1.4 Nomenclature (added 2 March 2008)

Historically there has been a fair amount of disparity in the nomenclature used in wave intensity analysis. Wave intensity itself, for example, was not defined in our early papers where we used the term dPdU. There is still no consensus of nomenclature amongst the different groups using wave intensity analysis. This brief section is meant as a guide to the different possible nomenclatures with some personal comments about their pros and cons, and provisional recommendations for their cardiovascular use in the last paragraph.

Wave intensity

Most authors have used the original definition of wave intensity dI = dPdU where dP is the change in pressure across a wavefront and dU is the change in velocity. This definition, however, has the disadvantage that the magnitude of the calculated dI depends upon the sampling rate which defines the wavefronts. Longer sampling times (lower sampling rates) increase the changes during the sampling interval, thereby increasing the magnitude of dI. An alternative definition of wave intensity dI' = (dP/dt)(dU/dt) eliminates this problems and enables the direct comparison of the magnitudes of wave intensity obtained at different sampling rates. The original definition dI has the advantage that the units, W/m2 have a direct meaning as the energy flux per unit area carried by the wave. The alternative definition, dI', does not have such easily understood units. In any case, it is imperative to cite the sampling rate used in any study so that comparisons with other results can be made.

Waves One of the biggest problems in the communication of wave intensity analysis arises from the different meanings of the word wave. As discussed at length in Section 1.2 What is a Wave?, the measured waveforms of pressure and velocity are treated as the superposition of succeeding wavefronts rather than the superposition of sinusoidal wavetrains, as is done in impedance analysis of arterial mechanics. Unfortunately, 'wave' can be used to describe any or all of these entities. I have therefore used the following conventions in these pages:

waveform = measured pressure or velocity waveforms

wavetrain = a sinusoidal wave

wavefront = a small, incremental wave

I do not advocate this particular usage universally; when it is clear either by definition or context, it would be appropriate to use 'wave' for any of these particular forms of wave. In this introduction, however, I have opted for this more stilted, but precise nomenclature.


wavefronts can travel either forward or backward; they can cause and increase or decrease in pressure and an increase or decrease in velocity. As we will see in the later analysis, there is a basic relationship between the incremental pressure and velocity that depends on the direction of travel of the wavefront:

dP± = ± ρc dU±         (Water hammer equation)

That is, in forward travelling wavefronts the sign of the change in pressure is equal to the sign of the change in velocity and in backward waves they are opposite. This can cause a lot of confusion when first exposed to wave intensity analysis. Wavefronts have three properties: direction of travel, type of pressure change and type of velocity change. Because of the water hammer equation any one property depends on the other two and so it is necessary to specify only two of them to fully describe the wavefront type. The various suggestions for nomenclature are listed by type:

Direction of travel:

forward - backward: These terms are obvious once the coordinate system is defined, but the choice of direction in the cardiovascular system is not always obvious. We have generally defined the forward direction as the direction of mean blood flow. In the arteries this is an obvious choice, but it is contentious in the veins.

proximal originating - distal originating: This terminology has been used to overcome the arbitrariness of 'forward - backward'. They are terms that are familiar to cardiologists where they refer to relative distance from the heart. This terminology can lead to problems in the venous system where blood flows from distal veins to proximal veins; opposite to the arteries. (Note that it is important to include 'originating' in this specification because the use of a location to describe direction depends on whether you use the origin or the destination to indicate direction. For example, a 'northerly' wind comes from the north whereas a wind with a 'northerly' velocity is going towards the north.)

