, we derive’area compliance’ and ‘area elastance’, where luminal area A replaces volume V. The rules for addition of compliances and elastances are discussed.


Compliance Elastance Distensibility Bulk modulus Volume elasticity Area compliance 


  1. 1.
    Baan J, van der Velde ET, de Bruin HG, Smeenk GJ, Koops J, van Dijk AD, et al. Continuous measurement of left ventricular volume in animals and humans by conductance catheter. Circulation. 1984;70:812–23.CrossRefPubMedGoogle Scholar
  2. 2.
    Hoeks AP, Brands PJ, Reneman RS. Assessment of the arterial distension waveform using Doppler signal processing. J Hypertens Suppl. 1992;10:S19–22.CrossRefPubMedGoogle Scholar
  3. 3.
    Peterson LH, Jensen RE, Parnell J. Mechanical properties of arteries in vivo. Circ Res. 1960;8:622–39.CrossRefGoogle Scholar
  4. 4.
    Hayashi K, Handa H, Nagasawa S, Okumura A, Moritake K. Stiffness and elastic behavior of human intracranial and extracranial arteries. J Biomech. 1980;13:175–84.CrossRefGoogle Scholar
  5. 5.
    Spronck B, Avolio AP, Tan I, Butlin M, Reesink KD, Delhaas T. Arterial stiffness index beta and cardio-ankle vascular index inherently depend on blood pressure but can be readily corrected. J Hypertens. 2017;35:98–104.CrossRefPubMedGoogle Scholar
  6. 6.
    Langewouters GJ, Wesseling KH, Goedhard WJ. The static elastic properties of 45 human thoracic and 20 abdominal aortas in vitro and the parameters of a new model. J Biomech. 1984;17:425–35.CrossRefPubMedGoogle Scholar
  7. 7.
    Fung YC. Biomechanics. mechanical properties of living tissues. New York & Heidelberg: Springer; 1981.Google Scholar
  8. 8.
    Love AEH. A treatise on the mathematical theory of elasticity. 4th ed. Cambridge: Cambridge University Press; 1952.Google Scholar
  9. 9.
    Randall OS, van den Bos GC, Westerhof N. Systemic compliance: does it play a role in the genesis of essential hypertension? Cardiovasc Res. 1984;18:455–62.CrossRefPubMedGoogle Scholar
  10. 10.
    Ioannou CV, Morel DR, Katsamouris AN, Katranitsa S, Startchik I, Kalangos A, et al. Left ventricular hypertrophy induced by reduced aortic compliance. J Vasc Res. 2009;46:417–25.CrossRefPubMedGoogle Scholar
  11. 11.
    Benetos A, Safar M, Rudnichi A, Smulyan H, Richard JL, Ducimetieere P, et al. Pulse pressure: a predictor of long-term cardiovascular mortality in a French male population. Hypertension. 1997;30:1410–5.CrossRefPubMedGoogle Scholar
  12. 12.
    Mitchell GF, Moye LA, Braunwald E, Rouleau JL, Bernstein V, Geltman EM, et al. Sphygmomanometrically determined pulse pressure is a powerful independent predictor of recurrent events after myocardial infarction in patients with impaired left ventricular function. Circulation. 1997;96:4254–60.CrossRefPubMedGoogle Scholar
  13. 13.
    Kawaguchi M, Hay I, Fetics B, Kass DA. Combined ventricular systolic and arterial stiffening in patients with heart failure and preserved ejection fraction: implications for systolic and diastolic reserve limitations. Circulation. 2003;107:714–20.CrossRefPubMedGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2019

Authors and Affiliations

  • Nicolaas Westerhof
    • 1
  • Nikolaos Stergiopulos
    • 2
  • Mark I. M. Noble
    • 3
  • Berend E. Westerhof
    • 1
  1. 1.Department of Pulmonary Diseases, Amsterdam Cardiovascular SciencesVU University Medical CenterAmsterdamThe Netherlands
  2. 2.Laboratory of Hemodynamics and Cardiovascular TechnologyEcole Polytechnique Fédérale de Lausanne (EPFL), Institute of BioengineeringLausanneSwitzerland
  3. 3.Cardiovascular Medicine, Department of Medicine and TherapeuticsUniversity of AberdeenAberdeenUnited Kingdom

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