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At least 127 records · Page 7Linked to original sources
PubMed2003

Fourier analysis of induced irregular astigmatism. Photorefractive keratectomy versus laser in situ keratomileusis in a bilateral cohort of hyperopic patients.

PURPOSE: To analyze corneal topographic data by Fourier analysis to determine differences in irregular astigmatism following spherical hyperopic correction by photorefractive keratectomy (PRK) or laser in situ keratomileusis (LASIK). SETTING: Department of Ophthalmology, St. Thomas' Hospital, London, United Kingdom. METHODS: Thirty-six eyes of 18 patients with moderate hyperopia had LASIK in 1 eye and PRK in the other eye. The flap was cut on a nasal hinge with a Moria LSK One microkeratome. The laser was a Summit SVS Apex Plus with an optical zone of 6.5 mm and a blending zone of 1.5 mm. Corneal topographic data were acquired with a TMS-1 topographer (Computed Anatomy Inc.) preoperatively and 1, 3, 6, and 12 months postoperatively. The ASCII files containing the dioptric power values were extracted and analyzed with custom-written software to extract the Fourier harmonics. RESULTS: The irregular astigmatism increased in both groups postoperatively, peaking at 3 months and then decreasing over the next 9 months. There was no statistically significant difference between the 2 groups at any time point (P<.05). The change in the topographically derived equivalent sphere showed undercorrection in both groups at all time points. Regular astigmatism showed a marginal statistically significant increase in the LASIK group at 12 months (P =.049). CONCLUSION: Irregular astigmatism, equivalent sphere, and regular astigmatism were not significantly different in the PRK and LASIK groups during the follow-up. Based on the corneal topography, the 2 procedures induced an equal amount of irregular astigmatism.

Adult↗
PubMed1990

[Comparative study of coronary artery disease using Fourier analysis in radionuclide ventriculography and coronary arteriography].

The results of rest blood-equilibrium radionuclide ventriculography (RVG) and of coronary arteriography were reviewed together. In 12 angiographically proved CAD patients, Fourier analysis correctly diagnosed 11, with an accuracy of 83.33% in localization 9 patients with myocardial infarction showed "empty" area in phase images. The phase analysis in RVG was considered a sensitive and accurate method in evaluating patients of CAD.

Adult↗
PubMed1985

[Phase and amplitude images using Fourier analysis in radioisotopic angiography. Comparison with contrast angiography for studying regional changes in ventricular contraction].

Phase-amplitude images and phase distribution histograms, derived from a temporal Fourier analysis of equilibrium ecg-gated blood pool studies, were used to assess the overall wall motion synchronism and to detect regional wall motion abnormalities in 69 consecutive patients with suspected or documented coronary artery disease, in whom biplane contrast left ventriculography and coronary angiography were performed. Four regions were considered on the 15 degrees caudal left-anterior oblique view radionuclide image, in order to identify the 7 conventional angiographic left ventricular wall segments (as the American Heart Association Council of Cardiovascular Surgery). Regional abnormalities on the phase-amplitude images from the 15 degrees caudal left anterior oblique view scans were studied in order to identify local hypokinesis, akinesis or dyskinesis (in accord to definitions used for contrast cineangiography) relative to seven conventional left ventricular wall segments. Results of phase-amplitude image analysis were compared with those of contrast cineangiography. The parametric images showed overall sensitivity of 82% and 92% respectively towards biplane and monoplane (left anterior oblique) contrast cineangiography, with a high degree of specificity (97%). Most akinetic and dyskinetic segments were correctly identified. A significant phase delay (greater than or equal to 70 degrees) from mean value, always occurred in dyskinetic segments and generally related to the severity of the wall motion abnormality. Lower accuracy was observed for hypokinetic regions; sensitivity was lower for apical and antero-lateral segments.(ABSTRACT TRUNCATED AT 250 WORDS)

Adult↗
PubMed1990

Fourier analysis of ventricular fibrillation of varied aetiology.

