An Innovative Method to Measure the Peripheral Arterial Elasticity: Spring Constant Modeling Based on the Arterial Pressure Wave with Radial Vibration

Article

Abstract

In this study, we propose an innovative method for the direct measurement of the peripheral artery elasticity using a spring constant model, based on the arterial pressure wave equation, vibrating in a radial direction. By means of the boundary condition of the pressure wave equation at the maximum peak, we can derive the spring constant used for evaluating peripheral arterial elasticity. The calculated spring constants of six typical subjects show a coincidence with their proper arterial elasticities. Furthermore, the comparison between the spring constant method and pulse wave velocity (PWV) was investigated in 70 subjects (21–64 years, 47 normotensives and 23 hypertensives). The results reveal a significant negative correlation for the spring constant vs. PWV (correlation coefficient = −0.663, p < 0.001). Multivariate analysis also indicates the same close relationship. Furthermore, within-operator and between-operator analyses show significantly high reproducibility. Therefore, the use of the spring constant method to assess the arterial elasticity is carefully verified, and it is shown to be effective as well as fast. This method should be useful for healthcare, not only in improving clinical diagnosis of arterial stiffness but also in screening subjects for early evidence of cardio-vascular diseases and in monitoring responses to therapy in the future.

Keywords

Elasticity Peripheral artery Radial vibration Spring constant Pulse wave velocity Healthcare 

