Simulation of ultrasonic pulse propagation, distortion, and attenuation in the human chest wall.

A finite-difference time-domain model for ultrasonic pulse propagation through soft tissue has been extended to incorporate absorption effects as well as longitudinal-wave propagation in cartilage and bone. This extended model has been used to simulate ultrasonic propagation through anatomically detailed representations of chest wall structure. The inhomogeneous chest wall tissue is represented by two-dimensional maps determined by staining chest wall cross sections to distinguish between tissue types, digitally scanning the stained cross sections, and mapping each pixel of the scanned images to fat, muscle, connective tissue, cartilage, or bone. Each pixel of the tissue map is then assigned a sound speed, density, and absorption value determined from published measurements and assumed to be representative of the local tissue type. Computational results for energy level fluctuations and arrival time fluctuations show qualitative agreement with measurements performed on the same specimens, but show significantly less waveform distortion than measurements. Visualization of simulated tissue-ultrasound interactions in the chest wall shows possible mechanisms for image aberration in echocardiography, including effects associated with reflection and diffraction caused by rib structures. A comparison of distortion effects for varying pulse center frequencies shows that, for soft tissue paths through the chest wall, energy level and waveform distortion increase markedly with rising ultrasonic frequency and that arrival-time fluctuations increase to a lesser degree.

The effect of abdominal wall morphology on ultrasonic pulse distortion. Part I. Measurements.

The relative importance of the fat and muscle layers of the human abdominal wall in producing ultrasonic wavefront distortion was assessed by means of direct measurements. Specimens employed included six whole abdominal wall specimens and twelve partial specimens obtained by dividing each whole specimen into a fat and a muscle layer. In the measurement technique employed, a hemispheric transducer transmitted a 3.75-MHz ultrasonic pulse through a tissue section. The received wavefront was measured by a linear array translated in the elevation direction to synthesize a two-dimensional aperture. Insertion loss was also measured at various locations on each specimen. Differences in arrival time and energy level between the measured waveforms and computed references that account for geometric delay and spreading were calculated. After correction for the effects of geometry, the received waveforms were synthetically focused. The characteristics of the distortion produced by each specimen and the quality of the resulting focus were analyzed and compared. The measurements show that muscle produces greater arrival time distortion than fat while fat produces greater energy level distortion than muscle, but that the distortion produced by the entire abdominal wall is not equivalent to a simple combination of distortion effects produced by the layers. The results also indicate that both fat and muscle layers contribute significantly to the distortion of ultrasonic beams by the abdominal wall. However, the spatial characteristics of the distortion produced by fat and muscle layers differ substantially. Distortion produced by muscle layers, as well as focal images aberrated by muscle layers, show considerable anisotropy associated with muscle fiber orientation. Distortion produced by fat layers shows smaller-scale, granular structure associated with scattering from the septa surrounding individual fat lobules. Thick layers of fat may be expected to cause poor image quality due to both scattering and bulk absorption effects, while thick muscle layers may be expected to cause focus aberration due to large arrival time fluctuations. Correction of aberrated focuses using time-shift compensation shows more complete correction for muscle sections than for fat sections, so that correction methods based on phase screen models may be more appropriate for muscle layers than for fat layers.

The effect of abdominal wall morphology on ultrasonic pulse distortion. Part II. Simulations.

