Isolating two sources of variability of subcortical stimulation to quantify fluctuations of corticospinal tract excitability

Three novel methods for determining motor threshold with transcranial magnetic stimulation outperform conventional procedures

Objective. Thresholding of neural responses is central to many applications of transcranial magnetic stimulation (TMS), but the stochastic aspect of neuronal activity and motor evoked potentials (MEPs) challenges thresholding techniques. We analyzed existing methods for obtaining TMS motor threshold and their variations, introduced new methods from other fields, and compared their accuracy and speed.Approach. In addition to existing relative-frequency methods, such as the five-out-of-ten method, we examined adaptive methods based on a probabilistic motor threshold model using maximum-likelihood (ML) or maximuma-posteriori(MAP) estimation. To improve the performance of these adaptive estimation methods, we explored variations in the estimation procedure and inclusion of population-level prior information. We adapted a Bayesian estimation method which iteratively incorporated information of the TMS responses into the probability density function. A family of non-parametric stochastic root-finding methods with different convergence criteria and stepping rules were explored as well. The performance of the thresholding methods was evaluated with an independent stochastic MEP model.Main Results. The conventional relative-frequency methods required a large number of stimuli, were inherently biased on the population level, and had wide error distributions for individual subjects. The parametric estimation methods obtained the thresholds much faster and their accuracy depended on the estimation method, with performance significantly improved when population-level prior information was included. Stochastic root-finding methods were comparable to adaptive estimation methods but were much simpler to implement and did not rely on a potentially inaccurate underlying estimation model.Significance. Two-parameter MAP estimation, Bayesian estimation, and stochastic root-finding methods have better error convergence compared to conventional single-parameter ML estimation, and all these methods require significantly fewer TMS pulses for accurate estimation than conventional relative-frequency methods. Stochastic root-finding appears particularly attractive due to the low computational requirements, simplicity of the algorithmic implementation, and independence from potential model flaws in the parametric estimators.

Motor potentials evoked by transcranial magnetic stimulation: interpreting a simple measure of a complex system

Transcranial magnetic stimulation (TMS) is a non-invasive technique that is increasingly used to study the human brain. One of the principal outcome measures is the motor-evoked potential (MEP) elicited in a muscle following TMS over the primary motor cortex (M1), where it is used to estimate changes in corticospinal excitability. However, multiple elements play a role in MEP generation, so even apparently simple measures such as peak-to-peak amplitude have a complex interpretation. Here, we summarize what is currently known regarding the neural pathways and circuits that contribute to the MEP and discuss the factors that should be considered when interpreting MEP amplitude measured at rest in the context of motor processing and patients with neurological conditions. In the last part of this work, we also discuss how emerging technological approaches can be combined with TMS to improve our understanding of neural substrates that can influence MEPs. Overall, this review aims to highlight the capabilities and limitations of TMS that are important to recognize when attempting to disentangle sources that contribute to the physiological state-related changes in corticomotor excitability.

Closed-loop optimal and automatic tuning of pulse amplitude and width in EMG-guided controllable transcranial magnetic stimulation

This paper proposes an efficient algorithm for automatic and optimal tuning of pulse amplitude and width for sequential parameter estimation (SPE) of the neural membrane time constant and input-output (IO) curve parameters in closed-loop electromyography-guided (EMG-guided) controllable transcranial magnetic stimulation (cTMS). The proposed SPE is performed by administering a train of optimally tuned TMS pulses and updating the estimations until a stopping rule is satisfied or the maximum number of pulses is reached. The pulse amplitude is computed by the Fisher information maximization. The pulse width is chosen by maximizing a normalized depolarization factor, which is defined to separate the optimization and tuning of the pulse amplitude and width. The normalized depolarization factor maximization identifies the critical pulse width, which is an important parameter in the identifiability analysis, without any prior neurophysiological or anatomical knowledge of the neural membrane. The effectiveness of the proposed algorithm is evaluated through simulation. The results confirm satisfactory estimation of the membrane time constant and IO curve parameters for the simulation case. By defining the stopping rule based on the satisfaction of the convergence criterion with tolerance of 0.01 for 5 consecutive times for all parameters, the IO curve parameters are estimated with 52 TMS pulses, with absolute relative estimation errors (AREs) of less than 7%. The membrane time constant is estimated with 0.67% ARE, and the pulse width value tends to the critical pulse width with 0.16% ARE with 52 TMS pulses. The results confirm that the pulse width and amplitude can be tuned optimally and automatically to estimate the membrane time constant and IO curve parameters in real-time with closed-loop EMG-guided cTMS.

