Hydrophone Spatial Averaging Correction for Acoustic Exposure Measurements from Arrays I: Theory and Impact on Diagnostic Safety Indexes.

This article reports underestimation of mechanical index (MI) and non-scanned thermal index for bone near focus (TIB) due to hydrophone spatial averaging effects that occur during acoustic output measurements for clinical linear and phased arrays. TIB is the appropriate version of thermal index (TI) for fetal imaging after 10 weeks from the last menstrual period according to the American Institute of Ultrasound in Medicine (AIUM). Spatial averaging is particularly troublesome for highly-focused beams and nonlinear, non-scanned modes such as acoustic radiation force impulse (ARFI) and pulsed Doppler. MI and variants of TI (e.g., TIB), which are displayed in real-time during imaging, are often not corrected for hydrophone spatial averaging because a standardized method for doing so does not exist for linear and phased arrays. A novel analytic inverse-filter method to correct for spatial averaging for pressure waves from linear and phased arrays is derived in this article (Part I) and experimentally validated in a companion article (Part II). A simulation was developed to estimate potential spatial-averaging errors for typical clinical ultrasound imaging systems based on the theoretical inverse filter and specifications for 124 scanner / transducer combinations from the U.S. Food and Drug Administration (FDA) 510(k) database from 2015-2019. Specifications included center frequency, aperture size, acoustic output parameters, hydrophone geometrical sensitive element diameter, etc. Correction for hydrophone spatial averaging using the inverse-filter suggests that maximally-achievable values for MI, TIB, thermal dose (t43), and spatial-peak-temporal-average intensity (Ispta) for typical clinical systems are potentially higher than uncorrected values by (means ± standard deviations) 9% ± 4% (ARFI MI), 19% ± 15% (ARFI TIB), 50% ± 41% (ARFI t43), 43% ± 39% (ARFI Ispta), 7% ± 5% (pulsed Doppler MI), 15% ± 11% (pulsed Doppler TIB), 42% ± 31% (pulsed Doppler t43), and 33% ± 27% (pulsed Doppler Ispta). These values correspond to frequencies of 3.2 ± 1.3 MHz (ARFI) and 4.1 ± 1.4 MHz (pulsed Doppler), and the model predicts that they would increase with frequency. Inverse filtering for hydrophone spatial averaging significantly improves accuracy of estimates of MI, TIB, t43, and Ispta for ARFI and pulsed Doppler signals.