SCALING IN COGNITION

Background: Interest in the analysis of RR interval variability by new dynamic methods is growing, because these methods give different, complementary information on heart rate behavior compared to the traditional measures of HRV. Several new methods have been recently introduced for studying complex heart rate dynamics, but the validity of these methods in analyzing RR interval behavior from Holter recordings is not well established.Methods: A real‐time microprocessor QRS detector system using a 1‐ms timing accuracy and a conventional 24‐hour ECG recording system with a sampling frequency of 128 Hz were compared in the measurement of new dynamic components of HRV in a sample of ten healthy subjects and ten patients with acute Ml.Results: Significant errors were observed in the analysis of approximate entropy (ApEn; mean difference 11 %) and in the short‐term scaling exponent value a1 (mean difference 3%) in detrended fluctuation analysis (DFA). In the Poincaré analysis, notable differences were also observed in short‐term instantaneous RR‐interval variability (SD1; mean difference 5%). In spectral analysis, low‐to‐high frequency ratio was also influenced by the sampling frequency (mean difference 14%). The magnitude of all these differences grew proportionately when the overall heart HRV diminished.Conclusions: The data suggest that conventional Holter recordings should be used with caution in the analysis of new dynamic HRV parameters, especially approximate entropy and the ratio between low and high frequency spectral components, particularly in patient populations with low total HRV.

Patients with sarcoidosis (Sarc) may have autonomic dysfunction, which could be evaluated by heart rate variability (HRV). Nonlinear HRV parameters such as detrended fluctuation analysis (DFA) have been demonstrated to be an important predictor of mortality. Whether DFA is a prognostic factor for patients with sarcoidosis remains unclear. Purpose of this study was the evaluation of this hypothesis. Methods: Sarc patients were included and underwent a 24-hour Holter as well as lung function tests, cardiac ultrasound and MRI examination for the assessment. The study population was prospectively examined with all-cause mortality as an end-point. HRV analysis included short-term α1 and long-term α2 scaling exponents from detrended fluctuation analysis (DFA) and approximate entropy (ApEn), (ii) time-domain indices and frequency domain indices. Results: 173 patients, mean aged: 46.78±14.57 yo, with disease duration of 4.20±5.85 yrs were evaluated. During a median follow-up period of 51.5±21.3 months, 14 deaths occurred; Cox-regression analysis demonstrated that the strongest predictors of all-cause mortality were α1 (p Conclusion: The DFA α1 is a strong and independent predictor of mortality in Sarcoidosis. This study highlights the importance of the non-linear dynamic indices in prognosis in Sarcoid population.

Low Scaling Exponent during Arrhythmia: Detrended Fluctuation Analysis is a Beneficial Biomedical Computation Tool

Stochastic fractal signals can be characterized by the Hurst coefficient H, which is related to the exponents of various power-law statistics characteristic of these processes. Two techniques widely used to estimate H are spectral analysis and detrended fluctuation analysis (DFA). This paper examines the analytical link between these two measures and shows that they are related through an integral transform. Numerical simulations confirm this relationship for ideal synthesized fractal signals. Their performance as estimators of H is compared based on a mean square error criterion and found to be similar. DFA measures are derived for physiological signals of heartbeat R-R intervals through the integral transform of a spectral density estimate. These agree with directly calculated DFA estimates, indicating that the relationship holds for signals with nonideal fractal properties. It is concluded that DFA and spectral measures provide equivalent characterizations of stochastic signals with long-term correlation.