Fast Fourier Transform analysis was used to study ventricular fibrillation induced by several different methods in 43 greyhounds anaesthetized with sodium pentobarbitone. The dominant frequency at the body surface of ventricular fibrillation induced electrically in non-ischaemic hearts was initially 9.9 +/- 0.7 Hz, remained above 9 Hz for 70 s and then rapidly fell to 5 Hz. The dominant frequency of ventricular fibrillation induced by acute occlusion (initially 12.3 +/- 0.2 Hz), or by reperfusion (12.2 +/- 0.4 Hz) of the anterior descending branch of the left coronary artery, showed a similar time-course. However, ventricular fibrillation induced by administration of potassium (4.8 +/- 0.8 Hz) or ouabain (7.1 +/- 1.1 Hz) was significantly slower. Fibrillation recorded from the endocardium of the heart initially showed a similar dominant frequency to that recorded at the body surface, but there was no significant fall in frequency over 3.3 mins. There was little difference in the time-course of fibrillation in the non-ischaemic heart recorded directly from the epicardium or from a surface lead. These findings may be of relevance to the poor response to DC countershock after prolonged ventricular fibrillation, hyperkalaemia or cardiac glycosides.

Animals↗
PubMed1998

Diagnosis of arrhythmogenic right ventricular cardiomyopathy by fourier analysis of gated blood pool single-photon emission tomography.

To evaluate the diagnostic performance of Fourier phase analysis of gated blood pool single-photon emission computed tomography (GBP SPECT) in arrhythmogenic right ventricular (RV) cardiomyopathy, 18 patients with confirmed arrhythmogenic RV cardiomyopathy underwent GBP SPECT and x-ray cineangiography. Results were compared with data obtained with GBP SPECT in 10 control subjects. This 3-dimensional method demonstrated good correlation with cineangiography for measurements of RV enlargement and extent of the disease; RV and left ventricular segments were analyzed with the same accuracy. Tomographic abnormalities were significant decreased RV ejection fraction, RV dilatation, nonsynchronized contraction of the ventricles, increased RV contraction dispersion, presence of segmental RV wall motion disorders and/or phase delays, and occasionally regional left ventricular abnormalities. RV-delayed phase areas were always present in our population. A scoring system with RV criteria was proposed to diagnose RV disease. Because Fourier analysis of GBP SPECT provides ventricular morphologic information for the right ventricle with the same accuracy as for the left ventricle, it may replace planar radionuclide studies. Therefore, this method is helpful in patients with a strong clinical suspicion of arrhythmogenic RV cardiomyopathy, and should be used as a screening method before right ventriculography.

Adolescent↗
PubMedDate not supplied

Elliptic Fourier analysis of mandibular shape.

Craniofacial growth and development involve both size and shape variations. Shape variations can be assessed independently from size using mathematical methods such as the elliptic Fourier analysis, which allows a global evaluation of the shape of organs identified by their outlines independently from size, spatial orientation, and relation to reference planes. The mandibular outlines were digitized from the tracings of the Bolton standards (lateral view) from 1 to 18 years of age, and the age differences in shape independently from size were quantified using the elliptic Fourier series. A "morphologic distance" MD (i.e., a measurement of differences in shape) between each younger mandible and the oldest one was computed using the relevant Fourier coefficients like the cartesian coordinates in standard metric measurements. MD equals 0 when the profiles are identical. MD (Y) between the Bolton standard at 18 years of age and all the other Bolton tracings were significantly correlated (correlation coefficient r = 0.987, P < or = 0.001) with age (X) (semi-logarithmic interpolation Y = -3.87.log(e) X + 13.593). Differences between the size-independent shape of the Bolton standard at 18 years and the relevant plot at 1 year were located at the chin, gonion, coronoid process, anterior border of the ramus. Size differences were measured from the areas enclosed by the mandibular outlines. Mandibular area (Y) increased about 2.58 times from 1 to 18 years of age (X) (Y = -0.071.X2 + 4.917.X + 35.904, r = 0.997, P < or = 0.001). The shape effect was largely overwhelmed by the very evident size increments, and it could be measured only using the proper mathematical methods. The method developed could also be applied to the comparison between healthy and diseased individuals.

