Numerical evaluation of the effect of electronically steering a phased array transducer: axially post-focal shifting

HIFU has been emerging as an effective and safe modality for the treatment of solid tumours and cancers. The focus shifting range of phased array HIFU transducer is an important safety concern because of the presence of grating lobe in the pre-focal region. However, previous studies were only based on linear acoustic wave model.

The nonlinear wave propagation from a 256-element phased array through multiple layered media was simulated using the angular spectrum approach (ASA) in marching fractional steps with the consideration of diffraction, attenuation and non-linearity effects by a second-order operator splitting scheme. The distribution of acoustic intensities, temperature elevations, lesion sizes and grating lobe levels were calculated at various axially post-focal shifting distances and driving frequencies.

Axially shifting HIFU focus leads to significant increase of the acoustic intensity at the grating lobe, but decrease at the main lobe. The influences on the acoustic field, thermal field and lesion sizes are determined by the shifting distance and driving frequency, and variations can be fit monotonically and linearly. Prediction accuracies by simple regression models are satisfactory. Irreversible tissue coagulation could be generated by the grating lobe at certain conditions.

The established nonlinear wave propagation algorithm allows the accurate description of HIFU field and consequently the evaluation of grating lobe and steerability of focus. The influence of focus shifting may be predicted simply. The treatment planning of phased array HIFU ablation could be optimised by setting the appropriate exposure and focus scanning schemes.