Linearization strategies for the Iterative Nonlinear Contrast Source method for full-wave simulation of nonlinear ultrasound fields

Verweij, Martin D.; Demi, Libertario; Dongen, Koen W. A. van

doi:10.1063/1.4749341

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“…This iterative solution method allows to model moderate losses and nonlinearity. Recently, linearization strategies [10] [11] have been presented in order to model a broader variety of contrasts. However, convergence is not always guaranteed for realistic speed of sound contrast.…”

Section: Introductionmentioning

confidence: 99%

Modeling three-dimensional nonlinear acoustic wave fields in media with spatially varying coefficient of nonlinearity, attenuation and speed of sound

Demi

Verweij

Dongen

2012

2012 IEEE International Ultrasonics Symposium

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Numerical methods capable of modeling nonlinear pressure wave fields propagating through inhomogeneous biomedical tissue are essential for the design and optimization of ultrasound transducers or devices. The Iterative Nonlinear Contrast Source (INCS) method is an accurate method for modeling three-dimensional nonlinear acoustic wave fields. Originally it was capable of modeling nonlinear wave fields in homogeneous lossy tissue. Recently, it has been extended to deal with spatially varying coefficient of nonlinearity and attenuation. The method recasts a generalized form of the Westervelt equation into an integral equation which was originally solved using a Neumann scheme. This scheme allows to model moderate losses and nonlinearity. Problems with the convergence may occur for realistic speed of sound contrast. Here, we present a different solution method which makes it possible to treat, besides spatially varying coefficient of nonlinearity and attenuation, also realistic speed of sound contrasts. The nonlinear integral equation is solved using a steepest descent scheme. The method has been used to compute the three-dimensional nonlinear pressure wave field generated by a 40 element linear array and propagating through a medium with spatially varying coefficient of nonlinearity, attenuation and speed of sound. Simulations have been performed up to the 5th harmonic component. I. INTRODUCTIONNowadays, the number of ultrasound medical applications based on nonlinear propagation is steadily growing. As an example, Tissue Harmonic Imaging [1] [2] and Super Harmonic Imaging [3], can be mentioned amongst diagnostic applications of ultrasound. Consequently, a significant amount of numerical methods capable of modeling nonlinear propagation have been developed. Existing methods may be divided into two categories, forward wave methods and full wave methods [4]. The Iterative Nonlinear Contrast Source (INCS) [5] [6] method is a full wave method, it does not favor a particular direction of propagation, and since it only requires two points per wavelength or period, it can deal with nonlinear ultrasound fields over computational domains measuring hundreds of wavelengths and periods. Originally, the method could model pressure wave field propagating through homogeneous nonlinear media with frequency power law attenuation [6] [7]. Recently, it has been extended to deal with spatially varying coefficient of nonlinearity and attenuation [8] [9]. The

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Section: Introductionmentioning

confidence: 99%