Factual errors in a recent paper by Westerhof, Segers and Westerhof in Hypertension

But facts are chiels that winna ding
An downa be disputed
– from A Dream by Robert Burns (1786)

(But facts are fellows that will not be overturned,
And cannot be disputed)

Wave separation, wave intensity, the reservoir-wave concept, and the instantaneous wave-free ratio (2015) N Westerhof, P Segers and BE Westerhof, Hypertension, DOI: 10.1161/HYPERTENSIONAHA.115.05567 Hereinafter referred to as [WSW].

This paper by three distinguished workers in the field of cardiovascular mechanics, concludes that both the reservoir pressure and instantaneous wave-free ratio are ’... both physically incorrect, and should be abandoned’. These are very strong conclusions which, if they were opinions could only be debated. Reading the paper in detail, however, reveals that it contains numerous factual errors in their discussion of these two entities. Since facts are different from opinions, we believe that it is essential that these errors be corrected before they gain credence by repetition.

False facts are highly injurious to the progress of science, for they often endure long; but false views, if supported by some evidence, do little harm, for every one takes a salutary pleasure in proving their falseness.
– Charles Darwin (1871)

Because we are naturally prejudiced about the validity of both the reservoir pressure (\(P_{res}\)) and instantaneous wave-free ratio (iFR), having been involved in the conception and development of both ideas, we will try to present our arguments as transparently and fairly as possible. As far as possible we will demonstrate the errors by direct quotations from the paper. The whole paper\(^1\) is available from the Hypertension web site and should be consulted directly if there are any questions about our treatment of the text.

Approximately two thirds of the paper is taken up with a discussion of wave separation and wave intensity from the point of view of the more usual Fourier-based methods of analysing cardiovascular mechanics, frequently called the impedance method. This part of the paper is, as far as we can see, both insightful and free of major errors. We found some of the discussion about wave intensity analysis thought-provoking and agree with most of their conclusions. We recommend the first two-thirds of this paper to anyone interested in arterial mechanics.

In contrast, the last third of the paper, starting with the final sentence of the section ’Summary of Wave Separation and WIA’ is riddled with errors of interpretation and, more importantly, contains a number of mistakes (or in Darwin’s terms ’false statements of fact’) that need to be corrected. Instead of dealing with these errors chronologically, we will point out the fundamental errors first and then deal with their sequelae.

The fundamental errors

The first major error is the assumption that RWC (Reservoir-Wave Concept) and iFR (Instantaneous wave-Free Ratio) are directly related and that conclusions drawn from either of the two ideas can be directly applied to the other. This assumption is not stated overtly but it permeates almost all of their discussion.

In fact, iFR makes no use of the reservoir-wave concept and we are unaware of any publications before WSW that imply that it does. We did look into the idea of applying the reservoir pressure to our coronary measurements and very quickly decided that it added nothing to the wave intensity analysis based on the measured pressure and flow. It is our belief that the reservoir pressure hypothesis is very likely to be inappropriate in the coronary arteries because of their limited compliance and their proximity to terminal reflection sites and other sources of backward travelling waves. We have used reservoir pressure analysis of pressure measured in various distal locations, e.g. the radial artery in the analysis of the CAFE study and while we have some reservations about their interpretation in relation to current theories about the reservoir pressure, one cannot contest their epidemiological predictive power.

Conversely, iFR played no role in the development of the reservoir-wave hypothesis which antedated iFR by more than a decade. After the development of iFR there has never been any attempt to apply that principle to the reservoir pressure Pr.

Examples of this basic error will be discussed at various points in the following discussion which concentrates on first Pr and then iFR.

The basic error about \(P_{res}\)

The first sentence of the second paragraph of the section Reservoir-Wave Concept states:

The RWC assumes that diastole (diastasis) is wave-free and that, therefore, the arterial system can be described by a reservoir (storage volume) and peripheral resistance (Frank Windkessel). (my italics)

This is simply wrong. Nowhere in our work do we assume that diastole is ’wave-free’. Wave-free is used in the description of iFR. In the derivation of Pr we assume only that the major part of the diastolic pressure waveform can be described by a falling exponential function, which is predicted by the overall mass conservation equation when there is no flow into the aortic root. This is also predicted in the Frank Windkessel model and that model was important in our original conception of the RWC. In fact, in our first paper on the subject (ref 36), we did not define a reservoir pressure, but called it the Windkessel pressure. Further work on the subject, experimental and theoretical, showed that the 2-element Windkessel was not a viable model. It was clear that what we had called the Windkessel pressure was propagating down the aorta and so we introduced the term ’reservoir pressure’ in our next paper (Wang et al. Am J Physiol 2005) and were careful to describe how it differed from the Windkessel pressure. All of our subsequent papers on RWC should make it clear that Pr is not the Windkessel pressure.

The basic error about iFR

The first sentence of the Section The Instantaneous Wave-Free Ratio states:

The iFR is the ratio of pressure and flow in the latter 75% of diastole.

This is blatantly untrue. The iFR is defined as the ratio of the pressure measured downstream of a coronary stenosis to the pressure measured upstream at a particular time during diastole (see our published equation below). We have never asserted that this ratio is a measure of coronary resistance. As shown below, this fallacy is repeated at least five times.