References

  1. 1.
    Armentano, R. L., J. G. Barra, J. Levenson, A. Simon, and R. H. Pichel. Arterial wall mechanics in conscious dogs. Circ. Res. 76:468–478, 1995.PubMedGoogle Scholar
  2. 2.
    Avigad, G., and E. Eisenstadt. Robustness of multi-objective optimal solutions to physical deterioration through active control. LNCS 6457:394–403, 2010.Google Scholar
  3. 3.
    Baker, P. D., D. R. Westenskow, and K. Kuck. Theoretical analysis of non-invasive oscillometric maximum amplitude algorithm for estimating mean blood pressure. Med. Biol. Eng. Comput. 35:271–278, 1997.PubMedCrossRefGoogle Scholar
  4. 4.
    Cohn, J. N., S. M. Finkelstein, G. McVeigh, D. J. Morgan, L. LeMay, J. Robinson, and J. Mock. Noninvasive pulse wave analysis for the early detection of vascular disease. Hypertension 26:503–508, 1995.PubMedGoogle Scholar
  5. 5.
    Fang, S. E., and R. Perera. Power mode shapes for early damage detection in linear structures. J. Sound Vib. 324:40–56, 2009.CrossRefGoogle Scholar
  6. 6.
    Fetics, B., E. Nevo, C. H. Chen, and D. A. Kass. Parametric model derivation of transfer function for noninvasive estimation of aortic pressure. IEEE Trans. Biomed. Eng. 46:698–706, 1999.PubMedCrossRefGoogle Scholar
  7. 7.
    Fey, J. F. Contemporary Sphygmology in Traditional Chinese Medicine. Beijing: People’s Medical Publishing House, p. 164, 2003; (in Chinese).Google Scholar
  8. 8.
    Hecht, E. Physics: Calculus (2nd ed.). Pacific Grove, CA: Brooks/Cole, pp. 408–429, 2000.Google Scholar
  9. 9.
    Jatoi, N. A., A. Mahmud, K. Bennett, and J. Feely. Assessment of arterial stiffness in hypertension: comparison of oscillometric (Arteriograph), piezoelectronic (Complior) and tonometric (SphygmoCor) techniques. J. Hypertens. 27:2186–2191, 2009.PubMedCrossRefGoogle Scholar
  10. 10.
    Kelly, R., C. Hayward, A. Avolio, and M. O’Rourke. Noninvasive determination of age-related changes in the human arterial pulse. Circulation 80:1652–1659, 1989.PubMedCrossRefGoogle Scholar
  11. 11.
    Lardner, T. J. Resonance and the aging spring. J. Appl. Mech. 69:397–398, 2002.CrossRefGoogle Scholar
  12. 12.
    Laurent, S., J. Cockcroft, L. V. Bortel, P. Boutouyrie, C. Giannattasio, D. Hayoz, B. Pannier, C. Vlachopoulos, I. Wilkinson, and H. Struijker-Boudier. Expert consensus document on arterial stiffness methodological issues and clinical applications. Eur. Heart J. 27:2588–2605, 2006.PubMedCrossRefGoogle Scholar
  13. 13.
    Lin Wang, Y. Y., W. C. Lia, H. Hsiu, and M. Y. Jan. Effect of length on the fundamental resonance frequency of arterial models having radial dilation. IEEE Trans. Biomed. Eng. 47:313–318, 2000.CrossRefGoogle Scholar
  14. 14.
    Liu, C. Y., C. C. Wei, and P. C. Lo. Variation analysis of sphygmogram to assess cardiovascular system under meditation. Evid. Based Complement Alternat. Med. 6:107–112, 2009.PubMedCrossRefGoogle Scholar
  15. 15.
    Mackenzie, I. S., I. B. Wilkinson, and J. R. Cockcroft. Assessment of arterial stiffness in clinical practice. QJM 95:67–74, 2002.PubMedCrossRefGoogle Scholar
  16. 16.
    Mancia, G., G. De Backer, and A. Dominiczak. 2007 Guidelines for the management of arterial hypertension. The task force for the management of arterial hypertension of the European Society of Hypertension (ESH) and the European Society of Cardiology (ESC). J. Hypertens. 25:1105–1187, 2007.PubMedCrossRefGoogle Scholar
  17. 17.
    McVeigh, G. E., C. W. Bratteli, D. J. Morgan, C. M. Alinder, S. P. Glasser, S. M. Finkelstein, and J. N. Cohn. Age-related abnormalities in arterial compliance identified by pressure pulse contour analysis: aging and arterial compliance. Hypertension 33:1392–1398, 1999.PubMedGoogle Scholar
  18. 18.
    Milnor, W. R. Hemodynamics, 2nd ed. Baltimore, MD: Williams & Wilkins Co, 1989, pp. 95–97, 106–108.Google Scholar
  19. 19.
    Munir, S., A. Guilcher, T. Kamalesh, B. Clapp, S. Redwood, M. Marber, and P. Chowienczyk. Peripheral augmentation index defines the relationship between central and peripheral pulse pressure. Hypertension 51:112–118, 2008.PubMedCrossRefGoogle Scholar
  20. 20.
    Nichols, W. W. Clinical measurement of arterial stiffness obtained from noninvasive pressure waveforms. Am. J. Hypertens. 18:3–10, 2005.CrossRefGoogle Scholar
