Statistical model of beam distortion by tissue inhomogeneities in tissue harmonic imaging

In tissue harmonic imaging (THI) the images are formed using the second harmonic component that is generated nonlinearly when ultrasound propagates inside the body. THI improves image resolution by reducing effects of phase distortion and reverberation in the body wall layer. A statistical investigation was performed to quantify improvement achieved with THI in the presence of tissue inhomogeneity. The investigation was both theoretical and experimental. In the theoretical model, a thin random phase screen located just in front of the source approximates the effect of inhomogeneity in the body wall layer. The phase variations across the screen are characterized statistically by zero mean, small variance, and Gaussian spatial correlation function. An analytical solution was derived for the expected value of the intensity of the second harmonic for a source that radiates a focused Gaussian beam. Contributions due to the coherent and scattered field components appear as separate terms in the solution. Validity of the statistical solution was established by comparison with ensemble averages of direct numerical simulations. Evolution of the beam profile and variation in energy content of the scattered second harmonic as a function of phase screen statistics are discussed. In comparison with the scattered field at the source frequency, the scattered field at the second-harmonic frequency is shown to be more localized about the beam axis. The results demonstrate clearly and quantitatively how distortions due to phase aberrations near the source are reduced by THI. Numerical simulations were also performed for beams radiated from a focused circular source with uniform amplitude. These results exhibit similar behavior. Dependence of results from the theoretical model on the distance between the source and phase screen was investigated. A transformation based on geometrical acoustics was obtained that approximates the mean scattered field due to a phase screen at a given distance away from the source using the solution obtained when the phase screen is in the source plane. Use of multiple phase screens to approximate thick inhomogeneous layers was also investigated. Experiments performed with a focused circular source and phase screens created with randomly indented plastic plates confirm the general theoretical approach.