Wave intensity analysis provides a method to calculate the properties of arterial waves that give rise to arterial blood pressure, based on measurements of pressure, P, and velocity, U, waveforms (Figure 1). Wave intensity analysis is applicable to the evaluation of circulatory physiology and quantifying the pathophysiology of disorders such as coronary artery disease. The method is based on discrete, successive wave fronts (wavelets) and is carried out in the time domain. These wavelets travel forward and backwards in the arteries with amplitudes Δ P {\textstyle \Delta P} and Δ U {\textstyle \Delta U} . The wave intensity, Δ I {\textstyle \Delta I} , of a particular wavelet is defined as Δ I = Δ P Δ U {\displaystyle \Delta I=\Delta P\Delta U} It is related to sound intensity in acoustics and describes the power per unit area carried by the wavelet. From the theory discussed below, there is a relationship between the pressure amplitude and the velocity amplitude of a wavelet Δ P ± = 1 2 ( Δ P ± ± ρ c Δ U ± ) {\displaystyle \Delta P_{\pm }={\frac {1}{2}}(\Delta P_{\pm }\pm \rho c\Delta U_{\pm })} where ρ is the density of blood and c is the wave speed of the wavelet. From these equations, generally known as the water hammer equations, it follows that the wave intensity for forward wavelets Δ I + > 0 {\textstyle \Delta I_{+}>0} and for backward wavelets Δ I − < 0 {\textstyle \Delta I_{-}<0} . The ability to determine the direction of a wavelet from its sign is the basis of the practical utility of wave intensity analysis.
Net wave intensity The pressure amplitude of a wavelet can be positive (compression) or negative (decompression) and the velocity amplitude can be positive (acceleration) or negative (deceleration). The measured changes Δ P {\displaystyle \Delta P} and Δ U {\displaystyle \Delta U} are the sums of the amplitudes of the forward and backward wavelets arriving at the measurement site at the time of the measurement and so the wave intensity Δ I {\displaystyle \Delta I} is sometimes called net wave intensity. The Δ I {\displaystyle \Delta I} in the Figure 2 shows the normal pattern in the aorta and illustrates four important features:
A large positive peak at the start of systole indicating a dominant forward wave due to the compression of the left ventricle. A period of relatively small negative wave intensity during mid-systole indicating a small level of reflected wave activity. A smaller positive peak at the end of systole indicating that the deceleration of blood at the end of systole is predominantly due to a forward deceleration wave instead of backward reflected waves. The very low level of net wave intensity during diastole Departures from this pattern of wave intensity is usually indicative of pathology.
Separation of forward and backward waves The additivity of the forward and backward wavelets coinciding at the site of measurement at a particular time can be combined algebraically with the water-hammer equations to calculate the magnitudes of the two wavelets Δ P ± = 1 2 ( Δ P ± ± ρ c Δ U ± ) {\displaystyle \Delta P_{\pm }={\frac {1}{2}}(\Delta P_{\pm }\pm \rho c\Delta U_{\pm })} This method assumes that the wave speed is constant. In general, the wave speed is a function of the pressure. A more complex method of separation involving integrals along the characteristics is available. The forward and backward waveforms follow from summing the magnitudes of the sequential wavelets P ± = Σ Δ P ± {\displaystyle P_{\pm }=\Sigma \Delta P_{\pm }} The pressure shown in Figure 1 is separated into its forward and backward components in Figure 3. This separation is carried out in the time domain and can be applied to irregular, non-periodic data. For periodic heart beats this separation coincides closely with the separation obtained using Fourier analysis methods.
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