• Korean Journal of Biological Psychiatry
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• v.16 no.2
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• pp.69-75
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• 2009

Objectives : The detrended fluctuation analysis is one of the nonlinear methods for the investigation of biological time series. It quantifies the fractal scaling properties and is known to be useful in the evaluation of long-range correlations in time series. The heart rate variability(HRV) of obstructive sleep apnea syndrome (OSAS) patients during nighttime was analyzed by detrended fluctuation analysis to assess its relationship with the severity of the symptoms. Methods : Fifty nine untreated male OSAS patients with moderate to severe symptoms(mean age=45.4${\pm}$11.7 years, apnea-hypopnea index, AHI${\geq}$15) underwent nocturnal polysomnography. Moderate(AHI=15-30, N=22) and severe(AHI>30, N=37) OSAS patients were compared for the indices derived from detrended fluctuation analysis and frequency domain analysis of HRV. Results : In the detrended fluctuation analysis, the alpha values were 0.75${\pm}$0.11 and 0.82${\pm}$0.07 for the severe and the moderate OSAS groups respectively. The difference was significant(p<.01). The alpha value had negative correlation with AHI(r=-.425, p=.001). Negative correlation coefficients were also found in the relationships between the alpha values and very low frequency(VLF)(r=-.425, p=.001), low frequency(LF)(r=-.633, p= <.001) and the LF/HF ratio(r=-.305, p=.019) respectively. LF/HF ratio(p=.005) was higher in the severe OSAS group compared to that of the moderate OSAS group. Conclusion : In this study, the detrended fluctuation analysis showed the significant difference between the two OSAS groups classified according to their severity of symptoms. The scaling exponent showed the negative correlation with AHI and indicies of frequency domain analysis. This result suggests that detrended fluctuation analysis can be helpful to estimate the severity of OSAS.

• Structural Engineering and Mechanics
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• v.63 no.6
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• pp.751-760
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• 2017

In recent years, multifractal-based analysis methods have been widely applied in engineering. Among these methods, multifractal detrended cross-correlation analysis (MFDXA), a branch of fractal analysis, has been successfully applied in the fields of finance and biomedicine. For its great potential in reflecting the subtle characteristic among signals, a structural health monitoring (SHM) system based on MFDXA is proposed. In this system, damage assessment is conducted by exploiting the concept of multifractal theory to quantify the complexity of the vibration signal measured from a structure. According to the proposed algorithm, the damage condition is first distinguished by multifractal detrended fluctuation analysis. Subsequently, the relationship between the q-order, q-order detrended covariance, and length of segment is further explored. The dissimilarity between damaged and undamaged cases is visualized on contour diagrams, and the damage location can thus be detected using signals measured from different floors. Moreover, a damage index is proposed to efficiently enhance the SHM process. A seven-story benchmark structure, located at the National Center for Research on Earthquake Engineering (NCREE), was employed for an experimental verification to demonstrate the performance of the proposed SHM algorithm. According to the results, the damage condition and orientation could be correctly identified using the MFDXA algorithm and the proposed damage index. Since only the ambient vibration signal is required along with a set of initial reference measurements, the proposed SHM system can provide a lower cost, efficient, and reliable monitoring process.

• Sleep Medicine and Psychophysiology
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• v.15 no.1
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• pp.5-11
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• 2008

Sleep is an essential process maintaining the life cycle of the human. In parallel with physiological, cognitive, subjective, and behavioral changes that take place during the sleep, there are remarkable changes in the electroencephalogram (EEG) that reflect the underlying electro-physiological activity of the brain. However, analyzing EEG and relating the results to clinical observations is often very hard due to the complexity and a huge data amount. In this article, I introduce several linear and non-linear tools, developed to analyze a huge time series data in many scientific researches, and apply them to EEG to characterize various sleep states. In particular, the spectral analysis, detrended fluctuation analysis (DFA), and synchrony analysis are administered to EEG recorded during nocturnal polysomnography (NPSG) processes and daytime multiple sleep latency tests (MSLT). I report that 1) sleep stages could be differentiated by the spectral analysis and the DFA ; 2) the gradual transition from Wake to Sleep during the sleep onset could be illustrated by the spectral analysis and the DFA ; 3) electrophysiological properties of narcolepsy could be characterized by the DFA ; 4) hypnic jerks (sleep starts) could be quantified by the synchrony analysis.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.64 no.2
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• pp.304-309
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• 2015

