| Background, Motivation and Objective: In the optimization and development of medical ultrasound transducers and imaging methods, a numerical model that predicts the occurring nonlinear acoustic pressure fields is an invaluable tool. A realistic model should be capable of handling a 3D, large-scale domain of interest, a pulsed excitation and a tissue-like medium exhibiting nonlinearity and a frequency power law-type of attenuation. In the recent years, we have developed the Iterative Nonlinear Contrast Source (INCS) method, a model that is well suited for computing large-scale, nonlinear ultrasound fields of phased array transducers in water. Until now, in this model attenuation had been neglected. Our objective is to resolve this issue. Statement of Contribution/Methods: In this contribution, we present an extended INCS method that includes medium attenuation and dispersion of an arbitrary behavior. The INCS method is based on a solution of the Westervelt equation, in which the nonlinear term is treated as a contrast source. The full nonlinear wavefield is then obtained by an iterative solution of the linearized wave problem using a Green’s function method. To include medium attenuation, the Green’s function of the lossy background medium is obtained by using a complex wavenumber. This requires an adaptation of the numerical evaluation method, which can be done at no extra cost in terms of memory and at a small cost in terms of computation time. Results: Numerical results for the lossy INCS method are presented for a phased array transducer (64 elements, 19.2 mm aperture, 12 mm elevation width) exciting a focused beam with a source pressure level of 250 kPa and a three-cycle pulse with 1 MHz center frequency, and propagating in liver, which exhibits a frequency power law attenuation with a power b = 1.14. Comparison of the linear, lossy field with results from the FieldII program show excellent agreement with a difference of at most 0.1dB. The nonlinear, lossy field is compared with the nonlinear field in a situation where the attenuation is neglected, and in a situation where a square power law attenuation (b = 2) has been employed. For these two cases we observe deviations in the axial profile of the second harmonic frequency component up to +5 dB and –2 dB at z = 60mm, respectively. Discussion and Conclusions: From the linear results we conclude that the improved INCS method correctly handles the attenuative medium behavior. From the nonlinear results we conclude that for a tissue-like medium the attenuation results in a significant reduction of the higher harmonics. Moreover, we conclude that a square power law and a frequency power law result in significantly differing nonlinear fields. In order to predict the nonlinear acoustic field of medical transducers as it occurs in a tissue-like medium, it is therefore essential to include a frequency power law attenuation in the model. |