Modeling nonlinear pressure fields in inhomogeneous attenuative media using a lossy Green's function and a contrast source

Attenuation or loss forms an important phenomenon in medical ultrasound. At ultrasonic frequencies, attenuation is mainly due to absorption. Experimental data reveal that attenuation acts according to a frequency power law. For a given penetration depth, this effect limits the frequency, and hence the attainable resolution, that is utilized in diagnostic ultrasound applications. Attenuation is also crucial for therapeutic applications where high intensity focused ultrasound fields are used for ablation and hyperthermia treatment. Modeling attenuative pressure fields in inhomogeneous media is therefore of great importance for the development of new ultrasound modalities and the optimization of treatment protocols. In this paper a compliance memory function is utilized to model attenuation. This function consists of two parts; a spatially independent and a spatially dependent part. The former accounts for the lossy background medium, the latter for variations in the attenuation parameters with respect to the background medium. The first part is accounted for by deriving the Green's function of the lossy background medium, whereas the second part leads to the formulation of attenuation contrast sources. The resulting integral equation for the acoustic wave field is solved with an iterative Neumann scheme. Each step involves the convolution of the attenuation contrast sources with the `lossy' Green's function. Finally, nonlinear contrast sources are included to extend the method to nonlinear acoustics, resulting in a new version of the Iterative Nonlinear Contrast Source (INCS) method. The presented approach shows excellent agreement with results obtained with the `contrast only' INCS method, which includes losses only via an attenuation contrast source. This agreement occurs both when nonlinear propagation is or is not taken into account. Moreover, the presented method shows a faster convergence ac compared to the `contrast only' method, and it automatically prevents for scattering artifacts caused by truncation of the numerical domain.