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We describe characterization of digital signals using analogs of thermodynamic quantities: the topological entropy, Shannon entropy, thermodynamic energy, partition function, specific heat at constant volume, and an idealized version of Shannon entropy in the limit of digitizing with infinite dynamic range and sampling rate. We show that analysis based on these quantities is capable of detecting differences between digital signals that are undetectable by conventional methods of characterization based on peak-to-peak amplitude or signal energy. We report the results of applying thermodynamic quantities to a problem from nondestructive materials evaluation: detection of foreign objects (FO) embedded near the surface of thin graphite/epoxy laminates using backscattered waveforms obtained by C-scanning the laminate. The characterization problem was to distinguish waveforms acquired from the region containing the FO from those acquired outside. In all cases the thermodynamic analogs exhibit significant increases (up to 20-fold) in contrast and for certain types of FO materials permit detection when energy or amplitude methods fail altogether.

Anisotropy of ultrasonic scattering and attenuation in heart tissue depends on the specific orientation of myofibers with respect to angle of insonification. The present study was designed to delineate the effect of the angle of insonification with respect to the alignment of myofibers on measurements of integrated backscatter. A transmural cube of myocardium was cut from the anterior wall of the left ventricles from 5 normal canine hearts and their transmural scattering behavior was studied with the use of reflection acoustic microscopy at 50 MHz. A theoretical model for scattering based on the Born approximation (weak scattering) was employed to predict the relationship between backscatter and angle of insonification. Insonification of the basal face (basal view) demonstrated a wide transmural variation in integrated backscatter (/spl sim/15 dB), while insonification of the lateral face (lateral view) had much reduced variation (/spl sim/4 dB), despite an equivalent overall shift in transmural fiber angle of /spl sim/85/spl deg/ across the ventricular wall. Integrated backscatter was greatest in the midmyocardium when the basal face was viewed and least in the midmyocardium when the lateral face was viewed. The backscatter in the subepicardial and subendocardial regions was similar for both views. The maximum difference in backscatter from basal and lateral views at the midmyocardial level was approximately 18 dB, which represents a 64-fold change in the intensity of ultrasonic backscatter. The mathematical model developed for scattering based on the Born approximation (weak scattering) predicted the observed relationship between backscatter and angle of insonification. The rapid angular variation of integrated backscatter perpendicular to the fiber direction and the slow variation at parallel incidence observed experimentally were predicted by the model. This angular variation is due to the specific shape and elastic properties assumed for the predominant myocardial scatterer. There was a strong relationship between backscatter and fiber orientation, indicating that the view chosen for insonification of myocardium in clinical imaging may influence the estimation of scattering behavior. The mathematical model utilized here predicts the anisotropic behavior of scattering and suggests that the principal scattering structure in normal myocardium may be a stiff collagen shell surrounding a more compliant myocyte. This model might provide a valid approach for the study of material properties of the heart with the use of ultrasound. >