Fourier Harmonic Analysis Research Articles

Changes in Corneal Topography after 25-Gauge Transconjunctival Sutureless Vitrectomy versus after 20-Gauge Standard Vitrectomy

To evaluate the changes in regular and irregular corneal astigmatism after 25-gauge transconjunctival sutureless vitrectomy and 20-gauge standard vitrectomy. Prospective observational comparative case series. Thirty-two eyes of 32 patients undergoing 25-gauge transconjunctival sutureless vitrectomy and 25 eyes of 24 patients undergoing 20-gauge standard vitrectomy. Corneal topography was obtained preoperatively and at 2 weeks and 1 month postoperatively. The dioptric data of the central 3-mm zone of the cornea were decomposed using Fourier harmonic analysis into spherical power, regular astigmatism, asymmetry, and higher-order irregularity. None of the 4 Fourier indices changed throughout the observation period in the 25-gauge group. In the 20-gauge group, regular astigmatism, asymmetry, and higher-order irregularity were increased significantly at 2 weeks after vitrectomy (P<0.05, Wilcoxon signed-ranks test) and returned to preoperative levels by 1 month. The spherical power in the 20-gauge group did not change after surgery. For regular astigmatism, asymmetry, and higher-order irregularity, the 20-gauge group showed significantly greater surgically induced changes than the 25-gauge group (P<0.05, Mann-Whitney U test). Twenty-five-gauge transconjunctival sutureless vitrectomy does not induce significant changes in corneal topography and exerts little influence on the optical quality of the cornea.

CFD Based Determination of Dynamic Stability Derivatives in Yaw for a Bird

Dynamic yaw stability derivatives of a gull bird are determined using Computational Fluid Dynamics(CFD) method. Two kinds of motions are applied for calculating the dynamic yaw stability derivatives C Nr and C Nβ . The first one relates to a lateral translation and, separately, to a yaw rotation. The second one consists of a combined translational and rotational motion. To determine dynamic yaw stability derivatives, the simulation of an unsteady flow with a bird model showing a harmonic motion is performed. The flow solution for each time step is obtained by solving unsteady Euler equations based on a finite volume approach for a small reduced frequency. Then, an evaluation of unsteady forces and moments for one cycle is conducted using harmonic Fourier analysis. The results of the dynamic yaw stability derivatives for both simulations of the model show a good agreement.

226 DAY LENGTH DOES NOT AFFECT LIVE SPERM NUCLEAR SHAPE IN THE STALLION

Fourier harmonic analysis (FHA) of sperm nuclei is a precise and objective method to evaluate shape of the sperm head, with the calculated harmonic amplitudes highly related to male fertility. The FHA approach has been developed for use in the bull and the boar but has not yet been applied to the stallion. Direct utilization of the previous fluorescent approaches to identify and image live sperm nuclei in the bull cannot be used in the stallion due to the increased thickness of the post-nuclear region and thin anterior region of the sperm head. An alternative approach was developed in which live and motile sperm were isolated after filtration of an ejaculate through a Sephadex G-15 column. The resulting live sperm were sonicated briefly to separate tails and heads. The heads were isolated on a 45–90 discontinous Percoll gradient, fixed with paraformaldehyde (0.2%), centrifuged onto glass slides, and dried. The slides were then stained with eosin (1%), cleared with water, and dried again; Permount was added, followed by a coverslip. Slides were imaged with phase contrast microscopy; digital images were acquired and evaluated with custom software to identify perimeter coordinates of sperm nuclei. The perimeter coordinates were next converted to Fourier harmonic amplitudes 0–5 (HA0–HA5) using trigonomic regression at 1 degree equally spaced angles. Fertility of bulls were previously reported to be most related to changes in HA0 and HA2 but no information is available on stallions. As fertility data on stallions is limited, to evaluate FHA in the equine, the day length (period of light) was increased in January from the ambient 9–10 h to 16. Semen samples from 5 light horse stallions were collected at weekly intervals for 8 weeks following the increase in light. It was hypothesized that fertility would increase for each stallion over the course of the experiment, as testosterone increases and spermatogenesis improves with increasing day length, as previously shown. Each week semen samples were evaluated for FHA live sperm nuclei, as described above. All parameter means and variations were recorded on 100 randomly selected sperm nuclei per semen sample evaluated. There was no difference relative to week 0 in the least squares mean or SD of HA0, HA1, HA2, HA3, HA4, or HA5 over the 8 weeks (P &gt; 0.05). However stallions were consistently different for all HAs (P &lt; 0.05). The overall mean HA0–HA5 � SEM were 1.973 � 0.38, 0.087 � 0.002, 0.721 � 0.021, 0.051 � 0.004, 0.208 � 0.014, and 0.031 � 0.002, respectively. Even though libido increased during the experiment, confirming the effect of light on the stallions, no affect on sperm nuclear shape or its variation was detected using FHA. Based on work in other species involving numbers of sperm inseminated, if large numbers of sperm from these stallions were inseminated in mares, we would predict no change in fertility due to season. Further research is needed to confirm this prediction.

