Skip to main content
SpringerLink
Log in
Book cover

Snapshots of Hemodynamics pp 185–193Cite as

Wave Intensity Analysis

  • Chapter
  • First Online:

  • 1616 Accesses

Abstract

Originally Wave Intensity was defined as the product of differences in pressure, dP=P(t + Δt)–P(t) and velocity, dv = v(t + Δt)–v(t), as dP·dv. This implies that their product, dP·dv is in Watt·m−2, and depends on the sampling time, Δt, which makes quantitative comparison between studies, when Δt is not reported, difficult. When flow, Q, instead of velocity is used Wave Intensity equals (dP)·(dQ) with units Watt. Wave Intensity can also be derived by differentiation as dP/dt·dQ/dt (in Watt s−2) and is called ‘time normalized Wave Intensity’. Flow and velocity are both used and also differentiated and differences in waves have been used. The main peaks of the Wave Intensity are in early and late ejection. Names of peaks have not been standardized. Wave Intensity Analysis is allowed in nonlinear and time-varying systems, but depends on contribution of heart and load.

In diastole dP and dQ are small and so dP·dQ is in diastole; this period has been labeled as ‘wave free’. Assuming a wave free period, the Reservoir-Wave Concept was introduced, based on a combination of a reservoir pressure given by Frank’s two-element Windkessel and an excess pressure, a wave related pressure.

The instantaneous wave Free Ratio, iFR, is proposed as a method to estimate stenosis severity in the coronary arterial system without the need for vasodilation. The iFR is defined as the ratio of distal and proximal pressures of a stenosis in the latter 75% of diastole, the so-called ‘wave free period’.

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

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   109.99
Price excludes VAT (USA)
  • Compact, lightweight 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

Learn about institutional subscriptions

References

  1. Parker KH, Jones CJ. Forward and backward running waves in the arteries: analysis using the method of characteristics. J Biomech Eng. 1990;112:322–6.

    Article  CAS  Google Scholar 

  2. Parker KH. An introduction to wave intensity analysis. Med Biol Eng Comput. 2009;47:175–88. Review

    Article  Google Scholar 

  3. Borlotti A, Khir AW, Rietzschel ER, De Buyzere ML, Vermeersch S, Segers P. Noninvasive determination of local pulse wave velocity and wave intensity: changes with age and gender in the carotid and femoral arteries of healthy human. J Appl Physiol (1985). 2012;113:727–35.

    Article  Google Scholar 

  4. Sugawara M, Niki K, Ohte N, Okada T, Harada A. Clinical usefulness of wave intensity analysis. Med Biol Eng Comput. 2009;47:197–206.

    Article  Google Scholar 

  5. Rivolo S, Nagel E, Smith NP, Lee J. Automatic selection of optimal Savitzky-Golay filter parameters for coronary wave intensity analysis. Conf Proc IEEE Eng Med Biol Soc. 2014;2014:5056–9.

    Google Scholar 

  6. Davies JE, Whinnett ZI, Francis DP, Manisty CH, Aguado-Sierra J, Willson K, et al. Evidence of a dominant backward-propagating suction wave responsible for diastolic coronary filling in humans, attenuated in left ventricular hypertrophy. Circulation. 2006;113:1768–78.

    Article  PubMed  Google Scholar 

  7. Hughes AD, Parker KH. Forward and backward waves in the arterial system: impedance or wave intensity analysis? Med Biol Eng Comput. 2009;47:207–10.

    Article  CAS  PubMed  Google Scholar 

  8. Westerhof N, Segers P, Westerhof BE. Wave separation, wave intensity, the reservoir-wave concept, and the instantaneous wave–free ratio: presumptions and principles. Hypertension. 2015;66:93–8. (and Hypertension 2015;66:e21)

    Article  CAS  PubMed  Google Scholar 

  9. Dujardin JP, Stone DN. Characteristic impedance of the proximal aorta determined in the time and frequency domain: a comparison. Med Biol Eng Comput. 1981;19:565–8.