On the body surface the electric field generated by the cardiac muscles consists of electric potential maxima and minima that increase and decrease during each cardiac cycle. The recording of these electric potentials as a function of time is called electrocardiography, and the resulting signal is called the electrocardiogram (ECG). The ECG signal is used extensively as a low cost diagnostic tool to provide information concerning the heart's state of health. Reliable and accurate detection of the QRS complex and R wave peak in ECG signals is essential in computer-based ECG analysis. In this paper we evaluate the significance of Detrended Fluctuation Analysis (DFA) for studying heart rate variability in children with sleep disordered breathing. An Enhanced Hilbert Transform (EHT) algorithm was used to derive the Heart Rate Variability (HRV) signal. We compare the DFA values with Approximate Entropy and Poincaré Plots of HRV signals as these are very useful in characterization and visualization of HRV data. Our data demonstrated differences in DFA parameters between periods of normal and abnormal breathing and also between sleep stages. These results suggest that DFA is suitable for the long-term analysis of non-stationary time series such as HRV signals and may also be applied in the detection of sleep disordered breathing.

Two kinds of nerves, acceleratory and inhibitory cardio-regulator nerves, innervate the heart. They are known to discharge concurrently to maintain an equilibrium state of the body. The nerves are also known to change their frequency of discharge in a reflexive manner to meet the demand from the periphery; such as augmentation of oxygen supply or vice versa. Consequently, the heart exhibits dynamic change in its pumping rate and force of contraction. If the control system fails, the heart exhibits unhealthy state. However, assessment of healthy/unhealthy status is uneasy because we are not able to monitor the nerve activities by non-invasive methods. Therefore, we challenged to detect state of the heart without nerve-recordings. We used the detrended fluctuation analysis (DFA) applying to heartbeat interval time series because DFA has been believed that it can quantify the state of heart. We performed DFA on the EKGs (electrocardiograms) from various living organisms including humans. The objective of this research was to determine whether the analytical technology, DFA, could function as a useful method for the evaluation of the subject’s quality of cardiovascular-related illness and transition to and from a normal healthy state. We found that DFA could describe brain-heart interaction quantitatively: the scaling exponents of (1) healthy, (2) sick-type (such as stressful or arrhythmic states), and (3) unpredictable-death type (such as ischemic heart disease) were corresponded to individuals who exhibited, (1) nearly one, (2) less than one, and (3) greater than one, respectively. We conclude that scaling exponents could determine whether the subjects are under sick or healthy conditions on the basis of cardiac physiology.

FUNDAMENTO: A variabilidade da frequência cardíaca (VFC) é um método diagnóstico não invasivo usado na avaliação da modulação autonômica do coração. A análise da VFC por métodos de dinâmica não linear no período pré-operatório da cirurgia de revascularização do miocárdio poderia ser preditora de morbidade no pós-operatório, como por exemplo, infecções pulmonares. OBJETIVO: Avaliar o comportamento da VFC pela dinâmica não linear, no período pré-operatório da cirurgia de revascularização do miocárdio e sua relação com a ocorrência de infecções pulmonares no período pós-operatório hospitalar. MÉTODOS: Foram avaliados 69 pacientes (média de idade de 58,6 ± 10,4 anos) com doença arterial coronariana e indicação eletiva de cirurgia de revascularização do miocárdio. Para quantificar a dinâmica não linear da VFC, foram realizadas: análise das flutuações depuradas de tendências (DFA), seus componentes de curto (α1) e longo (α2) prazos, entropia aproximada (-ApEn), expoente de Lyapunov (LE), e expoente de Hurst (HE) de séries temporais dos intervalos RR do ECG, captados com equipamento Polar S810i, na véspera da operação. RESULTADOS: Nos níveis de corte estipulado pela curva ROC, houve diferença significativa entre os grupos com e sem infecções pulmonares no pós-operatório de revascularização do miocárdio para a DFA total, entropia aproximada e expoente Lyapunov com p = 0, 0309, p = 0,0307 e p = 0,0006, respectivamente. CONCLUSÃO: Os métodos de dinâmica não linear, nos seus respectivos níveis de corte, permitiram diferenciar os casos que evoluíram com infecção pulmonar no pós-operatório de cirurgia de revascularização do miocárdio, sugerindo que, nesse grupo de pacientes, estes métodos podem ter caráter prognóstico.

