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PubMed1989

Fourier analysis of the nerve fiber layer by digital imaging techniques.

We introduce a new method to examine the retinal nerve fiber layer (RNFL) that may detect early changes in its structure due to glaucoma. Viewed in the conventional manner, in a plane perpendicular to the retina, we get an estimation of the structural integrity of the RNFL. Viewed from a plane parallel to the retina, the RNFL forms a contour surface of hills and valleys. In our method red free fundus slides are digitally acquired. A waveform, representing a topographic profile cut through the resulting representation of the RNFL contour surface, was analyzed using Fourier's transform. Three cycles/mm in the Fourier power spectrum was used as an arbitrary cutoff to discriminate normal from glaucomatous RNFL. The Fourier power spectrum from normal RNFL was shifted to higher spatial frequencies, while the power spectrum from glaucomatous RNFL was shifted to lower spatial frequencies. Thus, Fourier Analysis can reveal information about such a wave form which is not obvious by visual inspection or by densitometric techniques. This method may allow for an even earlier diagnosis of injury to the optic nerve due to glaucoma.

Fourier Analysis↗
PubMed1991

Evaluation with Fourier analysis on radionuclide angiography of viable but stunned myocardium in patients with right ventricular myocardial infarction.

Stunned myocardium of right ventricle was studied by radionuclide angiography (RNA) and Thallium myocardial scintigraphy (TL) in 39 patients with inferior myocardial infarction with and without right ventricular myocardial infarction (RVMI). RNA was performed within 1 week of the onset (acute phase) and after 1 month, when exercise cardiac scintigraphy (EX-TL) was also performed. The ejection fraction (EF) of each ventricle calculated from RNA and the phase and amplitude evaluated visually and quantitatively by Fourier analysis were compared between the acute phase and 1 month after the onset of myocardial infarction. The degree of visualization of right ventricle was examined in EX-TL 1 month after the onset. (1) In RNA obtained in the acute myocardial infarction, abnormalities in the right ventricle (delayed phase or low amplitude image) were observed in 18 (46%) but not in 21 (54%) of the 39 patients (N group). Of those 18 patients, the abnormalities in the right ventricle alleviated in 11 (RVMI-A group) but persisted in 7 (RVMI-B group) in RNA obtained 1 month after the onset. (2) In the acute phase, the right ventricular ejection fraction (RVEF) was 39.4 +/- 10.4% in N group, 30.8 +/- 5.3% in RVMI-A group, and 29.6 +/- 8.9% in RVMI-B group, with significant differences between N group and the other two groups (P less than 0.05) but no significant difference between RVMI-A and RVMI-B groups. (3) After 1 month, RVEF was 40.1 +/- 10.1% in N group, 42.2 +/- 8.4% in RVMI-A group, and 32.2 +/- 9.8% in RVMI-B group, being improved in RVMI-A group and showing a significant difference as compared with RVMI-B group (p less than 0.05). (4) In EX-TL of RVMI-A group, the right ventricle was visible although the uptake of TL was reduced in the entire right ventricle. In RVMI-B group, only part of the right ventricular free wall was visible with defects in the other areas of right ventricle. The sign of RVMI showed improvements in many of the patients after the acute phase, and their condition was considered to have been so-called stunned myocardium, which is a complex of symptoms of reversible myocardial ischemia, rather than RVMI.

Aged↗
PubMed1991

Fourier analysis of the nuclear and cytoplasmic shapes of living two-cell murine embryos.

Living two-cell mouse embryos were flushed out from the oviduct 17, 24 and 36 hours after fertilization in order to obtain cells in the G1S, early G2 and late G2 phases of the second cell cycle. The nuclei of the living cells were stained with Hoechst 33342. The coordinates of the contour shapes of the entire cells (cellular contours) were registered by contour image processing with a TV camera coupled with a computer; the contours of the nuclei were computed by means of a digitizer coupled with the computer. Fourier analysis of the cellular and nuclear contours revealed systematic modifications in the folding of the cells and nuclei in the course of the murine second cell cycle. The progression of cells through the second cell cycle was correlated with an increasing diversification of cellular and nuclear shape, with the diversification being much more pronounced in the nuclear shapes.

