Correction for Spatial Averaging Artifacts in Hydrophone Measurements of High-Intensity Therapeutic Ultrasound: An Inverse Filter Approach

High-intensity therapeutic ultrasound (HITU) pressure is often measured using a hydrophone. HITU pressure waves typically contain multiple harmonics due to nonlinear propagation. As harmonic frequency increases, harmonic beamwidth decreases. For sufficiently high harmonic frequency, beamwidth may become comparable to the hydrophone effective sensitive element diameter, resulting in signal reduction due to spatial averaging. An analytic formula for a hydrophone spatial averaging filter for beams with Gaussian harmonic radial profiles was tested on HITU pressure signals generated by three transducers (1.45 MHz, F/1; 1.53 MHz, F/1.5; 3.91 MHz, F/1) with focal pressures up to 48 MPa. The HITU signals were measured using fiber-optic and needle hydrophones (nominal geometrical sensitive element diameters: 100 and 400 μm). Harmonic radial profiles were measured with transverse scans in the focal plane using the fiber-optic hydrophone. Harmonic radial profiles were accurately approximated by Gaussian functions with root-meansquare (rms) differences between transverse scans and Gaussian fits less than 9% for frequencies up to approximately 50 MHz. The Gaussian harmonic beamwidth parameter σn varied with harmonic number n according to a power law, σn = σ1/nq where 0.5 <; q <; 0.6. RMS differences between experimental and theoretical spatial averaging filters were 11% ± 1% (1.45 MHz), 8% ± 1% (1.53 MHz), and 4% ± 1% (3.91 MHz). For the two more highly focused (F/1) transducers, the effect of spatial averaging was to underestimate peak compressional pressure (pcp), peak rarefactional pressure (prp), and pulse intensity integral (pii) by (mean ± standard deviation) (pcp: 4.9% ± 0.5%, prp: 0.4% ± 0.2%, pii: 2.9% ± 1%) and (pcp: 28.3% ± 9.6%, prp: 6% ± 2.4%, pii: 24.3% ± 6.7%) for the 100and 400-μm-diameter hydrophones, respectively. These errors can be suppressed by the application of the inverse spatial averaging filter.