Tremor classification and tremor time series analysis

The separation between physiologic tremor (PT) in normal subjects and the pathological tremors of essential tremor (ET) or Parkinson's disease (PD) was investigated on the basis of monoaxial accelerometric recordings of 35 s hand tremor epochs. Frequency and amplitude were insufficient to separate between these conditions, except for the trivial distinction between normal and pathologic tremors that is already defined on the basis of amplitude. We found that waveform analysis revealed highly significant differences between normal and pathologic tremors, and, more importantly, among different forms of pathologic tremors. We found in our group of 25 patients with PT and 15 with ET a reasonable distinction with the third momentum and the time reversal invariance. A nearly complete distinction between these two conditions on the basis of the asymmetric decay of the autocorrelation function. We conclude that time series analysis can probably be developed into a powerful tool for the objective analysis of tremors. (c) 1995 American Institute of Physics.     

Effects of simulated source of tremor on acoustic and airflow voice measures

To test the effects of different sources of tremor on the voice, tremor was simulated by external rhythmic perturbation of structures at the subglottal, glottal, and supraglottal levels in 10 healthy subjects. The acoustic and airflow signals simultaneously recorded during sustained phonation in the normal and the 3 simulated tremor conditions were analyzed and compared. Voice measures included: fundamental frequency, 2 short-term perturbation measures (jitter and shimmer), and 3 long-term tremor measures (prominence ratios of the spectral peaks of the acoustic frequency contour, acoustic amplitude contour, and airflow contour). Measures of fundamental frequency and percent shimmer were not significantly affected by the simulated tremors. Measures of percent jitter and the amplitudes of the long-term frequency and amplitude modulations were most prominently increased when respiratory drive was perturbed by simulated tremor. Spectral analysis of the acoustic amplitude contour was most useful in distinguishing the 3 sites of simulated tremor.     

Acoustic voice analysis in patients with essential tremor

To quantify several acoustic features of the voice in patients with essentialtremor (ET), 28 patients and 28 age- and sex-matched controls were studied. ET severity was assessed with the rating scale for tremor of Fahn, Tolosa, and Marín. The Computerized Speech Lab 4300 program (Kay Elemetrics) was used. Two-second samples of a sustained /a/ and a sentence were captured with a microphone and laryngograph equipment. Measures included fundamental frequency (F₀), frequency perturbation (fitter, Koike algorithm), intensity perturbation (shimmer, Horii algorithm), and harmonic-to-noise ratio (H/N, Yumoto algorithm) of the vowel /a/, and the frequency and intensity variability of the sentence, phonational range, and dynamic range at the natural frequency, maximum phonational time, and s/z ratio. All subjects underwent indirect laryngoscopy and/or laryngeal fibroscopy. When compared with controls, ET patients showed higher jitter, lower H/N ratio (the last one only with laryngographic signal), of the vowel /a/, lower frequency variability in the microphonc signal, lower intensity variability in the laryngographic signal of the sentence, and significantly lower dynamic range at natural frequency of phonation. ET patients reported higher frequency of the presence of high voice intensity, tremor, and struggle. Several acoustic parameters were influenced by the severity of the disease, including shimmer, jitter, H/N ratio, frequency variability of the sentence, and s/z ratio, although neither of the acoustic analysis values or the phonetometric measurements were affected by the presence of voice tremor or by a successful pharmacological treatment of ET.     

Scaling instability in self-potential earthquake-related signals

Scaling behavior of the temporal variability in self-potential data recorded in the frequency range during 1995 at Acapulco station (Mexico) was identified and analyzed. In this period, a strong earthquake (Ms=7.4) struck the monitored area on September 14, 1995. Using the detrended fluctuation analysis (DFA), which is a powerful method to detect scaling in nonstationary time series, deviations from stable power-law scaling were quantified. Our findings point to an evident unstable scaling behavior in self-potential data before the occurrence of the seismic event. These first results could be useful in the framework of earthquake prediction studies.     