Animals↗
PubMed1994

Shape of the human corpus callosum. Elliptic Fourier analysis on midsagittal magnetic resonance scans.

RATIONALE AND OBJECTIVES: Sex, age, or functional-asymmetry-related variations in the size and shape characteristics of the midsagittal magnetic resonance (MR) image of the human corpus callosum (CC) have been widely investigated in the last 10 years, with conflicting results. In the current study, the authors attempted to analyze the sex- and age-related shape differences of the human CC in a large sample of adult subjects from a mathematical standpoint. METHODS: On the midsagittal MR images of 143 neurologically intact adults (75 women, 68 men, 21 to 81 years of age) the outline of the CC was identified. The shape of the CC was quantified using elliptic Fourier analysis, which allows for a global evaluation of the shape of organs identified by their outlines independent of their size, spatial orientation, and relation to reference planes. Subjects were grouped by sex and age. RESULTS: The shape of the human CC within age and sex class was highly variable. The analysis of variance showed a significant effect of age; however no significant sex differences could be demonstrated. CONCLUSIONS: Larger sample sizes are required to definitively assess the normal shape variations in human CC. The method developed also could be applied to the comparison of healthy and diseased individuals.

Adult↗
PubMed1986

Fourier analysis of the cell shape of paired human urothelial cell lines of the same origin but of different grades of transformation.

The rationale of the present investigation is the observations made by many authors of changes in the molecular structure of the cell surface during the multistep process of malignant transformation. These changes may influence cell-matrix and cell-cell interactions and thereby cause changes in cell adhesiveness and cell shape. The aim of the present work was to investigate whether the development of various grades of transformation in vivo and in vitro of human urothelial cells is accompanied by significant changes in cell shape as measured by Fourier analysis. The following transformation grades (TGr) have been defined (Christensen et al. 1984; Kieler 1984): TGr I = nonmalignant, mortal cell lines that grow independently of fibroblasts and have a prolonged life span. TGr II = nonmalignant cell lines with an infinite life span. TGr III = malignant and immortal cell lines that grow invasively in co-cultures with embryonic chick heart fragments and possess tumorigenic properties after s.c. injection into nude mice. Comparisons of 4 pairs of cell lines were performed; each pair was of the same origin. Two pairs--each including a TGr I cell line (Hu 961b and Hu 1703S) compared to a TGr III cell line (Hu 961a or Hu 1703He)--were derived from two transitional cell carcinomas (TCC) containing a heterogeneous cell population. Two additional cell lines classified as TGr II (HCV-29 and Hu 609) were compared to two TGr III sublines (HCV-29T and Hu 609T, respectively) which arose by "spontaneous" transformation during propagation in vitro of the respective maternal TGr II-cell lines.(ABSTRACT TRUNCATED AT 250 WORDS)

Carcinoma, Transitional Cell↗
PubMed2002

Long-term results of a clinical trial on dermal substitution. A light microscopy and Fourier analysis based evaluation.

Although dermal substitution is a main topic of current wound healing research, there is a paucity of clinical trials with a long-term clinical and histopathological evaluation. A clinical trial was conducted to perform an intra-individual comparison of conventional treatment (split-thickness autograft) to a collagen/elastin dermal substitute in combination with an autograft. Promising results with this substitute were obtained with respect to dermal organisation and scar elasticity in animal studies and clinical trials with a short-term follow-up. Twenty-nine of the 42 pairs of the burn wounds and 28 of the 44 pairs of the scar reconstructions enrolled in the study were biopsied after 1 year. Promising but not statistically significant differences were found between substituted groups and control groups for epidermal thickness, basement membrane maturation, rete ridges (P=0.055), fibroblasts, myofibroblasts, inflammatory cells, vessels and extracellular matrix maturation. An objective and accurate technique, Fourier analysis, was used to evaluate collagen bundle orientation and packing. However, no statistically significant differences were obtained for these parameters. This microscopic evaluation provided no convincing evidence for a long-term effectiveness of a dermal substitute despite promising data over a short-term in in vitro and in vivo studies with the same material.

