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PubMed1989

Elliptic fourier analysis of cell and nuclear shapes.

The elliptic Fourier analysis (EFA) is proposed to characterize the cell and nuclear shape. The principal feature of this method is that it decomposes shapes with a closed contour into subshapes each of which maintains a closed contour. A set of homogeneous, nonredundant descriptors, independent of the contour rotation and translation, is computed from the elliptic Fourier coefficients. These descriptors also account for the contour size and resolution. The paired analysis of the cell and nuclear shape provides an exhaustive and accurate definition of the nucleoplasmic configuration.

Computer Simulation↗
PubMed1994

Fourier analysis versus multiple linear regression to analyse pressure-flow data during artificial ventilation.

Respiratory resistance (Rrs) and elastance (Ers) are commonly measured in artificially-ventilated patients or animals by multiple linear regression of airway opening pressure (Pao) versus flow (V') and volume (V), according to the first order model: Pao = P0 + Ers.V + Rrs.V', where P0 is the static recoil pressure at end-expiration. An alternative way to obtain Rrs and Ers is to derive them from the Fourier coefficients of Pao and V' at the breathing frequency. A potential advantage of the second approach over the first is that it should be insensitive to a zero offset on V' and to the corresponding volume drift. The two methods were assessed comparatively in six tracheotomized, paralysed and artificially ventilated rabbits with and without adding to V' an offset equal to 5% of the mean unsigned flow. The 5% flow offset did not modify the results of Fourier analysis, but increased Rrs and Ers from linear regression by 15.8 +/- 4.6% and 4.55 +/- 0.64%, respectively. Without additional offset, differences between the two methods averaged 30.2 +/- 14.0% for Rrs and 9.3 +/- 6.2% for Ers. The differences almost completely disappeared (2.47 and 0.61%, respectively) when the flow signal was zero-corrected using the assumption that inspired and expired volumes were the same. After induced bronchoconstriction, however, Ers was still slightly larger by linear regression than by Fourier analysis, which may result from nonlinearities and/or frequency dependence of the parameters. We conclude that the regression method requires zero flow correction and that Fourier analysis is an attractive alternative.

Algorithms↗
PubMed1989

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↗
PubMed2007

Variations of the mandibular shape in extant hominoids: Generic, specific, and subspecific quantification using elliptical fourier analysis in lateral view.

While a number of studies have documented the mandibular variations in hominoids, few focused on evaluating the variation of the whole outline of this structure. Using an efficient morphometrical approach, i.e. elliptical Fourier analysis, mandibular outlines in lateral view from 578 adult hominoids representing the genera Hylobates, Pongo, Gorilla, Pan, and Homo were quantified and compared. This study confirms that elliptical Fourier analysis provides an accurate characterization of the shape of the mandibular profile. Differences in mandibular shape between hominoid genera, species, subspecies, and to a lesser extent between sexes were demonstrated. Mandibles in great apes and hylobatids subspecies were generally less distinct from each other than were species. However, the magnitudes of differences among subspecies of Gorilla and Pongo approached or exceeded those between Pan troglodytes and P. paniscus. The powerful discrimination between taxa from the genus down to subspecific level associated to the relatively low level of intrageneric mandibular polymorphism in great apes provides strong evidences in support of the taxonomic utility of the shape of the mandibular profile in hominoids. In addition, morphological affinities between Pongo and Pan and the clear distinction between Homo and Pan suggest that the mandibular outline is a poor estimate of phylogenetic relationships in great apes and humans. The sexual dimorphism in mandibular shape exhibits two patterns of expression: a high degree of dimorphism in Gorilla, Pongo, and H. s. syndactylus and a relatively low one in modern humans and Pan. Besides, degree of mandibular shape dimorphism can vary considerably among closely related subspecies as observed in gorillas, arguing against the use of mandibular shape dimorphism patterns as characters in phylogenetic analyses. However, the quantification of the mandibular shape and of the variations among hominoids provides an interesting comparative framework that is likely to supply further arguments for a better understanding of the patterns of differentiation between living hominoids.

Animals↗
PubMed1993

Fourier analysis of shape changes in the Japanese skull: occipital view.

