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PubMed2000

Time-frequency analysis of heart rate variability using short-time fourier analysis.

This study was done to introduce new parameters derived by time frequency analysis of heart rate variability data. Four simulation experiments were carried out to compare the short-time Fourier transform (STFT) analysis method to the traditional overall spectral analysis method. Sinusoidal signals were generated with identical total power in the high-frequency band, but varying time-frequency and time-amplitude information. The STFT method was also applied to heart rate variability data from the stages of normal human sleep. Data analysis included computation of the power in the high-frequency band by overall spectral analysis. The instability coefficients (ICs) of the frequency and power in the high-frequency band were derived by STFT analysis. The ICs derived by the STFT method were able to describe time-frequency and time-amplitude variations in sinusoidal signals which contained identical total power in a specified frequency range. The ICs of the frequency and power were able to differentiate variations in vagal activity between the stages of human sleep and waking. The ICs represent new parameters derived by the STFT method, and allow the detection and quantification of short-lasting time-frequency and time-amplitude variations that remain obscured by overall spectral analysis.

Adult↗
PubMed2003

Fourier analysis of optical coherence tomography and scanning laser polarimetry retinal nerve fiber layer measurements in the diagnosis of glaucoma.

OBJECTIVE: To evaluate a new Fourier-based analysis method for diagnosing glaucoma using retinal nerve fiber layer (RNFL) thickness estimates obtained from the optical coherence tomograph (OCT) (OCT 2000) and the scanning laser polarimeter (GDx). METHODS: We obtained RNFL thickness estimates from 1 eye of 38 healthy individuals and 42 patients with early glaucomatous visual field loss using the OCT and GDx devices. The shape of the RNFL double-hump pattern was assessed using Fourier analysis, and values were entered into a linear discriminant analysis. Receiver operating characteristic (ROC) curves were used to compare the performance of the Fourier-based metrics against other commonly used RNFL analytical procedures. Reliability was assessed on independent samples by the split-half method. Correlations were calculated to determine the extent to which the Fourier discriminant measures and other RNFL measures covaried between the 2 devices and the relationship between these RNFL measures and visual field measures. RESULTS: Sensitivity and specificity for the linear discriminant function (LDF) based on the Fourier analysis of the OCT data were 76% and 90%, respectively, and the area under the ROC curve was 0.925 (SEM, 0.028). For the GDx data, the Fourier-based LDF yielded sensitivity and specificity of 82% and 90%, respectively, with an ROC curve area of 0.928 (SEM, 0.029). These values were better than those determined using the GDx number, a previous discriminant function using GDx variables and OCT thickness values. The Fourier-based LDFs and numerous other measures were significantly correlated between the 2 devices. For each device, the visual field measures correlated most highly with the Fourier-based LDF measure. CONCLUSIONS: For both devices, the LDF based on the output from a Fourier analysis of RNFL data resulted in better diagnostic capability compared with other common RNFL analytical procedures. That this technique improves RNFL analysis is also supported by the better correlations between visual field measures and the Fourier-based LDF measures.

Diagnostic Techniques, Ophthalmological↗
PubMed1990

Filters and Fourier analysis of gated blood pool studies: a search for the optimal combination.

Fourier analysis of gated blood pool studies is performed after filtering the raw data by a spatial median 3 x 3, 9 x 9 or temporo-spatial 9 x 9 x 9 filter. 20 patients and a dynamic cardiac phantom were studied to determine the quantitative effects of these filters and of multiharmonic Fourier filtering (MHFF). The filtered MHFF data, with or without preprocessing, were compared with a 3 D or 2 D filter to the raw data using a chi 2 distribution. The MHFF (two or three harmonics) procedure applied to the raw data of patients without any preprocessing produced the smallest chi 2 value, thus demonstrating the very close relationship between filtered images and raw data. Preprocessing the raw data by the median filter also preserved the signal when two or three harmonics were applied, whereas the 3 D and 2 D (9 x 9) filters did not. The phantom study also demonstrated that MHFF preserved the signal better than any other preprocessing. The median filter introduced a smaller distortion than the 2 D (9 x 9) and 3 D filters. It is concluded that MHFF applied with two or three harmonics on the raw data or after preprocessing by a median (3 x 3) filter is the most successful way of preserving the real signal. It is believed that the other filters should be avoided. The clinical advantage of MHFF processing is to provide both very accurate filtering and parametric images.