An attempt was made to develop a truly quantitative approach to temperature, based on models derived from nonlinear dynamics and chaos theory. Three different procedures for measuring the degree of complexity of the temperature curve were compared, and the possible correlations between these measurements and certain physiopathologically relevant parameters in healthy subjects were examined. Twenty-three healthy subjects (10 males, 13 females) between 18 and 85 years of age had their temperature measured every 10 min for at least 30 h. These time series were used to determine the approximate entropy (ApEn), a detrended fluctuation analysis (DFA), and the fractal dimension by the compass method (FD(c)). There was good correlation between the different methods of measuring the complexity of the curve [ r=-0.603 for ApEn vs. DFA ( p=0.002), r=0.438 for ApEn vs. FDc ( p=0.04) and r=-0.647 for DFA vs. FDc ( p=0.0008)]. Both the fractal dimension and the approximate entropy were inversely correlated with age [ r=-0.637 ( p=0.001) and r=-0.417 ( p=0.03), respectively], while the DFA increased with age ( r=0.413, p=0.04). The results thus suggest that complexity of the temperature curve decreases with age. The complexity of the temperature curve can be quantified in a consistent fashion. Age is associated with lower complexity of the temperature curve.

Work is needed to better understand the control of knee movement and knee health. Specifically, work is needed to further understand knee muscle force control variability and complexity and how it is organized on both sides of the body. The purpose of this study was to explore side-to-side comparisons of magnitude- and complexity-based measures of knee muscle force control to support future interpretations of complexity-based analyses and clinical reasoning in knee injury control. Participants (male/female n = 11/5) performed constant-force isometric efforts at 50% maximal effort. Force variability was quantified during the constant-force efforts using a coefficient of variation (CV%) and force complexity using approximate entropy (ApEn) and detrended fluctuation analysis (DFA) α. Outcomes were right/left and dominant/nondominant group-level and individual-level comparisons. A limb-symmetry index was calculated for each variable and clinically significant absolute asymmetry was defined (>15%). The only significant side-to-side difference was for right/left DFA α (p = 0.00; d = 1.12). Maximum absolute asymmetries were (right/left, dominant/nondominant): CV 18.2%, 18.0%; ApEn 34.5%, 32.3%; DFA α 4.9%, 5.0%. Different side-to-side comparisons yield different findings. Consideration for how side-to-side comparisons are performed (right/left, dominant/nondominant) is required. Because a significant difference existed for complexity but not variability, this indicates that both complexity-based and magnitude-based measures should be used when studying knee muscle force control.

Concurrent sympathetic activation and vagal withdrawal in hyperthyroidism: Evidence from detrended fluctuation analysis of heart rate variability

Detrended fluctuation analysis can detect the impairment of heart rate regulation in patients with heart failure with preserved ejection fraction

BackgroundDuring steady walking, gait parameters fluctuate from one stride to another with complex fractal patterns and long-range statistical persistence. When a metronome is used to pace the gait (sensorimotor synchronization), long-range persistence is replaced by stochastic oscillations (anti-persistence). Fractal patterns present in gait fluctuations are most often analyzed using detrended fluctuation analysis (DFA). This method requires the use of a discrete times series, such as intervals between consecutive heel strikes, as an input. Recently, a new nonlinear method, the attractor complexity index (ACI), has been shown to respond to complexity changes like DFA, while being computed from continuous signals without preliminary discretization. Its use would facilitate complexity analysis from a larger variety of gait measures, such as body accelerations. The aim of this study was to further compare DFA and ACI in a treadmill experiment that induced complexity changes through sensorimotor synchronization.MethodsThirty-six healthy adults walked 30 min on an instrumented treadmill under three conditions: no cueing, auditory cueing (metronome walking), and visual cueing (stepping stones). The center-of-pressure trajectory was discretized into time series of gait parameters, after which a complexity index (scaling exponent alpha) was computed via DFA. Continuous pressure position signals were used to compute the ACI. Correlations between ACI and DFA were then analyzed. The predictive ability of DFA and ACI to differentiate between cueing and no-cueing conditions was assessed using regularized logistic regressions and areas under the receiver operating characteristic curves (AUC).ResultsDFA and ACI were both significantly different among the cueing conditions. DFA and ACI were correlated (Pearson’s r = 0.86). Logistic regressions showed that DFA and ACI could differentiate between cueing/no cueing conditions with a high degree of confidence (AUC = 1.00 and 0.97, respectively).ConclusionBoth DFA and ACI responded similarly to changes in cueing conditions and had comparable predictive power. This support the assumption that ACI could be used instead of DFA to assess the long-range complexity of continuous gait signals. However, future studies are needed to investigate the theoretical relationship between DFA and ACI.