Adolescent↗
PubMed1996

Fourier analysis of cephalometric shapes.

Craniofacial growth and development involve both size and shape variations. Shape variations can be assessed independently from size using mathematical methods such as the Fourier series. A method for the reconstruction of outlines starting from selected landmarks and for their Fourier analysis has been developed and applied to analyze the age differences in shape in the tracings of the Bolton standards (lateral view) from 1 to 18 years of age. The size-independent shape of the Bolton standard at 18 years was larger at the chin, at the gonion, and in the anterior cranial base than the shape at 1 year of age. Conversely, the younger shape was larger in the middle part of face, corresponding roughly to the maxillary bone, than the older shape. When standardized for size, growth thus seemed to modify craniofacial shape with progressive lengthening and narrowing. This shape effect was largely overwhelmed by the very evident size increments, and it could be measured only using the proper mathematical methods.

Adolescent↗
PubMed2002

Evaluation of the end-expiratory pressure by multiple linear regression and Fourier analysis in humans.

This study was designed to compare the end-expiratory pressure (EEP) during mechanical ventilation (MV) measured dynamically (EEPdyn), by multiple linear regression (MLR) of the airway pressure (Pao) vs volume (V) and flow (V') and after Fourier analysis (FA) of the Pao and V'. Pao and V' were recorded from 32 ICU patients (II without respiratory disease, 10 COPD, II ARDS) under MV, at three levels of PEEPe (0, 5 and 10 hPa). Volume was calculated by numerical integration of V'. Data were analysed by MLR and FA, while the actual value of EEPdyn was recognised on the Pao signal at zero V' and V. EEPdyn, EEPMLR and EEPFA were compared for all patients, for each group of patients and for every level of applied PEEPe. Despite the different evaluation of respiratory mechanics between MLR and FA, the EEP values were always not significantly different between the three applied methods (P > 0.05). A high degree of correlation was found between them, taken two at a time (r > 0.99, P < 0.001). Two non-invasive analytical methods for the evaluation of respiratory mechanics during MV, MLR and FA offer a reliable and clinically useful estimation of EEP during MV.

Adult↗
PubMed1994

A discrete Fourier analysis for evolutionary trees.

Discrete Fourier transformations have recently been developed to model the evolution of two-state characters (the Cavender/Farris model). We report here the extension of these transformations to provide invertible relationships between a phylogenetic tree T (with three probability parameters of nucleotide substitution on each edge corresponding to Kimura's 3ST model) and the expected frequencies of the nucleotide patterns in the sequences. We refer to these relationships as spectral analysis. In either model with independent and identically distributed site substitutions, spectral analysis allows a global correction for all multiple substitutions (second- and higher-order interactions), independent of any particular tree. From these corrected data we use a least-squares selection procedure, the closest tree algorithm, to infer an evolutionary tree. Other selection criteria such as parsimony or compatibility analysis could also be used; each of these criteria will be statistically consistent for these models. The closest tree algorithm selects a unique best-fit phylogenetic tree together with independent edge length parameters for each edge. The method is illustrated with an analysis of some primate hemoglobin sequences.

Animals↗
PubMed1987

Fourier analysis of nuclear and cytoplasmic shape of blood lymphoid cells from healthy donors and chronic lymphocytic leukemia patients.

The folding rates of the contours of nuclei and entire lymphoid cells were analyzed by Fourier analysis of the shapes. Smears of peripheral blood from healthy subjects and from patients with chronic lymphocytic leukemia (CLL: type B, stage zero) were routinely prepared and stained. The shapes of lymphoid cells from CLL patients revealed a higher folding rate (from fifth to tenth harmonics) than did those of lymphocytes from healthy subjects. Accordingly, the roughness coefficient (describing the folding rate of the surface) for CLL cells was 0.036, as compared to 0.028 for the cells of healthy subjects. The shapes of nuclei of CLL lymphoid cells also had a higher folding rate than did those of lymphocytes from healthy subjects, but a significant difference was found only for the highest harmonic calculated (the tenth harmonic); the respective roughness coefficients for nuclei were 0.037 and 0.033.