Adult↗
PubMed1982

[Age-matched normal values of regional cerebral blood flow measurements by 133Xe inhalation and production of judgment image: as to initial slope index computed by Fourier analysis].

In order to investigate an influence of advancing age on regional cerebral blood [flow](rCBF), 125 measurements of rCBF were made by 133Xe inhalation method in 90 normal subjects without cerebral symptoms and risk factors of atherothrombotic stroke including hypertension, diabetes mellitus, and hyperlipidemia. There were 46 male and 44 female aged 19 to 80 years old (mean 42.5). The measurements were carried out in a quiet, semi-darkened room with the subjects at rest and eye closed. 133Xe inhalation system (Meditronic-Novo Diagnostic Systems, Inhalation Cerebrograph, Denmark) consists of 32 scintillation detectors, the lateral part of each hemisphere being covered by 16 detectors placed in parallel. One pair of the detectors is mounted in place over the brain stem and cerebellar region. Relationship of age and rCBF computed as the initial slope index (ISI) by Fourier analysis was investigated with both correlation and regression analyses, and age-matched normal values were calculated. End-tidal partial pressure for carbon dioxide (PECO2) was recorded from the face mask during the measurements along with the mean arterial blood pressure (MABP). ISI values were not corrected for changes in PECO2. PECO2 and MABP did not differ significantly among the normal subjects. There were no significant differences in the hemispheric mean ISI values between the right and left hemispheres. Mean brain ISI values showed significant negative correlation with advancing age (r = -0.67, p less than 0.001), and regression line was Y = -0.30X + 67.8. Ninety five per-cent confidence interval of the regression line was +/- 11.8. Regional ISI values also showed significant negative correlations with advancing age in the whole brain (p less than 0.001). There were no significant differences in the correlation coefficients obtained from parallel regions between the right and left hemispheres. The regional reduction of ISI values with advancing age was significantly greater in the regional distribution of the middle cerebral arteries bilaterally, compared with regions in the distribution of either the anterior cerebral, the posterior cerebral, or vertebrobasilar arteries (p less than 0.05). Regional hemispheric percent value of frontal lobe was greater than that of either parietal, temporal, occipital lobe, or brain stem and cerebellar region in the whole age. But, this hyperfrontal distribution became gradually obscured with advancing age, because reduction of ISI values with aging was significantly greater in the frontal than in other regions. It is concluded that measured rCBF of a patient have to be compared with age-matched normal values of mean brain and each region. Judgment image was produced with dividing patient value by 95% confidence limit of age-matched normal value. According to this image, regions in which rCBF significantly decrease or increase can be easily evaluated.

Adult↗
PubMed1999

Fourier analysis of fluctuations of oxygen tension and blood flow in R3230Ac tumors and muscle in rats.

Tumor hypoxia is a major barrier to tumor radiation therapy. Typically tumor hypoxia occurs in two forms: chronic and acute. Although the existence of acute hypoxia has long been acknowledged, its temporal characteristics have never been directly measured and documented. In this study tumor PO(2), blood flow (BF), and arterial blood pressure (BP) were measured simultaneously in nine Fischer 344 rats bearing R3230Ac rat mammary adenocarcinomas in the subcutis of the left hindleg. We measured PO(2) at a single location for 36-125 min using recessed-tip oxygen microelectrodes. Simultaneously, we measured tumor BF at two sites within the tumor using laser-Doppler flowmetry (LDF). Similar recordings were made in the quadriceps muscle of seven non-tumor-bearing rats. The PO(2), tumor BF, and BP records were subjected to Fourier analysis. PO(2) and BF showed low-frequency fluctuations (<2 cycles/min) in both tumor and muscle, but the magnitude of the changes in tumor was greater. Tumor BF showed more activity at low frequencies than muscle BF, and the magnitude tended to be greater. No strong correlations were found between PO(2) and BF power spectra for either tumor or muscle or between the frequency patterns of BP and tumor PO(2) spectra. These results quantitatively demonstrate, for the first time, that BF and PO(2) fluctuate at very low frequencies in tumors. In addition to having biological significance for tumor therapy, these fluctuations may have the potential to alter tumor cell behavior via induction of hypoxia reoxygenation injury and/or altered gene expression.