Fourier Analysis↗
PubMed1983

Fourier analysis of ground reaction forces in normals and patients with knee joint disease.

Fourier analysis was performed on the ground reaction force patterns during gait in 26 normals and 10 patients with knee joint disease prior to total knee replacement. A method was developed to determine the essential number of harmonics for each force component, based on data sampling rate and the level of accuracy required in reconstructing the original patterns. The criteria used to select the level of accuracy depend upon the type of analysis to be performed. Only the first two to four harmonics, plus the constant term, were found to be the dominating coefficients in describing each of the reaction force patterns, and they are subsequently used as the key parameters in differentiating normals and patients with knee joint disease. The advantages of this method and its implication to objective gait analysis in biomechanics are discussed.

Adult↗
PubMed2000

Fourier analysis of sinusoidally driven thalamocortical relay neurons and a minimal integrate-and-fire-or-burst model.

We performed intracellular recordings of relay neurons from the lateral geniculate nucleus of a cat thalamic slice preparation. We measured responses during both tonic and burst firing modes to sinusoidal current injection and performed Fourier analysis on these responses. For comparison, we constructed a minimal "integrate-and-fire-or-burst" (IFB) neuron model that reproduces salient features of the relay cell responses. The IFB model is constrained to quantitatively fit our Fourier analysis of experimental relay neuron responses, including: the temporal tuning of the response in both tonic and burst modes, including a finding of low-pass and sometimes broadband behavior of tonic firing and band-pass characteristics during bursting, and the generally greater linearity of tonic compared with burst responses at low frequencies. In tonic mode, both experimental and theoretical responses display a frequency-dependent transition from massively superharmonic spiking to phase-locked superharmonic spiking near 3 Hz, followed by phase-locked subharmonic spiking at higher frequencies. Subharmonic and superharmonic burst responses also were observed experimentally. Characterizing the response properties of the "tuned" IFB model leads to insights regarding the observed stimulus dependence of burst versus tonic response mode in relay neurons. Furthermore the simplicity of the IFB model makes it a candidate for large scale network simulations of thalamic functioning.

Animals↗
PubMedDate not supplied

Coincidence of adjacent periodicities of men investigated with the pergressive Fourier analysis.

The body temperature of 2 persons closed off to the outside world was pergressively analyzed with a short analyzing interval showing that the spontaneous and controlling rhythms of T = 30 h are present as previously demonstrated by ASCHOFF and BLUME. The characteristic properties and differences of both curves are described. Especially it is demonstrated that a transient process is present in the first curve, but not in the second curve. The presence of both rhythms is confirmed by the pergressive Fourier analysis of the first curve with a long analyzing interval. The problem to find out correct values for the parameters of hidden rhythms with the aid of the amplitude spectrum is pointed out. It is not present for the pergressive Fourier analysis.

Body Temperature↗
PubMed1998

The Fourier analysis of biological transients.

With modern computing technology the digital implementation of the Fourier transform is widely available, mostly in the form of the fast Fourier transform (FFT). Although the FFT has become almost synonymous with the Fourier transform, it is a fast numerical technique for computing the discrete Fourier transform (DFT) of a finite sequence of sampled data. The DFT is not directly equivalent to the continuous Fourier transform of the underlying biological signal, which becomes important when analyzing biological transients. Although this distinction is well known by some, for many it leads to confusion in how to interpret the FFT of biological data, and in how to precondition data so as to yield a more accurate Fourier transform using the FFT. We review here the fundamentals of Fourier analysis with emphasis on the analysis of transient signals. As an example of a transient, we consider the human saccade to illustrate the pitfalls and advantages of various Fourier analyses.

Computational Biology↗
PubMed1984

Fourier analysis of the shape of normal and transformed epithelial cells derived from human transitional epithelium.