  21. 21.
    Nichols, W. W., and M. F. O’Rourke. McDonald’s Blood Flow in Arteries (5th ed.). New York: Oxford University Press, pp. 49–58, 2005.Google Scholar
  22. 22.
    Nichols, W. W., and M. F. O’Rourke. McDonald’s Blood Flow in Arteries, 5th ed. New York: Oxford University Press, 2005, pp. 185, 245.Google Scholar
  23. 23.
    O’Rourke, M. F., and W. W. Nichols. Aortic diameter, aortic stiffness, and wave reflection increase with age and isolated systolic hypertension. Hypertension 45:652–658, 2005.PubMedCrossRefGoogle Scholar
  24. 24.
    Oliver, J. J., and D. J. Webb. Noninvasive assessment of arterial stiffness and risk of atherosclerotic events. Arterioscler. Thromb. Vasc. Biol. 23:554–566, 2003.PubMedCrossRefGoogle Scholar
  25. 25.
    Raamat, R., J. Talts, K. Jagomagi, and E. Lansimies. Mathematical modeling of non-invasive oscillometric finger mean blood pressure measurement by maximum oscillation criterion. Med. Biol. Eng. Comput. 37:784–788, 1999.PubMedCrossRefGoogle Scholar
  26. 26.
    Rajzer, M. W., W. Wojciechowska, M. Klocek, I. Palka, M. Brzozowska-Kiszka, and K. Kawecka-Jaszcz. Comparison of aortic pulse wave velocity measured by three techniques Complior SphygmoCor and Arteriograph. J. Hypertens. 26:2001–2007, 2008.PubMedCrossRefGoogle Scholar
  27. 27.
    Smith, S. A., J. M. Morris, and E. D. Gallery. Methods of assessment of the arterial pulse wave in normal human pregnancy. Am. J. Obstet. Gynecol. 190:472–476, 2004.PubMedCrossRefGoogle Scholar
  28. 28.
    Smulyan, H., D. S. Siddiqui, R. J. Carlson, G. M. London, and M. E. Safar. Clinical utility of aortic pulses and pressures calculated from applanated radial-artery pulses. Hypertension 42:150–155, 2003.PubMedCrossRefGoogle Scholar
  29. 29.
    Takazawa, K., N. Tanaka, M. Fujita, O. Matsuoka, T. Saiki, M. Aikawa, S. Tamura, and C. Ibukiyama. Assessment of vasoactive agents and vascular aging by the second derivative of photoplethysmogram waveform. Hypertension 32:365–370, 1998.PubMedGoogle Scholar
  30. 30.
    Urbina, E. M., R. V. Williams, B. S. Alpert, R. T. Collins, et al. Noninvasive assessment of subclinical atherosclerosis in children and adolescents. Hypertension 54:919–950, 2009.PubMedCrossRefGoogle Scholar
  31. 31.
    VanBavel, E., P. Siersma, and J. A. E. Spaan. Elasticity of passive blood vessels: a new concept. Am. J. Physiol. Heart Circ. Physiol. 285:1986–2000, 2003.Google Scholar
  32. 32.
    Wang Lin, Y. Y., C. C. Chang, J. C. Chen, H. Hsiu, and W. K. Wang. Pressure wave propagation in arteries: a model with radial dilation for simulating the behavior of a real artery. IEEE Eng. Med. Biol. Mag. 16:51–56, 1997.CrossRefGoogle Scholar
  33. 33.
    Wei, C. C., C. M. Huang, and Y. T. Liao. The exponential decay characteristic of the spectral distribution of blood pressure wave in radial artery. Comput. Biol. Med. 39:453–459, 2009.PubMedCrossRefGoogle Scholar
  34. 34.
    Wilkinson, I. B., S. A. Fuchs, I. M. Jansen, J. C. Spratt, G. D. Murray, J. R. Cockcroft, and D. J. Webb. Reproducibility of pulse wave velocity and augmentation index measured by pulse wave analysis. J. Hypertens. 16:2079–2084, 1998.PubMedCrossRefGoogle Scholar
  35. 35.
    Yamashina, A., H. Tomiyama, K. Takeda, H. Tsuda, T. Arai, K. Hirose, Y. Koji, S. Hori, and Y. Yamamoto. Validity, reproducibility, and clinical significance of non-invasive brachial-ankle pulse wave velocity measurement. Hypertens. Res. 25:359–364, 2002.PubMedCrossRefGoogle Scholar
  36. 36.
    Yasmin, and M. J. Brown. Similarities and differences between augmentation index and pulse wave velocity in the assessment of arterial stiffness. QJM 92:595–600, 1999.PubMedCrossRefGoogle Scholar
  37. 37.
    Yoon, Y. Z., M. H. Lee, and K. S. Soh. Pulse type classification by varying contact pressure. IEEE Eng. Med. Biol. Mag. 19:106–110, 2000.PubMedGoogle Scholar
  38. 38.
    Zill, D. G., and M. R. Cullen. Advanced Engineering Mathematics. Sudbury, MA: Jones & Bartlett Publishers, Inc., 2006.Google Scholar

Copyright information

© Biomedical Engineering Society 2011

Authors and Affiliations

  1. 1.Department of Information and Communication EngineeringChaoyang University of TechnologyTaichung CityTaiwan, ROC

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