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PubMed2000

Shape analysis of tumor cell nuclei in ependymomas by means of Fourier analysis.

OBJECTIVE: To study the prognostic significance of nuclear shape analysis in ependymomas. STUDY DESIGN: Tumor cell nuclei in surgical specimens of primary resected ependymomas from 30 patients were evaluated by means of Fourier analysis of nuclear contours, conventional morphometric features (nuclear area, shape factor) and the Ki-67 proliferation index. Fourier analysis can be used for decomposing an irregular nuclear contour by calculating "Fourier amplitudes." Tumors with different tumor grades according to the World Health Organization were compared, as were patients with and without recurrence of ependymomas. Planimetric data were further correlated with the Ki-67 index. RESULTS: t Test and multivariate analysis showed distinct differences between ependymomas with tumor grade 3 and the other tumor grades. Cross-validated, stepwise discriminant analysis with the event of recurrence as grouping variable revealed correct reclassification in 16/18 cases without recurrence and of 10/12 cases with recurrence. When considering just intracranial ependymomas with total surgical removal, Fourier amplitudes provided 100% correct reclassification concerning recurrence. Proliferation index, in contrast, showed considerable overlap between all tumor grades and between cases with and without recurrence. CONCLUSION: Quantification of the shape of tumor cell nuclei in ependymomas by means of Fourier analysis has prognostic significance and seems to be superior to the Ki-67 index.

Brain Neoplasms↗
PubMed2005

Analysis of GDx-VCC polarimetry data by Wavelet-Fourier analysis across glaucoma stages.

PURPOSE: The purpose of this study was to apply shape-based analysis techniques of retinal nerve fiber layer (RNFL) thickness to GDx-VCC (variable corneal and lens compensator; Laser Diagnostic Technologies, Inc., San Diego, CA) polarimetry data and to evaluate the techniques' ability to detect glaucoma in its earliest stages. Wavelet-based (wavelet-Fourier analysis [WFA]), Fourier-based (fast Fourier analysis [FFA]), and several previous variations of shape-based analysis were considered, as well as the standard metric nerve fiber indicator (NFI), and all were compared as a function of disease stage. METHODS: GDx-VCC scans of one eye of each of 67 patients with glaucoma and each of 67 healthy age-matched subjects provided RNFL thickness estimates at a fixed distance from the optic disc. Severity of disease was graded according to the Glaucoma Staging System and also by mean deviation (MD) from standard automated perimetry. WFA, FFA, and NFI procedures were performed including the following variations: use of signed or unsigned phase, inclusion of interocular or intraocular asymmetry of analysis parameters, and combination of features by principle components analysis or Wilks lambda. Independent samples (k-fold variation) were used for training and testing. Sensitivity, specificity, and receiver operating characteristic (ROC) area were obtained. RESULTS: Classification performance of WFA (ROC = 0.978) was significantly better than FFA (ROC = 0.938) and NFI (ROC = 0.900). This difference was largest for the earliest stages of glaucoma. Shape-based analysis methods performed better than NFI overall. Adding between-eye asymmetry measures helped FFA but not WFA. CONCLUSIONS: Shape-based analysis, and WFA in particular, makes an important improvement in detecting earliest glaucoma with polarimetry.

Aged↗
PubMed1981

Fourier analysis of cardiac action potentials.

Fourier analysis of the repolarization phases of cardiac action potentials showed clear differences in the frequency characteristics of atrial and ventricular recordings. The frequency spectrum of the atrial repolarization phase was in the range of 0-45Hz, with a predominant power spectral density between 0-15Hz. The frequency spectrum of the ventricular repolarization phase was in the range of 0-20Hz, with a predominant power spectral density between 0-10Hz. Physiological changes that accentuate the differences in shape between atrial and ventricular APs also accentuate the differences in frequency spectrum of their repolarization phases. Fourier analysis therefore could be a complement to the current methods used to describe and quantify differences in the shape of cardiac action potentials.

Action Potentials↗
PubMed1978

Fourier analysis of the echocardiogram.

Fourier analysis has been applied to the analysis of echocardiograms, with the result that anterior mitral leaflet waveforms have been classified in a manner which is unambiguous and which lends itself easily to present-day automated technology.

