This paper describes a novel tool for closed-loop system identification of the activation dynamics of the neural target of transcranial magnetic stimulation (TMS). The method operates in real time, selects ideal stimulus parameters, detects and processes the response, and estimates the input--output (IO) curve and the neural membrane time constant representing a first-order approximation of the activated neural target. First, the neural membrane response and depolarization factor, which leads to motor evoked potentials (MEPs) are analytically computed and discussed. Then, an integrated model is developed which combines the neural membrane time constant and the input--output curve in TMS. Identifiability of the proposed integrated model is discussed. A condition is derived, which assures SPE of the proposed integrated model. Finally, a real-time and sequential parameter estimation (SPE) formalism is described to identify the neural membrane time constant and IO curve parameters in closed-loop TMS, where TMS pulses are administered sequentially based on the automatic analysis of the electromyography (EMG) data in real time. Optimal sampling based on maximization of the Fisher information matrix (FIM) and more conventional and intuitive uniform sampling methods both are addressed in this paper. The effectiveness of the proposed parameter tuning method is evaluated via simulations. Without loss of generality, this paper focuses on a specific case of cTMS pulses. The method is directly applicable to other cTMS pulse shapes with no new point of principals. The Matlab code is available online on Github.

This paper discusses some of the practical limitations and issues, which exist for the input -- output (IO) slope curve estimation (SCE) in neural, brain and spinal, stimulation techniques. The drawbacks of the SCE techniques by using existing uniform sampling and Fisher-information-based optimal IO curve estimation (FO-IOCE) methods are elaborated. A novel IO SCE technique is proposed with a modified sampling strategy and stopping rule which improve the SCE performance compared to these methods. The effectiveness of the proposed IO SCE is tested on 1000 simulation runs in transcranial magnetic stimulation (TMS), with a realistic model of motor evoked potentials (MEPs). The results show that the proposed IO SCE method successfully satisfies the stopping rule, before reaching the maximum number of TMS pulses in 79.5% of runs, while the estimation based on the uniform sampling technique never converges and satisfies the stopping rule. At the time of successful termination, the proposed IO SCE method decreases the 95th percentile (mean value in the parentheses) of the absolute relative estimation errors (AREs) of the slope curve parameters up to 7.45% (2.2%), with only 18 additional pulses in average compared to that of the FO-IOCE technique. It also decreases the 95th percentile (mean value in the parentheses) of the AREs of the IO slope curve parameters up to 59.33% (16.71%), compared to that of the uniform sampling method. The proposed IO SCE also identifies the peak slope with higher accuracy, with the 95th percentile (mean value in the parentheses) of AREs reduced up to 9.96% (2.01%) compared to that of the FO-IOCE method, and up to 46.29% (13.13%) compared to that of the uniform sampling method.

Background: Neurons demonstrate very distinct nonlinear activation dynamics, influenced by the neuron type, morphology, ion channel expression, and various other factors. The measurement of the activation dynamics can identify the neural target of stimulation and detect deviations, e.g., for diagnosis. This paper describes a tool for closed-loop sequential parameter estimation (SPE) of the activation dynamics through transcranial magnetic stimulation (TMS). The proposed SPE method operates in real time, selects ideal stimulus parameters, detects and processes the response, and concurrently estimates the input-output (IO) curve and the first-order approximation of the activated neural target. Objective: To develop a SPE method to concurrently estimate the first-order activation dynamics and IO curve in closed-loop electromyography-guided (EMG-guided) TMS. Method: First, identifiability of the integrated model of the first-order neural activation dynamics and IO curve is assessed, demonstrating that at least two IO curves need to be acquired with different pulse widths. Then, a two-stage SPE method is proposed. It estimates the IO curve by using Fisher information matrix optimization in the first stage and subsequently estimates the membrane time constant as well as the coupling gain in the second stage. The procedure continues in a sequential manner until a stopping rule is satisfied. Results: The results of 73 simulation cases confirm the satisfactory estimation of the membrane time constant and coupling gain with average absolute relative errors (AREs) of 6.2% and 5.3%, respectively, with an average of 344 pulses (172 pulses for each IO curve or pulse width). The method estimates the IO curves' lower and upper plateaus, mid-point, and slope with average AREs of 0.2%, 0.7%, 0.9%, and 14.5%, respectively. Conclusions: SPE of the activation dynamics requires acquiring at least two IO curves with different pulse widths, which needs a TMS device with adjustable pulse duration. Significance: The proposed SPE method enhances the cTMS functionality, which can contribute novel insights in TMS studies.