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

Background: Strength-duration (SD) curve, rheobase and chronaxie parameters provide insights about neural activation dynamics and interdependence between pulse amplitude and duration, for diagnostics and therapeutic applications. The existing SD curve estimation methods are based on open-loop uniform and/or random pulse durations, which are chosen without feedback from neuronal data.

Objective: To develop a method for closed-loop estimation 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 based on the successive convergence of the SD curve parameters. The results are compared with various iterative uniform and random sampling techniques, where the SD curve estimation is updated after each sample.

Results: 250 simulation cases were run. The FIM method satisfied the stopping rule in 225 (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. In all 250 runs, the FIM method has chosen the minimum and maximum pulse durations as the optimal pulse durations for the SD curve estimation.

Conclusions: As proposed by the FIM method, the SD curve is identifiable by fitting to the data of the minimum and maximum pulse durations. However, the range of pulse duration should cover the vertical and horizontal parts of the SD curve. Also, 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 closed-loop and open-loop SD curve estimation.