Multiple Linear Regression Estimation of Onset Time Delay for Experimental Transcranial Narrowband Ultrasound Signals

Focused ultrasound is an emerging medical technique for transcranial procedures and requires the precise modeling of ultrasound signal propagation through the skull. To verify models, the onset time delay (OTD) between two signals measured at the same spatial location, with and without the presence of a skull in the path of the signal, is compared between simulations and experiments. Current methods to automatically identify OTD use correlation-based algorithms. However, these techniques suffer from poor results caused by signal distortion and low signal-to-noise ratios in experimental signals. In this study, we compare the effectiveness of machine learning (multiple linear regression) to three correlation-based time-delay estimation techniques in estimating the OTD of a signal pair. A sample of 1643 signal pairs, with the center frequencies of either 270 or 836 kHz, had their delays manually identified as a benchmark. Density, thickness, incidence angle, frequency, and x and y offsets from the center were used as predictors. We find that, compared with manual identification, machine learning is 80.4% more accurate than cross correlation across all test signals and is noise-independent through all noise bins. The median of the errors was less than 0.3 periods was observed for signals with a frequency of 270 kHz and less than 1.1 periods for signals with a frequency of 836 kHz, with little estimate bias. Overall, linear multivariable regression is determined to provide the best estimate of the OTD of two signals.