Echocardiography↗
PubMed1991

Simulated bipolar cells in fovea of human retina. V. Use of Fourier analysis to determine resolution.

Fourier analysis is used to study resolution of images processed by the matrix of simulated red-center (BCR) and green-center (BCG) bipolar cells (BC) of the human central fovea. Simulated achromatic and chromatic sine and square waves, and a two-bar stimulus are used to activate the BCs. Due to the "honeycomb" packing of the cones and BC matrices Fourier transforms are computed row by row using a one-dimensional FFT. Resolution computed by the Fourier transform is compared with the resolution index (RI), which is a method for determining resolution based on two-point discrimination in the space domain. In general the harmonic with the maximum amplitude gives the best correlation with RI for the three stimuli. Amplitudes at all spatial frequencies are enhanced by increasing the number of cycles in the sine and square wave gratings. Results with simulated BCs compare favorably with human and macaque psychophysics measuring contrast sensitivity. Square wave gratings are better than sine wave greetings for studying resolution.

Color Perception↗
PubMed2000

Evaluation of gastric motility by Fourier analysis of condensed images.

In this study Fourier analysis was applied to condensed images of gastric emptying with the aim of evaluating the amplitude and frequency of gastric contractions as well as gastric emptying in patients with various well-defined disorders. In 15 controls, 65 patients with progressive systemic sclerosis (PSS), 41 patients with diabetes mellitus type I (DM), 12 patients with pyloric stenosis and 9 patients who had undergone gastric surgery, gastric emptying was determined after ingestion of a semi-solid test meal. In addition, condensed images were generated to evaluate the amplitude and frequency of gastric contractions by means of Fourier analysis. In PSS and DM patients, gastric emptying and contraction amplitudes were significantly reduced (P<0.01). Patients with pyloric stenosis displayed regular peristalsis but significantly delayed emptying (P<0.01). Patients who had undergone gastric surgery showed normal or rapid gastric emptying associated with decreased amplitudes (P<0.01). The frequency of gastric contractions in the patient groups was not different from that in controls. This study showed Fourier analysis of condensed images to be a rapid and feasible approach for the evaluation of gastric contractions. Depending on the underlying disorder, gastric emptying and peristalsis showed both corresponding and discrepant findings. Data on gastric contractions provided additional information compared with results obtained by conventional emptying studies. Therefore, both parameters should be routinely assessed to further improve characterisation of gastric dysfunction by scintigraphy.

Adult↗
PubMed1991

Fourier analysis as a planimetric procedure--application to malignant and normal urothelial cells with reactive changes.

The shape of urothelial cell nuclei in 27 urinary cytological preparations has been quantified by means of Fourier analysis. Fourier amplitudes were calculated as parameters of the nuclear shape. The T-test and a discriminance analysis showed significant differences in nuclear shape between preparations with malignant urothelial cells and nonmalignant cells with reactive changes. Only one preparation was reclassified false-negatively. No preparation was reclassified false-positively. No significant differences were found between normal cells with and without reactive changes. Thus it can be concluded that nuclear shape is an important criterion for the diagnosis of urothelial carcinomas in urinary cytological preparations. Fourier analysis allows the complete reproduction of the convex shape of a nucleus and it seems to be useful as an additional quantitative procedure in the diagnosis of malignant tumours.

Carcinoma, Transitional Cell↗
PubMed1995

Quantitative analysis of the lens cell microstructure in selenite cataract using a two-dimensional Fourier analysis.

Using two-dimensional (2-D) Fourier methods, we analysed the cellular microstructure of three rat lenses: normal transparent, selenite-induced cataractous and selenite-treated plus a phase separation inhibitor (PSI) to prevent cataract. 2-D Fourier analysis of electron micrographs of the lens cells quantified the dimensions of the spatial fluctuations in electron density of the lens cell microstructure. The 2-D Fourier spectra of the transparent normal and PSI-treated lens cells were remarkably similar while those of the opaque selenite-treated lens cells were dramatically different. In the opaque cells the contributions of large Fourier components (larger than half the wavelength of light) in the 2-D Fourier spectra were much greater than in the transparent cells. The results of the 2-D Fourier analysis of electron micrographs are consistent with the theory of transparency of the eye.

