Pulse Wave Velocity Prediction and Compliance Assessment in Elastic Arterial Segments

  • Jeffrey S. Lillie
  • Alexander S. Liberson
  • Doran Mix
  • Karl Q. Schwarz
  • Ankur Chandra
  • Daniel B. Phillips
  • Steven W. Day
  • David A. Borkholder
Article

Abstract

Pressure wave velocity (PWV) is commonly used as a clinical marker of vascular elasticity. Recent studies have increased clinical interest in also analyzing the impact of heart rate, blood pressure, and left ventricular ejection time on PWV. In this article we focus on the development of a theoretical one-dimensional model and validation via direct measurement of the impact of ejection time and peak pressure on PWV using an in vitro hemodynamic simulator. A simple nonlinear traveling wave model was developed for a compliant thin-walled elastic tube filled with an incompressible fluid. This model accounts for the convective fluid phenomena, elastic vessel deformation, radial motion, and inertia of the wall. An exact analytical solution for PWV is presented which incorporates peak pressure, ejection time, ejection volume, and modulus of elasticity. To assess arterial compliance, the solution is introduced in an alternative form, explicitly determining compliance of the wall as a function of the other variables. The model predicts PWV in good agreement with the measured values with a maximum difference of 3.0%. The results indicate an inverse quadratic relationship (\(R^{2} = .99\)) between ejection time and PWV, with ejection time dominating the PWV shifts (12%) over those observed with changes in peak pressure (2%). Our modeling and validation results both explain and support the emerging evidence that, both in clinical practice and clinical research, cardiac systolic function related variables should be regularly taken into account when interpreting arterial function indices, namely PWV.

Keywords

Left ventricular ejection time Systemic vascular resistance Pulse wave velocity Peak pressure Blood pressure Wave propagation 

Supplementary material

13239_2014_202_MOESM1_ESM.docx (121 kb)
Supplementary material 1 (DOCX 99 kb)

