Comparative Physiology

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


To compare parameters in different mammals we make use of the so-called allometric equation: PA = PA0 Me, with PA the parameter of interest, PA0 a reference value, M body mass, and e the exponent. The RpC-time of aortic pressure decay in diastole, and heart period, Tperiod, both scale as M1/4, their ratio thus being independent of body mass and thus similar in mammals. Volume parameters such a heart size and Stroke Volume, SV, are proportional to body mass. Since CO equals HR times SV, CO is proportional to M3/4. Basal metabolism is proportional to CO, and thus also proportional to M3/4. The coupling parameters (Chap. 14 and 31) are independent of body mass. The ratio of peripheral resistance and aortic characteristic impedance is also independent of animal size, implying that normalized aortic input impedance is similar in mammals. These mass-independent relations imply that wave shapes of pressure and flow are similar, pressures equal, but CO=CO0M3/4 and Basal Metabolism, BMr=BMr0M3/4, depend on body mass. The quantitative similarity of pressures in mammals suggest that even borderline hypertension is abnormal.


Allometry Coupling parameters Pressure Stroke Volume Cardiac Output Heart Rate 


  1. 1.
    Schmidt-Nielsen K. Scaling. Why is animal size so important? vol. 57. London/New York: Cambridge Univ Press; 1984.CrossRefGoogle Scholar
  2. 2.
    Kleiber M. Body size and metabolic rate. Physiol Rev. 1947;27:511–41.CrossRefPubMedGoogle Scholar
  3. 3.
    Dubois D, Dubois EF. A formula to estimate the approximate surface area if height and weight be known. Arch Int Med. 1961;17:867–71.Google Scholar
  4. 4.
    Takai S, Shimaguchi S. Are height and weight sufficient for the estimation of human body surface area? Hum Biol. 1986;58:625–38.PubMedGoogle Scholar
  5. 5.
    White CR, Seymour RS. The role of gravity in the evolution of mammalian blood pressure. Evolution. 2014;68:901–8.CrossRefPubMedGoogle Scholar
  6. 6.
    White CR, Seymour RS. Mammalian basal metabolic rate is proportional to body mass2/3. Proc Natl Acad Sci U S A. 2003;100:4046–9.CrossRefPubMedPubMedCentralGoogle Scholar
  7. 7.
    Holt JP, Rhode EA, Kines H. Ventricular volumes and body weight in mammals. Am J Phys. 1968;215:704–14.Google Scholar
  8. 8.
    Altman PL, Dittmer DE (eds). Biological handbook. Bethesda, Fed Am Soc Exptl Biol. pp. 278, 320, 336–341; 1971.Google Scholar
  9. 9.
    Westerhof N, Elzinga G. Normalized input impedance and arterial decay time over heart period are independent of animal size. Am J Phys. 1991;261:R126–33.Google Scholar
  10. 10.
    Smulyan H, Marchais SJ, Pannier B, Guerin AP, Safar ME, London GM. Influence of body height on pulsatile hemodynamic data. J Am Coll Cardiol. 1998;31:1103–9.CrossRefGoogle Scholar
  11. 11.
    Savage VM, Deeds EJ, Fontana W. Sizing up allometric scaling theory. PLoS Comput Biol. 2008;4(9):e1000171.CrossRefPubMedPubMedCentralGoogle Scholar
  12. 12.
    Kumar NT, Liestøl K, Løberg EM, Reims HM, Mæhlen J. Postmortem heart weight: relation to body size and effects of cardiovascular disease and cancer. Cardiovasc Pathol. 2014;23:5–11.CrossRefPubMedGoogle Scholar
  13. 13.
    Elzinga G, Westerhof N. Matching between ventricle and arterial load. Circ Res. 1991;68:1495–500.CrossRefPubMedGoogle Scholar
  14. 14.
    Senzaki H, Chen C-H, Kass DA. Single beat estimation of end-systolic pressure-volume relation in humans: a new method with the potential for noninvasive application. Circulation. 1996;94:2497–506.CrossRefPubMedGoogle Scholar
  15. 15.
    West GB, Woodruff WH, Brown JH. Allometric scaling of metabolic rate from molecules and mitochondria to cells and mammals. PNAS. 2002;99:2473–8.CrossRefPubMedGoogle Scholar
  16. 16.
    Barth E, Stämler G, Speiser B, Schaper J. Ultrastructural quantification of mitochondria and myofilaments in cardiac muscle from 10 different animal species including man. J Mol Cell Cardiol. 1992;24:669–81.CrossRefPubMedGoogle Scholar
  17. 17.
    Dobson GP. On being the right size: heart design, mitochondrial efficiency and lifespan potential. Clin Exp Pharmacol Physiol. 2003;30:590–7.CrossRefPubMedGoogle Scholar
  18. 18.
    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
  19. 19.
    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
  20. 20.
    Martyn CN, Greenwald SE. Impaired synthesis of elastin in walls of aorta and large conduit arteries during early development as an initiating event in pathogenesis of systemic hypertension. Lancet. 1997;3502:953–5.CrossRefGoogle Scholar
  21. 21.
    Millar JS, Zammuto RM. Life histories of mammals: an analysis of life tables. Ecology. 1983;64:631–5.CrossRefGoogle Scholar
  22. 22.
    Levine HJ. Rest heart rate and life expectancy. J Am Coll Cardiol. 1997;30:1104–6.CrossRefPubMedGoogle Scholar
  23. 23.
    Gent S, Kleinbongard P, Dammann P, Neuhäuser M, Heusch G. Heart rate reduction and longevity in mice. Basic Res Cardiol. 2015;110:1–9.CrossRefGoogle Scholar
  24. 24.
    Samaras TT, Elrick H, Storms LH. Is height related to longevity? Life Sci. 2003;72:1781–802. Review.CrossRefPubMedGoogle Scholar
  25. 25.
    Reeve JC, Abhayaratna WP, Davies JE, Sharman JE. Central hemodynamics could explain the inverse association between height and cardiovascular mortality. Am J Hypertens. 2014;27:392–400.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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