Pitfalls in Normalizing Wave Intensity Indices to Body Size

Abstract

We read with interest the paper by Valdovinos et al. [1] which used wave intensity analysis (WIA) to evaluate single ventricle function in patients with a Fontan circulation. Since the control group was much younger than the Fontan group (2.5 vs 19 years), WIA variables were indexed to body surface area (BSA). With such indexing, both the peak intensity (0.61 vs 1.47 × 106 Wm−2 s−2 m−2) and energy flux (2.9 vs 6.9 × 104 Jm−2 s−2 m−2) of the forward compression wave (FCW) associated with early-systolic flow acceleration were markedly lower in Fontan patients, leading to the conclusion that ventricular contractility was impaired in this group. However, we have two concerns regarding the validity of indexing wave intensity to BSA as performed by Valdovinos et al. [1]. First, as discussed by Gunther [2], dimensional analysis can exquisitely predict allometric scaling of physical quantities with body weight, via a scaling exponent denoted b (see Table 10 in [2]). A quantity that scales with BSA would have b = 0.67, whereas blood pressure, which does not scale with body weight, has b = 0. Similarly, blood velocity scales very weakly with body weight, with b = 0.065. Given that wave intensity is calculated from pressure and velocity, it too is almost body size-independent, with b = 0.065. With an invariant heart rate between body sizes, as in Valdovinos et al. [1], b = 0.065 would also be expected for wave energy flux. These principles have significant implications for interpretation of data in [1]. Assuming body weights from [3] based on ages reported in [1] (13.5 and 69 kg), scaling with b = 0.065 would indicate that Fontan patients had similar or even higher FCW peak intensity compared with controls (approximately 0.98 vs 0.82 × 106 Wm−2 s−2, where control values were scaled to 69 kg), while FCW energy was 21% higher in the Fontan group (approximately 4.6 vs 3.8 × 106 Jm−2 s−2). This type of scaling would therefore fundamentally alter conclusions about differences in ventricular contractility in Fontan patients in [1]. The second concern is that scaling based on body size alone neglects physiological changes that occur during childhood and are independent of body size, which may also influence the dimensionless wave ratios reported in [1]. While there is evidence of reduced FCW magnitude in preand post-Fontan patients, using relatively wellmatched controls [4, 5], the issues we have raised emphasize the difficulty in making reliable comparisons between the unmatched groups in [1]. Given well-established allometric scaling principles [2], and in the absence of normative values, we suggest that wave intensity should not be indexed to body size.