Amifostine↗
PubMedDate not supplied

Study of the peripheral blood leucocyte population by Fourier analysis of the cell volume histogram.

The Fourier transformation is proposed as a technique for the description of cell volume histogram data. In order to test the applicability of this transformation, peripheral blood leucocytes were studied as model populations and the technique assessed by determining the extent to which the Fourier coefficients could be applied as descriptors of various pathologic abnormalities of the differential leucocyte count. Histograms of leucocyte volume distribution were plotted for 87 cases with a variety of abnormalities of the peripheral blood leucocyte population. These histograms were submitted to Fourier analysis and the coefficients thus obtained were used as the basis of a multivariate classification system designed to distinguish certain predefined abnormalities of the differential count. The results obtained suggest that Fourier analysis may prove a valuable technique for the interpretation of cell volume histogram data, and its potential applications are discussed.

Cell Count↗
PubMed1991

Fourier analysis of the cerebrovascular system.

We performed Fourier analysis of the middle cerebral artery blood flow velocity waveform envelope in 14 normal subjects (group A) and 15 patients, of whom five had arteriovenous malformations (group B), five had cerebral vasospasm (group C), and five had arterial hypertension (group D). Measurements were obtained under conditions of normocapnia, hypercapnia, and hypocapnia. The Fourier coefficients measured in the first five harmonics of the Doppler waveforms of group A were used as the reference baseline and were compared with the coefficients found in the other three groups. Group B showed significantly lower Fourier coefficients, while groups C and D showed higher coefficients (p less than 0.05). The elevation of the Fourier coefficients occurred in an alternating pattern in group C and a decremental pattern in group D. This distinction was attributed to possible differences in the underlying pathophysiological processes. The degree of vascular distensibility of the cerebral arterioles, inferred from the shape of the Fourier analysis curves, was compared in all four groups. Vascular distensibility was characterized as abnormal in arteriovenous malformations, vasospasm, and arterial hypertension. Fourier coefficients may be better indicators of cerebrovascular abnormalities than mean blood flow velocity in hypertension and pulsatility index in arteriovenous malformations, vasospasm, and hypertension.

Adult↗
PubMed1990

Recognition of cell surface modulation by elliptic Fourier analysis.

A development of elliptic Fourier analysis, consisting in an alignment of harmonics according to their clockwise or counter-clockwise rotation, resolves the discrepancy between calculated harmonic frequencies and observed morphological periodicities. The new technique is supported by consistent data of empiric and fractal contours, comparatively analyzed and visualized with and without harmonic alignment. The method is particularly suitable for the recognition of periodic modulations of the cell surface. A preliminary analysis of two different cell populations (echinocytes and chondrocytes) shows distinct patterns of surface modulation that allow an effective discrimination of the cell type, while providing relevant information about the respective cytological configurations.

Algorithms↗
PubMed1999

Do's and don'ts in Fourier analysis of steady-state potentials.

Fourier analysis is a powerful tool in signal analysis that can be very fruitfully applied to steady-state evoked potentials (flicker ERG, pattern ERG, VEP, etc.). However, there are some inherent assumptions in the underlying discrete Fourier transform (DFT) that are not necessarily fulfilled in typical electrophysiological recording and analysis conditions. Furthermore, engineering software-packages may be ill-suited and/or may not fully exploit the information of steady-state recordings. Specifically: * In the case of steady-state stimulation we know more about the stimulus than in standard textbook situations (exact frequency, phase stability), so 'windowing' and calculation of the 'periodogram' are not necessary. * It is mandatory to choose an integer relationship between sampling rate and frame rate when employing a raster-based CRT stimulator. * The analysis interval must comprise an exact integer number (e.g., 10) of stimulus periods. * The choice of the number of stimulus periods per analysis interval needs a wise compromise: A high number increases the frequency resolution, but makes artifact removal difficult; a low number 'spills' noise into the response frequency. * There is no need to feel tied to a power-of-two number of data points as required by standard FFT, 'resampling' is an easy and efficient alternative. * Proper estimates of noise-corrected Fourier magnitude and statistical significance can be calculated that take into account the non-linear superposition of signal and noise. These aspects are developed in an intuitive approach with examples using both simulations and recordings. Proper use of Fourier analysis of our electrophysiological records will reduce recording time and/or increase the reliability of physiologic or pathologic interpretations.

