[Fourier analysis of flicker ERG response. I. Fourier analysis of photopic ERG response by flicker stimulation of square wave (author's transl)].
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Rapid detection of spatial pattern by Fourier analysis.
Fast Fourier transform analysis can be used to accurately and rapidly detect pattern in large two-dimensional arrangements of points, such as the locations of cells in culture or plants in a unit square. We present here a sample study of pattern in spatial random point processes. This is evidently the first time that Fourier transform-based cross-correlation techniques have been applied to the analysis of point processes of biological origin. Radial profiles of the power spectra and autocorrelation estimates revealed a nearly constant interpore distance of 0.49 +/- 0.04 mm in the locations of eccrine gland pores on the surface of human skin. Additionally, gland-free areas may exist near hair follicles.
Algorithms↗
[Analysis of circadian blood pressure profiles using Fourier analysis].
Blood pressure is subject to considerable circadian and situational fluctuation. In 24-h blood-pressure monitoring the severity of arterial hypertension is generally classified on the basis of the arithmetic mean of the diastolic blood pressure between 07.00 and 22.00 hours. In the present study Fourier analysis was used to generate continuous functions from the discrete blood-pressure values measured during 24-h blood-pressure monitoring in a sample of 50 normotensive persons aged from 25 to 80 years. A common reference profile was then constructed from these 50 profiles. This reference profile is characterized by the fact that the sum of the integrals over the squares of the distances between the individual profiles and the reference profile is the smallest possible. The reference profile is thus the best approximation of all normotensive profiles and practically ignores individual blood pressure fluctuations. The individual 24-h profiles of 80 patients with untreated arterial hypertension were classified on the basis of the daytime mean as mild, moderate or severe arterial hypertension and also each is described by a Fourier series. The pathological profiles were then compared with the normotensive reference profile. The comparison was made, not only with respect to the absolute pressure over 24 h, but also with respect to the circadian fluctuations in blood pressure. Comparison of the profiles shows that the Fourier analysis of 24-h blood-pressure profiles presented here permits reliable analysis and classification of arterial hypertension and can thus be used for more precise evaluation of the influence of antihypertensives on 24-h blood-pressure profiles.
Adult↗
Improved detection of anterior left ventricular aneurysm with multiharmonic fourier analysis.
Single and multiharmonic Fourier analysis of LAO 30-45 degrees gated blood-pool studies were performed in a selected group of 30 patients with a left ventricular anterior aneurysm proven by contrast angiography. The sensitivity of the first harmonic phase image for the diagnosis of ventricular aneurysm was 80%. The clear phase shift (greater than 110 degrees) between the normal and the aneurysmal areas was missing in six patients. Peak acceleration images (negative maximum of the second derivative of the Fourier series) were calculated for each pixel with the analytical Fourier formula using two or three harmonics. A clear phase shift (greater than 126 degrees) than appeared in all the patients. This improvement was related to the increased weight of the second and third harmonics in the aneurysmal area when compared to control patients or to patients with dilative cardiomyopathy. Multiharmonic Fourier analysis clearly improved the sensitivity of the diagnosis of anterior left ventricular aneurysm on LAO 30 degrees-45 degrees gated blood-pool images.
Cardiomyopathy, Dilated↗
Size and shape of the hominoid distal femur: fourier analysis.
A quantitative description of the shape of the distal femur is provided by Fourier analysis. Fourier analysis also facilitates the separation of the size and shape components which allows the removal of the distorting effect of size. Hence, comparisons between the hominoid groups can be based solely on shape. A sample of 91 hominoid distal femora from the Cleveland Museum of Natural History was used to make comparisons based on size and shape as well as shape only. It is suggested that unless the effect of size is minimized or removed, generally not possible with the traditional metrical approach, measures of biological distance will be distorted.
Animals↗
Elliptic Fourier analysis of megakaryocyte nuclei in chronic myeloproliferative disorders.
Elliptic Fourier analysis was applied to megakaryocyte nuclei in bone marrow biopsies from 15 patients with chronic myelocytic leukemia with megakaryocyte predominance and from 15 patients with chronic megakaryocytic granulocytic myelosis. To assess the reliability of this procedure, the biopsies were evaluated also by the semiautomatic measurement of nuclear area and form factor, and both methods were compared with respect to the degree of morphologic differences obtained between these two types of chronic myeloproliferative disorders (CMPDs). Discriminant analysis revealed correct reclassification of all cases both for elliptic Fourier analysis and for semiautomatic planimetry, whereas discriminant scores were much higher for Fourier analysis. Thus, simple planimetric features such as nuclear area and form factor, in contrast to Fourier analysis, are not able to detect the full degree of morphologic differences between megakaryocyte nuclei in different CMPDs. Elliptic Fourier analysis therefore seems to be a useful procedure for the accurate description of such complicated structures as megakaryocyte nuclei in CMPD.
Analysis of Variance↗
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↗
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↗
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↗
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↗
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↗
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↗
Monitoring of cerebral perfusion during anesthesia by time-compressed Fourier analysis of the electroencephalogram.
Time-compressed Fourier analysis of the electroencephalogram has proven to be a useful analytical procedure during anesthesia and surgery which simplifies data interpretation by presenting the EEG in a time-compressed frequency domain rather than the conventional time domain. This method of data analysis graphically accentuates the electroencephalographic correlates of ischemia-induced cerebral dysfunction and other cerebral oxygen consumption abnormalities. The ability to accentuate trends in frequency and power is derived from sequential plotting of spectra to produce a graph with three dimensional axes of frequency, time, and power. In carotid endarterectomies the system has proven more useful than the conventional EEG in assessing the need for a vascular shunt to maintain internal carotid flow during endarterectomy. In open-heart surgery time-compressed EEG spectral analysis has allowed early recognition of cerebral ischemia resulting from arterial hypotension and venous hypertension. Five cases are presented which demonstrate the ability of our system to reflect developing cerebral ischemia.
Aged↗
Fourier analysis of the cranium in trisomy 21.
A comparative study of individuals exhibiting the trisomy 21 syndrome (Down's) and a normal group has shown statistically significant differences in cranial shape (norma lateralis). These differences illustrate the departure from normal growth seen in individuals displaying the trisomy 21 syndrome. Fourier analysis is a preferred method since it is more efficient than conventional techniques in the analysis of complex shapes. Fourier analysis is also attractive because the series terms are orthogonal, hence independent; further, the Fourier approach allows for the control of size differences. A three-way analysis of variance was used to test for significant differences between mean Fourier coefficients. The results showed significant difference between individuals with trisomy 21 and controls. Age differences were also significant, only sex differences tended to be non-significant. Finally, the trisomy 21 sample is twice as variable as the controls.
Age Factors↗
Shape description in osteology using automatic Fourier analysis. Example of the human atlas.
An image analysing procedure for the shape characterisation in osteology is described. We used expansion in Fourier series of an equiangular polar representation of the contour. Fourier analysis is an information preserving technique, and it is therefore possible to reconstruct the original contour from the shape descriptors (Fourier coefficients and descriptors). The properties of the truncated expansion of the Fourier series can be used for smoothing effect and noise reduction, for interpolated reconstruction, and for data compression. Fourier analysis also allows a quantitative description of the shape. The first components describe the gross feature, the following ones the fine details.
Cervical Atlas↗
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↗
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↗
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↗