Detrended fluctuation analysis (DFA) is a scaling analysis method used to estimate long-range power-law correlation exponents in noisy signals. Many noisy signals in real systems display trends, so that the scaling results obtained from the DFA method become difficult to analyze. We systematically study the effects of three types of trends — linear, periodic, and power-law trends, and offer examples where these trends are likely to occur in real data. We compare the difference between the scaling results for artificially generated correlated noise and correlated noise with a trend, and study how trends lead to the appearance of crossovers in the scaling behavior. We find that crossovers result from the competition between the scaling of the noise and the “apparent” scaling of the trend. We study how the characteristics of these crossovers depend on (i) the slope of the linear trend; (ii) the amplitude and period of the periodic trend; (iii) the amplitude and power of the power-law trend, and (iv) the length as well as the correlation properties of the noise. Surprisingly, we find that the crossovers in the scaling of noisy signals with trends also follow scaling laws—i.e., long-range power-law dependence of the position of the crossover on the parameters of the trends. We show that the DFA result of noise with a trend can be exactly determined by the superposition of the separate results of the DFA on the noise and on the trend, assuming that the noise and the trend are not correlated. If this superposition rule is not followed, this is an indication that the noise and the superposed trend are not independent, so that removing the trend could lead to changes in the correlation properties of the noise. In addition, we show how to use DFA appropriately to minimize the effects of trends, how to recognize if a crossover indicates indeed a transition from one type to a different type of underlying correlation, or if the crossover is due to a trend without any transition in the dynamical properties of the noise.

Detrended fluctuation analysis (DFA) is a scaling analysis method used to quantify long-range power-law correlations in signals. Many physical and biological signals are “noisy,” heterogeneous, and exhibit different types of nonstationarities, which can affect the correlation properties of these signals. We systematically study the effects of three types of nonstationarities often encountered in real data. Specifically, we consider nonstationary sequences formed in three ways: (i) stitching together segments of data obtained from discontinuous experimental recordings, or removing some noisy and unreliable parts from continuous recordings and stitching together the remaining parts—a “cutting” procedure commonly used in preparing data prior to signal analysis; (ii) adding to a signal with known correlations a tunable concentration of random outliers or spikes with different amplitudes; and (iii) generating a signal comprised of segments with different properties—e.g., different standard deviations or different correlation exponents. We compare the difference between the scaling results obtained for stationary correlated signals and correlated signals with these three types of nonstationarities. We find that introducing nonstationarities to stationary correlated signals leads to the appearance of crossovers in the scaling behavior and we study how the characteristics of these crossovers depend on (a) the fraction and size of the parts cut out from the signal, (b) the concentration of spikes and their amplitudes (c) the proportion between segments with different standard deviations or different correlations and (d) the correlation properties of the stationary signal. We show how to develop strategies for preprocessing “raw” data prior to analysis, which will minimize the effects of nonstationarities on the scaling properties of the data, and how to interpret the results of DFA for complex signals with different local characteristics.

Significance: Shift work is a risk factor for hypertension, inflammation, and cardiovascular disease, even after controlling for traditional risk factors. Shift workers frequently undergo circadian misalignment (i.e., misalignment between the endogenous circadian system and 24-h environmental/behavioral cycles). This misalignment has been proposed to explain, in part, why shift work is a risk factor for hypertension, inflammation, and cardiovascular disease. However, the impact of circadian misalignment per se on 24-h blood pressure and inflammatory markers is poorly understood. We show—under highly controlled laboratory conditions—that short-term circadian misalignment increases 24-h blood pressure and inflammatory markers in healthy adults. Our findings may help explain why shift work increases hypertension, inflammation, and cardiovascular disease risk.

Circadian rhythmicity of cardiac ion-channel expression and of an index of myocardial repolarization is under the control of Klf15, a clock-dependent oscillator that is required for generating transient outward potassium current, and deficiencies or excesses of which cause loss of rhythmic variation in myocardial and abnormal repolarization, and an enhanced susceptibility to ventricular arrhythmias. Several physiological parameters in the cardiovascular system show diurnal variation. Mukesh Jain and colleagues now provide a link between circadian rhythms and arrhythmogenesis in mice. They show that the transcription factor Klf15 is regulated by components of the circadian clock, and Klf15 in turn regulates expression of the ion channel KChIP2. In gain- and loss-of-function experiments, the authors show that Klf15 regulates temporal variation in cardiac repolarization and susceptibility to arrhythmias. The findings raise the possibility that circadian factors contribute to the diurnal variation seen in occurrence of sudden cardiac death. Sudden cardiac death exhibits diurnal variation in both acquired and hereditary forms of heart disease1,2, but the molecular basis of this variation is unknown. A common mechanism that underlies susceptibility to ventricular arrhythmias is abnormalities in the duration (for example, short or long QT syndromes and heart failure)3,4,5 or pattern (for example, Brugada’s syndrome)6 of myocardial repolarization. Here we provide molecular evidence that links circadian rhythms to vulnerability in ventricular arrhythmias in mice. Specifically, we show that cardiac ion-channel expression and QT-interval duration (an index of myocardial repolarization) exhibit endogenous circadian rhythmicity under the control of a clock-dependent oscillator, krüppel-like factor 15 (Klf15). Klf15 transcriptionally controls rhythmic expression of Kv channel-interacting protein 2 (KChIP2), a critical subunit required for generating the transient outward potassium current7. Deficiency or excess of Klf15 causes loss of rhythmic QT variation, abnormal repolarization and enhanced susceptibility to ventricular arrhythmias. These findings identify circadian transcription of ion channels as a mechanism for cardiac arrhythmogenesis.