Scaling characteristics of ocean wave height time series

Fluctuations in the significant wave height can be quantified by using scaling statistics. In this paper, the scaling properties of the significant wave height were explored by using a large data set of hourly series from 25 monitoring stations located off the west coast of the US. Detrended fluctuation analysis (DFA) was used to investigate the scaling properties of the series. DFA is a robust technique that can be used to detect long-range correlations in nonstationary time series. The significant wave height data was analyzed by using scales from hourly to monthly. It was found that a common scaling behavior can be observed for all stations. A breakpoint in the scaling region around 4-5 days was apparent. Spectral analysis confirms this result. This breakpoint divided the scaling region into two distinct parts. The first part was for finer scales (up to 4 days) which exhibited Brown noise characteristics, while the second one showed 1/f noise behavior at coarser scales (5 days to 1 month). The first order and the second order DFA (DFA1 and DFA2) were used to check the effect of seasonality. It was found that there were no differences between DFA1 and DFA2 results, indicating that there is no effect of trends in the wave height time series. The resulting scaling coefficients range from 0.696 to 0.890 indicating that the wave height exhibits long-term persistence. There were no coherent spatial variations in the scaling coefficients.     

Non-uniform scaling behavior in ultra-low-frequency (ULF) earthquake-related geomagnetic signals

Investigating highly non-stationary time series, which typically exhibit long-range correlations, is a classic problem in physics. Here, we analyze the scaling properties of the dynamics of ultra-low-frequency (ULF) geomagnetic data (in the frequency range between 1 mHz and 10 Hz) observed at Izu Peninsula in Japan. On the basis of the detrended fluctuation analysis (DFA), deviations from uniform power-law scaling were quantified. Our findings point out to a significant non-uniform scaling behavior in ULF geomagnetic data in relationship with the occurrence of intense seismic clusters.     

Dynamics of Parkinsonian tremor during deep brain stimulation

The mechanism by which chronic, high frequency, electrical deep brain stimulation (HF-DBS) suppresses tremor in Parkinson's disease is unknown. Rest tremor in subjects with Parkinson's disease receiving HF-DBS was recorded continuously throughout switching the deep brain stimulator on (at an effective frequency) and off. These data suggest that the stimulation induces a qualitative change in the dynamics, called a Hopf bifurcation, so that the stable oscillations are destabilized. We hypothesize that the periodic stimulation modifies a parameter affecting the oscillation in a time dependent way and thereby induces a Hopf bifurcation. We explore this hypothesis using a schematic network model of an oscillator interacting with periodic stimulation. The mechanism of time-dependent change of a control parameter in the model captures two aspects of the dynamics observed in the data: (1) a gradual increase in tremor amplitude when the stimulation is switched off and a gradual decrease in tremor amplitude when the stimulation is switched on and (2) a time delay in the onset and offset of the oscillations. This mechanism is consistent with these rest tremor transition data and with the idea that HF-DBS acts via the gradual change of a network property. (c) 2001 American Institute of Physics.     

Scaling analysis of paces of fetal breathing, gross-body and extremity movements

Using detrended fluctuation analysis (DFA), we studied the scaling properties of the time instances (occurrence) of the fetal breathing, gross-body, and extremity movements scored on a second by second basis from the recorded ultrasound measurements of 49 fetuses. The DFA exponent α of all the three movements of the fetuses varied between 0.63 and 1.1. We found an increase in α obtained for the movement due to breathing as a function of the gestational age while this trend was not observed for gross-body and extremity movements. This trend was argued as the indication of the maturation of lung and functional development of respiratory aspect of the fetal central nervous system. This result may be useful in discriminating normal fetuses from high-risk fetuses.     

Detrended fluctuation analysis of heart intrabeat dynamics

We investigate scaling properties of electrocardiogram (ECG) recordings of healthy subjects and heart failure patients based on detrended fluctuation analysis (DFA). While the vast majority of scaling analysis has focused on the characterization of the long-range correlations of interbeat (i.e., beat-to-beat) dynamics, in this work we consider instead the characterization of intrabeat dynamics. That is, here we use DFA to study correlations for time scales smaller than one heart beat period (about 0.75 s). Our results show that intrabeat dynamics of healthy subject are less correlated than for heart failure dynamics. As in the case of interbeat dynamics, the DFA scaling exponents can be used to discriminate healthy and pathological data. It is shown that 0.5 h recordings suffices to characterize the ECG correlation properties.     

Detrending fluctuation analysis based on high-pass filtering

Detrended fluctuation analysis (DFA) is a scaling method commonly used for detecting long-range correlations in non-stationary time series. The DFA method uses a trend based on polynomial fitting to extract and quantify fluctuations at different time scales. Basically, such procedure acts as a (non-dynamical) high-pass filter that removes time series components below a given time scale. As an alternative to the polynomial fitting approach, this paper proposes a DFA method based on well-known high-pass filters (e.g., Butterworth, elliptic, etc.). Numerical results show that the proposed DFA approach yields results similar to traditional DFA method. Maybe, the main advantage of the proposed DFA method is that efficient implementations of high-pass filters are available commercially.     

