Needle hydrophone transfer function model for characterizing therapeutic transducers

A rigid piston model has been developed to predict needle hydrophone transfer functions. The model predicts that “effective” sensitive element diameter depends on the frequency and can exceed geometrical sensitive element diameter by a factor of up to 2.25. The model predicts harmonic distortion for hydrophone measurements of focused pressure waves, which were modeled using nonlinear plane wave theory for spectral characteristics and Gaussian radial pressure distributions. The pressure wave model was validated by comparing to hydrophone (sensitive element diameter: 85 microns) measurements performed in focal planes of source transducers (3.5 MHz, 64 mm diameter, 89 mm focus and 5 MHz, 19 mm diameter, 38 mm focus). Root mean squared difference (RMSD) between the model fit and measured relative strengths of the first four harmonics was 9% (3.5 MHz transducer) and 11% (5 MHz transducer) where Blackstock’s sigma parameter (JASA, 39, 1019–1026, 1966), which measures extent of nonlinearity, was optimized to fit the data. RMSD between model and measured half width half maxima was 10 ± 5%. Tone bursts from each transducer were measured using needle hydrophones (sensitive element diameters: 200, 400, 600, and 1000 microns). RMSD between model and measured harmonic distortion was 12 ± 4% for the first four harmonics.A rigid piston model has been developed to predict needle hydrophone transfer functions. The model predicts that “effective” sensitive element diameter depends on the frequency and can exceed geometrical sensitive element diameter by a factor of up to 2.25. The model predicts harmonic distortion for hydrophone measurements of focused pressure waves, which were modeled using nonlinear plane wave theory for spectral characteristics and Gaussian radial pressure distributions. The pressure wave model was validated by comparing to hydrophone (sensitive element diameter: 85 microns) measurements performed in focal planes of source transducers (3.5 MHz, 64 mm diameter, 89 mm focus and 5 MHz, 19 mm diameter, 38 mm focus). Root mean squared difference (RMSD) between the model fit and measured relative strengths of the first four harmonics was 9% (3.5 MHz transducer) and 11% (5 MHz transducer) where Blackstock’s sigma parameter (JASA, 39, 1019–1026, 1966), which measures extent of nonlinearity, was optimized to fit...