Applicable range of Photoplethysmography (PPG) becomes wider as a non-invasive physiological measurement technique. However, PPG waveform is easy to be distorted by ambient light or vascular variation from temperature changes. Especially, irregular variation of PPG waveform caused by ambient temperature not only severely distorts the PPG, but also leads miss interpretation in clinical applications. Therefore, the investigation of between temperature and PPG waveform is quite important in using PPG. The purpose of this research is to quantify the PPG waveform characteristic and to investigate the waveform variation following the temperature change on measuring site. To quantify the fluctuation of PPG waveform, we use two techniques; detrended fluctuation analysis (DFA) and AC/DC analysis of PPG. We record PPG under temperature stress, which applied by medical use heat pack ($40^{\circ}C$) and ice pack ($0^{\circ}C$). Ten participants were applied to the experiment, and the result was evaluated to approve the temperature effect with statistical method, Wilcoxon signed rank test. The result shows that the AC component (p<0.05) and perfusion index DFS scale exponent (p<0.01) of PPG have the significance to temperature stress except for a DC component of PPG.

• Korean Journal of Biological Psychiatry
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• v.19 no.1
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• pp.65-69
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• 2012

Objectives : Much is still unknown about the neurophysiological mechanisms or dynamics of the sleep onset process. Detrended fluctuation analysis (DFA) is a new tool for the analysis of electroencephalography (EEG) that may give us additional information about electrophysiological changes. The purpose of this study is to analyze long-range correlations of electroencephalographic signals by DFA and their changes in the sleep onset process. Methods : Thirty channel EEG was recorded in 61 healthy subjects (male:female=34:27, age=$27.2{\pm}3.0$ years). The scaling exponents, alpha, were calculated by DFA and compared between four kinds of 30s sleep-wakefulness states such as wakefulness, transition period, early sleep, and late sleep (stage 1). These four states were selected by the distribution of alpha and theta waves in O1 and O2 electrodes. Results : The scaling exponents, alpha, were significantly different in the four states during sleep onset periods, and also varied with the thirty leads. The interaction between the sleep states and the leads was significant. The means (${\pm}$ standard deviation) of alphas for the states were 0.94 (${\pm}0.12$), 0.98 (${\pm}0.12$), 1.10 (${\pm}0.10$), 1.07 (${\pm}0.07$) in the wakefulness, transitional period, early sleep and late sleep state respectively. The mean alpha of anterior fifteen leads was greater than that of posterior fifteen leads, and the two regions showed the different pattern of changes of the alpha during the sleep onset periods. Conclusions : The characteristic findings in the sleep onset period were the increasing pattern of scaling exponent of DFA, and the pattern was slightly but significantly different between fronto-temporal and parieto-occipital regions. It suggests that the long-range correlations of EEG have a tendency of increasing from wakefulness to early sleep, but anterior and posterior brain regions have different dynamical process. DFA, one of the nonlinear analytical methods for time series, may be a useful tool for the investigation of the sleep onset period.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.11 no.7
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• pp.2491-2496
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• 2010

The DFA(detrended fluctuation analysis) which is included the correlation property of the EEG is used to analysis the depth of anesthesia. We studied ASA I or II adult patients supported by the society of anesthesiologists. Patients with history of dementia and neurological disorder are excluded. Average age is $48.9{\pm}10.9$ old, average weight is $57.1{\pm}8.2$ kg and average hight is $158{\pm}6.6$cm of the patients under the operation. Anesthesia medicine is Sevoflurane and the stages of anesthesia are 6 stages, that is pre-operation, induction, right after induction, stop the medicine and post-operation. Among the scaling exponent ${\alpha}1$, ${\alpha}2$, ${\alpha}3$ we know that ${\alpha}1$, ${\alpha}3$, were well appeared to discriminate pre-operation, induction, right after induction, stop the medicine and post-operation. So we confirmed that the parameters is useful to the depth of anesthesia.