Non-linear characteristics and long-range correlations in Asian stock markets

We test several non-linear characteristics of Asian stock markets, which indicates the failure of efficient market hypothesis and shows the essence of fractal of the financial markets. In addition, by using the method of detrended fluctuation analysis (DFA) to investigate the long range correlation of the volatility in the stock markets, we find that the crossover phenomena exist in the results of DFA. Further, in the region of small volatility, the scaling behavior is more complicated; in the region of large volatility, the scaling exponent is close to 0.5, which suggests the market is more efficient. All these results may indicate the possibility of characteristic multifractal scaling behaviors of the financial markets.     

Analysis of temporal fluctuations in Bach’s sinfonias

The correlation structures in 15 Bach’s sinfonias were analyzed. Each sinfonia is characterized by the superposition of three voices. Each voice is a sequence of pitches. Each voice was transformed in a time series, in which the sampling time was given by the smallest pitch duration in that voice. The scaling properties of the three voices of each sinfonia was quantified by means of the estimate of the scaling exponent, performed using the power spectral density (PSD) and the detrended fluctuation analysis (DFA). The results show that the voice time series are persistent. The DFA was applied not only to any single voice time series, but also to couples (2-DFA) of voices and to the triple (3-DFA) of voices. It was found that the first voice of each sinfonia modulates the scaling behavior of the whole sinfonia.     

Randomness and changes of heart rate and respiratory frequency during high altitude mountain ascent without acclimatization

The aim of this study was to detect and compare the changes in the time-frequency and fractal scaling behaviors of heart rate (HR) and respiratory frequency (Rf), recorded simultaneously during a high altitude mountain ascent. The time-frequency analysis was performed using the local cosine4 orthonormal bases of Coifman, Malvar and Meyer, whose spectrum is not redundant as those computed with the short Fourier transform. The fractal scaling behavior was obtained using the detrended fluctuation (DFA) and the wavelet leaders (WL) analysis. Results showed that the high altitude mountain ascent differently affected HR and Rf variability. Rf average values increased (p=0.0003) while HR average values did not change. The scaling variability of HR was altered during the mountain ascent, which was detected by the increasing HR short range DFA exponents with altitude (p<0.03). Rf scaling variability remained unchanged. These differences between HR and Rf alterations were also observed for the local cosine4 power law behavior since power law exponents, in absolute values, increased for HR (p<0.003) while those of Rf did not change. Furthermore, the ratio of low over the whole local spectrum energy of Rf decreased with altitude (p=0.04) in contrast to HR. In most of these HR and Rf analyses, one of the two time series was significantly modified but not both. Moreover, the Rf local cosine4 spectrum had higher entropy compared to HR (p<0.01), the difference between the Rf and the HR entropy increased (p=0.04) during the mountain ascent. In consequence, Rf had more randomness than HR and altitude increased this difference.     

Regular and stochastic behavior of Parkinsonian pathological tremor signals

Regular and stochastic behavior in the time series of Parkinsonian pathological tremor velocity is studied on the basis of the statistical theory of discrete non-Markov stochastic processes and flicker-noise spectroscopy. We have developed a new method of analyzing and diagnosing Parkinson's disease (PD) by taking into consideration discreteness, fluctuations, long- and short-range correlations, regular and stochastic behavior, Markov and non-Markov effects and dynamic alternation of relaxation modes in the initial time signals. The spectrum of the statistical non-Markovity parameter reflects Markovity and non-Markovity in the initial time series of tremor. The relaxation and kinetic parameters used in the method allow us to estimate the relaxation scales of diverse scenarios of the time signals produced by the patient in various dynamic states. The local time behavior of the initial time correlation function and the first point of the non-Markovity parameter give detailed information about the variation of pathological tremor in the local regions of the time series. The obtained results can be used to find the most effective method of reducing or suppressing pathological tremor in each individual case of a PD patient. Generally, the method allows one to assess the efficacy of the medical treatment for a group of PD patients.     