Artifacts↗
PubMed1984

Quantification of segmental wall motion by length-based Fourier analysis.

A new method for evaluating segmental wall motion by length-based Fourier analysis is described. Fourier analysis is performed on a series of lengths from a center to edges of the ventricle, generating parameters of percent length shortening (%LS) and phase of the segment (length-based phase). The reproducibility of the result was good, since the algorithm was automatic except for the setting of the ventricular region as a mask image to exclude surrounding blood pools. This program can be applied for quantification of ventricular wall-motion abnormalities in gated blood-pool studies, and for analysis of the timing of ventricular contraction in gated blood-pool emission computed tomography to detect the site of an accessory conduction pathway in patients with Wolff-Parkinson-White syndrome.

Arrhythmias, Cardiac↗
PubMed1980

Patterns of ventricular emptying by Fourier analysis of gated blood-pool studies.

Temporal Fourier analysis was applied to the processing of ECG-gated cardiac blood-pool studies on a pixel-by-pixel basis, to yield information about the pattern of ventricular emptying in normal hearts and in others with conduction abnormalities. The transform data at the fundamental frequency (the heart rate) were used to construct two types of display: (a) a distribution histogram of the pixel phase values, and (b) a cinematic display of the wave of emptying as it spread over the cardiac chambers. Preliminary results indicate that temporal Fourier analysis permits visualization of the pattern of ventricular emptying, which may prove useful in the study of motion abnormalities and asynergies, including those resulting from myocardial hypertrophy or conduction abnormalities, and as an aid in the optimum placement of pacemakers.

Arrhythmias, Cardiac↗
PubMed1996

Characterization of left atrial appendage Doppler flow in atrial fibrillation and flutter by Fourier analysis.

The aim of this study was to characterize left atrial appendage mechanical function in atrial fibrillation and flutter by Fourier analysis to analyze frequency and regularity of flow. Left atrial appendage function is central to a patient's risk for thromboembolism. Although the function of the appendage can be analyzed by Doppler echocardiography in sinus rhythm, its mechanical function in atrial fibrillation and flutter has not been well characterized. This lack of adequate definition is caused by the complexity and temporal variability of the Doppler flow profiles. We assessed left atrial appendage function in 21 cases of atrial fibrillation (n - 11) and flutter (n = 10) and five in sinus rhythm with transesophageal Doppler echocardiography. Doppler profiles were examined by Fourier analysis, and the power spectra compared and analyzed between patients with atrial fibrillation and flutter. Left atrial appendage Doppler flow in atrial fibrillation produced Fourier spectra over a narrow band of frequencies with a peak frequency of 6.2 +/- 1.0 Hz, significantly higher than in atrial flutter (3.9 +/- 0.6 Hz, p < 0.00001). Additionally, a significant difference in subharmonic modulation (spectral power below the peak frequency) was observed between atrial appendage flow in atrial fibrillation and flutter, because 37% +/- 16% of the total spectral power was achieved before the dominant frequency in atrial fibrillation compared with 20% +/- 14% in atrial flutter (p = 0.02). Conversely, patients in sinus rhythm exhibited broad-banded Fourier spectra with most of the power in discrete frequency spikes at harmonics above the fundamental frequency with very little subharmonic modulation (1% +/- 0.05%). Left atrial appendage function in atrial fibrillation and flutter can be well characterized by Fourier analysis of Doppler flow. Atrial fibrillation has higher dominant frequencies and greater subharmonic modulation compared with flutter. Moreover, atrial fibrillation demonstrated quasiperiodic contraction patterns typically found in chaotic systems. Fourier analysis of left atrial appendage contraction patterns may therefore have significant promise in providing insights into mechanisms of atrial fibrillation and thromboembolism.

Aged↗
PubMed2005

Efficacy of the phase images in Fourier analysis using gated cardiac POOL-SPECT for determining the indication for cardiac resynchronization therapy.