Photographs (norma occipitalis) of Japanese adult skulls (n = 171) were mathematically described with Fourier analysis to assess shape changes over time. The materials used were adult male skulls excavated from the Kanto District and covered four age-periods; Jomon (2000-1000 BC). Kamakura (14C. AD), Muromachi (15C. AD). and Edo (18C. AD). Mean raw data values, containing both size and shape information of each vector, were compared for the four age-periods. Statistically significant differences among the four age-periods were found using an ANOVA. The form of the Jomon skulls displayed the most difference among the four groups. This trend was especially evident at the parietal margin. Fourier analysis was subsequently undertaken to detect the presence of secular changes in skull form after standardization for size. Once the effect of size was removed, the occipital shape of the Jomon skulls was found to be essentially similar to those of the more recent age-periods.(ABSTRACT TRUNCATED AT 400 WORDS)

Adult↗
PubMed1999

Receptor test (pupillary dilatation after application of 0.01% tropicamide solution) and determination of central nervous activation (Fourier analysis of pupillary oscillations) in patients with Alzheimer's disease.

Memory loss and severe cognitive deficits in Alzheimer patients are supposed to be related to a reduction of acetylcholine as well as to central nervous deactivation. For the investigation of cholinergic deficits and deactivation, we used computer-assisted pupillometry. Cholinergic deficits caused by a particularly severe loss of cholinergic neurons may be responsible for cognitive and mnemonic performance deficits. The control of the pupillary diameter represents a balance between cholinergic and adrenergic innervation and is influenced directly or indirectly by central and autonomic nervous system inputs. Either of these systems could be affected in Alzheimer patients. A reduced innervation of the target muscle through neuronal cell death, axon retraction, reduced release, increased reuptake of altered amounts or function of neurotransmitter receptors seems to affect the pupillary response to cholinergic antagonists in Alzheimer patients. There is, however, no relationship between pupillary diameter and central deactivation, but between central nervous activation and pupillary oscillations which reflect the physiological corticodiencephalic activity, a relationship has to be assumed. Frequencies and amplitudes of pupillary oscillations measured by means of Fourier analysis are modulated corticodiencephalically. Therefore, Alzheimer patients were compared to healthy controls with respect to their pupillary diameters and responses to an acetylcholine antagonist. Twenty-nine patients, aged between 55 and 85 years, suffering from mild to moderate Alzheimer's disease (AD) and 29 normal controls of similar age (56-85 years) participated in the study. The cholinergic receptors of the pupil were blocked by the acetylcholine antagonist tropicamide. It could be assumed that the larger the pupillary dilatation, the larger the extent of cognitive deficits. Alzheimer patients show abnormal acetylcholine neurotransmission. Changes of pupillary diameter after instillation of 1 drop of 0.01% tropicamide solution were measured and Fourier analysis of pupillary oscillations was performed. Times of measurement were: 0 (baseline), 20, 40, 60, 80, and 100 min. After 4 min tropicamide was instilled. Forty min after the instillation of tropicamide into the left eye, the Alzheimer patients showed a pronounced dilatation of 41.57%. The dilatation in normal controls was 28.5%. Fourier analysis of pupillary oscillations (sum of frequency bands = power) demonstrated a marked deactivation (low amplitudes in low-frequency bands, but in contrast to our expectations no higher amplitudes in the higher frequency bands) in patients with AD which remained constant at all times of measurement. By means of discriminant analysis of pupillary diameter and pupillary oscillations (frequency band 0.00-1 Hz), 89. 7% were correctly predicted to be Alzheimer patients, 89% to be normal controls.

Aged↗
PubMed1986

Length-based Fourier analysis in the pre-excitation syndrome.

Length-based Fourier analysis (LFA) was applied to tomographic gated blood-pool study, and phase and percent-shortening diagrams were generated. In 22 patients with pre-excitation syndrome and ten control subjects, the most basal short-axis section was used for tomographic analysis. When the initial abnormal phase was considered as the location of accessory conduction pathway (ACP), correct diagnosis for the localization of ACP was given in 19 of 22 patients. In ten control subjects, no specific segments of initial phase were noted, although six patients had initial phase in the septal or paraseptal segments. The tomographic LFA was more effective for pinpointing the segment of the earliest phase than tomographic count-based phase analysis. The LFA provided objective three-dimensional information for contraction sequence. Because movements of ventricular edges are essential in tomography, the LFA was considered to be a reasonable approach for the analysis of tomographic gated blood-pool study.