Corneal Irregular Astigmatism After Hyperopic Laser In Situ Keratomileusis

To evaluate the changes in irregular astigmatism after hyperopic laser in situ keratomileusis (LASIK). In a prospective case series, 15 eyes of 12 patients who had hyperopic LASIK were evaluated. Corneal topography was obtained before and after hyperopic LASIK. Corneal irregular astigmatism (asymmetry and higher-order irregularity) was calculated using Fourier harmonic analysis of the topography data. Hyperopic LASIK significantly increased the asymmetry component at 3 (P = 0.0085) and 6 months (P = 0.0307) postoperatively. The mean higher-order irregularity was not significantly changed at any postoperative time-point (P = 0.222). The achieved change in the spherical equivalent was significantly correlated with the post/preoperative ratio of asymmetry (R = 0.695, P = 0.0030). Hyperopic LASIK significantly increases the asymmetry component of the cornea, which is correlated with the achieved change in the spherical equivalent.

SEST: A new error separation technique for ultra-high precision roundness measurement

In order to further improve the rotation accuracy of ultraprecision roundness measuring instruments, a new single-step rotation error separation technique (SEST) is proposed to accurately separate instrument spindle rotation error and workpiece roundness error. This is done by first selecting an appropriate rotation angle and rotating the workpiece through a small angle with respect to the instrument spindle, and then measuring mixed errors A(n) and B(n) including workpiece error g(θ) and spindle rotation error z(θ) before and after rotation, and finally achieving accurate separation of z(θ) and g(θ) through Fast Fourier Transformation and harmonic analysis. Theoretical analysis and simulation results indicate that the signals in the harmonic range 1–100 upr can be totally separated from the wide range of harmonics measured when rotation angle error Δα < 0.01° is achieved by optimizing the rotation angle α. In comparison with the multi-step separation technique commonly used in roundness measuring instruments, SEST can be used to totally eliminate any harmonics singularity in the range of 1–100 upr and to make the error separation system very simple, shorten the separation process and reduce the separation time.

Visual acuity measurements using Fourier series harmonic analysis of videokeratography data in eyes after penetrating keratoplasty

Fourier harmonic analysis can decompose videokeratography data into spherical power, regular astigmatism, and irregular astigmatism (asymmetry and higher-order irregularity). The aim of this study was to evaluate whether determination of cylinder power by Fourier analysis facilitates measurements of visual acuity and refraction in eyes after penetrating keratoplasty. Cross-sectional study. Sixty-six eyes of 56 subjects who had undergone penetrating keratoplasty. Spectacle-corrected visual acuity was measured in 2 ways: by the conventional and the Fourier methods. In the conventional method, the refraction was determined subjectively by reference to the measurement results of the autokeratometer and autorefractometer. In the Fourier method, the magnitude and axis of regular astigmatism were calculated by Fourier analysis of the videokeratography data, and spherical lenses were adjusted until best spectacle-corrected visual acuity was attained. Logarithm of the minimum angle of resolution (logMAR) visual acuity and refraction used for correction. The spectacle-corrected visual acuity obtained with the Fourier method (logMAR, 0.23+/-0.32; Snellen equivalent, 20/34) was significantly better than that attained with the conventional method (logMAR, 0.31+/-0.29; Snellen equivalent, 20/41; P<0.001, paired t test). The cylinder power used for spectacle-corrected visual acuity measurements was significantly lower with the Fourier method (-2.41+/-1.26 diopters [D]) than with the conventional method (-3.53+/-1.64 D; P<0.001). The spherical equivalent at the final refraction was not different between groups (P = 0.207). Fourier analysis of videokeratography data significantly facilitates determination of refraction and measurement of best spectacle-corrected visual acuity in eyes with corneal irregular astigmatism, such as eyes that have undergone penetrating keratoplasty.

