Phase Corrected Scattering Integral and the acoustic field in biomedical tissue with speed of sound and density variations

The acoustic field in an inhomogeneous medium can be expressed as the sum of incident and scattered parts, and different approximations are used to find the scattered part. We have previously considered the phase corrected scattering integral (PCSI) approach for the field within and near to midscale inhomogeneities with sound speed variations. The PCSI with a simple ray model used to find the phase correction gives good results in cases far beyond the limits of the Born approximation. In the present study we first examine the behaviour of the PCSI approximation in the far field, and compare it with a Kirchhoff (lumped phase) approximation. We then consider media with both sound speed and density variations, and show that the scattering integral can be recast into a form that allows the PCSI method to effectively calculate the contribution due to each effect separately. Comparison with exact results shows that the PCSI is remarkably accurate. We conclude that the PCSI method is effective for estimating the acoustic field in biomedical tissue, with characteristic weak scattering and irregular geometry.