Effect of nonstationarities on detrended fluctuation analysis

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 amplitude, 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.Comment: 17 pages, 10 figures, corrected some typos, added one referenc

Effect of Trends on Detrended Fluctuation Analysis

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 superimposed trend are not independent, so that removing the trend could lead to changes in the correlation properties of the noise.Comment: 20 pages, 16 figure

Deterministic Chaos and Fractal Complexity in the Dynamics of Cardiovascular Behavior: Perspectives on a New Frontier

Physiological systems such as the cardiovascular system are capable of five kinds of behavior: equilibrium, periodicity, quasi-periodicity, deterministic chaos and random behavior. Systems adopt one or more these behaviors depending on the function they have evolved to perform. The emerging mathematical concepts of fractal mathematics and chaos theory are extending our ability to study physiological behavior. Fractal geometry is observed in the physical structure of pathways, networks and macroscopic structures such the vasculature and the His-Purkinje network of the heart. Fractal structure is also observed in processes in time, such as heart rate variability. Chaos theory describes the underlying dynamics of the system, and chaotic behavior is also observed at many levels, from effector molecules in the cell to heart function and blood pressure. This review discusses the role of fractal structure and chaos in the cardiovascular system at the level of the heart and blood vessels, and at the cellular level. Key functional consequences of these phenomena are highlighted, and a perspective provided on the possible evolutionary origins of chaotic behavior and fractal structure. The discussion is non-mathematical with an emphasis on the key underlying concepts

Plasma brain natriuretic peptide as a surrogate marker for cardioembolic stroke

<p>Abstract</p> <p>Background</p> <p>Cardioembolic stroke generally results in more severe disability, since it typically has a larger ischemic area than the other types of ischemic stroke. However, it is difficult to differentiate cardioembolic stroke from non-cardioembolic stroke (atherothrombotic stroke and lacunar stroke). In this study, we evaluated the levels of plasma brain natriuretic peptide in acute ischemic stroke patients with cardioembolic stroke or non-cardioembolic stroke, and assessed the prediction factors of plasma brain natriuretic peptide and whether we could differentiate between stroke subtypes on the basis of plasma brain natriuretic peptide concentrations in addition to patient's clinical variables.</p> <p>Methods</p> <p>Our patient cohort consisted of 131 consecutive patients with acute cerebral infarction who were admitted to Kagawa University School of Medicine Hospital from January 1, 2005 to December 31, 2007. The mean age of patients (43 females, 88 males) was 69.6 ± 10.1 years. Sixty-two patients had cardioembolic stroke; the remaining 69 patients had non-cardioembolic stroke (including atherothrombotic stroke, lacunar stroke, or the other). Clinical variables and the plasma brain natriuretic peptide were evaluated in all patients.</p> <p>Results</p> <p>Plasma brain natriuretic peptide was linearly associated with atrial fibrillation, heart failure, chronic renal failure, and left atrial diameter, independently (F_4,126= 27.6, p < 0.0001; adjusted R²= 0.45). Furthermore, atrial fibrillation, mitral regurgitation, plasma brain natriuretic peptide (> 77 pg/ml), and left atrial diameter (> 36 mm) were statistically significant independent predictors of cardioembolic stroke in the multivariable setting (Χ²= 127.5, p < 0.001).</p> <p>Conclusion</p> <p>It was suggested that cardioembolic stroke was strongly predicted with atrial fibrillation and plasma brain natriuretic peptide. Plasma brain natriuretic peptide can be a surrogate marker for cardioembolic stroke.</p

The Prognostic Value of Non-Linear Analysis of Heart Rate Variability in Patients with Congestive Heart Failure—A Pilot Study of Multiscale Entropy

