Optimal Estimation of Neural Recruitment Curves Using Fisher Information: Application to Transcranial Magnetic Stimulation

This paper presents a novel method for fast and optimal determination of recruitment (input–output, IO) curve parameters in neural stimulation. A sequential parameter estimation (SPE) method was developed based on the Fisher information matrix (FIM), with a stopping rule based on successively satisfying a specified estimation tolerance. Simulated motor responses evoked by transcranial magnetic stimulation (TMS) were used as a test bed. Performance of FIM-SPE was characterized in 10 177 simulation runs for various IO parameter values corresponding to different virtual subjects, compared with uniform sampling. Unlike uniform sampling, FIM-SPE identifies and samples the areas of the IO curve that contain maximum information about the curve parameters. For the most relaxed stopping rule, the median number of samples required for convergence was only 17 for FIM-SPE versus 294 for uniform sampling. For the highest reliability stopping rule, more than 92% of the FIM-SPE runs converged, with a median of 88 samples, whereas all uniform sampling runs reached 1000 samples without converging. Compared to uniform sampling, FIM-SPE reduced estimation errors up to two-fold and required ten times fewer stimuli. FIM-SPE could improve the speed and accuracy of determination of IO curves for neural stimulation. A software implementation of the algorithm is provided online.