    Article  CAS  PubMed  Google Scholar 

  10. Khir AW, O’Brien A, Gibbs JS, Parker KH. Determination of wave speed and wave separation in the arteries. J Biomech. 2001;34:1145–55.

    Article  CAS  PubMed  Google Scholar 

  11. Davies JE, Whinnett ZI, Francis DP, Willson K, Foale RA, Malik IS, et al. Use of simultaneous pressure and velocity measurements to estimate arterial wave speed at a single site in humans. Am J Physiol Heart Circ Physiol. 2006;290:H878–85.

    Article  CAS  PubMed  Google Scholar 

  12. Kolyva C, Spaan JA, Piek JJ, Siebes M. Windkesselness of coronary arteries hampers assessment of human coronary wave speed by single-point technique. Am J Phys. 2008;295:H482–90.

    CAS  Google Scholar 

  13. Sen S, Escaned J, Malik IS, Mikhail GW, Foale RA, Mila R, et al. Development and validation of a new adenosine-independent index of stenosis severity from coronary wave-intensity analysis: results of the ADVISE (ADenosine vasodilator independent stenosis evaluation) study. J Am Coll Cardiol. 2012;59:1392–402.

    Article  CAS  Google Scholar 

  14. Wang JJ, O’Brien AB, Shrive NG, Parker KH, Tyberg JV. Time-domain representation of ventricular-arterial coupling as a windkessel and wave system. Am J Physiol Heart Circ Physiol. 2003;284:H1358–68.

    Article  CAS  PubMed  Google Scholar 

  15. Westerhof N, Elzinga G, Sipkema P. An artificial arterial system for pumping hearts. J Appl Physiol. 1971;31:776–81.

    Article  CAS  PubMed  Google Scholar 

  16. Westerhof N, Lankhaar JW, Westerhof BE. The arterial Windkessel. Med Biol Eng Comput. 2009;47:131–41.

    Article  PubMed  Google Scholar 

  17. Lighthill MJ. Waves in fluids. Cambridge: Cambridge University Press; 1978.

    Google Scholar 

  18. Tyberg JV, Davies JE, Wang Z, Whitelaw WA, Flewitt JA, Shrive NG, et al. Wave intensity analysis and the development of the reservoir-wave approach. Med Biol Eng Comput. 2009;47:221–32.

    Article  PubMed  Google Scholar 

  19. Tyberg JV, Shrive NG, Bouwmeester JC, Parker KH, Wang JJ. The reservoir-wave paradigm: potential implications for hypertension. Curr Hypertens Rev. 2008;4:203–13.

    Article  Google Scholar 

  20. Hametner B, Wassertheurer S, Hughes AD, Parker KH, Weber T, Eber B. Reservoir and excess pressures predict cardiovascular events in high-risk patients. Int J Cardiol. 2014;171:31–6.

    Article  PubMed  Google Scholar 

  21. Mynard JP. Assessment of conceptual inconsistencies in the hybrid reservoir-wave model. Conf Proc IEEE Eng Med Biol Soc. 2013;2013:213–6.

    PubMed  Google Scholar 

  22. Davies JE, Baksi J, Francis DP, Hadjiloizou N, Whinnett ZI, Manisty CH, et al. The arterial reservoir pressure increases with aging and is the major determinant of the aortic augmentation index. Am J Physiol Heart Circ Physiol. 2010;298:H580–6.

    Article  CAS  PubMed  Google Scholar 

  23. Sen S, Asrress KN, Nijjer S, Petraco R, Malik IS, Foale RA, et al. Diagnostic classification of the instantaneous wave-free ratio is equivalent to fractional flow reserve and is not improved with adenosine administration. Results of CLARIFY (Classification Accuracy of Pressure-Only Ratios Against Indices Using Flow Study). J Am Coll Cardiol. 2013;61:1409–20.

    Article  Google Scholar 

  24. Johnson NP, Kirkeeide RL, Asrress KN, Fearon WF, Lockie T, Marques KM, et al. Does the instantaneous wave-free ratio approximate the fractional flow reserve? J Am Coll Cardiol. 2013;61:1428–35.