AIMS: The influences of nonstationarity and nonlinearity on heart rate time series can be mathematically qualified or quantified by multiscale entropy (MSE). The aim of this study is to investigate the prognostic value of parameters derived from MSE in the patients with systolic heart failure. METHODS AND RESULTS: Patients with systolic heart failure were enrolled in this study. One month after clinical condition being stable, 24-hour Holter electrocardiogram was recording. MSE as well as other standard parameters of heart rate variability (HRV) and detrended fluctuation analysis (DFA) were assessed. A total of 40 heart failure patients with a mea age of 56±16 years were enrolled and followed-up for 684±441 days. There were 25 patients receiving β-blockers treatment. During follow-up period, 6 patients died or received urgent heart transplantation. The short-term exponent of DFA and the slope of MSE between scale 1 to 5 were significantly different between patients with or without β-blockers (p = 0.014 and p = 0.028). Only the area under the MSE curve for scale 6 to 20 (Area(6-20)) showed the strongest predictive power between survival (n = 34) and mortality (n = 6) groups among all the parameters. The value of Area(6-20)21.2 served as a significant predictor of mortality or heart transplant (p = 0.0014). CONCLUSION: The area under the MSE curve for scale 6 to 20 is not relevant to β-blockers and could further warrant independent risk stratification for the prognosis of CHF patients

Reduced Physiological Complexity in Robust Elderly Adults with the APOE ε4 Allele

BACKGROUND:It is unclear whether the loss of physiological complexity during the aging process is due to genetic variations. The APOE gene has been studied extensively in regard to its relationship with aging-associated medical illness. We hypothesize that diminished physiological complexity, as measured by heart rate variability, is influenced by polymorphisms in the APOE allele among elderly individuals. METHODOLOGY/PRINCIPAL FINDINGS:A total of 102 robust, non-demented, elderly subjects with normal functions of daily activities participated in this study (97 males and 5 females, aged 79.2+/-4.4 years, range 72-92 years). Among these individuals, the following two APOE genotypes were represented: epsilon4 non-carriers (n = 87, 85.3%) and epsilon4 carriers (n = 15, 14.7%). Multi-scale entropy (MSE), an analysis used in quantifying complexity for nonlinear time series, was employed to analyze heart-rate dynamics. Reduced physiological complexity, as measured by MSE, was significantly associated with the presence of the APOE epsilon4 allele in healthy elderly subjects, as compared to APOE epsilon4 allele non-carriers (24.6+/-5.5 versus 28.9+/-5.2, F = 9.429, p = 0.003, respectively). CONCLUSIONS/SIGNIFICANCE:This finding suggests a role for the APOE gene in the diminished physiological complexity seen in elderly populations

Percutaneous coronary angioplasty versus coronary artery bypass grafting in treatment of unprotected left main stenosis (NOBLE) : a prospective, randomised, open-label, non-inferiority trial

Background Coronary artery bypass grafting (CABG) is the standard treatment for revascularisation in patients with left main coronary artery disease, but use of percutaneous coronary intervention (PCI) for this indication is increasing. We aimed to compare PCI and CABG for treatment of left main coronary artery disease. Methods In this prospective, randomised, open-label, non-inferiority trial, patients with left main coronary artery disease were enrolled in 36 centres in northern Europe and randomised 1: 1 to treatment with PCI or CABG. Eligible patients had stable angina pectoris, unstable angina pectoris, or non-ST-elevation myocardial infarction. Exclusion criteria were ST-elevation myocardial infarction within 24 h, being considered too high risk for CABG or PCI, or expected survival of less than 1 year. The primary endpoint was major adverse cardiac or cerebrovascular events (MACCE), a composite of all-cause mortality, non-procedural myocardial infarction, any repeat coronary revascularisation, and stroke. Non-inferiority of PCI to CABG required the lower end of the 95% CI not to exceed a hazard ratio (HR) of 1 . 35 after up to 5 years of follow-up. The intention-to-treat principle was used in the analysis if not specified otherwise. This trial is registered with ClinicalTrials.gov identifier, number NCT01496651. Findings Between Dec 9, 2008, and Jan 21, 2015, 1201 patients were randomly assigned, 598 to PCI and 603 to CABG, and 592 in each group entered analysis by intention to treat. Kaplan-Meier 5 year estimates of MACCE were 29% for PCI (121 events) and 19% for CABG (81 events), HR 1 . 48 (95% CI 1 . 11-1 . 96), exceeding the limit for non-inferiority, and CABG was significantly better than PCI (p=0 . 0066). As-treated estimates were 28% versus 19% (1 . 55, 1 . 18-2 . 04, p= 0 . 0015). Comparing PCI with CABG, 5 year estimates were 12% versus 9% (1 . 07, 0 . 67-1 . 72, p= 0 . 77) for all-cause mortality, 7% versus 2% (2 . 88, 1 . 40-5 . 90, p= 0 . 0040) for non-procedural myocardial infarction, 16% versus 10% (1 . 50, 1 . 04-2 . 17, p= 0 . 032) for any revascularisation, and 5% versus 2% (2 . 25, 0 . 93-5 . 48, p= 0 . 073) for stroke. Interpretation The findings of this study suggest that CABG might be better than PCI for treatment of left main stem coronary artery disease.Peer reviewe

