Wave equation based analysis of phase aberrations in inhomogeneous tissue

An analysis of phase aberrations and correction algorithms in ultrasound echography is presented. A wave equation for time-harmonic waves in an inhomogeneous energy absorbing tissue is developed, which separates scales that can be treated by geometrical acoustics and scales that have to be treated by perturbation methods. In the experiments sound waves in water are generated and registered by a linear phased array and reflected by a point scatterer. A sample of pork tissue is placed between the array and the point scatterer. Various mixtures of muscle cells and fat with different structures are used. The analysis shows that when the dimensions of inhomogeneities are sufficiently large compared to the transducer dimensions, the amplitude fluctuations over the transducer increase as the distance between the tissue and the transducer is increased. As the dimensions of the tissue decrease, amplitude fluctuations become important at all distances. This happens within the regime of geometrical acoustics. In some experiments highly irregular mixtures of muscle cells and fat induce large variations in the amplitude of the wave over the transducer. As a result the signals are very weak for some elements. These large variations may create problems for correction algorithms that correlate the signals of neighbouring elements of the transducer