Wave Intensity Analysis

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


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 ddQ 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’.


Wave intensity: differences Wave intensity: differentials ‘Wave free’ period Reservoir-wave concept Instantaneous wave free ratio Stenosis Coronary 


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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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