Skip to main content

Cardiovascular Allometry: Analysis, Methodology, and Clinical Applications

  • Chapter
  • First Online:
Book cover Sex-Specific Analysis of Cardiovascular Function

Part of the book series: Advances in Experimental Medicine and Biology ((AEMB,volume 1065))

Abstract

The classic works of “On Growth and Form” and “The Problem of Relative Growth” that began a century ago have so fittingly, albeit unintentionally, become pertinent to the modern-day clinical treatment strategy of the many patients with cardiovascular disease. This chapter uses allometry, which was established for comparative biology, to explore physiological and pathological differences due to differential growth, which may lead to differing diagnostic and treatment approaches for male versus female patients. Men and women have obvious differences in body and heart weights, as well as different geometries and structures of their blood vessels; the analysis in this chapter extends to their hemodynamic functional differences. This includes dimensional analysis to establish criteria for characterizing functions based on allometric formulations. The clinical applications of sex differences are analyzed for arterial stenosis, aneurysm, atherosclerosis, hypertension, and coronary revascularization. Allometric approaches are applied specifically to isolated cases of systolic hypertension to delineate the intermingled relations of aging and sex differences. This chapter aims to provide some preliminary insights into the usefulness of cardiovascular allometry. Its future impact on clinical diagnosis remains largely unexplored.

Allometry. Artwork by Piet Michiels, Leuven, Belgium

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 189.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 249.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 329.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Allebeck P, Bergh C. Height, body mass index and mortality: do social factors explain the association? Public Health. 1992;106:375–82.

    Article  CAS  PubMed  Google Scholar 

  2. Berger DS, Li JK-J. Concurrent compliance reduction and increased peripheral resistance in the manifestation of isolated systolic hypertension. Am J Cardiol. 1990;65:67–71.

    Article  CAS  PubMed  Google Scholar 

  3. Berger D, Li JK-J, Laskey WK, Noordergraaf A. Repeated reflection of waves in the systemic arterial system. Am J Physiol (Heart & Circ Physiol). 1993;33(264):H269–81.

    Article  Google Scholar 

  4. Calder WA III. Size, function and life history. New York: Dover; 1996.

    Google Scholar 

  5. Caro CG. Discovery of the role of wall shear in atherosclerosis. Arterioscler Thromb Vasc Biol. 2009;29:158–61.

    Article  CAS  PubMed  Google Scholar 

  6. Caro CG, Fitzgerald JM, Schroter RC. Atheroma and arterial wall shear observation, correlation and proposal of a shear dependent mass transfer mechanism for altherogenesis. Proc R Soc Lond B. 1971;177:109–33.

    Article  CAS  PubMed  Google Scholar 

  7. Chen C-H, Ting C-T, Lin S-J, Hsu T-L, S-J Ho PC, Chang M-S, O’Connor F, Spurgeon H, Lakatta E, Yin FCP. Which arterial and cardiac parameters best predict left ventricular mass? Circulation. 1998;98:422–8.

    Article  CAS  PubMed  Google Scholar 

  8. Comerota AJ, Salles-Cunha SX, Daoud Y, Jones L, Beebe HG. Gender differences in blood velocities across carotid stenosis. J Vasc Surg. 2004;40:939–44.

    Article  PubMed  Google Scholar 

  9. Coutinho T, Borlaug BA, Pellikka PA, Turner ST, Kullo IJ. Sex differences in arterial stiffness and ventricular-arterial interactions. J Am Coll Cardiol. 2013;61:96–103.

    Article  PubMed  Google Scholar 

  10. Dawson TH. Engineering design of the cardiovascular system of mammals. Englewood Cliffs: Prentice-Hall; 1991.

    Google Scholar 

  11. DeBakey ME, Lawrie GM, Glaeser DH. Patterns of atherosclerosis and their surgical significance. Ann Surg. 1985;201:115–31.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  12. Dickerson JA, Nagaraja HN, Raman SV. Gender-related differences in coronary artery dimensions: a volumetric analysis. Clin Cardiol. 2010;33:E44–9.

    Article  PubMed  Google Scholar 

  13. Dodge JT Jr, Brown BG, Bolson EL, Dodge HT. Lumen diameter of normal human coronary arteries. Influence of age, sex, anatomic variation, and left ventricular hypertrophy or dilation. Circulation. 1992;86:232–46.