Effect on pressure:

compression - expansion: This terminology arises from gas dynamics and refers to the sign of the change in pressure. 'Compression' refers to an increase in pressure and 'expansion' refers to a decrease in pressure. This is natural in gas dynamics where the terms refer to the changes in volume of the gas; as pressure decreases the volume increases. Unfortunately, the descriptive nature of the terms do not work in elastic vessels where a decrease in pressure results in a decrease in the diameter of the vessel. This notation can lead to statements that are difficult to understand such as 'an expansion wave cause the artery to contract'.

compression - decompression: These terms also refer to the change in pressure; 'compression' is an increase in pressure and 'decompression' is a decrease in pressure.

compression - rarefaction: Another possible choice for describing the change in pressure; 'rarefaction' is the opposite of compression, but is less appropriate for descriptions of liquids than gases.

pushing - pulling: These are colloquial terms that may be easier for non-specialists to understand.

blowing - sucking: These are also colloquial terms that enable the non-specialist to easily grasp the direction of change in pressure due to the intervention at the end of the vessel. The intention with this nomenclature is to describe the changes in pressure at the end of the tube but it could be interpreted as the changes relative to ambient pressure. With this interpretation, it could be understood that a 'sucking' wave will produce a pressure lower than the external pressure, which in elastic vessels would cause collapse.

Effect on velocity:

acceleration - deceleration: This terminology describes the wavefronts through their effect on the velocity. 'Acceleration' increases the velocity and 'deceleration' decreases the velocity. Because cardiologists are usually interested in perfusion, identifying waves by their effect on the velocity could be useful. There is, however, a subtle dependence on the choice of coordinate system (see above).

Wave patterns There has been some suggestion that the pattern of wavefronts seen using wave intensity analysis should be defined. This has been done for the ECG in electrocardiology and there are many other examples in different areas of clinical cardiology - the 'E' and 'A' waves during left ventricular filling, the 'x-descent' and 'y-descent' in the venous pressure waveform spring to mind. This is obviously important if wave intensity analysis is to gain clinical applications. It seems to me, however, that it is premature to devise such systems of nomenclature until there is more agreement about the clinical application of wave intensity analysis. The only two waves (here I am using the term to mean an observable collection of wavefronts) that are currently unambiguous are the forward compression wave generated at the start of systole by the contraction of the ventricle and the forward decompression wave at the end of systole resulting from the slowing down and eventual relaxation of contraction at the end of systole. Other waves have been seen and described in different papers, but the patterns of waves are generally very different depending upon the site of measurement and the clinical condition being investigated.

Alice and Humpty Dumpty by Sir John Tenniel (1871).
from Lenny's Alice in Wonderland Site.

The problem with nomenclature was summed up nicely by Humpty Dumpty in Alice Through the Looking Glass; "When I use a word, it means just what I choose it to mean -- neither more nor less." There is no problem in written work if the terminology is defined clearly. The problem arises when the words are received with a different meaning from that with which they were sent.

My current preferences are to describe wavefronts as forward - backward where the direction is defined by the mean direction of blood flow. Despite my background in gas dynamics, I also favour compression - decompression to describe wavefronts with increasing - decreasing pressures. With these conventions, we can say 'a forward travelling compression wavefront causes acceleration of the flow', 'a backward travelling compression wavefront causes deceleration of the flow', 'a backward travelling decompression wavefront causes deceleration' and 'a backward travelling decompression wave causes acceleration'.

There has been a suggestion that 'causes' in the preceding sentences is not appropriate since it could equally well be stated that 'a forward travelling acceleration wave causes compression'. Because of the inextricably linked nature of pressure and velocity in elastic tube waves, this is perfectly true; one causes the other and the other causes the one. The suggestion of replacing 'causes' with 'is associated with' weakens the direct causal link between the two properties and is more appropriate to the description of simple correlation studies where no mechanism of effect is necessary.

(An excellent example of this sort of 'mechanism free' correlation is the comparison of the total USA traffic fatality rate and the tonnage of fresh lemons imported to the USA from Mexico from 1996-2000 which has an R2=0.97. )

Examples of mutual causative effects are common. Consider, for example, the gravitation between the Earth and the Moon. It is equally accurate to say that 'the Earth causes the Moon to orbit the Earth' and that 'the Moon causes tides on the Earth'. The mutual attractive nature of gravity makes both statements true and unambiguous. The mechanical linkage between pressure and velocity is similar so that stating that pressure changes causes velocity changes does not imply that velocity changes cannot cause pressure changes.