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Time-series analysis--spectral analysis and the search for cycles.

In summary, spectral analysis is one analytic strategy for analyzing time-series data. Specifically, spectral analysis enables researchers to detect cyclicity and determines the variance in the data accounted for by cyclic activity. Results describe cycle frequency, period, and amplitude. Unlike cosinor analysis (Lentz, 1990b), spectral analysis does not directly determine peak time nor directly indicate time-ordered relationships, as does autocorrelation (Taylor, 1990). Cyclic relationships between time-series data can be detected using coherency (Gottman & Ringland, 1981), an extension of spectral analysis which is beyond the scope of this article. A word of caution is in order for the uninitiated researcher. Spectral analysis, as well as autocorrelation and cosinor analysis, entails within-subject analysis of single variables. Currently, means of determining relationships between time series, such as cross-correlation and coherency, are bivariate. The need to analyze the pattern of individual variables within-subject, followed by examination of bivariate relationships between pairs of variables, is wisely balanced by limited numbers of variables and small sample size.

Nursing Research

Assessment of autonomic function in humans by heart rate spectral analysis.

Spectral analysis of spontaneous heart rate fluctuations were assessed by use of autonomic blocking agents and changes in posture. Low-frequency fluctuations (below 0.12 Hz) in the supine position are mediated entirely by the parasympathetic nervous system. On standing, the low-frequency fluctuations increase and are jointly mediated by the sympathetic and parasympathetic nervous systems. High-frequency fluctuations, at the respiratory frequency, are decreased by standing and are mediated solely by the parasympathetic system. Heart rate spectral analysis is a powerful noninvasive tool for quantifying autonomic nervous system activity.

Adult

Characterizing rumination patterns of dairy cows using spectral analysis.

Spectral analysis techniques were used to characterize the cyclical variation in rumination behavior of cows. Four Holstein cows were fed twice daily a diet of 60% high-moisture shelled corn-based concentrate, 15% first-cut alfalfa-grass hay and 25% second-cut alfalfa silage. The number of minutes that each cow spent ruminating was determined for 15-min intervals during six consecutive days. Rumination data then were characterized using Fourier harmonic analysis to decompose the total sum of squares into 288 orthogonal components due to different rumination wavelengths. Rumination patterns for all cows consisted mainly of wavelengths that were harmonics of a 24-h cycle, indicating a circadian pattern of rumination. Differences in rumination patterns between cows occurred mainly at wavelengths of less than 2 h. Rumination patterns of two of the four cows were more complex, and consisted of high-frequency, non-24-h harmonic wavelengths in addition to the circadian pattern. Spectral analysis can be used to identify the component cycles of rumination patterns of individual animals, which can then be used to determine the effects of dietary or other manipulations on rumination behavior.

Animals

Autonomic control of heart rate during exercise studied by heart rate variability spectral analysis.

Spectral analysis of heart rate variability (HRV) might provide an index of relative sympathetic (SNS) and parasympathetic nervous system (PNS) activity during exercise. Eight subjects completed six 17-min submaximal exercise tests and one resting measurement in the upright sitting position. During submaximal tests, work rate (WR) was increased for the initial 3 min in a ramp fashion until it reached constant WRs of 20 W, or 30, 60, 90, 100, and 110% of the predetermined ventilatory threshold (Tvent). Ventilatory profile and alveolar gas exchange were monitored breath by breath, and beat-to-beat HRV was measured as R-R intervals of an electrocardiogram. Spectral analysis was applied to the HRV from 7 to 17 min. Low-frequency (0-0.15 Hz) and high-frequency (0.15-1.0 Hz) areas under power spectra (LO and HI, respectively) were calculated. The indicator of PNS activity (HI) decreased dramatically (P less than 0.05) when the subjects exercised compared with rest and continued to decrease until the intensity reached 60% Tvent. The indicator of SNS activity (LO/HI) remained unchanged up to 100% Tvent, whereas it increased abruptly (P less than 0.05) at 110% Tvent. The results suggested that (cardiac) PNS activity decreased progressively from rest to a WR equivalent to 60% Tvent, and SNS activity increased only when exercise intensity exceeded Tvent.

Adult

Effect of low-dose atropine on heart rate fluctuations during orthostatic load: a spectral analysis.

