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B-mode echograms were simulated by employing the impulse response method in transmission and reception using a discrete scatterer tissue model, with and without attenuation. The analytic signal approach was used for demodulation of the RF A-mode lines. The simulations were performed in 3-D space and compared to B-mode echograms obtained from experiments with scattering tissue phantoms. The average echo amplitude appeared to increase towards the focus and to decrease beyond it. In the focal zone, the average amplitude increased proportionally to the square root of the scatterer density. The signal to noise ratio (SNR) was found to be independent of depth, i.e., 1.91 as predicted for a Rayleigh distribution of gray levels, although a minimum was found in the focal zone at relatively low scatterer densities. The SNR continuously increased with increasing scatterer density and reached the limit of 1.91 at relatively high densities (greater than 10(4) cm-3). The lateral full width at half maximum (FWHM) of the two dimensional autocovariance function of the speckle increased continuously from the transducer face to far beyond the focus and decreased thereafter due to the diffraction effect. The lateral FWHM decreased proportionally to the logarithm of the scatterer density at low densities and reached a limit at high densities. Introduction of attenuation in the simulated tissue resulted in a much more pronounced depth dependence of the texture. The axial FWHM was independent of the distance to the transducer to a first approximation and decreased slightly with increasing scatterer density until a limit was reached at densities larger than 10(3) cm-3. This limit was in agreement with theory. The experiments confirmed the simulations and it can be concluded that the presented results are of great importance to the understanding of B-mode echograms and to the potential use of the analysis of B-mode texture for tissue characterization.

A study was performed to find and test quantitative methods of analysing echographic signals for the differentiation of diffuse liver diseases. An on-line data acquisition system was used to acquire radiofrequency (RF) echo signals from volunteers and patients. Several methods to estimate the frequency-dependent attenuation coefficient were evaluated, in which a correction for the frequency and depth-dependent diffraction and focusing effects caused by the sound beam was applied. Using the estimated value of the attenuation coefficient the RF signals themselves were corrected to remove the depth dependencies caused by the sound beam and by the frequency-dependent attenuation. After this preprocessing the envelope of the corrected RF signals was calculated and B-mode images were reconstructed. The texture was analysed in the axial direction by first- and second-order statistical methods. The accuracy and precision of the attenuation methods were assessed by using computer simulated RF signals and RF data obtained from a tissue-mimicking phantom. The phantom measurements were also used to test the performance of the methods to correct for the depth dependencies. The echograms of 163 persons, both volunteers and patients suffering from a diffuse liver disease (cirrhosis, hepatitis, haemochromatosis), were recorded. The mutual correlations between the estimated parameters were used to preselect parameters contributing independent information, and which can subsequently be used in a discriminant analysis to differentiate between the various diseased conditions.

B-mode echograms were simulated by employing the impulse response method in transmission and reception using a discrete scatterer tissue model, with and without attenuation. The analytic signal approach was used for demodulation of the RF A-mode lines. The simulations were performed in 3-D space and compared to B-mode echograms obtained from experiments with scattering tissue phantoms. The average echo amplitude appeared to increase towards the focus and to decrease beyond it. In the focal zone, the average amplitude increased proportionally to the square root of the scatterer density. The signal to noise ratio (SNR) was found to be independent of depth, i.e., 1.91 as predicted for a Rayleigh distribution of gray levels, although a minimum was found in the focal zone at relatively low scatterer densities. The SNR continuously increased with increasing scatterer density and reached the limit of 1.91 at relatively high densities (greater than 10(4) cm-3). The lateral full width at half maximum (FWHM) of the two dimensional autocovariance function of the speckle increased continuously from the transducer face to far beyond the focus and decreased thereafter due to the diffraction effect. The lateral FWHM decreased proportionally to the logarithm of the scatterer density at low densities and reached a limit at high densities. Introduction of attenuation in the simulated tissue resulted in a much more pronounced depth dependence of the texture. The axial FWHM was independent of the distance to the transducer to a first approximation and decreased slightly with increasing scatterer density until a limit was reached at densities larger than 10(3) cm-3. This limit was in agreement with theory. The experiments confirmed the simulations and it can be concluded that the presented results are of great importance to the understanding of B-mode echograms and to the potential use of the analysis of B-mode texture for tissue characterization.

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In search of the optimal display of echographic information for the detection of focal lesions, a systematic study was performed considering a wide range of gray level transforms (i.e., lookup tables). This range comprised power functions of the echo envelope signal (1/8 less than or equal to n less than or equal to 8), power functions of the logarithmic transform and a sigmoid function. The implications of the transforms on the first order statistics (histogram, "point signal-to-noise ratio" SNRp) and on the second order statistics (autocorrelation function) could be derived both analytically, and from the analysis of simulated and experimentally obtained echograms of homogeneously scattering tissue models. These results were employed to estimate the lesion signal-to-noise ratio SNRl, which specifies the detectability of a lesion by an ideal observer. It was found, both theoretically and practically, that the intensity display corresponds to the optimal transform (i.e., n = 2) for a low contrast lesion. When the data were first logarithmically compressed, the lesion SNR appeared to increase with increasing power (1/8 less than or equal to n less than or equal to 8). A logarithmic transform followed by a sigmoid compression did not produce much improvement. These effects of gray level transforms on the SNRl were shown to be relatively small, with the exception of powers n greater than 2 when applied to linear (i.e. amplitude) data. In the case of high lesion contrast, the sequence of log compression, followed by a square law produced the optimum SNRl. This sequence is equivalent to the processing within echographic equipment, where the TV monitor has a gamma of the order of 2.

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