Identifiability analysis and noninvasive online estimation of the first-order neural activation dynamics in the brain with transcranial magnetic stimulation

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. ### Competing Interest Statement The authors have declared no competing interest.