    Article  PubMed  Google Scholar 

  14. Fisher M, Fieman S. Geometric factors of the bifurcation in carotid atherogenesis. Stroke. 1990;21:267–71.

    Article  CAS  PubMed  Google Scholar 

  15. Fisher LD, Kennedy JW, Davis KB, et al. Association of sex, physical size, and operative mortality after coronary artery bypass in the Coronary Artery Surgery Study (CASS). J Thorac Cardiovasc Surg. 1982;84:334–41.

    PubMed  CAS  Google Scholar 

  16. Gasowski J, Wang JG, Staessen JA. Clinical trials in isolated systolic hypertension. Curr Hypertens Rep. 10 1999; 1:387–393.

    Article  CAS  PubMed  Google Scholar 

  17. Gatzka CD, Cameron JD, Kingwell BA, Dart AM. Relation between coronary artery disease, aortic stiffness, and left ventricular structure in a population sample. Hypertension. 1998;32:575–8.

    Article  CAS  PubMed  Google Scholar 

  18. Gertler MM, Garn SM, White PD. Young candidates for coronary heart disease. JAMA. 1951;147:621–5.

    Article  CAS  Google Scholar 

  19. Gosling RG, Dunbar G, King DH, Newman DL, Side CD, Woodcock JP, Fitzgerald DE, Keates JS, MacMillan D. The quantitative analysis of occlusive peripheral arterial disease by a non-intrusive ultrasonic technique. Angiology. 1971;22:52–5.

    Article  CAS  PubMed  Google Scholar 

  20. Green HD. Circulatory system: physical principles. In: Glasser O, editor. Medical physics 2. New York: Year Book Publishers; 1950.

    Google Scholar 

  21. Gunther B. Allometric ratios, invariant numbers and the theory of biological similarity. Physiol Rev. 1975;55:659.

    Article  CAS  PubMed  Google Scholar 

  22. Gunther B, DeLa Barra L. Physiometry of the mammalian circulatory system. Acta Physiol Lat-Am. 1966a;16:32.

    PubMed  CAS  Google Scholar 

  23. Gunther B, DeLa Barra L. Theories of biological similarities, non-dimensional parameters and invariant numbers. Bull Math Biophys. 1966b;28:9–102.

    Article  Google Scholar 

  24. Gunther B, Guerra B. Biological similarities. Acta Physiol Lat-Am. 1955;5:169.

    PubMed  CAS  Google Scholar 

  25. Hales S. Statical essays containing haemostaticks. London: Innys and Manby; 1733.

    Google Scholar 

  26. Hansen F, Mangell P, Sonesson B, Länne T. Diameter and compliance in the human common carotid artery–Variations with age and sex. Ultrasound Med Biol. 1995;21(1):1–9.

    Article  CAS  Google Scholar 

  27. Huxley, J.S. Problems of relative growth. Methuen, London, 1932.

    Google Scholar 

  28. Iberall AS. Anatomy and steady flow characteristics of the arterial system with an introduction of its pulsatile characteristics. Math Biosci. 1967;1:375–95.

    Article  Google Scholar 

  29. Kannam JP, Levy D, Larson M, Wilson PWF. Short stature and risk for mortality and cardiovascular events: the Framingham Heart Study. Circulation. 1994;90:2241–7.

    Article  CAS  PubMed  Google Scholar 

  30. Karreman G. Some contributions to the mathematical biology of blood circulation. Reflections of pressure wave in the arterial system. Bull Math Biophys. 1952;14:327–50.

    Article  Google Scholar 

  31. Kerkhof PLM, Heyndrickx GR, Li JK. Hemodynamic determinants and ventriculo-arterial coupling are sex-associated in heart failure patients. Conf Proc IEEE Eng Med Biol Soc. 2016 Aug; 2016:3286–3289. https://doi.org/10.1109/EMBC.2016.7591430. PMID: 28227219

  32. Kim S, Apple S, GS Mintz TMM, DA Canos AM, Weissman NJ. The importance of gender on coronary artery size: in-vivo assessment by intravascular ultrasound. Clin Cardiol. 2004;27:291–4.

    Article  PubMed  Google Scholar 

  33. Kim H, Kim M, W Shim SO, Kim M, Park SM, Kim YH, Na JO, Shin MS, Yoon HJ, Shin GJ, Cho Y, Kim S, Hong K, Cho KI. Sex difference in the association between brachial pulse pressure and coronary artery disease: the Korean women’s chest pain registry (KoROSE). J Clin Hypertens (Greenwich). 2017;19:38–44.

