Fourier coefficient description of left ventricular shape.

A method of quantifying the shape of the left ventricle of the heart as seen in 2D echocardiograms was developed. It is based on describing the shape in terms of the coefficients a fifth-order trigonometric Fourier series. Such a series has eleven Fourier coefficients which is too large a number for clinical application so pairs of coefficients are combined to give six coefficients (alpha 0, alpha 1, ... , alpha 5). A trial was conducted to test the ability of the coefficient description to classify subjects as having normal right ventricles or ventricles with an apical abnormality. The tests showed that one of the coefficients (alpha 2) was higher for the subjects with an apical abnormality and that this difference increased with exercise. This is as was expected. However, it was found to be difficult to get a reliable estimate of alpha 2 from a single scan of a patient and that it is therefore probably necessary to average data from several scans to obtain a reliable alpha 2 value for a single patient.

Intrinsic echolocation capability of Hector's dolphin, Cephalorhynchus hectori.

A sonar system's echolocation capabilities can be inferred from the ambiguity distribution (defined here in terms of the conventional signal response function) of each of its transmitted signals. Several records of sounds emitted by Hector's dolphin are analyzed. The computed ambiguity distributions indicate that the sonar clicks of Hector's dolphins should be capable of resolving the ranges of targets as close together as 2 cm apart, but that target velocities cannot be resolved to any useful degree from a single echo.

From living being to medical image--bridging the dimensionality gap.

The human body is viewed, in the context of medical imaging, as a multiplicity of three-dimensional time-varying images, coinciding in time and space. Medical imaging modalities that are well established, or are undergoing clinical trials, or are at the tentative proposal stage, are tabulated. Also listed are the types of radiation and other physical processes employed to gather the image data, the physical parameters which can be imaged, and the physiological attributes represented by these parameters. Image reconstruction algorithms are reviewed and possible improvements are assessed. The processing of multidimensional information is emphasised as of primary concern for future progress in medical imaging. Such processing is seen to be developing along two converging paths: the processing of information from coincident images of different parameter distributions, and the processing of time-sequential images of a single parameter distribution. The images referred to have three spatial dimensions, implying that a challenge for future medical imaging systems is conjectured to be the efficient distillation of useful information (which must include the most effective means of image display) from multiple sets of time-varying volume data. Medical diagnosis can always profit from improved interpretation of information provided by the multifarious types of radiation and other physical processes which are employed in established and tentative medical imaging techniques. There is a premium on parameter sets that provide independent information and on processes, such as magnetic fields, ultrasound, and low frequency electric currents, which are free of the stigma associated with ionising radiations. Promising avenues of exploration are identified.

Assessment of the significance and severity of premenstrual tension--I. A new model.

A method is proposed for analysing daily mood scores for premenstrual tension (PMT) in single menstrual cycles by fitting an approximation function consisting of the first two harmonics of a Fourier series. On the basis of harmonic analysis of 133 cycles of daily mood scores obtained from women perceiving themselves to have the premenstrual syndrome (PMS), the severity of PMT is taken to be the difference between the mean and the fitted function at a point 92% of the way through the menstrual cycle. The significance of the severity is calculated statistically. Significant PMT was detected in 70% of the 133 cycles; this compared with an 8% incidence in women who considered that they did not have PMS. The method improves on previously described methods for detecting PMT by: (1) using statistical criteria; (2) modelling cycles with asymmetric and double peaks; (3) using a difference rather than a ratio as the severity estimate; (4) smoothing the data and (5) giving valid estimates when data points are missing. There was no evidence for the presence of distinct periodicities with wavelengths less than half that of the menstrual cycle.

Modification of spectra of pulses from ultrasonic transducers by scatters in non-attenuating and in attenuating media.

When an ultrasonic pulse is scattered off a particle, the spectrum of the scattered pulse differs from that which was transmitted. A mathematical analysis is presented to show that the center frequency of the backscattered pulse is greater than that of the transmitted pulse and that the bandwidth decreases slightly when the spectrum of the pulse is Gaussian in shape. The results of measurements designed to test the theory are presented. The magnitude of the shift in center frequency for pulses backscattered off subwavelength-diameter wires is found to be similar to that predicted by the analysis. It is shown that characteristics of the spectra of the backscattered pulses can differ from those predicted if the shape of the spectrum is not truly Gaussian (as is assumed in most published analyses, including that introduced here). In medical ultrasonic imaging, the pulses are modified by scattering and absorption. The analysis is extended to account for the effects of both interactions. This allows the bandwidth and center frequency of pulses backscattered from tissues and received by medical ultrasonic scanners to be predicted.

Fourier transform magnitudes are unique pattern recognition templates.

Fourier transform magnitudes are commonly used in the generation of templates in pattern recognition applications. We report on recent advances in Fourier phase retrieval which are relevant to pattern recognition. We emphasise in particular that the intrinsic form of a finite, positive image is, in general, uniquely related to the magnitude of its Fourier transform. We state conditions under which the Fourier phase can be reconstructed from samples of the Fourier magnitude, and describe a method of achieving this. Computational examples of restoration of Fourier phase (and hence, by Fourier transformation, the intrinsic form of the image) from samples of the Fourier magnitude are also presented.

Speckle processing gives diffraction-limited true images from severely aberrated instruments.

Speckle images of spatially incoherent objects viewed under severe seeing conditions are formed in the optical laboratory (organized for simulations of stellar speckle interferometry). The brightest pixel in each speckle image is shifted to the center of image space, and the translated image is added to all other speckle images that have been similarly processed. A recognizable diffraction-limited version of the true image of the object results, even when the imaging instrument is defocused such that, under perfect seeing conditions, the Airy disk is spread over an area comparable with that covered by a typical speckle image.

A possible conformation for double-stranded polynucleotides.

A model is presented for double-stranded polynucleotides which involves side-by-side meshing of the two strands rather than double helical intertwining. The sugar-phosphate backbone has a twisted strip-like character, yet base-pairing of the Watson-Crick type is still possible. Structural features of the basic model are described and coordinates are presented for a representative example. The structure has, on the whole, reasonable sterochemical contacts, and can be shown to produce a fiber diffraction pattern with x-rays not unlike that of the B form of DNA.