The acoustic field in biomedical tissue with midscale inhomogeneities

Biomedical ultrasound is often used for investigations within and close to tissue inhomogeneities, such as lesions and plaques, that are midsized compared with the ultrasound wavelength. The scaled wavenumber is typically in the range 1 to 100. Even with small (less than 10%) sound speed variations, such objects are associated with very complicated diffractive field magnitude modulations. The corresponding phase modulations are much more regular, and this observation is the basis for the method described in this paper. The acoustic field can be expressed in terms of a scattering integral. For biomedical parameters, calculations with the widely used Born approximation give accurate results in only very limited circumstances. In this paper we demonstrate the importance of the initial phase estimate, and introduce the phase corrected scattering integral (PCSI) method. We show that remarkably accurate results for the acoustic field can be obtained from a single evaluation of the scattering integral if this incorporates an initial estimate of the phase modulation imposed by the inhomogeneity. A simple ray model can be used to find the phase correction. The PCSI method deals very effectively with scattering due to small changes in sound speed and irregular geometry, both characteristic of biomedical problems.