Lifestyle modification and metformin as long-term treatment options for obese adolescents: study protocol

<p>Abstract</p> <p>Background</p> <p>Childhood obesity is a serious health concern affecting over 155 million children in developed countries worldwide. Childhood obesity is associated with significantly increased risk for development of type 2 diabetes, cardiovascular disease and psychosocial functioning problems (i.e., depression and decreased quality of life). The two major strategies for management of obesity and associated metabolic abnormalities are lifestyle modification and pharmacologic therapy. This paper will provide the background rationale and methods of the REACH childhood obesity treatment program.</p> <p>Methods/design</p> <p>The REACH study is a 2-year multidisciplinary, family-based, childhood obesity treatment program. Seventy-two obese adolescents (aged 10-16 years) and their parents are being recruited to participate in this randomized placebo controlled trial. Participants are randomized to receive either metformin or placebo, and are then randomized to a moderate or a vigorous intensity supervised exercise program for the first 12-weeks. After the 12-week exercise program, participants engage in weekly exercise sessions with an exercise facilitator at a local community center. Participants engage in treatment sessions with a dietitian and social worker monthly for the first year, and then every three months for the second year. The primary outcome measure is change in body mass index and the secondary outcome measures are changes in body composition, risk factors for type 2 diabetes and cardiovascular disease, changes in diet, physical activity, and psychosocial well-being (e.g., quality of life). It is hypothesized that participants who take metformin and engage in vigorous intensity exercise will show the greatest improvements in body mass index. In addition, it is hypothesized that participants who adhere to the REACH program will show improvements in body composition, physical activity, diet, psychosocial functioning and risk factor profiles for type 2 diabetes and cardiovascular disease. These improvements are expected to be maintained over the 2-year program.</p> <p>Discussion</p> <p>The findings from this study will advance the knowledge regarding the long-term efficacy and sustainability of interventions for childhood obesity.</p> <p>Trial Registration</p> <p>ClinicalTrials.gov number NCT00934570</p

Complex systems and the technology of variability analysis

Characteristic patterns of variation over time, namely rhythms, represent a defining feature of complex systems, one that is synonymous with life. Despite the intrinsic dynamic, interdependent and nonlinear relationships of their parts, complex biological systems exhibit robust systemic stability. Applied to critical care, it is the systemic properties of the host response to a physiological insult that manifest as health or illness and determine outcome in our patients. Variability analysis provides a novel technology with which to evaluate the overall properties of a complex system. This review highlights the means by which we scientifically measure variation, including analyses of overall variation (time domain analysis, frequency distribution, spectral power), frequency contribution (spectral analysis), scale invariant (fractal) behaviour (detrended fluctuation and power law analysis) and regularity (approximate and multiscale entropy). Each technique is presented with a definition, interpretation, clinical application, advantages, limitations and summary of its calculation. The ubiquitous association between altered variability and illness is highlighted, followed by an analysis of how variability analysis may significantly improve prognostication of severity of illness and guide therapeutic intervention in critically ill patients