Evidence of wave trapping in the arteries

There is evidence of wave trapping in many old experiments, although the authors generally did not interpret their data in terms of this concept.

MacDonalds' Blood Flow in Arteries

In the second edition of his book , MacDonald discussed the possibility of a 'standing wave' in the aorta. In it there is much information about the phenomenon that we are calling 'wave trapping'. There are a number of relevant comments. For example:

'It might, therefore, seem obvious that the arterial tree which has many discontinuities of this sort would create large reflections and that there are no grounds for argument. The case for the contrary is probably best summed up by the remark that Womersley made when he was first confronted with the problem - "If you wanted to design a perfect sound-absorber you could hardly do better than a set of tapering and branching tubes with considerable internal damping such as the arterial tree."'

'The Experiments of Peterson and Shepard (1955) furthermore appear to bear this out because they showed that a large pressure wave created by a rapid injection pulse of blood retrogradely into a femora artery caused no detectable effect in the pressure-curve recorded at the root of the aorta.'

After a brief discussion of the effects of multiple reflections and dissipation on a wave arriving back at the ascending aorta, MacDonald also notes:

'This conclusion is consonant with the findings of Starr (1957) in human cadavers. He created a single transient wave in the aorta of an an amplitude approximately the amplitude of the pulse wave. A reflected wave is just detectable at the arch but there is no sign of a secondary reflection.'

All of these observations are interpreted in terms of dissipation, which certainly must be considered in the interpretation of cardiovascular measurements. However, there is no mention of the asymmetry of the reflection coefficient for waves approaching a bifurcation from different directions (although it is clearly present in the theoretical results that are given). We would suggest that this asymmetry could explain many of the observations.

The occlusion experiments of Westerhof and colleagues

A landmark series of experiments by Westerhof and his colleagues also demonstrates the phenomenon of 'wave trapping' although, again, the data were not originally interpreted in this way. The experiment involved the creation of total occlusions by the inflation of intra-arterial balloons at different locations in the cardiovascular system of a dog and measuring their affect on the pressure and flow measured at the ascending aorta. The occlusions were created temporarily at four locations (see figure): 'high' - where the aorta leaves the vertebral column, 'dia' - at the level of the diaphragm, 'mid' - at the level of the renal arteries and 'low' - just above the aorto-iliac bifurction.

The results of the careful and innovative experiment are very informative about arterial haemodynamics in general and they deserve careful study by anyone interested in this subject. However, for the purposes of the current discussion, the most significant result is the comment: 'Haemodynamic effects of low aortic occlusion... were small and were not tabulated.'. In other words, the haemodynamic effects at the ascending aorta of a total occlusion of the aorto-iliac bifurcation were not large enough to be tabulated.

The occlusion experiments of Khir and Parker

Khir performed a very similar experiment in the laboratories of J.V. Tyberg using snares rather than intra-arterial balloons to produce occlusions at the same sites in the aorta. The results were interpreted using wave intensity analysis and are discussed at various places in these notes. Again, the implications for the discussion of wave trapping are summarised by the statement: However, with the distal occlusions, neither the arrival time nor the size of the reflection was different from that of the control, which was somewhat surprising..' It was, in fact, contemplation of these experimental results that led us to the idea of wave trapping.

References:

Khir A and Parker KH (2005) Wave intensity in the ascending aorta: effects of arterial occlusion. J. Biomech. 38, 647-655.

MacDonald DA (1960) Blood Flow in the Arteries, 2^nd Ed., Edward Arnold, London, Chapter 12.

Peterson LH and Shepard RB (1955) Symposium on applied physiology in modern surgery; some relationships of blood pressure to cardiovascular system. S. Clin. N. Amer., 35, 1613-1628.

Starr I(1957) Studies made by simulating systole at necropsy. X. State of peripheral circulation in cadavers. J. Appl. Physiol. 11, 174-180.

Van Den Bos GC, Westerhof N, Elzinga G, and Sipkema P (1976) Reflection in the systemic arterial system: effects of aortic and carotid occlusion. Cardiovasc. Res. 10, 565–573.

Westerhof N, Sipkema P, Van Den Bos GC and Elzinga G (1972) Forward and backward waves in the arterial system. Cardiovas. Res. 6, 648–656.