    Article  Google Scholar 

  34. Kostis JB, Cabrera J, Cheng JQ, Cosgrove NM, Deng Y, Pressel SL, Davis BR. Association between chlorthalidone treatment of systolic hypertension and long-term survival. JAMA. 2011;306:2588–93.

    Article  CAS  PubMed  Google Scholar 

  35. Lambert R, Teissier G. Theorie de la similitude biologique. Ann Physiol Physiocochem Biol. 1927;3:212.

    Google Scholar 

  36. Li JK-JA. New similarity principle for cardiac energetics. Bull Math Biol. 1983a;45:1005–11.

    Article  CAS  PubMed  Google Scholar 

  37. Li JK-J. Hemodynamic significance of metabolic turnover rate. J Theor Biol. 1983b;103:333–8.

    Article  CAS  PubMed  Google Scholar 

  38. Li JK-J. Comparative cardiac mechanics: Laplace’s law. J Theor Biol. 1986a;118:339–43.

    Article  CAS  PubMed  Google Scholar 

  39. Li JK-J. Time domain resolution of forward and reflected waves in the aorta. IEEE Trans Biomed Eng. 1986b;BME-33:783–5.

    Article  Google Scholar 

  40. Li JK-J. Dominance of geometric over elastic factors in pulse transmission through arterial branching. Bull Math Biol. 1986c;48:97–l03.

    PubMed  CAS  Google Scholar 

  41. Li JK-J. Arterial system dynamics. New York: New York University Press; 1987.

    Google Scholar 

  42. Li JK-J. Laminar and turbulent flow in the mammalian aorta: Reynolds number. J Theor Biol. 1988;135:409–14.

    Article  CAS  PubMed  Google Scholar 

  43. Li JK-J. Increased arterial pulse wave reflections and pulsatile energy loss in acute hypertension. Angiol, J Vasc Dis. 1989;40:730–5.

    CAS  Google Scholar 

  44. Li JK-J. Feedback effects in heart-arterial system interaction. In: Sideman S, Beyar R, editors. Interactive phenomenon in the cardiac system. New York: Plenum; 1993. p. 325–33.

    Chapter  Google Scholar 

  45. Li JK-J. Comparative cardiovascular dynamics of mammals. Boca Raton: CRC Press; 1996.

    Google Scholar 

  46. Li JK-J. A new description of arterial function: the compliance-pressure loop. Angiol, J Vasc Dis. 1998;49:543–8.

    CAS  Google Scholar 

  47. Li JK-J. The arterial circulation: physical principles and clinical application. Totowa: Humana Press; 2000.

    Book  Google Scholar 

  48. Li JK-J. Dynamics of the vascular system. Singapore: World Scientific; 2004.

    Book  Google Scholar 

  49. Li JK-J, Atlas G. Left ventricle–arterial system interaction in heart failure. Clin Med Insights: Cardiol. 2015;(Suppl):93–9. https://doi.org/10.4137/CMC.S18742.

  50. Li JK-J, Noordergraaf A. Similar pressure pulse propagation and reflection characteristics in aortas of mammals. Am J Phys. 1991;261:R519–21.

    CAS  Google Scholar 

  51. Li JK-J, Zhu Y. Arterial compliance and its pressure-dependence in hypertension and vasodilation. Angiol J Vasc Dis. 1994;45:113–7.

    CAS  Google Scholar 

  52. Li JK-J, Melbin J, Riffle RA, Noordergraaf A. Pulse wave propagation. Circulation Res. 1981;49:442–52.

    Article  CAS  PubMed  Google Scholar 

  53. Li JK-J, Melbin J, Noordergraaf A. Directional disparity of pulse wave reflections in dog arteries. Am J Phys. 1984;247:H95–9.

    CAS  Google Scholar 

  54. Li JK-J, Cui T, Drzewiecki G. A nonlinear model of the arterial system incorporating a pressure-dependent compliance. IEEE Trans Biomed Eng. 1990;BME-37:673–8.

    Article  Google Scholar 

  55. Li JK-J, Zhu Y, Nanna M. Computer modeling of the effects of aortic valve stenosis and arterial system afterload on left ventricular hypertrophy. Comput Biol Med. 1997;27:477–85.

