Response to: ‘Allometric scaling of endothelium-dependent vasodilation: Brachial artery flow-mediated dilation coming of age’

We sincerely thank Drs Al Mheid and Quyyumi for their interest in our critique of the percentage flow-mediated dilation ratio index (FMD%). ¹ We can respond to the two ‘interpretative challenges’ raised in the final two paragraphs of their editorial. ² First, it was questioned whether FMD% might ultimately represent a useful integrative exposure of cardiovascular disease outcome; that is, whether a small FMD% integrates the prognostic utility of both a large baseline diameter (D_base) and a small change in diameter (D_diff). Second, it was questioned whether FMD% or D_diff should be scaled to indicators of body size other than D_base.

Historically, the dependency of FMD% on D_base has been consistently viewed as a problem to eradicate. For example, the interpretation of FMD% has been said to be sound only for relatively small arteries in adults and relatively large arteries in children, ³ only if study samples or conditions are similar in terms of D_base, ⁴ or only if D_base, D_diff and, potentially, shear rate are all scrutinised together. ⁵ Importantly, the now widespread idea that FMD% should be normalised for shear rate was first rationalised primarily on the basis of eradicating D_base dependency. ⁶ Therefore, if the substantial dependency of FMD% on D_base is now thought to be useful, then it follows that past and present efforts to eradicate D_base-dependency have been unnecessary. This seems like a significant juxtaposition.

Like other researchers, we maintain that the dependency of FMD% on D_base is a significant measurement problem to eradicate. It must have been deemed important to scale D_diff to D_base, otherwise researchers would have selected D_diff as the primary outcome rather than FMD%. We found a slightly negative correlation between D_diff and D_base in the MESA (Multi-Ethnic Study of Atherosclerosis) dataset. This means that, irrespective of the physiological mechanisms for this scaling relationship, FMD% is a poor choice of index to describe it because FMD% assumes direct and consistent proportionality. The result is that FMD% exaggerates substantially the negative correlation between D_base and the flow-mediated response. It seems incongruous to now accept these erroneous scaling properties of FMD% as being potentially useful.

To ascertain whether FMD% is a useful integrative index, one has to first quantify precisely the clinical importance of its components; the D_base-free flow-mediated response per se and D_base per se. It is possible that at least some of the prognostic utility of FMD% is explained by the prognostic utility of D_base. If this is the case, then the clinical usefulness of obtaining an additional measurement of D_diff needs careful consideration. This is because the measurement of D_diff (or FMD%), in response to reactive hyperaemia, is more costly, requires more equipment and more training, and is less reproducible than measurements of D_base. ¹ Therefore, it seems important to ascertain the relative prognostic utility of FMD%, D_base and the D_base-free flow-mediated response per se. Then it can be seen clearly whether the measurement of D_diff is worth the additional effort and cost.

In response to the second ‘interpretive challenge’ that was raised, it is important to distinguish between the scaling properties of a ratio index and the scaling of any physiological variable for body size. Allometry is relevant to many physiological variables, but these variables need not be themselves ratios. For example, cardiac dimensions of mass and volume can be scaled for body size, ⁷ but these variables are not already ratio indices like FMD%. Appropriate scaling should be considered for all ratio indices, irrespective of whether the denominator of the ratio is a body size variable or not. Recently, Curran-Everrit ⁸ included gene expression, cerebral oxygen uptake and ribonucleic acid amongst the list of physiological ratios that should be analysed allometrically, even though their denominators are not necessarily body size variables. In the case of FMD%, D_base happens to be a variable related to body size but, more importantly, it is the denominator of FMD%. Therefore, the appropriate scaling of a ratio index for its denominator is paramount before any further consideration of body size scaling is made. This established philosophy informs our scrutiny of the FMD% ratio index.