Application of Fourier harmonic analysis to the electromechanical response of an electroactive material

Signal decomposition through Fourier analysis can aid quantification of the electromechanical properties (induced strain and polarization) of electroactive materials. Spectral analysis of the strain and polarization, obtained from the Fourier transform, provides a unique characterization tool that better conveys material response than can be accomplished with polynomial fitting. The derived coefficients can be mapped onto those in the Devonshire phenomenology. The technique is demonstrated by analysis of a lead magnesium niobate relaxor ferroelectric [0.9875(0.935PMN–0.065PT)–0.0125BT or 0.9233PMN–0.06419PT–0.0125BT] operating in the electrostrictive regime. Fourier analysis, applied to a materials response, provides the first quantitative linkage to materials coefficients. A generalized mathematical approach has been derived that equates a Fourier series expression, from the transform of a time-domain electromechanical response, to the basic underlying physics developed in Devonshire theory. Thus, the electrostrictive strain and polarization coefficients are calculated directly from the harmonic spectrum of the response. A benefit of the Fourier transform approach is the direct calculation of electrostrictive (and piezoelectric) coefficients with quantitative criterion for truncation and a “goodness of fit” criterion related to the zero frequency component. The real strength of the approach lies in its ability to accommodate electromechanical hysteresis and provide a distinct quantification of a given strain response. This is accomplished while faithfully describing the true harmonic content of the signal. The coefficients provide a descriptive fingerprint for use of the material under varying conditions.

Fourier series harmonic analysis of corneal topography following suture removal after penetrating keratoplasty.

To evaluate quantitatively the influence of suture removal after penetrating keratoplasty on corneal refraction including irregular astigmatism. Subjects were 42 eyes of 39 patients with clear corneal grafts who underwent suture removal after penetrating keratoplasty. Videokeratography data taken before and after suture removal were decomposed using Fourier harmonic analysis into spherical power, regular astigmatism, and irregular astigmatism (asymmetry and higher order irregularity). On average, spherical power significantly increased after suture removal (p < 0.0001, paired t test), and regular astigmatism did not change significantly (p = 0.247). Suture removal significantly decreased asymmetry (p < 0.0001) and higher order irregularity (p < 0.0001). Suture removal after penetrating keratoplasty induces myopic shift and reduction in irregular astigmatism of the cornea.

Vibration modelling with fast Gaussian wavelet algorithm

Vibration signals are considered as nonstationary signals with transients. Conventional harmonic Fourier analysis finds it difficult to model the vibration signals. In this paper, a novel approach using the global Fourier transforms and local wavelet analysis is presented for vibration analysis and modelling. Time–frequency wavelet analysis has been proven a useful tool for the detection of vibration transients. However, current algorithms with discrete or continuous wavelet transforms for vibration analysis are either low resolution of features or very time consuming. We developed a fast Gaussian wavelet algorithm with very narrow band-pass filtering technique. The time–frequency maps with high frequency resolution enable us to observe the evolution in time of significant frequencies identified by global Fourier analysis, so that the transients and the regular signals can be distinguished. These regular significant frequencies are selected to be the basis of vibration modelling. The coefficients of the model are identified by a least-squares algorithm, which ensures that the error is minimised. To demonstrate this approach a machine spindle vibration signal is analysed, and the main features of the vibration signal are extracted, which are useful for system monitoring and further analysis.