Adenocarcinoma↗
PubMed2004

Corneal regular and irregular astigmatism assessed by Fourier analysis of videokeratography data in normal and pathologic eyes.

PURPOSE: To assess corneal regular and irregular astigmatism using Fourier series harmonic analysis of videokeratography data in normal subjects, as well as in subjects with pathologic and postsurgical conditions. STUDY DESIGN: Retrospective, case-control study. PARTICIPANTS: Two hundred normal eyes, 58 eyes with keratoconus, 24 eyes with suspect keratoconus, 100 eyes that underwent LASIK, 101 eyes that underwent photorefractive keratectomy (PRK), and 79 eyes that underwent penetrating keratoplasty (PK). METHODS: Videokeratography data were decomposed, using Fourier analysis, into spherical power, regular astigmatism, asymmetry, and higher order irregularity. RESULTS: The normal range of the Fourier indices was defined as the mean +/-2xstandard deviation in the normal eyes, which were 40.81-47.13 diopters (D) for spherical power, 0-1.04 D for regular astigmatism, 0.02-0.68 D for asymmetry, and 0.05-0.17 for higher order irregularity. The keratoconus and suspect keratoconus groups showed significantly greater values in all indices than did the normal group (P<0.001 or 0.0001, Mann-Whitney test with Bonferroni correction). Eyes that had undergone LASIK and PRK had significantly smaller spherical power and regular astigmatism (P<0.0001) and significantly larger asymmetry (P<0.0001) than the normal eyes. All indices were significantly greater in the PK group than in the normal group (P<0.0001). Among the eyes tested in this study, eyes with keratoconus had the largest asymmetry, whereas eyes that had undergone PK had the most irregular corneas. CONCLUSIONS: The normal range was defined for the corneal irregular astigmatism index (asymmetry and higher order irregularity) to support future studies in this field. Eyes with ocular pathologic and postsurgical conditions were evaluated using the normal range.

Adolescent↗
PubMed1998

The use of Fourier analysis in the calculation of trough to peak ratio from ambulatory blood pressure measurements.

The trough:peak (T:P) ratio serves as an index of efficacy of antihypertensive drugs with respect to their dose and dose interval. There is no consensus regarding the method for the calculation of the T:P ratio. We assessed the influences of curve smoothing, the average fall in 24-h mean arterial pressure (MAP) and the length of the peak effect period on the result of T:P ratio calculation. Forty-two patients with essential hypertension (aged 27-81 years; 20 males) had a 24-h ambulatory blood pressure (BP) measurement on two occasions. The first was performed at baseline, the second after 12 weeks of treatment with a beta-blocker, angiotensin-converting enzyme inhibitor, calcium slow-channel blocker, diuretic or a centrally acting drug, all taken once daily. BP data were analysed both by Fourier analysis (FA) with four harmonics and by time block analysis (TBA). The peak effect was defined as the maximum drop in MAP over a period of 0 to 3 h following drug intake at any time in the 24 h, and the trough effect as the fall in MAP over the last 2 h of the dose interval. FA gave higher T:P ratio values than TBA (0.51 vs 0.43; P < 0.05) and the variability of the results was reduced by FA (FA: 0.49-0.52; TBA: 0.35-0.46). A greater fall in 24-h MAP was associated with a higher T:P ratio (r = 0.42, P < 0.02; TBA: r = 0.31, P = 0.09). Half of the patients whose fall in 24-h MAP after treatment was <10 mm Hg, had higher trough BP values, resulting in negative T:P ratios. With increasing length of the peak period, the calculated peak effect was reduced and the T:P ratio increased (both FA and TBA: P < 0.001). The mean trough responses during the last 2 h of the dose interval were similar after TBA and FA. Based on these data, we recommend the use of FA for calculation of T:P ratios, especially when the magnitude of the antihypertensive effect is small. We also suggest using peak- and trough-effect periods of 2 h each. Whenever T:P ratios are calculated, the method used for curve smoothing and the length of peak- and trough-effect periods should be specified in order to obtain meaningful results. T:P ratios need to be interpreted individually together with the magnitude of the antihypertensive drug effect and the circadian BP profile.

