Modeling nonlinear medical ultrasound via a linearized contrast sourcemethod

Research on nonlinear medical ultrasound has been increased over the lastdecade and has resulted in a wide range of numerical methods for the modeling ofthe nonlinear distortion of a propagating pressure wave. However, when appliedto realistic configurations, the majority of these methods are eithercomputationally expensive or limited by the applied approximations. TheIterative Nonlinear Contrast Source (INCS) method is able to accurately computethe pulsed nonlinear pressure wave field that is generated in a largethree-dimensional domain by an arbitrary transducer transmitting under a largesteering angle. The method is based on the Neumann iterative solution of anonlinear integral equation that is equivalent to the Westervelt equation. Toimprove the performance of the method, it would be beneficial to employiterative schemes (e.g. Conjugate Gradient based schemes) that are efficient forsolving linear integral equations. This motivates the development of alinearized version of the INCS method, as presented in this paper. To test thepresented approach, a Bi-CGSTAB scheme is used to solve the linearizedWestervelt equation. For the one-dimensional case, results are obtained andcompared with the solution obtained with the original INCS method, and theFubini solution. All the results have been obtained up to the third harmoniccomponent and are in agreement with each other.