Late stage coarsening in concentrated ice systems

We have developed a dedicated, automated cryomicroscope for the study of ice coarsening in binary aqueous systems. This, together with new image analysis procedures, can provide wide ranging characterisation capabilities for the study of isothermal coarsening of ice crystal ensembles. Single particle tracking has elucidated hitherto unattainable mechanistic detail of coarsening kinetics. Ice crystal faceting has been shown to be an important factor. Ice crystals, with an average size in the mesoscopic range, have a significant tendency to evolve their initial kinetic growth forms towards the equilibrium Wulff shape. By Fourier harmonic analysis, the time evolution of the state of roughness of the prism plane of ice can be monitored, both for growing and dissolving crystals.Results are presented for fructose/water at three temperatures, -20, -19 and -17°C. On the basis of recent high pressure studies on ice roughening, the highest temperature may be near the onset of a (high order) thermodynamic roughening transition of the prism plane; pronounced faceting of both the prism and the basal plane of ice is expected at the lower temperatures. We describe coarsening of non-interacting, faceted crystals at -19°C, and that of initially percolated networks of aggregated ice crystals at -20°C. The onset of faceting of ice prism planes at -17°C was monitored using Fourier harmonics to characterise the ‘sharpness’ of hexagonal contours of ice crystals viewed normal to their basal plane. A tentative analysis of the results suggests an estimate of the dimensionless step free energy of the prism face, γ, of 7×10-3.The coarsening kinetics observed for dilute ice crystal ensembles did not conform with classical continuum theories such as the LSW treatment. This was indicated by the measured size distribution, the scaling dependence of the mean radius and crystal number density with time, and by single particle tracking showing that an asymptotic steady state was not reached. The lack of a sharply defined critical radius, demarcating growing particles from those which dissolve, does not then permit an assignment of excess chemical potentials to individual ice crystals on the basis solely of their observed curvature. While faceting and shape changes are important, the overall kinetics are broadly consistent with diffusion control.More concentrated ice systems at -20°C form networks of aggregated faceted crystals under the action of van der Waals attractive forces. These initially percolated structures are linear chains of crystals with occasional branches. On ripening, the chains thicken and progressively break. The tendency for linear chains may reflect a preference for basal face ice contacts. This is being investigated further.

Corneal astigmatism after scleral buckling surgery assessed by Fourier analysis of videokeratography data.

To evaluate quantitatively the changes in corneal curvature, including irregular astigmatism, after scleral buckling surgery for retinal detachment. In 29 eyes of 29 patients undergoing scleral explant surgery, videokeratographic measurements were carried out before and 1 week, 1 month, and 3 months after surgery. Using Fourier harmonic analysis, dioptric data on mire rings were decomposed into spherical, regular astigmatic, and irregular astigmatic (decentration and higher order irregularity) components. The irregular astigmatic component significantly increased at 1 week postoperatively but returned to the preoperative level 1 month after surgery. The regular astigmatism also displayed a transient increase up to 1 month after surgery. The increases in regular astigmatism were significant in eyes that had scleral buckling of < or =180 degrees but not in eyes with buckles extending >180 degrees. Changes in irregular astigmatism after retinal detachment surgery were quantitatively evaluated. The scleral buckling surgery causes a transient increase in irregular astigmatism as well as regular astigmatism.

Computer-assisted skull identification system using video superimposition

This system consists of two main units, namely a video superimposition system and a computer-assisted skull identification system. The video superimposition system is comprised of the following five parts: a skull-positioning box having a monochrome CCD camera, a photo-stand having a color CCD camera, a video image mixing device, a TV monitor and a videotape recorder. The computer-assisted skull identification system is composed of a host computer including our original application software, a film recorder and a color printer. After the determination of the orientation and size of the skull to those of the facial photograph using the video superimposition system, the skull and facial photograph images are digitized and stored within the computer, and then both digitized images are superimposed on the monitor. For the assessment of anatomical consistency between the digitized skull and face, the distance between the landmarks and the thickness of soft tissue of the anthropometrical points are semi-automatically measured on the monitor. The wipe images facilitates the comparison of positional relationships between the digitized skull and face. The software includes the polynomial functions and Fourier harmonic analysis for evaluating the match of the outline such as the forehead and mandibular line in both the digitized images.

