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