Adult↗
PubMed2000

Fourier analysis of facial profiles of young twins.

Twins studies provide a powerful approach to determining the relative contribution of genetics and environment to observed variation. Such studies assume trait differences in monozygous (MZ) twins are due to environmental factors and those in dizygous (DZ) twins are due to both genetic and environmental factors. This study quantitated facial profiles of twins using Fourier equations, determining their value in profile analysis and the assessment of the genetic contribution to facial shape. Standardized profile slide photographs of 79 pairs of 4-6 year-old twins (37 MZ pairs, 42 DZ pairs) were scanned and x and y coordinates were extracted from each profile using sellion and Camper's plane as references. The coordinates were subjected to Fourier analysis and the normalised vertex projection coefficients were studied. The means of the differences between coefficients for MZ co-twins did not differ significantly from that of DZ co-twins, although the DZ group showed higher mean differences in the higher harmonics. Subjective examination of superimposed reconstructions showed wider variation between DZ co-twins than MZ co-twins. Correct classification of twins by discriminant function analysis using Fourier coefficients was similar for both groups (MZ: 70.3%; DZ: 73.8%). Fourier analysis could quantitate facial profiles of young children and differentiate some details, but was unable to discriminate between genetic and environmental influences, and any possible interactions between these influences, on their overall facial profiles at this developmental stage.

Child↗
PubMed1995

Computerized analysis of interstitial infiltrates on chest radiographs: a new scheme based on geometric pattern features and Fourier analysis.

RATIONALE AND OBJECTIVES: Detection of interstitial infiltrates on chest radiographs is difficult and subjective. Therefore, we developed a computerized method to provide quantitative analysis of lung texture to increase diagnostic accuracy. METHODS: Two hundred chest radiographs--100 healthy and 100 abnormal with interstitial infiltrates--were digitized using a laser scanner. They were analyzed by an automated computerized scheme that uses a combination of two methods for detection of interstitial infiltrates: a lung texture analysis based on the Fourier transform and a geometric pattern feature analysis based on filtering techniques. RESULTS: The overall sensitivity and specificity of the computerized scheme were 92% and 90%, respectively. The scheme achieved a sensitivity of 80% in subtle cases (n = 15) and 88% in cases with localized interstitial disease (n = 26), whereas the specificity remained unchanged. There was good correlation between the computer output and the radiologists' severity rating. CONCLUSION: This enhanced computerized scheme exhibits high sensitivity and specificity with a large database.

Adolescent↗
PubMed1995

Fourier analysis of video-keratographic data. A tool for separation of spherical, regular astigmatic and irregular astigmatic corneal power components.

Topographic analysis of the cornea and computation of changes in corneal topography is difficult because of the lack of a standardized concept for analysing topographic information. We have used Fourier series harmonic analysis to decompose the often very complex information given in topographic images (TMS-1 video-keratograph). The polar data values arising from each mire were separated into spherical (average power), regular astigmatic (2' harmonic) and non-regular astigmatic components. The non-regular astigmatic components were further divided into a decentration component (1' harmonic) and a higher order irregular refractive component (root mean square (r.m.s.) of the residual between original data and the sum of spherical, 1' and 2' order components). Algorithms for utilizing the Fourier analysis technique on subjective refractive and on keratometric changes in regular astigmatism were also derived. Averages of the separate refractive components were calculated for groups of normal (right and left eye of 25 patients), keratoconic (13 eyes), and transplanted eyes (20 eyes), and average topographic maps were reconstructed and imaged. Changes in the separate topographic refractive components were compared with subjective refractive changes in eyes that had undergone combined myopic-astigmatic excimer laser ablation (8 eyes). Fourier series analysis was found superior to conventional keratometry in predicting spherical and regular astigmatic changes in subjective refraction. Fourier series analysis seems to be a powerful tool to decompose the information of complex topographic corneal images into rational optical components.

Algorithms↗
PubMed1997

Quantitative characterization of vascular endothelial cell morphology and orientation using Fourier transform analysis.