A Century of Interplay Between Taylor Series, Fourier Series and Brownian Motion

This article is an extended version of a lecture given in Oxford on 12 May 1995 at the invitation of the London Mathematical Society and the British Society for the History of Mathematics.Contents1. A few figures2. Taylor series before 1900. A strange statement of Borel3. Fourier series before 1900. A strange field4. Brownian motion around 1900. A rising subject5. Fourier and Taylor series after 1900. A revival6. Lacunarity and randomness7. The appearance of random series of functions8. The Wiener theory of Brownian motion9. The merging of Brownian motion and random Fourier series10. The non-differentiability and local behaviour of Brownian motion11. Three ways to figure out the Brownian motion12. The plane Brownian motion13. Applications of Brownian motion to Taylor series and analytic functions14. Applications of Brownian motion to Fourier series and harmonic analysis

Corneal versus scleral tunnel incision in cataract surgery: A randomized study

Purpose: To compare the induced regular and irregular astigmatism after scleral and corneal tunnel incision.Setting: University hospital outpatient cataract clinic.Methods: One hundred phacoemulsification patients with less than 1.0 diopter (D) of preoperative astigmatism were randomly assigned to have a clear corneal incision (50 patients) or a scleral tunnel incision (50 patients). All incisions were 3.5 to 4.0 mm wide and were made in the steepest axis of the corneal astigmatism. The surgically induced astigmatism was analyzed by vector analysis from keratometric data, as well as by Fourier harmonic series analysis of the topographic data.Results: One day after surgery, the surgically induced astigmatism (vector analysis, keratometry) was 1.41 D ± 0.66 (SD) and 0.55 ± 0.31 D in the corneal incision group and the scleral incision group, respectively (P < .01). Six months after surgery, the induced astigmatism was 0.72 ± 0.35 D and 0.36 ± 0.21 D in the two groups, respectively (P < .01). The corneal topography data confirmed the regular astigmatism changes found by conventional keratometry. However, in addition, Fourier harmonic series analysis of the topography data showed significantly more irregular induced astigmatism with the corneal approach than with the scleral approach.Conclusion: The clear corneal incision induces significantly more regular as well as irregular astigmatism than the scleral tunnel incision.

Cranio-Facial Identification

This article constitutes a review of the literature and an evaluation of the anatomical relationships between skull and face including the soft tissue thickness at various anthropometrical points of the skull, along with a comparison of the methodologies involved in the three techniques, that is, photographic, video and computer-assisted superimposition techniques used in forensic science. In addition, an evaluation of cosistency between skull and face is discussed from the aspect of personal identification. Forensic examiner must be well versed in the anatomy of skull and face for effective utilization of the superimposition technique. When evaluating anatomical consistency between these parts, special attention should be paid their outline, the facial tissue thickness at the anthropometrical points, and positional relationships between skull and face. Data on the thickness of facial soft tissue has been accumulated for each race, Caucasoid, Negroid and Mongoloid. The positional relation of the eyebrow and eye to the orbit, the ala to the nasal aperture, and the lips to the teeth has been investigated by many researchers. Over the last two decades, video superimposition technique has widely been used for identifying unknown skull. The video superimposition presents enormous advantage over the conventional photographic superimposition. This technique allows the fade-out of either the skull or facial image on the monitor for overall assessment of how well the two images match. This also allows the various sectioning images of the skull and facial images for evaluating the positional relationships between the skull and face. In this technique, however, the anthropometrical examination including soft tissue thickness could not directly be performed on the TV monitor. On the other hand, in the last ten years, the computer-assisted cranio-facial superimposition has been developed. The use of a video-computer with appropriate software allows to take the images of the skull and facial photograph with only one camera and to directly compare the digitized both images on the monitor. The computer technology has also been used to determine the size of natural head and optimum objective length. The software such as the polynomial functions and Fourier harmonic analysis has been applied to evaluate the fit between the outline of skull and facial photograph. It is suggested that the outline from the forehead to the gnathion in the lateral or oblique view is the preferable portion for personal identification, and the cranio-facial superimposition method is reliable for personal identification when two or more facial photographs taken from different angles are used in the examination. The computer-assisted skull identification system using video superimposition is useful to demonstrate the cosistency between skull and facial photograph because the quantitative data including anthropometrical measurements obtained from this system provide objective and reliable results in skull identification.