Spectral analysis was utilized in order to determine the influence of low (0.7 microgram/kg)-dose atropine sulfate injections on the isolated spectral power components of heart rate fluctuations in contrast to moderate (0.02 mg/dose)-dose atropine and unmedicated states in human subjects during orthostatic load. Low-dose atropine decreased mean heart rate and increased respiration-related spectral power compared with controls in both the supine and standing posture. In supine subjects total power (0.01-0.5 Hz) was unchanged compared with controls due to a decreasing trend of low-frequency (0.01-0.05 Hz) and mid-frequency (0.05-0.15 Hz) heart rate spectral power. Standing upright, there was a distinct increase in total power with significantly higher values than in the controls resulting from an enormous activation of mid-frequency heart rate fluctuations. The peak frequency of the mid-frequency component was increased with a strong tendency compared with controls. Moderate-dose atropine increased mean heart rate and decreased total power, mid-frequency and respiration-related heart rate spectral power and peak frequency compared with controls in both positions. Our results suggest that low-dose atropine affects the interaction between sympathetic and parasympathetic limbs in the autonomic control of cardiac function in a complex manner producing a differentiated pattern of heart rate fluctuations dependent on the body posture. We suggest that low-dose atropine augments and moderate-dose atropine attenuates the vagal cardiac efferent activity in each position.

Adult

Contributions of sympathetic and vagal mechanisms to the genesis of heart rate fluctuations during orthostatic load: a spectral analysis.

Spectral analysis was utilized in order to determine the influence of postural change on heart rate fluctuations and respiratory frequencies and to evaluate the frequency-specific contributions of both vagal and beta-adrenergic mechanisms to the genesis of the heart rate fluctuations during change in posture. In unmedicated subjects the total power (0.01-0.5 Hz) of heart rate fluctuations and the relative power at the mid-frequency band (0.05-0.15 Hz) were significantly increased in response to postural change, while the relative power of high-frequency fluctuations (0.15-0.5 Hz) was significantly depressed. Low-frequency fluctuations (0.01-0.05 Hz) were unchanged. The respiratory frequency was non-significantly slowed. The coherence between heart rate and respiration showed a significant reduction during orthostatic load. The heart rate fluctuations above 0.05 Hz were abolished by vagal blockade, during supine rest, while beta-adrenergic blockade reduced fluctuations at the mid-frequency band. Combined blockade caused a depression of heart rate fluctuations over the entire frequency range. On standing, vagal blockade or autonomic double blockade caused a decrease in heart rate fluctuations at each frequency band. After beta-adrenergic blockade alone, mid-frequency and high-frequency fluctuations were significantly reduced. The coherence between heart rate and respiration was nearly abolished under vagal blockade in each body posture. We conclude that the increased sympathetic outflow during orthostatic load is reflected by a marked increase in heart rate spectral power densities in the mid-frequency range.(ABSTRACT TRUNCATED AT 250 WORDS)

Adult

The information carried by spindle afferents on motor unit activity as revealed by spectral analysis.

Spectral analysis was used to study the effects of motor unit activity on the discharge patterns of muscle spindle endings. Spindle afferents of hind-limb muscles of the cat were recorded during electrical stimulation of one or more motor units, and, for comparison, while the receptors discharged in the absence of induced extrafusal activity ('background discharge'). The stimulus sequences used were random, but had characteristic frequency components representing an underlying rhythm, similar to those of trains in real alpha-motoneuron output. The computed afferent spectra and coherences between stimulus and afferent trains indicate that the discharge patterns of muscle spindles carry information on the activity of particular subsets of motor units. The spectra also demonstrate a complex interaction of internal spindle (pacemaker) mechanisms and external (modulating) processes which determine the discharge patterns of primary and secondary endings. In addition, they reveal interesting differences between primaries and secondaries, possibly indicative of a particular role for each type of ending in motor control.

Action Potentials

[Continuous frequency analysis (spectral trend analysis) in the evaluation of long-term EEG recordings].

This study demonstrates the possibilities of continuous frequency analysis supporting the evaluation of long lasting EEG recordings which present problems in analysing large amount of data. Avoiding some disadvantages of the usual presentation of power spectra by compressed spectral array compression of the spectral data will be obtained in a more suitable way by sequential plots of the data on the abscissa as time axis. The spectra will be separated in only a few number of frequency bands. A special conversion procedure (linear multiplication of the data within each frequency band by logarithmic calculated factors) provides for the essential enhancement of low spectral power in the upper EEG frequency domain preserving the full dynamic of spectral variations. The efficiency of this spectral trend analysis is shown by two examples: (1) In the study of the variations of cerebral excitability in a patient with epileptic seizures depending on the waking-sleeping-cycle (Fig. 3), and (2) in the documentation of the EEG dynamics in the course of intensive care monitoring. Fig. 5 shows the development of a cerebral autorhythmicity representing reintegration of cerebral function in a patient with severe head injury.