In the study of human cognitive activity using electroencephalogram (EEG), the brain dynamics parameters and characteristics play a crucial role. They allow to investigate the changes in functionality depending on the environment and task performance process, and also to access the intensity of the brain activity in various locations of the cortex and its dependencies. Usually, the dynamics of activation of different brain areas during the cognitive tasks are being studied by spectral analysis based on power spectral density (PSD) estimation, and coherence analysis, which are de facto standard tools in quantitative characterization of brain activity. PSD and coherence reflect the strength of oscillations and similarity of the emergence of these oscillations in the brain, respectively, while the concept of stability of brain activity over time is not well defined and less formalized. We propose to employ the detrended fluctuation analysis (DFA) as a measure of the EEG persistence over time, and use the DFA scaling exponent as its quantitative characteristics. We applied DFA to the study of the changes in activation in brain dynamics during mental calculations and united it with PSD and coherence estimation. In the experiment, EEGs during resting state and mental serial subtraction from 36 subjects were recorded and analyzed in four frequency ranges: θ1 (4.1–5.8 Hz), θ2 (5.9–7.4 Hz), β1 (13–19.9 Hz), and β2 (20–25 Hz). PSD maps to access the intensity of cortex activation and coherence to quantify the connections between different brain areas were calculated, the distribution of DFA scaling exponent over the head surface was exploited to measure the time characteristics of the dynamics of brain activity. Obtained arrangements of DFA scaling exponent suggest that normal functioning of the brain is characterized by long-term temporal correlations in the cortex. Topographical distribution of the DFA scaling exponent was comparable for θ and β frequency bands, demonstrating the largest values of DFA scaling exponent during cognitive activation. The study shows that the long-term temporal correlations evaluated by DFA can be of great interest for diagnosis of the variety of brain dysfunctions of different etiology in the future.

Detrended fluctuation analysis (DFA) of heart rate variability appears to yield improved prognostic power in cardiovascular disease, through calculation of the fractal scaling exponent α. We have recently used Taylor series approximations to propose that DFA is closely related to standard spectral analysis measures. We now present a direct analytical approach using integration and explicit expressions for the steps involved in DFA. This demonstrates clearly how DFA corresponds to standard spectral analysis.

Prognostic techniques play a critical role in predicting upcoming faults and failures in machinery or a system by monitoring any deviation in the operation. This paper presents a novel method to analyze multidimensional sensory data and use its characteristics in bearing health prognostics. Firstly, detrended fluctuation analysis (DFA) is exploited to evaluate the long-range correlations in ball bearing vibration data. The results reveal the existence of the crossover phenomenon in vibration data with two scaling exponents at the short-range and long-range scales. Among several data sets, applying the DFA method to vibration signals shows a consistent increase in the short-range scaling exponent toward bearing failure. Finally, Kendall’s tau is used as a ranking coefficient to quantify the trend in the scaling exponent. It was found that the Kendall’s tau coefficient of the vibration scaling exponent could provide an early warning signal (EWS) for bearing failure.