• Korean Journal of Oriental Medicine
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• v.14 no.1
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• pp.85-89
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• 2008

This study is to investigate cardiotonic effect of acupuncture on heart rate variability(HRV) analyzed by a nonlinear way(DFA, Detrended Fluctuation Analysis). It was designed as a randomized, single-blind, waiting list-controlled, cross-over study. We assessed heart rate and R-R intervals in Circadian electrocardiography with a Holter monitoring device for twelve hospitalized participants. The compatible analytical program, Zymed, was used for generating the signals of R-R intervals from 24 hour-ECG. In DFA analysis, we produced DFA alpha 1, alpha 2 parameters according to the process of Cygwin module of Linux server. We tested if there was any difference between HRV parameters using SPSS, a statistical package. There was no difference between acupuncture and no treatment group in DFA alpha 2 parameter {95% Confidence Interval (-)0.058 - 0.037, P = .565}. Two group all showed large intra-individual variations. Consequently, acupuncture treatment did not modulate the complexity of HRV in a DFA analysis. This study can be a rationale for acupuncture's properties on cardiovascular and autonomic systems.

• The Bulletin of The Korean Astronomical Society
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• v.41 no.1
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• pp.81.2-81.2
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• 2016

Many signals in the nature have power-law behaviors, namely they are "scale-free". The method of detrended fluctuation analysis (DFA), as one of the popular methods (e.g., Rescaled range analysis and Spectral analysis) for determining scale-free nature of time series, has a very important advantage that the DFA can be applied to both stationary and non-stationary signals. The analysis of time series using the DFA has been broadly used in physiology, finance, hydrology, meteorology, geology, and so on. We performed the DFA of 16 Spaceweather HMI Active Region Patch (SHARP) parameters for 38 HMI Active Region Patches (HARPs) obtained by Solar Dynamics Observatory (SDO) from May 2010 to June 2014. The main results from this study are as follows. (1) The most of the time series data are non-stationary. (2) The DFA scaling exponents of "mean vertical current density" for 38 HARPs have a negative correlation coefficient (-0.41) with flare index. (3) The DFA scaling exponents of parameters such as "Sum of the absolute value of net currents per polarity", "Absolute value of the net current helicity", and "Mean photospheric excess magnetic energy density" for the most active HARPs having more than 10 major flares, have positive correlation coefficients (0.64, 0.59, and 0.53, respectively) with the ratio of "the number of CMEs associated with major flares" to "the number of major flares". Physical interpretations on our results will be discussed.

• Sleep Medicine and Psychophysiology
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• v.14 no.1
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• pp.42-48
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• 2007

Introduction: Detrended fluctuation analysis (DFA) is used as a way of studying nonlinearity of EEG. In this study, DFA is applied on sleep EEG of normal subjects to look into its nonlinearity in terms of EEG channels and sleep stages. Method: Twelve healthy young subjects (age：$23.8{\pm}2.5$ years old, male：female=7：5) have undergone nocturnal polysomnography (nPSG). EEG from nPSG was classified in terms of its channels and sleep stages and was analyzed by DFA. Scaling exponents (SEs) yielded by DFA were compared using linear mixed model analysis. Results: Scaling exponents (SEs) of sleep EEG were distributed around 1 showing long term temporal correlation and self-similarity. SE of C3 channel was bigger than that of O1 channel. As sleep stage progressed from stage 1 to slow wave sleep, SE increased accordingly. SE of stage REM sleep did not show significant difference when compared with that of stage 1 sleep. Conclusion: SEs of Normal sleep EEG showed nonlinear characteristic with scale-free fluctuation, long-range temporal correlation, self-similarity and self-organized criticality. SE from DFA differentiated sleep stages and EEG channels. It can be a useful tool in the research with sleep EEG.

• Journal of the Korean Society of Radiology
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• v.7 no.1
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• pp.25-30
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• 2013

In this work, we investigate the statistical properties of gamma exposure rates using well-known analysis methods, such as Autocorrelation Function Analysis(ACF), Rescaled Range Analysis(R/S Analysis), and Detrended Fluctuation Analysis(DFA). Especially, DFA is an important method to reliably detect long-range correlations in non-stationary time series. Our data are measured by Gangneung regional radiation monitoring station over the period of 1998 to 2011. First, we find a crossover indicating two different governing regimes in fluctuations of gamma exposure rates. Within a year, they show a strong long-ranged memory while this property vanishes over the range of time period longer than one year. Second, our finding is very securely supported by a variety of analysis tools. Those tools yield many relevant exponents which satisfies the well known relation between them.