Cell Nucleus↗
PubMed2003

Ultrastructural characterization and Fourier analysis of fiber cell cytoplasm in the hyperbaric oxygen treated guinea pig lens opacification model.

The structural characteristics of differentiated fiber cells in control and hyperbaric oxygen (HBO)-treated guinea pig lenses were examined by transmission electron microscopy (TEM). Emphasis was placed on cell damage, membrane integrity, and cytoplasmic texture. Given the faint gross opacities observed in HBO-treated lenses in previous studies, it was hypothesized that subtle but significant morphological differences due to oxidative damage exist between control and treated animals. Experimental animals received either 70 or 85 treatments with HBO (2.5 atm of 100% O(2) for 2.5 hr, 3 times per week for 5-7 months). All specimens were obtained within 24 hr of death. Freshly cut Vibratome lens sections were fixed and processed for low and high-magnification thin-section TEM analysis. Cytoplasmic texture was analyzed using Fourier and autocorrelation image processing techniques. Low-magnification analysis revealed relatively insignificant differences in general appearance between the fiber cells of the inner fetal and embryonic nuclei in control and HBO-treated guinea pigs. Both groups demonstrated cells of similar morphology with equivalent membrane complexity and homogeneous cytoplasmic texture. Evidence of any major cellular damage or extracellular space debris was not obvious. High-magnification analysis of the cytoplasm of the treated lenses exhibited a mild, yet detectable increase in texture compared with controls and was confirmed by Fourier analysis. Cytoplasmic texture increased in complexity with additional treatments. The absence of major cellular damage in the lenses of HBO-treated animals suggests a less conspicuous source of light scattering. The small changes in cytoplasmic organization observed between treated and control animals may entirely account for the increase in nuclear light scattering observed by slit lamp. The results obtained with this guinea pig/HBO model parallel many of the morphological data associated with human nuclear cataracts. The high-angle scattering observed in the lens of the HBO-treated guinea pig may represent the type of cytoplasmic reorganization that occurs with mild oxidation, effectively making it a valuable model for human lens aging.

Animals↗
PubMed1999

The method of linear transformation in revealing EEG polyharmonic components in comparison to the Fourier analysis.

The method of linear transformation (LT) in the modification known as method of Buys Ballot was examined in its ability to reveal polyharmonic periodicities in EEG signals. Applying this method to simulated signals-additive mixtures of sinusoids, periodic squared waves and Gaussian noise some rules were found, which can be used in analyzing of EEG signals. The results were compared to that of Discrete Fourier analysis. The conclusion was made that in contrast to the method of Fourier giving the frequency contents, LT method is able to reveal not only the mono- but also polyharmonic components with their waveshape (the reconstruction) even if their frequency bands are overlapping.

Algorithms↗
PubMed1986

Ejection fraction by combined inverse Fourier analysis and second-derivative technique: correlation with isocontour method.

In order to measure ejection fractions (EFs) from nuclear ventriculograms, we devised a semi-automated edge-detection technique based on a combination of inverse Fourier analysis and second-derivative techniques. Initial clinical studies showed that, for the left ventricle, our method gives EF values statistically identical with those obtained using a conventional isocontour technique. For the right ventricle, however, the values obtained using the two methods were somewhat more at variance. Despite requiring a longer processing time, the results obtained with our method are reproducible because less operator intervention is necessary.

Fourier Analysis↗
PubMed1982

Temporal Fourier analysis applied to equilibrium radionuclide cineangiography. Importance in the study of global and regional left ventricular wall motion.

