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An introduction to wave intensity analysis

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Abstract

Wave intensity analysis applies methods first used to study gas dynamics to cardiovascular haemodynamics. It is based on the method of characteristics solution of the 1-D equations derived from the conservation of mass and momentum in elastic vessels. The measured waveforms of pressure P and velocity U are described as the summation of successive wavefronts that propagate forward and backward through the vessels with magnitudes dP ± and dU ±. The net wave intensity dPdU is the flux of energy per unit area carried by the wavefronts. It is positive for forward waves and negative for backward waves, providing a convenient tool for quantifying the timing, direction and magnitude of waves. Two methods, the PU-loop and the sum of squares, are given for calculating the wave speed c from simultaneous measurements of P and U at a single location. Given c, it is possible to separate the waveforms into their forward and backward components. Finally, the reservoir-wave hypothesis that the arterial and venous pressure can be conveniently thought of as the sum of a reservoir pressure arising from the total compliance of the vessels (the Windkessel effect) and the pressure associated with the waves is discussed.

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Notes

  1. The material in this paper form the basis for a web site An Introduction to Wave Intensity Analysis http://www.bg.ic.ac.uk/research/intro_to_wia. The site contains some additional material and a number of examples which could not be included in this work for reasons of space.

  2. The elemental wavefronts should not be confused with solitons, which are solitary wave solutions of the nonlinear Korteweg–de Vries equation originally derived to model shallow water hydrodynamics. The soliton is another example of a solitary wave that cannot be analysed easily using Fourier methods although it can be described easily as successive wavefronts.

  3. In this case, they are generally referred to as Riemann invariants.

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  1. Department of Bioengineering, Imperial College, London, UK

    Kim H. Parker

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  1. Kim H. Parker
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Correspondence to Kim H. Parker.

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Parker, K.H. An introduction to wave intensity analysis. Med Biol Eng Comput 47, 175–188 (2009). https://doi.org/10.1007/s11517-009-0439-y

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