A 15-Min Method for Hydrophone Spatial Averaging Correction in Transcranial Neuromodulation System Characterization

The International Transcranial Ultrasonic Stimulation Safety and Standards Consortium (ITRUSST) has identified hydrophone spatial averaging as a potentially significant source of error in transcranial ultrasonic stimulation (TUS) system characterization. Expected spatial averaging error correction factors for TUS systems were computed using 74 TUS system specification sets obtained from 60 peer-reviewed publications. Studies that used hydrophones with nominal diameters larger than the ITRUSST recommended maximum (750 μm at 500 kHz) were excluded. Multiplicative factors required to correct for hydrophone spatial averaging errors for acoustic intensity were found to be 1.10 ± 0.07 for all 24 human parameter sets, 1.12 ± 0.14 for all 50 animal parameter sets and 1.18 ± 0.17 for 26 animal parameter sets with frequencies exceeding 500 kHz. This analysis confirms that hydrophone spatial averaging is typically a significant source of error in TUS system characterization. This note provides researchers with a method to correct for these errors using their own TUS system specifications. The method requires less than 15 min with a scientific calculator, spreadsheet or MATLAB script.