Erythrocytes↗
PubMed1986

[Qualitative determination of infarct segment by Fourier analysis using gated cardiac pool emission computed tomography].

As a new method for regional wall motion analysis, the tomographic functional images, including "coronal", "sagittal" and "four-chamber" sections, were produced by applying the fundamental Fourier analysis using gated cardiac pool emission computed tomography (POOL-SPECT). Segmental wall motion was qualitatively assessed from the functional images in 10 normal subjects and in 48 patients with myocardial infarction. The results were compared with those assessed by gated blood pool planar images (modified LAO 45), two-dimensional echocardiography (2DE) or contrast left ventriculography (LVG). The following results were obtained. 1. POOL-SPECT imaging could separate the ventricle in three dimensions from the neighboring cardiovascular system by avoiding the overlapping blood pool to make accurate recognition of regional wall motion. 2. The functional tomograms had greater clinical efficacy in the diagnosis of infarcted segments than did the conventional equilibrium method, with high sensitivity (93/99, 93.9%), specificity (128/141, 90.8%) and accuracy (221/240, 92.1%), especially in the apical and inferoposterior portions. 3. Tomographic functional imaging facilitated estimating segmental cardiac performance from spatial and temporal aspects. The amplitude image which expresses regional stroke volume was readily available to detect hypokinesis and akinesis. The phase image of the initial cardiac movement was very useful for diagnosing dyskinesis. 4. In comparing the qualitative analysis with 2DE or LVG, complete agreement was observed in 80% (128/160) and 85.1% (149/175) of segments, though POOL-SPECT imaging showed underestimations in 11% of the segments. In conclusion, POOL-SPECT can be performed repeatedly without potential risks and the tomographic functional images derived from application of Fourier analysis to POOL-SPECT images are very useful for qualitative and three-dimensional analysis of regional wall motion. Thus, this technique may be a promising procedure in clinical investigations, obviating the disadvantages of conventional methods.

Adult↗
PubMed1993

Fourier analysis of blood pressure profiles.

This short review deals with the use of the Fourier technique to analyze diurnal blood pressure (BP) profiles obtained by noninvasive ambulatory monitoring. A Fourier series with four harmonics strikes an acceptable balance between the accuracy and complexity required to model the diurnal profile accurately in most subjects. A weighting procedure makes it possible to allow for the varying time intervals between consecutive pressure readings. Studies based on a single recording are insufficient to characterize an individual with respect to the statistical parameters describing the diurnal BP profile, regardless of whether they are obtained by Fourier analysis or by other methods. The Fourier approach provides the means to translate 24 h BP profiles into interpretable statistical parameters, such as the amplitude and acrophase of the overall model and the harmonics. These parameters can subsequently be used in further statistical analyses. In conclusion, the Fourier approach makes the description of complex, asymmetrical, and multiphasic BP profiles possible. By using the procedures of linear multiple regression, commonly provided by software packages, the calculations can be readily implemented on microcomputers without requiring advanced skills in mathematics or programming techniques.

Blood Pressure↗
PubMed1985

Characterization and automatic identification of ECG conduction abnormalities using segmental multiharmonic Fourier analysis of gated blood-pool scintigrams.

This study of biventricular segmental timing sequences compared patterns of the first-harmonic phase with those of multiharmonic Fourier-analysis-derived parameters to determine their suitability for the classification of patients using an automatic pattern recognition scheme. The study involved nine patients with normal ECGs, six with left bundle branch block, 4 with right bundle branch block, and 6 with right-ventricular pacemakers; all patients had normal left-ventricular function. The segmental sequence described by the time of end systole was similar to that described by the first-harmonic phase, with a lower correlation using the time of maximum filling rate, and a rather poor correlation of the time of maximum ejection rate with the other parameters. Thus, despite theoretical difficulties, timing patterns described by phase best agreed with those of the time of end systole. Intersegmental timing differences were used as criteria for discriminating between groups by means of a sequential logic tree. Using either phase, time of end systole or time of maximum ejection rate, all patients were correctly classified into the four ECG categories. More intersegmental timing differences were useful as criteria for phase (57) than for the time of end systole (45) or the time of maximum ejection rate (30). The first-harmonic phase was more efficient than the time of end systole for separating patient groups. Sequential biventricular timing disorders can be objectively classified using either first-harmonic or multiharmonic Fourier analysis, and their patterns can be automatically recognized and used for classification.

