Computation of steered nonlinear fields using offset KZK axes

Fox, P.D., Bouakaz, A. and Tranquart, F. (2005) Computation of steered nonlinear fields using offset KZK axes. Proceedings of the IEEE International Ultrasonics Symposium, Rotterdam. 17 - 20 Sep 2005. pp. 1984-1987 .

Abstract

Introduction/Background: Commercial medical scanners utilise electronic beam steering and the second harmonic signals generated by tissue nonlinear processes to form images at the second harmonic frequency. Furthermore, characteristics of nonlinearly generated harmonics within the beam itself contribute to improvements in lateral resolution and quality of the reconstructed image. Fully understanding these harmonic features offers new possibilities for redesigning or optimising array transducers to attain better imaging performances, as well as in other areas such as contrast agent responses and microbubble destruction strategies for drug delivery. However, such an understanding is hindered at present by the computational difficulty in accurately predicting all the nonlinear characteristics of steered beams. This paper addresses this issue, presenting a KZK based method for analysing beams steered at arbitrary angles.
Method: The parabolic KZK equation is often used to study nonlinear characteristics of medical ultrasound beams. This equation is traditionally applied in a propagation direction perpendicular to the surface of the transducer, and has been shown to model the pulse propagation well along the central axis of the transducer [1]. However, its accurate angle of application is restricted to within approximately only 16 degrees away from the central transducer axis due to the underlying approximations employed in the derivation of the KZK equation. This restriction causes a problem for studying steered beams, since typical steering ranges up to the order of 45 degrees away from the transducer centreline. To overcome this problem whilst at the same time exploiting the traditional KZK benefits, we develop an iterative method for displacing the KZK axes away from the central transducer axis to investigate arbitrary beam or field angles of interest.
Results/Conclusions: The implemented algorithm is based on a time domain solution of the KZK equation, on a standard 3GHz PC with 2GB RAM producing runtimes in the order of a few hours per investigation angle. The transducer used is a 64 element linear phased array operating at 1.7MHz (height 10.5 mm, width 0.27mm, kerf 0.065mm) with beam steering at 0 and 45 degrees. Validation of the basic KZK algorithm without steering has been given previously at linear pressures (54kPa) against both experimental measurements and Field II and at nonlinear pressures (700kPa) against measurements described previously in [1]. The KZK axes are swept over a range of angles covering the full spectrum 499 of -90 to +90 degrees relative to transducer centreline, in order to investigate the entire emitted field for both steered and unsteered beams. Element pitch is then increased to investigate grating lobes. All results are decomposed into first and second harmonic fields to compare relative frequency domain properties. The overall contribution is a better characterisation of linear and nonlinear field characteristics at high angles than is possible with the traditional KZK approach.

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