Modeling nonlinear medical ultrasound via a linearized contrast source method

Research on nonlinear medical ultrasound has been increased over the last decade and has resulted in a wide range of numerical methods for the modeling of the nonlinear distortion of a propagating pressure wave. However, when applied to realistic configurations, the majority of these methods are either computationally expensive or limited by the applied approximations. The Iterative Nonlinear Contrast Source (INCS) method is able to accurately compute the pulsed nonlinear pressure wave field that is generated in a large three-dimensional domain by an arbitrary transducer transmitting under a large steering angle. The method is based on the Neumann iterative solution of a nonlinear integral equation that is equivalent to the Westervelt equation. To improve the performance of the method, it would be beneficial to employ iterative schemes (e.g. Conjugate Gradient based schemes) that are efficient for solving linear integral equations. This motivates the development of a linearized version of the INCS method, as presented in this paper. To test the presented approach, a Bi-CGSTAB scheme is used to solve the linearized Westervelt equation. For the one-dimensional case, results are obtained and compared with the solution obtained with the original INCS method, and the Fubini solution. All the results have been obtained up to the third harmonic component and are in agreement with each other.