Closed-Loop Phase Selection in EEG-TMS Using Bayesian Optimization

Research on transcranial magnetic stimulation (TMS) combined with encephalography feedback (EEG-TMS) has shown that the phase of the sensorimotor mu rhythm is predictive of corticospinal excitability. Thus, if the subject-specific optimal phase is known, stimulation can be timed to be more efficient. In this paper, we present a closed-loop algorithm to determine the phase linked to the highest excitability with as few trials as possible. We used Bayesian optimization with different configurations as an automated, online search tool in an EEG-TMS simulation exneriment. From a sample of 38 healthy participants (25 f, 18 m), we selected all participants with a significant single-subject phase effect (N = 5) for the simulation. We then simulated 1000 experimental sessions per participant where we used Bayesian optimization to find the optimal phase. We tested two objective functions: Fitting a sinusoid in Bayesian linear regression or Gaussian Process regression. We additionally tested adaptive sampling using a knowledge gradient as the acquisition function compared with random sampling. We evaluated the algorithm's performance in a fast optimization (100 trials) and a long-term optimization (1000 trials). We found that for fast optimization, the Bayesian linear regression in combination with adaptive sampling gives the best results with a mean phase location accuracy of 79 % after 100 trials. With either sampling approach, Bayesian linear regression performs better than Gaussian Process regression in the fast optimization. In the long-term optimization, Bayesian regression with random sampling shows the best trajectory, with a rather steep improvement and good final performance of 87 % mean phase location accuracy. In summary, we could show the suitability of closed-loop Bayesian optimization for phase selection. We show that we can increase the speed and accuracy by using prior knowledge about the expected function shape compared with traditional Bayesian optimization with Gaussian Process regression.