Fast breathhold cardiovascular magnetic resonance (CMR) has become a reference standard for the measurement of cardiac volumes, function, and mass. The implications of this for sample sizes for remodeling studies in heart failure (HF) have not been elucidated. We determined the reproducibility of CMR in HF and calculated the sample size requirements and compared them with published values for echocardiography. Breathhold gradient echo cines of the left ventricle were acquired in 20 patients with HF and 20 normal subjects. Sample size values were calculated from the interstudy standard deviation of the difference. The percentage variability of the measured parameters in our HF group of intraobserver (2.0-7.4%), interobserver (3.3-7.7%), and interstudy (2.5-4.8%) measurements was slightly larger than for our normal group (1.6-6.6%, 1.6-7.3%, and 2.0-7.3%, respectively) but remained comparable with previous studies in normal subjects. The calculated sample sizes in patients with HF for CMR to detect a 10-ml change in end-diastolic volume (n = 12) and end-systolic volume (n = 10), a 3% change in ejection fraction (n = 15), and a 10-g change in mass was (n = 9) were substantially smaller than recently published values for two-dimensional echocardiography (reduction of 81-97%). Breathhold CMR is a fast comprehensive technique for the assessment of cardiac volumes, function, and mass in HF that is accurate but also highly reproducible. This allows a considerable reduction in the patient numbers required to prove a hypothesis in research studies, which suggests a potential for important research cost savings.

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The diagnostic and prognostic power of the fractal complexity measure ‘α’ of detrended fluctuation analysis (DFA) has remained mysterious because there has been no explanation of its meaning, particularly in relation to spectral analysis. First, we present a mathematical analysis of the meaning of α, in weighted power‐spectral terms. Second, we test this hypothesis and observe correlations between DFA‐based and weighted spectral methods of 0.97 (P < 0.0001) for α1 and 0.98 (P < 0.0001) for α2. Third, we predict mathematically that even in conventional (unweighted) spectral analysis there should be approximate counterparts to DFA, namely that α1 and α2 behave broadly in proportion to the conventional (unweighted) ratios LF/(HF + LF) and VLF/(LF + VLF), respectively, where HF is high frequency, LF is low frequency and VLF is very low frequency. Fourth, we test this hypothesis by physiologically manipulating spectral ratios in healthy volunteers in two ways. The effect of 0.1 Hz controlled breathing on LF/(HF + LF) correlates markedly with the effect on α1 (r= 0.73, P= 0.01); the effect on VLF/(LF + VLF) correlates markedly with that on α2 (r= 0.76, P < 0.01). Likewise, with voluntary periodic breathing the reduction in α2 correlates strongly with that in VLF/(LF + VLF) (r= 0.88, P < 0.001); effects on α1 and LF/(HF + LF) again clearly correlate (r= 0.73, P= 0.01). Finally, we examine published literature to identify previously undiscussed evidence of the relationship between α1 and LF/(HF + LF). We conclude that the α1 and α2 indices are simply frequency‐weighted versions of the spectral ratios LF/(HF + LF) and VLF/(LF + VLF), respectively, multiplied by two (giving a range of 0‐2). We can now understand fractal manifestations of physiological abnormalities: depressed baroreflex sensitivity → low LF/HF → low LF/(HF + LF) → low α1, while periodic breathing → high VLF/LF → high VLF/(LF + VLF) → high α2. Prognostic associations of α are no longer mysterious.