Bundle-Branch Block↗
PubMed1997

Fourier analysis of circadian blood pressure profile in secondary hypertension.

Different types of statistical methods have been used for circadian blood pressure (BP) rhythm analysis in secondary forms of hypertension. In the present study, we used the two-step statistical approach by Fourier analysis with four harmonics for the parametrization of the diurnal BP pattern in secondary hypertension. In 43 essential hypertensives (EH), eight patients with aldosterone producing adenoma (APA), 25 with idiopathic hyperaldosteronism (IHA), four with glucocorticoid remediable hyperaldosteronism (GRH) and seven with renovascular hypertension (RVH), 24-h ambulatory BP was measured. The diurnal BP and heart rate (HR) rhythm was present in more than 70% of patients with secondary hypertension, without significant differences with EH and despite the attenuation in the degree of the nocturnal BP fall. In conclusion, the statement that secondary hypertension is characterized by an abnormal diurnal rhythm of BP is a gross over-simplification. Our findings suggest that the two-step method with four harmonics Fourier analysis may represent a useful method and a more complete statistical approach to providing circadian parametrization of the 24-h profile in secondary hypertension.

Blood Pressure↗
PubMed1989

[Digital subtraction angiography and Fourier analysis of the left ventriculography: new methods of analyzing left ventricular function].

To evaluate two new methods of analyzing left ventricular function, digital subtraction left ventriculography (DSLV) and Fourier analysis of left ventriculography (FALV) were performed after conventional left ventriculography (LV) in 17 consecutive catheterized cases. Ejection fraction of FALV and LV corresponded closely with the correlation coefficient of 0.906, while segmental wall motion corresponded less with the range of correlation coefficients from 0.56 for the apical segment to 0.94 for the anterior wall. In 10 cases with asynergic segments of the left ventricle, Fourier analysis showed less hypokinesis in four (all had hypokinesis at the septal segment), the same degree in five and more in one case, suggesting the possibility of FALV to evaluate three-dimensional left ventricular function in a single projection.

Angiography, Digital Subtraction↗
PubMed1970

Fourier Analysis on GL(n,R).

Two problems of Fourier analysis on GL(n,R) are studied. The first concerns the decomposition of the additive Fourier operator in terms of the group representation theory of G. The second concerns the analytic continuation of certain zeta-functions defined on G. It is found that the generalized Gamma functions of Gelfand and Graev arise naturally in the solution of both these problems.

Journal Article↗
PubMed2000

Fourier analysis of irregular astigmatism after implantation of 3 types of intraocular lenses.

PURPOSE: To evaluate irregular astigmatism after silicone, acrylic, and poly(methyl methacrylate) (PMMA) intraocular lens (IOL) implantation using Fourier analysis of videokeratography data. METHODS: Two hundred forty eyes having phacoemulsification and IOL implantation were randomly assigned to 1 of 3 groups: 3.5 mm incision and silicone IOL, 4.1 mm incision and acrylic IOL, or 6.5 mm incision and PMMA IOL. All eyes had videokeratographic examinations preoperatively and 2, 4, and 10 days and 1 and 3 months postoperatively. The dioptric data of the central cornea were decomposed into spherical equivalent, regular astigmatism, and irregular astigmatism (decentration and higher-order irregularity) components using Fourier analysis. RESULTS: Regular astigmatism in the PMMA group was greater than in the silicone and acrylic groups. Decentration in all 3 groups increased significantly postoperatively but virtually returned to preoperative levels by 10 days. No significant difference was observed among the 3 groups. Higher-order irregularity significantly increased after surgery in all 3 groups. The higher-order irregularity in the PMMA group persisted for up to 1 month, while that in the silicone and acrylic groups returned to preoperative levels by 4 days, resulting in significant differences between these groups 10 days and 1 month after IOL implantation. CONCLUSION: Irregular astigmatism, both the decentration and higher-order irregularity components, increased significantly after 3 types of scleral tunnel incisions for silicone, acrylic, or PMMA IOL implantation but returned to preoperative levels soon after surgery except for the higher order irregularity after PMMA IOL implantation.

Acrylic Resins↗
PubMed2006

A fourier analysis on the maximum acceptable grid size for discrete proton beam dose calculation.