The aim of this paper is to show the possibility of objective mathematical description of changes occurring in the shape of cells in the process of transformation. The evaluation of the changes in cell shape of the chosen cell lines differing in transformation grade was performed by the use of Fourier analysis of the shape. Any two-dimensional contour can be described with specific accuracy in a mathematical manner using the closed form Fourier series of cosines. The components forming the analysed shape, called harmonics, are independent and uncorrelated measures of their contribution to the total shape. The shape of each cell can be represented by the spectrum of harmonic amplitudes. To quote the paper by Healy-Williams and Williams (1981): "The observed shape is partitioned into series, where gross shape, as elongation or triangularity, is measured by the harmonic amplitudes of the lower harmonic order and increasingly fine scaled surface sculpture is measured at higher orders". The statistically evaluated results allow the objective comparison of the cell shapes of several compared cell lines differing in transformation grades. Malignant transformation is supposed to be a multistep process. The different grades of transformation could be defined by several parameters as changes in the morphology of the cells, their ability to compete with fibroblasts, their life span, their angiogenic potency, their invasiveness in vitro and their tumorigenicity in nude mice. In this paper several human urothelial cell lines of normal and tumor origin differing in their transformation grade (TGr I-III) were compared by the use of Fourier analysis of their shape. TGr I cultures have finite life span but do not need intermittent collagenase treatment to prevent fibroblast overgrowth. TGr II cultures acquire infinite growth potential, here defined as capacity to survive at least 70 passages. They are neither tumorigenic nor invasive. TGr III cultures show infinite growth transformation, increased angiogenicity and ability to invade normal host tissue in vitro. They produce progressively growing tumors in nude mice. The following human uroepithelial cell lines differing in the degree of transformation were studied and compared by statistical evaluation of the harmonic amplitudes describing mathematically the cell shape: Two cell lines derived from human transitional cell carcinoma (TCC): 1. Hu 1703S classified as TGr I, 2. Hu 1703He classified as TGr III. It was found that these two cell lines differ in all harmonics. Two cell lines derived from morphological normal human bladder epithelium: 3. HCV-29 classified as TGr II.(ABSTRACT TRUNCATED AT 400 WORDS)

Carcinoma, Transitional Cell↗
PubMedDate not supplied

Improvement in Fourier analysis of gated blood-pool studies using single photon emission computed tomography: methodology and clinical feasibility.

We have developed a new method for obtaining reconstructed left ventricular (LV) planar images acquired from multidirectional views using gated blood-pool single photon emission computed tomography (SPECT), and have applied Fourier analysis to these planar images. In this paper, we describe the methodology of our new technique and discuss its feasibility for the detection of LV wall motion abnormalities (WMA) in patients with coronary artery disease (CAD). Sagittal long-axis, horizontal long-axis and short-axis sections of the LV were generated from the reconstructed transaxial tomograms. Sections covering only the LV at the same phase of the cardiac cycle were added to reconstruct planar images. Fourier analysis was then performed to construct phase and amplitude images. In 42 patients with significant WMA, a comparative study concerning the detection of WMA was performed between conventional and SPECT methods. The SPECT method had greater sensitivity in all segments of the LV, with no significant loss in specificity. In particular, the sensitivity of the SPECT method was significantly greater than that of the conventional method for inferior and posterior WMA (91% vs 57%; and 76% vs 35%, respectively). The method described here shows greater clinical effectiveness for the detection of LV WMA in patients with CAD.

Adult↗
PubMed1988

Models for preattentive texture discrimination: Fourier analysis and local feature processing in a unified framework.

Spatial frequency analysis and local feature analysis may be considered to be examples of a class of models for texture discrimination. In this theoretical framework, texture discrimination relies on differences in the distribution of responses generated in linear receptive fields placed randomly on the texture. If the set of receptive fields is taken to be a collection of gratings, spatial-frequency analysis is recovered. If the set of receptive-fields is taken to be a collection of local feature templates, a corresponding local-feature model is recovered. In order to test such models, it is necessary to construct distinct texture pairs that elicit similar distributions of responses for all of the postulated receptive field profiles: the model prediction is that such textures are not discriminable. A method is provided for construction of such textures which test generic models within this framework. This framework includes not only strict Fourier analysis, but also models which postulate a collection of arbitrarily-shaped local feature detectors, and models which postulate both Fourier analysis and local feature detection.

Form Perception↗
PubMed2000

Algorithm for application of Fourier analysis for biorhythmic baselines of pharmacodynamic indirect response models.