Evaluating surgically induced astigmatism by Fourier analysis of corneal topography data

Purpose: To evaluate surgically induced astigmatism using Fourier harmonic series analysis of corneal topography data.Setting: Aarhus Kommunehospital, Aarhus University, Denmark.Methods: We evaluated the results of 46 phacoemulsifications with a 4 or 6 mm scleral tunnel sutureless incision based on the axis of the steepest meridian. We performed conventional keratometry and corneal topography before and up to 1 month after surgery. Using Fourier analysis, the corneal topographic images were broken into spherical power, regular astigmatism, and nonregular astigmatism for individual or aggregate analysis of surgically induced astigmatism. The induced refractive change (average of the difference between preoperative and postoperative corneal topographies) was analyzed and normalized according to the surgical meridian and to right/left eye.Results: Regular astigmatism calculated by Fourier analysis of mires from the keratometer zone correlated well with conventional keratometry readings. Surgery induced a localized flattening in the superior region and a with-the-rule regular astigmatism component in the central area.Conclusion: Surgically induced corneal topography changes can be analyzed by Fourier series harmonic analysis, allowing aggregate data to be broken into optically meaningful quantities.

Evolutive spectral analysis of sunspot data over the past 300 years

We analyse the series of the Wolf sunspot number in the frequency domain to determine the dimension of the solar cycle system by using the properties of its strange attractor and to study the stability in time of this dimensionality and of the main quasiperiodicities. The two classical methods of time series analysis, Fourier harmonic and Blackman-Tukey spectral analysis, have been applied first to the series of the annual Wolf sunspot numbers to determine its overall character. To detect stationarity, periodic regression based upon the three most statistically significant quasi-periods and especially a moving form of the maximum entropy spectrum analysis (mesa) have been used. Both analyses show a splitting of the 11-year cycle before 1800, when a ± 55-year cycle is dominant, and a single 11-year and + 100-year peak after 1800. Moreover, these quasi-periods are very sensitive to the time interval over which the analysis is carried out. The reason is that the sunspot numbers constitute a widely non-stationary process, which therefore implies that Fourier techniques are not useful to predict solar activity and must be used as fitting procedure only. The minimum cross-entropy method serves to improve the maximum entropy spectrum. With a good a priori estimate and data containing a low noise level, this method allows the detection of very close peaks and the refinement of the main frequencies; it does not split nor introduce artificial peaks. The Thomson model was also applied for its superior bias control, its excellent leakage resistance and a better statistical information. The same methods were then used to study the 22-year magnetic cycle, which is formed by taking into account the change in polarity of the succeeding 11 -year cycle. The moving form of mesa confirms the 22-year cycle to be highly stable in contrast to the instability in the period of the 11-year sunspot series. This suggests the importance of working with the more invariant 22-year magnetic series to explain the complex, non-stationary behaviour of the sunspot series and of the solar—terrestrial interactions. Finally, we tried to see if the system generated by the sunspot data was allowing the existence of an attractor and tried to determine the minimum number of variables necessary to describe this system. It is shown that the dimension of the attractor is highly unstable varying from 2.21 to 4.95 in a quasi-cyclic way.

Characterizing rumination patterns of dairy cows using spectral analysis.

Spectral analysis techniques were used to characterize the cyclical variation in rumination behavior of cows. Four Holstein cows were fed twice daily a diet of 60% high-moisture shelled corn-based concentrate, 15% first-cut alfalfa-grass hay and 25% second-cut alfalfa silage. The number of minutes that each cow spent ruminating was determined for 15-min intervals during six consecutive days. Rumination data then were characterized using Fourier harmonic analysis to decompose the total sum of squares into 288 orthogonal components due to different rumination wavelengths. Rumination patterns for all cows consisted mainly of wavelengths that were harmonics of a 24-h cycle, indicating a circadian pattern of rumination. Differences in rumination patterns between cows occurred mainly at wavelengths of less than 2 h. Rumination patterns of two of the four cows were more complex, and consisted of high-frequency, non-24-h harmonic wavelengths in addition to the circadian pattern. Spectral analysis can be used to identify the component cycles of rumination patterns of individual animals, which can then be used to determine the effects of dietary or other manipulations on rumination behavior.