Regional and global left ventricular wall motion was assessed in 120 patients using radionuclide cineangiography (RCA) and contrast angiography. Functional imaging procedures based on a temporal Fourier analysis of dynamic image sequences were applied to the study of cardiac contractility. Two images were constructed by taking the phase and amplitude values of the first harmonic in the Fourier transform for each pixel. These two images aided in determining the perimeter of the left ventricle to calculate the global ejection fraction. Regional left ventricular wall motion was studied by analyzing the phase value and by examining the distribution histogram of these values. The accuracy of global ejection fraction calculation was improved by the Fourier technique. This technique increased the sensitivity of RCA for determining segmental abnormalities especially in the left anterior oblique view (LAO).

Adult↗
PubMed1992

Automated detection and quantification of venous beading using Fourier analysis.

Venous beading associated with diabetic retinopathy is currently assessed by means of subjective comparison to standard photographs from the modified Airlie House classification scheme. We describe a computerized grading scheme for venous beading. The algorithm, based on Fourier analysis of vessel width measurements, generates a venous beading index (VBI) for digitized colour fundus photographs. Colour photographs of local vessel segments about 1200 microns in length were evaluated by experienced graders. A comparison between the VBI and subjective grading showed good agreement. The mean VBI values across the four levels of clinical grading were significantly different (p = 0.000). Multiple comparison testing indicated that the VBI was able to significantly differentiate between all four categories except the "questionable" (grade 1) category (p < 0.05). We also found that progression of venous beading can be followed with the VBI. The results indicate that further development of automated grading of venous beading is warranted.

Algorithms↗
PubMed2005

A fourier analysis of the dose grid resolution required for accurate IMRT fluence map optimization.

We present a theoretical and empirical analysis of the errors associated with the spatial discretization of the dose grid employed in optimized intensity modulated radiation therapy (IMRT) treatment plans. An information theory based Fourier analysis of the accuracy of discrete representations of three-dimensional dose distributions is presented. When applied to beamlet-based IMRT dose distributions, the theory produces analytic integrals that can bound worst case aliasing errors that can occur regardless of the location and orientation of the dose grid. The predictions of this theory are compared to empirical results obtained by solving a linear-programming based fluence-map optimization model to global optimality. A reasonable agreement between worst case estimates and the empirical results is attributed to the fact that the optimization takes advantage of aliasing to produce an optimal plan. We predicted and empirically demonstrated that an isotropic dose grid with <2.5 mm spacing is sufficient to prevent dose errors larger than a percent. However, we noted that in practice this resolution is mostly needed in high-dose target regions. Finally, a multiresolution 2-4-6 mm spacing model was developed and empirically tested where these spacings were applied to targets, structures, and tissue, respectively.

Algorithms↗
PubMed1992

The inheritance of vertebral shape in the mouse. I. A study using Fourier analysis to examine patterns of inheritance in the morphology of cervical and upper thoracic vertebrae.

The shapes of cervical and upper thoracic vertebrae from large samples of 2 inbred strains of mice and their F1 offspring were examined using Fourier analysis to investigate in detail the distributions and magnitudes of differences in vertebral shape between different strains of mice, the relationships between parents and offspring and any differences in the inheritance of vertebral shape between successive vertebral levels. Consistent with the findings of an earlier study there was evidence for considerable differences between vertebral levels in the degree to which offspring resemble one or other parent. The results demonstrate that the inheritance of vertebral morphology conforms to a model in which F1s between inbred strains form a triangular relationship with their parents. Furthermore, this relationship varies between vertebral levels. The significance of these findings is considered in relation to the understanding of the mechanisms of character inheritance and evolution and some new directions for research into vertebral column morphogenesis are proposed.

Animals↗
PubMed1985

Fourier analysis of ECochG templates.

Computer templates of the action potential/summating potential waveforms from electrocochleograms have been analysed in the frequency domain following the Fast Fourier Transform. Analysis in the frequency domain is compared with standard time domain analysis and some inadequacies of the latter technique are shown. A simple account of the principles of Fourier analysis is given which may be of assistance to the general reader, particularly as computer packages currently being marketed with electric response audiometry equipment make this analytical technique readily available.

Action Potentials↗