    Article  CAS  PubMed  Google Scholar 

  56. Li JK-J, Zhu Y, O’Hara D, Khaw K. Allometric hemodynamic analysis of isolated systolic hypertension and aging. Cardiovasc Eng. 2007;7:135–9.

    Article  PubMed  Google Scholar 

  57. Loiselle DS, Gibbs CL. Species differences in cardiac energies. Am J Phys. 1979:490–8.

    Google Scholar 

  58. Martin RR, Haines H. Application of Laplace’s law to mammalian hearts. Comp Biochem Physiol. 1970;34:959.

    Article  CAS  PubMed  Google Scholar 

  59. Mates RE, Gupta RL, Bell AC, Klocke FJ. Fluid dynamics of coronary artery stenosis. Circ Res. 1978;42:152–62.

    Article  CAS  PubMed  Google Scholar 

  60. McDonald DA. Blood flow in arteries, vol. 1960. London: Arnold; 1974.

    Google Scholar 

  61. McMahon TA. Size and shape in biology. Science. 1973;179:1201–4.

    Article  CAS  PubMed  Google Scholar 

  62. McMahon TA, Bonner JT. On size and life. New York: Scientific American Library; 1983.

    Google Scholar 

  63. Mehta LS, Beckie TM, DeVon HA, et al. Acute myocardial infarction in women: a scientific statement from the american heart association. Circulation. 2016;133:916–47.

    Article  CAS  PubMed  Google Scholar 

  64. Noordergraaf A, Li JK-J, Campbell KB. Mammalian hemodynamics: a new similarity principle. J Theor Biol. 1979;79:485.

    Article  CAS  PubMed  Google Scholar 

  65. O’Rourke MF, Hashimoto J. Mechanical factors in arterial aging: a clinical perspective. J Am Coll Cardiol. 2007;50:1–13.

    Article  PubMed  Google Scholar 

  66. Palmer JR, Rosenberg L, Shapiro S. Stature and the risk of myocardial infarction in women. Am J Epidemiol. 1990;132:27–32.

    Article  CAS  PubMed  Google Scholar 

  67. Peterson ED, Lansky AJ, Kramer J, Anstrom K, Lanzilotta MJ. Effect of gender on the outcomes of contemporary percutaneous coronary intervention. Am J Cardiol. 2001;88:359–64.

    Article  CAS  PubMed  Google Scholar 

  68. Redfield MM, Jacobsen SJ, Borlaug BA, Rodeheffer RJ, Kass DA. Age- and gender-related ventricular-vascular stiffening: a community-based study. Circulation. 2005;112:2254–62.

    Article  PubMed  Google Scholar 

  69. Rexrode KM, Hennekens CH, Willett WC, et al. A prospective study of body mass index, weight change, and risk of stroke in women. JAMA. 1997;277:1539–45.

    Article  CAS  PubMed  Google Scholar 

  70. Rich-Edwards JW, Manson JE, Stampfer MJ, et al. Height and the risk of cardiovascular disease in women. Am J Epidemiol. 1995;142:909–17.

    Article  CAS  PubMed  Google Scholar 

  71. Robard S, Williams F, Williams C. The spherical dynamics of the heart. Am Heart J. 1959;57:348–60.

    Article  Google Scholar 

  72. Rosen R. Optimality principles in biology. London: Butterworth; 1967.

    Book  Google Scholar 

  73. Scheel P, Ruge C, Schoning M. Flow velocity and flow volume measurements in the extracranial carotid and vertebral arteries in healthy adults: reference data and the effects of age. Ultrasound Med Biol. 2000;26:1261–6.

    Article  CAS  PubMed  Google Scholar 

  74. Schulz UG, Rothwell PM. Major variation in carotid bifurcation anatomy: a possible risk factor for plaque development? Stroke. 2001;32:2522–9.

    Article  CAS  PubMed  Google Scholar 

  75. Sheifer SE, Canes MR, Weinfurt KP, Arora UK, Mendekohn FO, Gersh BJ, Weissman NJ. Sex differences in coronary artery size assessed by intravascular ultrasound. Am Heart J. 2000;139:649–53.

    Article  CAS  PubMed  Google Scholar 

  76. Skurnick JH, Aladjem M, Aviv A. Sex differences in pulse pressure trends with age are cross-cultural. Hypertension. 2010;55:40–7.