Temporal variations of long-term correlations in seismic activity fluctuations

The scaling behavior of the 1998-2009 seismicity in Guerrero, southern Mexico, was studied by means of the detrended fluctuation analysis (DFA). We found that inter-seismic periods are correlated with a transition in the scaling behavior at about 200 seismic events. Correlations are relatively weak for small time scales. However, for large time scales, correlations are associated with a 1/f fractional process, indicating that the seismicity pattern emerges from a self-organized critical state. Temporal variations of the scaling exponent along years computed from the DFA indicate the presence of a quasi-biennial cycle in the seismicity correlations. This cyclic behavior was apparently triggered by the large 2001-2002 slow slip event in the Guerrero seismic gap. Besides, the significant seismic events (M_w>5) originate, on the average, at deeper regions in each cycle.     

脑电信号的标度分析及其在睡眠状态区分中的应用

脑电信号具有长程幂律相关性及多重分形的标度特性,并随生理病理状态改变.本文首次针对睡眠脑电信号应用单重分形去趋势波动分析(detrended fluctuation analysis,简记为DFA)方法与多重分形奇异谱对睡眠脑电信号的标度特征进行系统的对比研究.发现DFA标度指数α对于不同导联和样本组间的差异较为敏感,随睡眠状态的变化不规律;而多重分形奇异强度区间Δα随睡眠状态的变化更为规律,睡眠Ⅰ期至Ⅳ期不断增大,并且导联间差异和样本组间差异均较小.多重分形Δα参数更适合作为判定睡眠状态的定量参数.     

Vocal Tremor Reduction with Deep Brain Stimulation: A Preliminary Report

Vocal tremor has been a challenging problem for patients and their physicians. In some cases, it has been possible to lesson the symptom's tremor through medications and/or voice therapy. However, in most cases no good treatment has been available. Chronic stimulation of the thalamus has been successful in controlling tremors of the upper limb and other portions of the body. Our preliminary experience suggests that it may also be helpful in controlling vocal tremor.     

Investigating the temporal variation of the scaling behavior in rainfall data measured in central Argentina by means of detrended fluctuation analysis

Investigation of the time variant scaling behavior of six monthly rainfall series recorded in central Argentina from 1860 to 2006 by using detrending fluctuation analysis (DFA) was performed. Changes in precipitation extremes are analyzed for several regions of Argentina using long-term monthly rainfall data (back to 1860) recorded by rain gauges extended for more than 10 latitude-degrees, from subtropical regions until 39^° S. A moving window was employed in order to analyze statistical changes. Three different types of time patterns can be distinguished: (i) eastern stations show visible crossovers between persistent and random behavior; (ii) north-western stations are characterized by random behavior approximately at any time and do not present visible crossovers between different types of scaling behaviors; (iii) one station (i.e. Corrientes) shows a peculiar pattern, since it is characterized by several crossovers from persistent to random behavior, indicating a more fluctuating time dynamics without a well defined trend. The obtained results can be interpreted in the context of the climatological conditions of Central Argentina, which is characterized by the continental heat low in the northwest region, by the subtropical rainforest in the eastern provinces and by a transition zone (from maritime to continental regime) fluctuating with the South Atlantic high-pressure cell.     

Qualitative assessment of gene expression in affymetrix genechip arrays

Affymetrix Genechip microarrays are used widely to determine the simultaneous expression of genes in a given biological paradigm. Probes on the Genechip array are atomic entities which by definition are randomly distributed across the array and in turn govern the gene expression. In the present study, we make several interesting observations. We show that there is considerable correlation between the probe intensities across the array which defy the independence assumption. While the mechanism behind such correlations is unclear, we show that scaling behavior and the profiles of perfect match (PM) as well as mismatch (MM) probes are similar and immune-to-background subtraction. We believe that the observed correlations are possibly an outcome of inherent non-stationarities or patchiness in the array devoid of biological significance. This is demonstrated by inspecting their scaling behavior and profiles of the PM and MM probe intensities obtained from publicly available Genechip arrays from three eukaryotic genomes, namely: Drosophila melanogaster (fruit fly), Homo sapiens (humans) and Mus musculus (house mouse) across distinct biological paradigms and across laboratories, with and without background subtraction. The fluctuation functions were estimated using detrended fluctuation analysis (DFA) with fourth-order polynomial detrending. The results presented in this study provide new insights into correlation signatures of PM and MM probe intensities and suggests the choice of DFA as a tool for qualitative assessment of Affymetrix Genechip microarrays prior to their analysis. A more detailed investigation is necessary in order to understand the source of these correlations.