3.1 Wave intensity

Wave intensity is defined as

dI = dPdU

where dP is the change of pressure across a wavefront and
           dU is the change in velocity across a wavefront

It has the units of power/area (W/m²) and has the very useful property that it is positive for forward travelling wavefronts, both compression and decompression, and negative for backward wavefronts. If, as is often the case, there are simultaneous forward and backward waves in the artery, the wave intensity is the algebraic sum of the wave intensities of the two wavefronts intersecting at the measurement site at the time of measurement. The sign of the net wave intensity therefore reveals immediately if the forward or backward waves are dominant.

The first measurement of wave intensity in man. The figure shows our first measurement of wave intensity in human ascending aorta. The top trace is the pressure P, the middle trace is the velocity U (measured using a catheter) and the bottom trace is the wave intensity dI calculated from P and U. The large negative peaks indicate a dominant backward wave in mid-systole that varies with the respiratory cycle (see the detail).

We now know that this pattern of wave intensity is pathological but at the time we were expecting large reflections and presumed they were normal. When we didn't see such large negative peaks in the following patients, we assumed that it was a failure in equipment or analysis and wasted a lot of time checking our methods before realising that our expectations were wrong.

One of the advantages of wave intensity analysis is that it is carried out in the time domain which makes it easy to relate the findings to particular points in the cardiac cycle. For example, it is clear that the large positive peak of wave intensity at the start of systole is due to the forward compression wave caused by the contraction of the ventricle. The second large positive peak at the end of systole was initially unexpected. Being positive, it indicates that there is a dominant forward travelling wave at the end of systole that is primarily responsible for stopping the flow of blood from the heart. This observation was one of the first insights from wave intensity analysis.

Note that this definition of wave intensity has the disadvantage that its magnitude depends upon the sampling interval over which dP and dU are measured. An alternative definition that does not suffer from this problem is

dI' = (dP/dt)(dU/dt)

where dP/dt and dU/dt are the time derivatives (rather than differences). If the magnitude of wave intensity is being compared between studies done under different sampling conditions, this definition of wave intensity should be used. In any case, the sampling rate should always be specified so that the results can be expressed in either form.