Fourier Transform methods were used to quantify mean elongation, mean orientation, and standard deviation of orientations of cultured vascular endothelial cells. Images of cell populations, which had been subjected to 11 and 20 hours of shear stress at 30 dynes/cm2 and 20 hours of no shear, were analyzed by Fourier Transform methods. Measurements of cell morphology and orientation characteristics were also obtained using a manual method for comparison purposes. The results of the study showed that mean cell orientation can be determined accurately with the Fourier Transform methods. Attempts to determine the standard deviation of cell orientations, however, resulted in poorer estimates of mean elongation and standard deviation of orientations except in the case of exposure of endothelial cells to 20 hours of shear, where the actual standard deviation of orientations was low. When the value for standard deviation of orientations was constrained to zero, a minimum possible mean elongation was determined reliably using the Fourier Transform methods. Use of the Fourier Transform methods in determining morphological and orientation characteristics of cell monolayers is fast and objective and may provide a basis for identifying other characteristics of cell shape.

Animals↗
PubMed1991

Spatial Fourier analysis of video photobleaching measurements. Principles and optimization.

The major use of the fluorescence recovery after photobleaching (FRAP) technique is to measure the translational motion of the molecular components in various condensed media. In a conventional laser spot photobleaching experiment, a photomultiplier is used to measure the total brightness levels of the bleached region in the sample, so no spatial information can be directly obtained. In video-FRAP, a series of images after photobleaching is acquired, allowing the spatial character of the recovery to be determined; this permits direct detection of both anisotropic diffusion and flow. To utilize all of the available image data to determine the transport coefficients, a two-dimensional spatial Fourier transform analysis of the images after photobleaching was employed. The change in the transform between two time points reflects the action of diffusion during the interim. An important advantage of this method, which involves taking the ratio of image transforms at different time points, is that it does not require a specific initial condition to be created by laser photobleaching. The ability of the analysis to extract transport coefficients from computer-simulated diffusional recovery is assessed in the presence of increasing amounts of noise. Experimental data analysis from the diffusion of proteins in viscous solutions and from the diffusion of protein receptors on cell surfaces demonstrate the feasibility of the Fourier analysis to obtain transport coefficients from the video FRAP measurement.

Biophysical Phenomena↗
PubMed2005

Automated magnification calibration in transmission electron microscopy using Fourier analysis of replica images.

The magnification factor in transmission electron microscopy is not very precise, hampering for instance quantitative analysis of specimens. Calibration of the magnification is usually performed interactively using replica specimens, containing line or grating patterns with known spacing. In the present study, a procedure is described for automated magnification calibration using digital images of a line replica. This procedure is based on analysis of the power spectrum of Fourier transformed replica images, and is compared to interactive measurement in the same images. Images were used with magnification ranging from 1,000 x to 200,000 x. The automated procedure deviated on average 0.10% from interactive measurements. Especially for catalase replicas, the coefficient of variation of automated measurement was considerably smaller (average 0.28%) compared to that of interactive measurement (average 3.5%). In conclusion, calibration of the magnification in digital images from transmission electron microscopy may be performed automatically, using the procedure presented here, with high precision and accuracy.

Automation↗
PubMed2004

Vicinal fluorine-fluorine coupling constants: Fourier analysis.

Stereochemical dependences of vicinal fluorine-fluorine nuclear magnetic resonance coupling constants (3JFF) have been studied with the multiconfigurational self-consistent field in the restricted active space approach, with the second-order polarization propagator approximation (SOPPA), and with density functional theory. The SOPPA results show the best overall agreement with experimental couplings. The relationship with the dihedral angle between the coupled fluorines has been studied by Fourier analysis, the result is very different from that of proton-proton couplings. The Fourier coefficients do not resemble those of a typical Karplus equation. The four nonrelativistic contributions to the coupling constants of 1,2-difluoroethane configurations have been studied separately showing that up to six Fourier coefficients are required to reproduce the calculated values satisfactorily. Comparison with Fourier coefficients for matching hydrogen fluoride dimer configurations suggests that the higher order Fourier coefficients (Cn> or =3) originate mainly from through-space Fermi contact interaction. The through-space interaction is the main reason 3JFF do not follow the Karplus equation.

Journal Article↗