Relation between primary tumor shape and biological behavior in breast cancer.

The aim of this study was to investigate the biological significance of tumor shape in breast cancer by considering the shape not as a casual event but as an expression of the behavior and natural history of the tumor. The shape was studied by an analytical morphometry procedure and was related to axillary metastases, which up to now are the most meaningful prognostic factors in this disease. Fifty cases of infiltrating breast carcinoma (25 N+ and 25 N-) were investigated. The shape, studied on subgross sections of the tumor, was considered as the result of two components: the subtle contour irregularities and the main distortions of the figure. The procedures used allowed us to distinguish and to parametrize these two components in order to submit them to univariate analysis (Student's t test), a principal components analysis and, finally, a multivariate discriminant analysis (Hotelling test). The utilized analytical procedures by work-station S.A.M. (S.A.M. work station is a product of "Metamorphosis") consisted of three steps: 1) Extraction of tumor function curve obtained by Kth order polynominals which gives a smoothing effect to the original curve; 2) Evaluation of contour irregularities by Fourier harmonic analysis; 3) Evaluation of shape asymmetry by SAE (shape asymmetry evaluator). We considered also the roundness factors of the original and function curves and finally the maximum tumor diameter. Three parameters relating to contour irregularities (sum and mean value of Fourier harmonic amplitude and percentage of superimposed points) and parameters relating to main distortions of the figure (mean value of SAE) were highly significant (p less than 0.001). The roundness factor of the original curve was more significant (p less than 0.001) than that of the function curve (p less than 0.01) whereas maximum tumor diameter was not significant when tested by Student's t test. Multivariate discriminant analysis allowed 20% of error to be reached by using 3 parameters relating to the shape analysis and the two roundness factors. By using 8 parameters, including maximum tumor diameter, the percentage error was 16%. The results obtained, while they stress the usefulness of the employed procedure, reveal that shape of the tumor, together with its dimensions, is an important expression of the biological behavior relating to metastatic spread.

Radionuclide Phase Imaging of Ventricular Tachycardia

The emptying sequence of ventricular blood pool was studied by scintigraphic regional phase mapping in 10 patients with monomorphic and sustained ventricular tachycardia (VT) and compared to an electrophysiological study in order to assess the scintigraphic accuracy for the noninvasive localization of abnormal site of activation. All patients underwent both phase imaging and electrical mapping studies. There were 6 coronary artery disease patients, 3 patients with arrhythmogenic right ventricular disease and 1 patient with dilatative cardiomyopathy. Phase image studies were performed by first harmonic Fourier analysis of radionuclide angiography either during sinus rhythm or during spontaneous or catheter-induced VT. Eleven morphologically distinct VTs with a heart rate ranging from 145 to 260 beats min^-1 (mean 173 ± 32 beats min^-1) were imaged. Endocardial catheter mapping was accomplished in 9 different VT morphologies. Three patients also had epicardial intraoperative mapping. The site of origin of VT by a scintigraphic method was defined as the area of earliest regional contraction on the biventricular scintigram. By separating the right ventricle into 5 segments and the left ventricle into 7 segments, with multiple view cardiac imaging, a close correspondence between the site of origin determined by electrophysiological study and the region of earliest emptying of radioactivity was observed in 7 of 9 (77%) VTs. In 2 patients the extension of regional akinesia during VT prevented us from an accurate mapping of the regional time sequence of contraction. Scintigraphic phase mapping has inherent limitations due to wall motion dependency and relatively low resolution power but it is feasible in selected patients with monomorphic, inducible and long-sustained VT in whom adequate time for data collection is provided. In this subset of patients the site of origin of VT could be localized on a 'segmental' basis with close correspondence to electrophysiological mapping studies.