Closed-Loop Estimation Method of Neurostimulation Strength-Duration Curve Using Fisher Information Optimization

Background: The existing estimation methods of strength-duration (SD) curve are based on open-loop uniform and/or random pulse durations, which are chosen without feedback from neuronal data. Objective: To develop a closed-loop estimation method of the SD curve, where the pulse durations are adjusted iteratively using the neuronal data. Method: In the proposed method, after the selection of each pulse duration through Fisher information matrix (FIM) optimization, the corresponding motor threshold (MT) is computed, the SD curve estimation is updated, and the process continues until satisfaction of a stopping rule. Results: 250 simulation cases were run, and the results were compared with the iterative random and uniform sampling methods. The FIM method satisfied the stopping rule in 90% runs and estimated the rheobase (chronaxie in parenthesis) with an average absolute relative error (ARE) of 1.57% (2.15%), with an average of 85 samples. At the FIM termination sample, methods with two and all random pulse durations, and uniform methods with descending, ascending and random orders led to 5.69% (20.09%), 2.22% (3.93%), 7.34% (40.90%), 3.10% (4.44%), and 2.05% (3.45%) AREs. Conclusions: The FIM method proposes the SD identification by fitting to the data of the minimum and maximum pulse durations. The range of pulse duration should cover the vertical and horizontal parts of the SD curve. Iterative random or uniform samples from only the vertical or horizontal areas of the curve might not result in satisfactory estimation. Significance: This paper provides insights about pulse durations selection for SD curve estimation.