References

  1. 1.
    Allen, J., and A. Murray. Age-related changes in the characteristics of the photoplethysmographic pulse shape at various body sites. Pysiol. Meas. 24:297–307, 2003.CrossRefGoogle Scholar
  2. 2.
    Asamar, R. Arterial Stiffness and Pulse Wave Velocity, Clinical Applications. New York: Elsevier, 1999.Google Scholar
  3. 3.
    Blacher, J., R. Asmar, S. Djane, G. M. London, and M. E. Safar. Aortic pulse wave velcity as a marker of cardiovascular risk in hypertensive patients. Hypertension 33:1111–1117, 1999.CrossRefGoogle Scholar
  4. 4.
    Blacher, J., A. P. Guerin, B. Pannier, et al. Impact of aortic stiffness on survival in end stage renal disease. Circulation 99(18):2434–2439, 1999.CrossRefGoogle Scholar
  5. 5.
    Bramwell, J. C., and A. V. Hill. Velocity of transmission of the pulse wave and elasticity of arteries. Lancet 1:891–892, 1922.CrossRefGoogle Scholar
  6. 6.
    Cascaval, C. R. A Boussinesq model for pressure and flow velocity waves in arterial segments. Math. Comput. Simul. 82:1047–1055, 2012.CrossRefMATHMathSciNetGoogle Scholar
  7. 7.
    Chen, Y., W. Changyun, T. Guocai, B. Min, and G. Li. Continuous and noninvasive blood pressure measurement: a novel modeling methodology of the relationship between blood pressure and pulse wave velocity. Ann. Biomed. Eng. 37(11):2222–2233, 2009.CrossRefGoogle Scholar
  8. 8.
    Chiu, Y. C., W. P. Arand, and G. S. Shroff. Determination of pulse wave velocities with computerized algorithms. Am. Heart J. 5(121):1460–1469, 1991.CrossRefGoogle Scholar
  9. 9.
    Formaggia, L., D. Lamponi, and A. Quarterroni. One dimensional models for blood flow in arteries. J. Eng. Math. 47:251–276, 2003.CrossRefMATHGoogle Scholar
  10. 10.
    Freis, E. D. Hemodynamics of hypertension. Physiology 40:27, 1960.Google Scholar
  11. 11.
    Freis, E. D., and I. M. Khatri. Hemodynamic changes during sleep in hypertensive patients. J. Appl. Physiol. 22:867, 1967.Google Scholar
  12. 12.
    Fullwood, L., M. Hawkins, A. J. Cowley, and A. F. Mueller. The integrated response of the cardiovascular system to food. Digestion 52:184–193, 1992.CrossRefGoogle Scholar
  13. 13.
    Hughes, D., F. Babbs, and C. Geddes. Measurement of Young’s modulus of elasticity of the canine aorta with ultrasound. Ultrasound Imaging 1(4):356–367, 1979.CrossRefGoogle Scholar
  14. 14.
    Karr, A., and S. George. Theoretical and Experimental Determination of Arterial Pulse Propagation Speed. Illinois: Northwestern University, 1982.Google Scholar
  15. 15.
    Kim, E. J., C. G. Park, J. D. Park, D. J. Oh, et al. Relationship between blood pressure parameters and pulse wave velocity in normotensive and hypertensive subjects: invasive study. J. Hum. Hypertens. 21:141–148, 2007.CrossRefGoogle Scholar
  16. 16.
    Klabunde, R. Cardiovascular Physiology Concepts (2nd ed.). Philadelphia, USA: Lippincott Williams & Wilkins, 2011.Google Scholar
  17. 17.
    Klingensmith, M., L. Chen, S. Glasgow, T. Goers, and S. Melby (eds.). Chapter 1: General and perioperative care of the surgical patient. In: The Washington Manual of Surgery, Lippincott Williams & Wilkins, 2008.Google Scholar
  18. 18.
    Kobayashi, T., S. Ichikawa, Y. Takeuchi, T. Togawa, and W. Chen. Continuous estimation of systolic blood pressure using the pulse arrival time and intermittent calibration. Med. Biol. Eng. Comput. 38:569–574, 2000.CrossRefGoogle Scholar
  19. 19.
    Kung, E., and C. Taylor. Development of a physical Windkessel module to re-create in vivo vascular flow impedance for in vitro experiments. Cardiovasc. Eng. Tech. 2(1):2–14, 2011.CrossRefGoogle Scholar
  20. 20.
    Laurent, S., H. S. Boulder, et al. Expert consensus document on arterial stiffness: methodological issues and clinical applications. Eur. Heart J. 27:2588–2605, 2006.CrossRefGoogle Scholar
  21. 21.
    Lebrun, C. E., Y. T. Van Der Schouw, A. A. Bak, et al. Arterial stiffness in postmenopausal women, determinants of pulse wave velocity. J. Hypertens. 20(11):2165–2172, 2002.CrossRefGoogle Scholar
  22. 22.
    London, G. M., and J. N. Cohn. Prognostic application of arterial stiffness, task forces. Am. J. Hypertens. 15(8):754–758, 2002.CrossRefGoogle Scholar
  23. 23.
    Meaume, S., A. Benetos, O. F. Henry, et al. Aortic pulse wave velocity predicts cardiovascular mortality in subjects > 70 years of age. Arterioscler. Thrombosis Vasc. Biol. 21:2046–2050, 2001.CrossRefGoogle Scholar
  24. 24.
    Nurnberger, J., A. Saez, S. Dammer, A. Mitchell, R. Wenzel, T. Philipp, and R. Schafers. Left ventricular ejection time: a potential determinant of pulse wave velocity in young, healthy males. J. Hypertens. 21(11):2125–2132, 2003.CrossRefGoogle Scholar
  25. 25.
    Ohnishi, H., S. Saitoh, S. Takagi, et al. Pulse wave velocity as an indicator of atherosclerosis in impaired fasting glucose, the tanno and sobetsu study. Diabetes Care 26(2):437–440, 2003.CrossRefGoogle Scholar
  26. 26.
    O’Rourke, M. McDonald’s Blood Flow in Arteries: Theoretical, Experimental and Clinical Principles (5th ed.). USA: Oxford University Press, 2005.Google Scholar
  27. 27.
    Papageogiou, G., and N. Jones. Physical modeling of the arterial wall. Part 1: Testing of tubes of various materials. J. Biomed. Eng. 9(2):153–156, 1987.CrossRefGoogle Scholar
  28. 28.
    Poon, C. C. Y., and Y. T. Zhang. Cuff-less and noninvasive measurements of arterial blood pressure by pulse transit time. Proceedings of the 2005 IEEE Engineering in Medicine and Biology 27th Annual Conference, Shanghai, 2005.Google Scholar
  29. 29.
    Safar, M. E., O. Henry, and S. Meaume. Aortic pulse wave velocity, an independent marker of cardiovascular risk. Am. J. Geriatric Cardiol. 11:295–298, 2002.CrossRefGoogle Scholar
  30. 30.
    Salvi, P., C. Palombo, G. Salvl, C. Labat, G. Parati, and A. Benetos. Left ventricular ejection time, not heart rate, is an independent correlate of aortic pulse wave velocity. J. Appl. Physiol. 115(11):1610–1617, 2013.CrossRefGoogle Scholar
  31. 31.
    Sherwin, S. J., V. Franke, J. Peiro, and K. Parker. One-dimensional modeling of a vascular network in space-time variables. J. Eng. Math. 47:217–250, 2003.CrossRefMATHMathSciNetGoogle Scholar
  32. 32.
    Sutton-Terrel, K., R. H. Mackey, R. Holukbov, et al. Measurement variation of aortic pulse wave velocity in the elderly. Am. J. Hypertens. 14:463–468, 2001.CrossRefGoogle Scholar
  33. 33.
    Varble, N. A Hemodynamic Investigation of a Complete Arteriovenous Model of the Arm, Arteriovenous Fistula, and Distal Revascularization and Interval Ligation. Masters Thesis, 2011. https://ritdml.rit.edu/handle/1850/14265. Accessed 17 Feb 2013.
  34. 34.
    Vardoulis, O., T. G. Papaioannou, and N. Stergiopoulas. On the estimation of total arterial compliance from aortic pulse wave velocity. Ann. Biomed. Eng. 40(12):2619–2626, 2012.CrossRefGoogle Scholar
  35. 35.
    Vlachopoulos, C., K. Aznouridis, and C. Stefenadis. Prediction of cardiovascular events and all-cause mortality with arterial stiffness. JACC 55(13):1318–1327, 2010.CrossRefGoogle Scholar
  36. 36.
    Whitham, G. B. Linear and Nonlinear Waves. New York: Wiley-Interscience, 1999.CrossRefMATHGoogle Scholar

Copyright information

© Biomedical Engineering Society 2014

Authors and Affiliations

  • Jeffrey S. Lillie
    • 1
  • Alexander S. Liberson
    • 1
  • Doran Mix
    • 2
  • Karl Q. Schwarz
    • 2
  • Ankur Chandra
    • 2
  • Daniel B. Phillips
    • 1
  • Steven W. Day
    • 1
  • David A. Borkholder
    • 1
    • 2
  1. 1.Rochester Institute of TechnologyRochesterUSA
  2. 2.University of RochesterRochesterUSA

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