We developed an analytical method for determining the maximum acceptable grid size for discrete dose calculation in proton therapy treatment plan optimization, so that the accuracy of the optimized dose distribution is guaranteed in the phase of dose sampling and the superfluous computational work is avoided. The accuracy of dose sampling was judged by the criterion that the continuous dose distribution could be reconstructed from the discrete dose within a 2% error limit. To keep the error caused by the discrete dose sampling under a 2% limit, the dose grid size cannot exceed a maximum acceptable value. The method was based on Fourier analysis and the Shannon-Nyquist sampling theorem as an extension of our previous analysis for photon beam intensity modulated radiation therapy [J. F. Dempsey, H. E. Romeijn, J. G. Li, D. A. Low, and J. R. Palta, Med. Phys. 32, 380-388 (2005)]. The proton beam model used for the analysis was a near monoenergetic (of width about 1% the incident energy) and monodirectional infinitesimal (nonintegrated) pencil beam in water medium. By monodirection, we mean that the proton particles are in the same direction before entering the water medium and the various scattering prior to entrance to water is not taken into account. In intensity modulated proton therapy, the elementary intensity modulation entity for proton therapy is either an infinitesimal or finite sized beamlet. Since a finite sized beamlet is the superposition of infinitesimal pencil beams, the result of the maximum acceptable grid size obtained with infinitesimal pencil beam also applies to finite sized beamlet. The analytic Bragg curve function proposed by Bortfeld [T. Bortfeld, Med. Phys. 24, 2024-2033 (1997)] was employed. The lateral profile was approximated by a depth dependent Gaussian distribution. The model included the spreads of the Bragg peak and the lateral profiles due to multiple Coulomb scattering. The dependence of the maximum acceptable dose grid size on the orientation of the beam with respect to the dose grid was also investigated. The maximum acceptable dose grid size depends on the gradient of dose profile and in turn the range of proton beam. In the case that only the phantom scattering was considered and that the beam was aligned with the dose grid, grid sizes from 0.4 to 6.8 mm were required for proton beams with ranges from 2 to 30 cm for 2% error limit at the Bragg peak point. A near linear relation between the maximum acceptable grid size and beam range was observed. For this analysis model, the resolution requirement was not significantly related to the orientation of the beam with respect to the grid.

Algorithms↗
PubMed2000

Fourier analysis of acetabular shape in native American Arikara populations before and after acquisition of horses.

The goal of this study was to identify changes in acetabular morphology associated with the use of horses by Native Americans. Previous studies reported "elongate" acetabula in horseback-riding members of the Omaha and Ponca populations. Such a difference in acetabular shape is a potentially useful osteological marker of habitual horseback riding. This report compares acetabula of adult males from two Native American Arikara populations known to have differed substantially in their use of horses. Population samples were from separate sites in South Dakota: Larson (nonriding) and Leavenworth (riding). Outlines of acetabular rims were digitized and analyzed, using a simplified 12-point Fourier analysis. A Fourier series with six terms accurately described acetabular shape. Significant differences (P<0.10) between riding and nonriding populations were observed in two Fourier coefficients. Acetabula of riding Arikara were found to have smaller B(4) coefficients (P = 0. 061) and more positive B(2) coefficients (P = 0.080), indicating expanded anterior-superior borders relative to acetabula of non-riding Arikara.

Acetabulum↗
PubMed1984

Fourier analysis of effects of varying pressure waveforms in electrical lung analogs.

Six voltage waveforms were devised to simulate pressure curves of varying configuration for use in artificial ventilation. These waveforms were subjected to Fourier analysis and terms of the resulting series applied to a simple two-branch resistive-capacitive circuit intended to represent a lung analog using computer simulation. Current (analogous to flow) and charge (analogous to volume) in each branch could be graphically displayed. Differences among the waveforms in such attributes as efficiency, inspiratory work, volume introduced per unit of mean pressure applied, and relative volume distribution between the two branches could be demonstrated. All waveforms were capable of delivering a predetermined volume to the circuit with adjustment of their peak pressure (voltage). It was not possible to designate any of the waveforms as "superior" since advantage in one attribute, such as efficiency, was accompanied by deficiencies in other characteristics such as uneven volume distribution. Despite obvious severe limitations on physiological interpretations of such data, Fourier analysis of respiratory waveforms appears to be a useful teaching, illustrative, and exploratory method.

Computers↗