BACKGROUND: Although cardiac resynchronization therapy (CRT) improves quality of life and survival for patients with heart failure, exact methods to estimate the effect of cardiac asynchrony have not yet been defined. METHODS AND RESULTS: Initially, to examine whether the phase analysis images in the Fourier analysis using gated cardiac pool single photon emission computed tomography (POOL-SPECT) could be used to evaluate cardiac asynchrony, 19 consecutive patients with dilated cardiomyopathy were studied. Interventricular asynchrony was defined by whether the peak of the picture elements of the right ventricle in the phase histogram fitted that of the left ventricle and intraventricular asynchrony by whether the phase image was described homogenously or not. The patients with both inter- and intraventricular asynchrony had significant deterioration in both left ventricular ejection fraction (p<0.01) and New York Heart Association functional class (p<0.01). To evaluate the efficacy of these phase images for CRT setting, 7 patients were tested before and after CRT. During a 3.9+/-3.6 month follow-up period, all patients had an improvement in their condition, and the inter- and intraventricular asynchrony significantly improved after CRT. The degrees of the inter- and intraventricular asynchrony were related to the degree of cardiac depression pre CRT. CONCLUSION: These results have shown that the phase images from POOL-SPECT are useful for assessing the effect of CRT in patients with heart failure, which suggests that it may provide information about the indication for CRT.

Adult↗
PubMed2000

[Central nervous system activation in opioid dependent patients, evaluation with Fourier analysis of pupillary oscillations].

The aim of the present investigation was to determine whether Fourier analysis of pupillary oscillations permits detection of differences in the activation of the central nervous system of opioid-addicted patients. We analysed pupillary oscillations during the recording period of static pupillometry, which lasted 25.6 s. Using Fourier analysis, the spectrum was divided into five frequency bands (0.0-0.20, 0.21-0.40, 0.41-0.60, 0.61-0.80, 0.81-1.0 Hz); the total spectrum (0-1 Hz) was also assessed. Three groups of patients were selected: the group addicted to heroin (consuming exclusively heroin) consisted of 26 patients with a mean age of 25.0 +/- 6.3 years, the methadone substitution group of 20 patients with a mean age of 30.9 +/- 8.2 years, and the morphine substitution group of 20 patients with a mean age of 33.2 +/- 4.6 years. The 3 patient groups were compared with normal controls of similar age (25.1 +/- 4.6 years). In the frequency band of 0.0-0.20 Hz the morphine group showed significantly lower amplitudes than the heroin group. Also in the frequency band of 0.41-0.60 Hz the morphine group differed significantly from the other groups concerning lower amplitudes, reflecting deactivation. In the total spectrum of 0 to 1 Hz the differences between these two groups were significant. Comparison with normal controls also showed significant differences. The groups were further divided according to dose (high/low): Patients of the heroin group as well as those of the methadone and morphine groups who had consumed higher doses showed greater activation of the central nervous system. In conclusion the morphine group was more deactivated than the methadone and heroin group and patients who received higher doses of the substances showed greater central nervous activation. Thus, the measurement of central nervous activation by means of Fourier analysis of pupillary oscillations might be useful in monitoring substitution therapy.

Adult↗
PubMed1994

Fourier analysis in the objectivisation of auditory brain stem responses in newborns.

Fourier analysis (FFT) of auditory brain stem responses induced by stimuli of 90, 70 and 40 dB HL was carried out in group of 45 full-term and pre-term neonates. It was stated that with postnatal newborn's development complex IV/V was observed more frequently for the more immature newborn. It influences also the power strength spectrum obtained. In responses with IV/V complex the frequency range is considerable and significantly reduced by about 100-200 Hz. It was observed that general state of newborn at the birth influences the frequency range as well as from the shape of score reproducibility and reliability of spectrum is significantly better. It was noticed also that the shape and form of spectrum in about threshold and threshold responses is significantly similar irrespective of the intensity of threshold stimulus. The shape and form of responses spectra for stimuli of 30-40 dB HL (in a group of children with normal hearing) and of 80-90 dB HL (in a group of children with severe hearing impairment) are identical. The above findings allow us to show the importance of Fourier analysis for objectivisation of subjective evaluation of auditory brain stem responses.

Auditory Threshold↗