    Article  PubMed  Google Scholar 

  25. Nijjer SS, de Waard GA, Sen S, van de Hoef TP, Petraco R, Echavarría-Pinto M, et al. Coronary pressure and flow relationships in humans: phasic analysis of normal and pathological vessels and the implications for stenosis assessment: a report from the Iberian-Dutch-English (IDEAL) collaborators. Eur Heart J. 2016;37:2069–80.

    Article  PubMed  Google Scholar 

  26. Fok H, Guilcher A, Brett S, Jiang B, Li Y, Epstein S, et al. Dominance of the forward compression wave in determining pulsatile components of blood pressure: similarities between inotropic stimulation and essential hypertension. Hypertension. 2014;64:1116–23.

    Article  CAS  PubMed  Google Scholar 

  27. Schultz MG, Davies JE, Roberts-Thomson P, Black JA, Hughes AD, Sharman JE. Exercise central (aortic) blood pressure is predominantly driven by forward traveling waves, not wave reflection. Hypertension. 2013;62:175–82.

    Article  CAS  PubMed  Google Scholar 

  28. Davies JE, Sen S, Broyd C, Hadjiloizou N, Baksi J, Francis DP, et al. Arterial pulse wave dynamics after percutaneous aortic valve replacement: fall in coronary diastolic suction with increasing heart rate as a basis for angina symptoms in aortic stenosis. Circulation. 2011;124:1565–72.

    Article  PubMed  Google Scholar 

  29. Narayan O, Davies JE, Hughes AD, Dart AM, Parker KH, Reid C, et al. Central aortic reservoir-wave analysis improves prediction of cardiovascular events in elderly hypertensives. Hypertension. 2015;65:629–35. Erratum in: Hypertension 2015;66:e28

    Article  CAS  PubMed  Google Scholar 

  30. Weber T, Wassertheurer S, Rammer M, Haiden A, Hametner B, Eber B. Wave reflections, assessed with a novel method for pulse wave separation, are associated with end-organ damage and clinical outcomes. Hypertension. 2012;60:534–41.

    Article  CAS  PubMed  Google Scholar 

  31. Davies JE, Lacy P, Tillin T, Collier D, Cruickshank JK, Francis DP, et al. Excess pressure integral predicts cardiovascular events independent of other risk factors in the conduit artery functional evaluation substudy of Anglo-Scandinavian cardiac outcomes trial. Hypertension. 2014;64:60–8.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  32. Mitchell GF, Gudnason V, Launer LJ, Aspelund T, Harris TB. Hemodynamics of increased pulse pressure in older women in the community-based age, gene/environment susceptibility-Reykjavik study. Hypertension. 2008;51:1123–8.

    Article  CAS  PubMed  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Pulmonary Diseases, Amsterdam Cardiovascular Sciences, VU University Medical Center, Amsterdam, The Netherlands

    Nicolaas Westerhof & Berend E. Westerhof

  2. Laboratory of Hemodynamics and Cardiovascular Technology, Ecole Polytechnique Fédérale de Lausanne (EPFL), Institute of Bioengineering, Lausanne, Switzerland

    Nikolaos Stergiopulos

  3. Cardiovascular Medicine, Department of Medicine and Therapeutics, University of Aberdeen, Aberdeen, United Kingdom

    Mark I. M. Noble

Authors
  1. Nicolaas Westerhof
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Nikolaos Stergiopulos
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Mark I. M. Noble
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Berend E. Westerhof
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer International Publishing AG, part of Springer Nature

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Westerhof, N., Stergiopulos, N., Noble, M.I.M., Westerhof, B.E. (2019). Wave Intensity Analysis. In: Snapshots of Hemodynamics. Springer, Cham. https://doi.org/10.1007/978-3-319-91932-4_23

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-91932-4_23

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-91931-7

  • Online ISBN: 978-3-319-91932-4

  • eBook Packages: MedicineMedicine (R0)

Publish with us

Policies and ethics

Search

Navigation