The change of an indirect pharmacological response R(t) can be described by a periodic time-dependent production rate kin(t) and a first-order loss constant kout. If kin(t) follows some biological rhythm (e.g., circadian), then the response R(t) also displays a periodic behavior. A new approach for describing the input function in indirect response models with biorhythmic baselines of physiologic substances is introduced. The present approach uses the baseline (placebo) response Rb(t) to recover the equation for kin(t). Fourier analysis provides an approximate equation for Rb(t) that consists of terms (usually two or three) of the Fourier series (harmonics) that contribute most to the overall sum. The model differential equation is solved backward for kin(t), yielding the equation involving Rb(t). A computer program was developed to perform the square L2-norm approximation technique. Fourier analysis was also performed based on nonlinear regression. Cortisol suppression after inhalation of fluticasone propionate (FP) was modeled based on the inhibition of the secretion rate kin(t) using ADAPT II. The pharmacodynamic parameters kout and IC50 were estimated from the model equation with kin(t) derived by the new approach. The proposed method of describing the input function needs no assumption about the behavior of kin(t), is as efficient as methods used previously, and is more flexible in describing the baseline data than the nonlinear regression method.

Administration, Inhalation↗
PubMed1989

Spreading of cells on various substrates evaluated by Fourier analysis of shape.

In order to evaluate in mathematical terms the morphological changes occurring in the course of cell spreading, Fourier analysis of shape was applied. Human urothelial Hu 961 b cells plated on type IV collagen, fibronectin, laminin, glass and bovine serum albumin (BSA) were studied. Fourier parameters describing cell shape as well as surface areas covered by the cells on the substrate were subjected to statistical analysis. Using analysis of variance and discriminant analysis it was found that parameters describing cell shape (both gross shape of cells and their fine scale contour foldings) possessed a higher power of discrimination between the cells spread on various substrates than the differences in cell surface areas. In the course of observation (75 and 150 min) the highest number of attached cells and highest degree of spreading were found when cells were plated on type IV collagen. Moderate alterations in cell shape and moderate increase of surface area were seen in the group of cells seeded on fibronectin, whereas the cells plated on laminin, glass and BSA revealed a moderate increase of surface area, but no changes in their shape were observed. The differences in attachment of cells and in the degree of their spreading might be due to the variation in expression of plasma membrane receptors for various substrates. The Fourier analysis of cell shape coupled with measurement of surface area is a good tool for quantitative evaluation of cell spreading and can be used for discrimination between cells spread on different substrates.

Cell Adhesion↗
PubMed2002

A Fourier analysis approach for capillary polarimetry.

A new method of fringe interrogation based on Fourier analysis was implemented and tested for a capillary polarimetry detector. It has significant advantages over the previously employed depth of modulation (DOM) approach, including speed and alignment insensitivity. The new and old methods were compared using a set of interference fringes typically used to facilitate nanoliter volume polarimetric determinations. Polarimetric response was calculated with both methods over the range from 0 degrees to 180 degrees. The results were found to be in good agreement with Malus Law and indicate that an fast Fourier transform (fft) could be used for real-time capillary scale polarimetry in a probe volume of 40 nL.

Electrophoresis, Capillary↗
PubMed1994

[A new method for measuring central activation: fourier analysis of pupillary oscillations in depressed patients].

While the changes in pupillary size during wakefulness and drowsiness are easy to understand, the origin of pupillary oscillations is quite mysterious. Waves of spontaneous pupillary constriction and dilation accompany periods of increasing sleepiness and spontaneous arousal. Lowenstein et al. (1963) demonstrated that in the dark, the pupils of young normal alert subjects show waves of dilatation and contraction lasting from about 4 to 40 s and measuring up to 0.5 mm. Furthermore, superimposed fast and very extensive oscillations were observed. The first described oscillations seemed to reflect central nervous activation. Therefore we analysed pupillary oscillations during the recording period of static pupillometry (described by the authors in 1992) which lasted for 25.6 s. Before calculating the Fourier analysis, blinks have to be identified and eliminated by means of a new technique which is called "smoothing". Using the Fourier analysis, the spectrum was divided into 5 frequency bands (0.0-0.2; 0.21-0.4; 0.41-0.60; 0.61-0.8; 0.81-1 Hz). We were also interested in the total spectrum. In order to demonstrate utilisation of the new technique, 146 male and female depressed patients (ICD-Diagnosis 296.1, 296.3, 296.1, 296.3 + 300, respectively, 300.4, 301.1, 296.1, 296.3 + 290, respectively), aged between 18 and 45 years, were investigated by means of pupillometry, followed by analysis of pupillary oscillations. The whole group of depressive patients who received antidepressive medication was compared with 64 healthy subjects of similar age to demonstrate differences in the frequency bands.(ABSTRACT TRUNCATED AT 250 WORDS)

Adolescent↗
PubMed1996

Evaluating surgically induced astigmatism by Fourier analysis of corneal topography data.