Wavefront propagation through the abdominal wall was simulated using a finite-difference time-domain implementation of the linearized wave propagation equations for a lossless, inhomogeneous, two-dimensional fluid as well as a simplified straight-ray model for a two-dimensional absorbing medium. Scanned images of six human abdominal wall cross sections provided the data for the propagation media in the simulations. The images were mapped into regions of fat, muscle, and connective tissue, each of which was assigned uniform sound speed, density, and absorption values. Propagation was simulated through each whole specimen as well as through each fat layer and muscle layer individually. Wavefronts computed by the finite-difference method contained arrival time, energy level, and wave shape distortion similar to that in measurements. Straight-ray simulations produced arrival time fluctuations similar to measurements but produced much smaller energy level fluctuations. These simulations confirm that both fat and muscle produce significant wavefront distortion and that distortion produced by fat sections differs from that produced by muscle sections. Spatial correlation of distortion with tissue composition suggests that most major arrival time fluctuations are caused by propagation through large-scale inhomogeneities such as fatty regions within muscle layers, while most amplitude and waveform variations are the result of scattering from smaller inhomogeneities such as septa within the subcutaneous fat. Additional finite-difference simulations performed using uniform-layer models of the abdominal wall indicate that wavefront distortion is primarily caused by tissue structures and inhomogeneities rather than by refraction at layer interfaces or by variations in layer thicknesses.

Simulation of ultrasonic pulse propagation through the abdominal wall.

Ultrasonic pulse propagation through the abdominal wall has been simulated using a model for two-dimensional propagation through anatomically realistic tissue cross sections. The time-domain equations for wave propagation in a medium of variable sound speed and density were discretized to obtain a set of coupled finite-difference equations. These difference equations were solved numerically using a two-step MacCormack scheme that is fourth-order accurate in space and second-order accurate in time. The inhomogeneous tissue of the abdominal wall was represented by two-dimensional matrices of sound speed and density values. These values were determined by processing scanned images of abdominal wall cross sections stained to identify connective tissue, muscle, and fat, each of which was assumed to have a constant sound speed and density. The computational configuration was chosen to simulate that of wavefront distortion measurements performed on the same specimens. Qualitative agreement was found between those measurements and the results of the present computations, indicating that the computational model correctly depicts the salient characteristics of ultrasonic wavefront distortion in vivo. However, quantitative agreement was limited by the two-dimensionality of the computation and the absence of detailed tissue microstructure. Calculations performed using an asymptotic straight-ray approximation showed good agreement with time-shift aberrations predicted by the full-wave method, but did not explain the amplitude fluctuations and waveform distortion found in the experiments and the full-wave calculations. Visualization of computed wave propagation within tissue cross sections suggests that amplitude fluctuations and waveform distortion observed in ultrasonic propagation through the abdominal wall are associated with scattering from internal inhomogeneities such as septa within the subcutaneous fat. These observations, as well as statistical analysis of computed and observed amplitude fluctuations, suggest that weak fluctuation models do not fully describe ultrasonic wavefront distortion caused by the abdominal wall.

Measurements of ultrasonic pulse distortion produced by human chest wall.

Ultrasonic wavefront distortion produced by transmission through human chest wall specimens was measured over a two-dimensional aperture. Measured pulse wavefronts were sometimes disrupted by secondary wavefronts produced by interaction between the transmitted pulses and the bone and cartilage structures of the rib cage. The secondary wavefronts produced large distortions in the received waveforms and interfered with the determination of the wavefront distortion caused by soft-tissue inhomogeneities. The effects of secondary wavefronts were minimized by reducing the region of analysis. Differences in arrival time and energy level between these restricted regions and references that account for geometric delay and spreading were computed. Spectral changes were assessed by calculating a waveform similarity factor that is decreased from 1.0 by changes in waveform shape. For 16 different intercostal spaces, the arrival time fluctuations of the measured waveforms had an average (+/-s.d.) rms value of 21.3 (+/-8.4) ns and an average correlation length of 2.50 (+/-0.62) mm. The energy level fluctuations had an average rms value of 1.57 (+/-0.45) dB and an average correlation length of 1.98 (+/-0.33) mm, and the average waveform similarity factor was 0.964 (+/-0.012). For soft-tissue inhomogeneities in chest wall specimens, the average rms arrival time and energy level fluctuations were less than half those measured for the abdominal wall. However, although the average correlation length of the arrival time fluctuations was less than half that found for the abdominal wall, the average correlation length of the energy level fluctuations was similar to that of the abdominal wall.

