The dependence of FMD% on baseline diameter: a problem solved by allometric scaling.

DeVan et al. [1] undertook a comprehensive cross-sectional study involving the independent variables of IFG (impaired fasting glucose) and exercise training status. In keeping with the effects of many other independent variables, including age [2,3], exercise [4], red wine [5] and cardiovascular disease [6], both FMD% [percentage FMD (flow-mediated dilation)] and Dbase (baseline artery diameter) were found to be different between the study samples. For example, Dbase was 0.46 mm larger in non-exercising older adults with IFG than the trained older adults with IFG, whereas FMD% was 3.6 % higher in the latter sample. Brachial FMD% is mathematically equivalent to the ratio of Dpeak (peak diameter) divided by Dbase, i.e. Dpeak/Dbase, where ‘1’ is the power exponent assumed ubiquitously whenever FMD% is selected as a study outcome. Given that Dbase is the denominator in the FMD% ratio statistic, it can be questioned to what extent the sample differences in Dbase are explaining the sample differences in FMD% [2,3]. This statistical issue may confound the findings of the otherwise completely sound study rationale and design in [1]. Figure 1 presents the relationship (r = − 0.74) between the sample mean values of FMD% and Dbase reported in [1]. One of the most consistent findings in FMD% research is this moderateto-strong negative correlation between Dbase and FMD%, and this is not surprising given that Dbase is inherent in the FMD% calculation. However, it is only recently that this correlation has been recognized as a fundamental scaling problem with the FMD% ratio statistic [2,3]. DeVan et al. [1] reported that FMD%, the study outcome, was covariate-adjusted for Dbase in their statistical analyses. However, this is not the correct approach to ensure that the change in artery diameter is independent from variability in Dbase [2,3]. With this approach, one is attempting to statistically adjust the ratio of Dpeak/Dbase by Dbase yet again. This approach might make the distributional properties of the FMD% ratio even less Gaussian thereby influencing population estimates of FMD [3]. The FMD% ratio is clearly an unsuccessful attempt to adjust the change in diameter for variability in Dbase in a consistent manner. The correct approach for quantifying a change in artery diameter that is truly independent from initial diameter is via allometric scaling.