Adolescent

Quantification of chorea in Huntington's disease by power spectral analysis.

A spectral analysis technique for quantifying dyskinesia in patients with diagnosis of Hungtington's Disease (chorea) (H.D.) is described. Spectral analysis involves computation of the magnitude of abnormal involuntary movements (AIMS) and of their distribution in frequency. It has the advantage of providing an objective measure of such movements. Three H.D. patients under different drug regimens and three age-matched controls have been evaluated and representative time records and power spectra are presented. Analysis established marked differences in the amplitude and shape of the normal and patient spectra. In addition, spectral analysis proved sensitive to differences in drug treatments among patients suggesting its additional use in evaluating the efficacy of therapeutic agents in the treatment of movement disorders.

Adult

Noninvasive determination of baroreflex sensitivity in man by means of spectral analysis.

The spectral analysis technique was applied for noninvasive assessment of heart-rate baroreflex sensitivity (BRS). The coherence between fluctuation of blood pressure and heart rate at 0.1 Hz and at respiratory frequency is high. This fact enables the assessment of BRS by means of calculating the modulus (or gain) of the transfer function between variations in blood pressure and heart rate. The noninvasive continuous blood pressure registration according to Penáz was used. During voluntarily controlled breathing intervals, the amplitude of 0.1 Hz and respiratory peaks in the spectra of heart rate and blood pressure changed markedly. Nevertheless, the average sensitivity of the baroreflex (modulus) changed insignificantly. This result indicated that the stability of BRS can be advantageous for the use of BRS in clinical practice. The difference between the modulus at 0.1 Hz and at the breathing rate indicates that baroreflex is only one of the factors causing respiratory arrhythmia. We also compared the determination of BRS by spectral analysis with the following alternative method: both lower extremities were occluded for 5 minutes. The release of pressure in the occluding cuffs decreased blood pressure which was followed by a baroreceptor-mediated increase of heart rate. Both methods correlated, but more detailed analysis revealed the role of the low pressure receptors in BRS determined by spectral analysis.

Blood Pressure

Myocardial wall motion evaluation using amplitude frequency spectral analysis.

Frequency spectral analysis of cardiac wall motion as calculated from the recorded video kymogram are demonstrated. Characteristic harmonics following the fundamental frequency of the cardiac rate have been demonstrated to have an alternating sequential energy distribution as measured from the free margin of the left ventricle of humans. The characteristic patterns occur in approximately 80% of the 50 patients evaluated. The correlation of these harmonics with physiologic events is not yet complete. Amplitude frequency spectral analysis offers an objective method for analysis of cardiac kymography not otherwise possible.

Adult

[The spectral analysis of heart rate variability. A comparative study between nonparametric and parametric spectral analysis in short series].

OBJECTIVE: to compare parametric (AR) and non parametric (FFT) spectral analysis results obtained in 512 beats series. INTERVENTIONS: 104 healthy subjects with normal physical examination and electrocardiogram were studied. The Ecg was recorded at rest, with controlled breathing at 15 cycles/min., and sampled at 300 Hz. The spectral VLF, LF and HF were calculated with FFT algorithm. For the same series, an auto-regressive analysis (AR) with optimized choice of the order of the model (AIC criterion) have been computed, VLF, LF and HF components were identified by AR spectral decomposition. RESULTS: In both groups, athletes and sedentary, there were no statistically differences between VLF, LF, HF and LF/HF spectral indices computed by the two methods. CONCLUSION: the results suggest that with controlled breathing it does not seems to exist any advantage in the use of AR spectral analysis to compute spectral components of heart rate variability, which is much more laborious that fixed bands non parametric FFT analysis.

Adolescent

Diagnosis of carotid stenosis by bruit spectral analysis.

Bruit spectral analysis provides an improved noninvasive method of quantifying the severity of carotid stenosis, and the method of Lees estimates the residual luminal diameter. Although the analysis required is complex, the test can be easily performed using the Spectraview, a microcomputer-based device which records and processes the sound information. The present study evaluated 44 cervical bruits in patients and found that in 84 percent of the vessels the estimated luminal size was within 1 mm of the angiographic lumen. Although substantial experience is required to obtain the maximum diagnostic accuracy, work with the technique during 18 months indicates that is provides more information from arterial bruits thn traditional phonoangiography.