Measurement and correction of ultrasonic pulse distortion produced by the human breast.

Ultrasonic wavefront distortion produced by transmission through breast tissue specimens was measured in a two-dimensional aperture. Differences in arrival time and energy level between the measured waveforms and references that account for geometric delay and spreading were calculated. Also calculated was a waveform similarity factor that is decreased from 1.0 by changes in waveform shape. For nine different breast specimens, the arrival time fluctuations had an average (+/- s.d.) rms value of 66.8 (+/- 12.6) ns and an associated correlation length of 4.3 (+/- 1.1) mm, while the energy level fluctuations had an average rms value of 5.0 (+/- 0.5) dB and a correlation length of 3.4 (+/- 0.8) mm. The corresponding waveform similarity factor was 0.910 (+/- 0.023). The effect of the wavefront distortion on focusing and the ability of time-shift compensation to remove the distortion were evaluated by comparing parameters such as the -30-dB effective radius, the -10-dB peripheral energy ratio, and the level at which the effective radius departs from an ideal by 10% for the focus obtained without compensation, with time-shift estimation and compensation in the aperture, and with time-shift estimation and compensation performed after backpropagation. For the nine specimens, the average -10-dB peripheral energy ratio of the focused beams fell from 3.82 (+/- 1.83) for the uncompensated data to 0.96 (+/- 0.18) with time-shift compensation in the aperture and to 0.63 (+/- 0.07) with time-shift compensation after backpropagation. The average -30-dB effective radius and average 10% deviation level were 4.5 (+/- 0.8) mm and -19.2 (+/- 3.5) dB, respectively, for compensation in the aperture and 3.2 (+/- 0.7) mm and -22.8 (+/- 2.8) dB, respectively, for compensation after backpropagation. The corresponding radius for the uncompensated data was not meaningful because the dynamic range of the focus was generally less than 30 dB in the elevation direction, while the average 10% deviation level for the uncompensated data was -4.9 (+/- 4.1) dB. The results indicate that wavefront distortion produced by breast significantly degrades ultrasonic focus in the low MHz frequency range and that much of this degradation can be eliminated using wavefront backpropagation and time-shift compensation.

Measurements of ultrasonic pulse arrival time and energy level variations produced by propagation through abdominal wall.

Ultrasonic pulse arrival time and energy level variations introduced by propagation through human abdominal wall specimens have been measured. A hemispheric transducer transmitted an ultrasonic pulse that was detected by a linear array transducer after propagation through an abdominal wall section. The array was translated in the elevation direction to collect data over a two-dimensional aperture. Differences in arrival time and energy level between the measured waveforms and calculated references that account for geometric delay and spreading were found. Plots of waveforms compensated for geometric path, maps of time delay differences and energy level fluctuations, and statistics derived from these for water paths and tissue paths characterize the measurement system and describe the time delay differences and energy level fluctuations caused by 14 different human abdominal wall specimens. Repeated measurements using the same specimens show that individual tissue path measurements are reproducible, the results depend on specimen position, and frozen storage of a specimen for three months does not appear to alter the time delay differences and energy level fluctuations produced by the specimen. Comparison of measurements at room and body temperature indicates that appreciably higher time delay differences occur at body temperature while energy level fluctuations and time delay difference patterns are less affected. For the 14 different abdominal wall specimens, the rms time delay differences and energy level fluctuations have average values of 43.0 ns and 3.30 dB, respectively, and the associated correlation lengths of the time delay differences and energy level fluctuations are 7.90 and 2.28 mm, respectively. The spatial patterns of time delay difference and energy level fluctuation in the reception plane appear largely uncorrelated, although some background variations in energy level fluctuation are similar to features in time delay difference maps. The results provide important new information about the variety and range of ultrasonic wave front arrival and energy variations caused by transmission through abdominal wall.