PURPOSE: To evaluate surgically induced astigmatism using Fourier harmonic series analysis of corneal topography data. SETTING: Aarhus Kommunehospital, Aarhus University, Denmark. METHODS: We evaluated the results of 46 phacoemulsifications with a 4 or 6 mm scleral tunnel sutureless incision based on the axis of the steepest meridian. We performed conventional keratometry and corneal topography before and up to 1 month after surgery. Using Fourier analysis, the corneal topographic images were broken into spherical power, regular astigmatism, and nonregular astigmatism for individual or aggregate analysis of surgically induced astigmatism. The induced refractive change (average of the difference between preoperative and postoperative corneal topographies) was analyzed and normalized according to the surgical meridian and to right/left eye. RESULTS: Regular astigmatism calculated by Fourier analysis of mires from the keratometer zone correlated well with conventional keratometry readings. Surgery induced a localized flattening in the superior region and a with-the-rule regular astigmatism component in the central area. CONCLUSION: Surgically induced corneal topography changes can be analyzed by Fourier series harmonic analysis, allowing aggregate data to be broken into optically meaningful quantities.

Adult↗
PubMed2000

Fourier analysis of nerve fiber layer measurements from scanning laser polarimetry in glaucoma: emphasizing shape characteristics of the 'double-hump' pattern.

PURPOSE: The pattern of the distribution of nerve fiber layer (NFL) thickness values across the retina may provide an early anatomic indication of glaucomatous disruption. We developed a method of analyzing polarimetry measurements that emphasizes the shape of the pattern of NFL thickness values. Sensitivity and specificity for detecting glaucoma was obtained for these measures and compared with those for conventional measures. METHODS: Nerve fiber thickness was inferred from retardation shift measured by a scanning laser polarimeter (Laser Diagnostic Technologies, Inc., San Diego, CA) in 34 healthy subjects (68 eyes) and 34 patients with glaucoma (68 eyes). Fourier analysis was performed on the polarimetry data to emphasize the shape in the evaluation of the distribution of thickness values around the optic disc (along a 1.7-disc diameter ring). This was computed separately on superior and inferior hemiretinas. RESULTS: Significant differences were found in the Fourier shape measures between healthy subjects and patients with glaucoma. The sensitivity and specificity using Fourier coefficients with this particular sample was 96% and 90%, respectively. CONCLUSION: The evaluation of NFL measurements with Fourier analysis to emphasize the holistic shape of the "double-hump" pattern was found to be a useful tool as an analysis strategy.

Adult↗
PubMed1985

Fourier analysis and the Farnsworth-Munsell 100-Hue test.

A mathematical method based on Fourier analysis devised for the assessment of score charts for the Farnsworth--Munsell 100-Hue test is described. The method facilitates the analysis of features of the shape of the score chart in an objective and quantitative manner. The calculations are easily performed by a microcomputer.

Color Perception Tests↗
PubMed1985

Fourier analysis of infantile stridor: preliminary data.

Preliminary data from 3 patients suggest that computerized (Fourier) analysis of infantile stridor can be instructive. Several recordings are quickly collected with a microphone and digital oscilloscope at the patient's bedside. The data are later sent to a computer for spectral analysis. Averaging of several spectra from each patient depicts only those sounds that are consistent from sample to sample. Subtraction of background noise from the averaged stridor removes all but those sounds that are produced by the patient. The results show that the spectra are relatively consistent from sample to sample within the same patient, and that different patients with different pathologies have distinct patterns in their spectra. It thus appears that further acoustical studies of infantile stridor will be productive. We are optimistic that data from a larger series of patients will indicate those spectral patterns which are characteristic of a specific laryngotracheal pathology, and perhaps facilitate rapid diagnosis without invasive procedures. An additional potential of this analysis is that pre- and post-operative spectra can be subtracted to show those sounds that improved or worsened. Such serial comparisons during the management of airway problems could be useful in evaluating treatment.

Female↗