    Article  CAS  PubMed  Google Scholar 

  77. Smulyan H, Marchais SJ, Pannier B, Guerin AP, Safar ME, London GM. Influence of body height on pulsatile arterial hemodynamic data. J Am Coll Cardiol. 1998;31:1103–9.

    Article  CAS  PubMed  Google Scholar 

  78. Sonesson B, Hansen F, Stale H, Lanne T. Compliance and diameter in the human abdominal aorta.- the influence of age and sex. Eur J Vasc Surg. 1993;7:690–7.

    Article  CAS  PubMed  Google Scholar 

  79. Staessen JA, Thijs L, Fagard R, O’Brien ET, Clement D, de Leeuw PW, Mancia G, Nachev C, Palatini P, Parati G, Tuomilehto J, Webster J. Predicting cardiovascular risk using conventional vs ambulatory blood pressure in older patients with systolic hypertension. Systolic hypertension in Europe Trial Investigators. JAMA. 1999;282:539–46.

    Article  CAS  PubMed  Google Scholar 

  80. Stahl WR. Similarity analysis of biological systems. Persp Biol Med. 1963a;6:291.

    Article  CAS  Google Scholar 

  81. Stahl WR. The analysis of biological similarity. Adv Biol Med Phys. 1963b;9:356.

    Google Scholar 

  82. Stahl WR. Organ weights in primates and other mammals. Science. 1965;150:1039–42.

    Article  CAS  PubMed  Google Scholar 

  83. Tarbell JM, Shi Z-D, Dunn J, Hanjoong J. Fluid mechanics, arterial disease, and gene expression. Annu Rev Fluid Mech. 2014;46:591–614.

    Article  PubMed  PubMed Central  Google Scholar 

  84. Thompson DW. On growth and form. Cambridge: Cambridge University Press; 1917.

    Book  Google Scholar 

  85. Thubrikar MJ, Robicsec F. Pressure-induced arterial wall stress and atherosclerosis. Ann Thorac Surg. 1995;59:1594–603.

    Article  CAS  PubMed  Google Scholar 

  86. Vouyouka AG, Kent KC. Arterial vascular disease in women. J Vasc Surg. 2007;46:1295–302.

    Article  PubMed  Google Scholar 

  87. Waaler HT. Height, weight and mortality: the Norwegian experience. Acta Med Scand Suppl. 1984;679:1–56.

    PubMed  CAS  Google Scholar 

  88. Wainwright SA. Axis and circumference. The cylindrical shape of plants and animals. Cambridge, MA: Harvard Univrsity Press; 1988.

    Book  Google Scholar 

  89. Weintraube WS, Wenger NK, Kosinski AS, Douglas Jr JS, Liberman HA, Morris DC, King SB III. Percutaneous transluminal angioplasty in women compared with men. J Am Coll Cardiol. 1994;24:81–90.

    Article  Google Scholar 

  90. West GB, Brown JH, Enquist BJ. A general model for the origin of allometric scaling laws in biology. Science. 1997;276:122–6.

    Article  CAS  PubMed  Google Scholar 

  91. Westerhof N, Bosman F, DeVries CJ, Noordergraaf A. Analog studies of the human systemic arterial tree. J Biomech. 1969;2:121–43.

    Article  CAS  PubMed  Google Scholar 

  92. White L, Haines H, Adams T. Cardiac output related to body weights in small mammals. Comp Biochem Physiol. 1968;27:559–65.

    Article  Google Scholar 

  93. Zanchetti A, Grassi G, Mancia G. When should antihypertensive drug treatment be initiated and to what levels should systolic blood pressure be lowered? A critical reappraisal. J Hypertens. 2009;27:923–34.

    Article  CAS  PubMed  Google Scholar 

  94. Zarins CK, Giddens DP, Bharadvaj BK, Sottiurai VS, Mabon RF, Glagov S. Carotid bifurcation atherosclerosis. Quantitative correlation of plaque localization with flow velocity profiles and wall shear stress. Circ Res. 1983;53:502–14.

    Article  CAS  PubMed  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to John K.-J. Li .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer International Publishing AG, part of Springer Nature

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Li, J.KJ. (2018). Cardiovascular Allometry: Analysis, Methodology, and Clinical Applications. In: Kerkhof, P., Miller, V. (eds) Sex-Specific Analysis of Cardiovascular Function. Advances in Experimental Medicine and Biology, vol 1065. Springer, Cham. https://doi.org/10.1007/978-3-319-77932-4_14

Download citation

Publish with us

Policies and ethics