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 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.