Closed-Loop Estimation of Neurostimulation Strength-Duration Curve Using Fisher Information Optimization and Comparison With Uniform and Random Methods

Background: Strength-duration (SD) curve, rheobase and chronaxie parameters provide insights about the interdependence between stimulus strength and stimulus duration (or pulse width), and the neural activation dynamics such as the membrane time constant, which are useful for diagnostics and therapeutic applications. The existing SD curve estimation methods are based on open-loop uniform and/or random selection of the pulse widths. Objective: To develop a method for closed-loop estimation of the SD curve. Method: In the proposed method, after the selection of each pulse width 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 uniform methods where pulse widths are chosen in ascending, descending and random orders, and with methods with two and all non-uniform random pulse widths. Results: 160 simulation cases were run. The FIM method satisfied the stopping rule in 144 runs, and estimated the rheobase (chronaxie in parenthesis) with an average absolute relative error (ARE) of 1.73% (2.46%), with an average of 82 samples. At this point, methods with two and all random pulse widths, and uniform methods with descending, ascending and random orders led to 5.66% (20.27%), 2.15% (4.51%), 8.57% (54.96%), 3.52% (5.45%), and 2.19% (4.40%) AREs, which are greater than that achieved through the FIM method. In all 160 runs, The FIM method has chosen the minimum and maximum pulse widths as the optimal pulse widths. Conclusions: The SD curve is identifiable by acquiring the SD data from the minimum and maximum pulse widths achieved through the FIM optimization. The SD data at random or uniform pulse widths from only the vertical area or lower plateau of the curve might not result in satisfactory estimation. Significance: This paper provides insights about pulse widths selection in closed-loop and open-loop SD curve estimation methods. ### Competing Interest Statement The authors have declared no competing interest.