Aged

[Evaluation of the degree of carotid stenosis by spectral analysis of the Doppler signal. Comparison of the results of spectral analysis, angiography and anatomo-pathology].

With the single Doppler spectrum analysis, one can appreciate the degree of the carotid stenosis according to the importance of the haemodynamic disturbances induced by the stenosis. The purpose of our study is to show the possibilities and the limitations of this method. Spectrum disturbances were classified in 5 grades, each of them being related to the importance of the stenosis. The degree of stenosis has been evaluated by the C.W. Doppler spectrum analysis, the angiographies and the anatomical study of the endarteriectomies. We considered that we had a perfect concordance between the results of the different methods when the degree of stenosis measured on the angiographies or on the endarteriectomies was compatible with the spectrum analysis classification: grade I: stenosis inferior to 40% (in area), 23% (in diameter); grade II: stenosis ranging between 40 and 60% in area (23 and 40 in diameter); grade III: stenosis of 60 to 75% in area (40 to 50% in diameter) and of particular shape (extended plaque); grade IV: stenosis ranging between 60 and 90% in area (40 to 70% in diameter); grade V: stenosis higher than 90% in area (70% in diameter). The confrontation of spectrum analysis and angiographic date concerns 58 bifurcations. We got a perfect correlation in 93% of the cases. The confrontation of the spectrum analysis method and the anatomical study of the endarteriectomies concerns 38 bifurcations. We got a perfect correlation in 92% of the cases. The appreciation of the carotid stenosis degree is now performed in routine at the Hospital. For some patients, the endarteriectomy has been decided from the clinical and the spectrum analysis data, and an electro-encephalogram with compression. However these date are generally completed with an angiography with venous punction.

Carotid Arteries

Detection of technical error during arterial surgery by pulsed Doppler spectral analysis.

Pulsed Doppler spectral analysis of midstream flow was compared with arteriography in 90 patients following carotid endarterectomy (N = 60) or lower-extremity bypass grafting (N = 30) for the detection of unsuspected technical error. Spectral changes in the velocity waveform indicating flow disturbance were identified in the endarterectomy or anastomotic sites of 11 patients (12%). All were associated with an anatomic defect apparent on arteriography. The revision of major defects in six patients (7%) corrected the flow disturbance. The absence of flow disturbance in 79 patients (88%) predicted a technically satisfactory arterial reconstruction. Intraoperative assessment by pulsed Doppler spectral analysis is a noninvasive, rapid, and accurate method for detecting technical errors during arterial surgery. The high sensitivity of this method makes it suitable for use as a screening test, resulting in the selective use of operative arteriography.

Angiography

Quantification of cardiovascular instability in premature infants using spectral analysis of waveforms.

Spectral analysis was applied to blood pressure and cerebral blood flow velocity recordings in premature infants with respiratory distress in order to quantify respiration-induced cardiovascular variability. Aortic blood pressure was transduced via an umbilical arterial catheter and cerebral blood flow velocity measured in the anterior cerebral artery using a 10 MHz continuous wave Doppler velocimeter in 16 infants less than or equal to 32 wk gestational age. Spectral analysis of the resulting waveforms revealed heart rate and respiratory rate components whose relative amplitudes (heart rate/respiratory rate amplitude ratio) represent an index of that component of variability induced by respiratory events. The mean (heart rate/respiratory rate amplitude) ratio was 47.2 in spontaneously breathing infants and rose to 165.9 in infants who were ventilated during muscle paralysis (p = 0.0003). Cerebral blood flow velocity recordings showed R components in only 22 of 38 simultaneous recordings. This method can be used to quantify respiration-induced cardiovascular variability and its response to therapy, and may provide a means of identifying infants at risk from brain injury due to an inability to regulate cerebral blood flow.

Blood Flow Velocity

EEG operant conditioning in a monkey model: II. EEG spectral analysis.

EEG power spectral analysis was studied from 14 (alumina-gel) chronically epileptic, undrugged monkeys during an EEG operant conditioning experiment. The composite profile of the average epileptic monkey shows the majority of power to be below 10 Hz. Because of the large variance in the data, no significant changes in the EEG power spectra could be detected as a function of conditioning. The possible reasons for this large variance are discussed. Hypothesis from previous human "biofeedback" studies would allow the prediction that those frequencies corresponding to the mu and sensory-motor-rhythm should negatively covary with seizure frequency. Data from this study did not support such assertions. The method of using spectral analysis for quantifying changes in the EEG which covary with operant conditioning is evaluated.

Animals