Finding synaptic couplings from a biophysical model of motor evoked potentials after theta-burst transcranial magnetic stimulation

OBJECTIVE

We aimed to use measured input-output (IO) data to identify the best fitting model for motor evoked potentials.

METHODS

We analyzed existing IO data before and after intermittent and continuous theta-burst stimulation (iTBS & cTBS) from a small group of subjects (18 for each). We fitted individual synaptic couplings and sensitivity parameters using variations of a biophysical model. A best performing model was selected and analyzed.

RESULTS

cTBS gives a broad reduction in MEPs for amplitudes larger than resting motor threshold (RMT). Close to threshold, iTBS gives strong potentiation. The model captures individual IO curves. There is no change to the population average synaptic weights post TBS but the change in excitatory-to-excitatory synaptic coupling is strongly correlated with the experimental post-TBS response relative to baseline.

CONCLUSIONS

The model describes population-averaged and individual IO curves, and their post-TBS change. Variation among individuals is accounted for with variation in synaptic couplings, and variation in sensitivity of neural response to stimulation.

SIGNIFICANCE

The best fitting model could be applied more broadly and validation studies could elucidate underlying biophysical meaning of parameters.

Detection of motor-evoked potentials below the noise floor: rethinking the motor stimulation threshold

Objective. Motor-evoked potentials (MEPs) are among the most prominent responses to brain stimulation, such as supra-threshold transcranial magnetic stimulation and electrical stimulation. Understanding of the neurophysiology and the determination of the lowest stimulation strength that evokes responses requires the detection of even smaller responses, e.g. from single motor units. However, available detection and quantization methods suffer from a large noise floor. This paper develops a detection method that extracts MEPs hidden below the noise floor. With this method, we aim to estimate excitatory activations of the corticospinal pathways well below the conventional detection level.Approach. The presented MEP detection method presents a self-learning matched-filter approach for improved robustness against noise. The filter is adaptively generated per subject through iterative learning. For responses that are reliably detected by conventional detection, the new approach is fully compatible with established peak-to-peak readings and provides the same results but extends the dynamic range below the conventional noise floor.Main results. In contrast to the conventional peak-to-peak measure, the proposed method increases the signal-to-noise ratio by more than a factor of 5. The first detectable responses appear to be substantially lower than the conventional threshold definition of 50µV median peak-to-peak amplitude.Significance. The proposed method shows that stimuli well below the conventional 50µV threshold definition can consistently and repeatably evoke muscular responses and thus activate excitable neuron populations in the brain. As a consequence, the input-output (IO) curve is extended at the lower end, and the noise cut-off is shifted. Importantly, the IO curve extends so far that the 50µV point turns out to be closer to the center of the logarithmic sigmoid curve rather than close to the first detectable responses. The underlying method is applicable to a wide range of evoked potentials and other biosignals, such as in electroencephalography.

A formalism for sequential estimation of neural membrane time constant and input--output curve towards selective and closed-loop transcranial magnetic stimulation

OBJECTIVE

To obtain a formalism for real-time concurrent sequential estimation of neural membrane time constant and input--output (IO) curve with transcranial magnetic stimulation (TMS).

APPROACH

First, the neural membrane response and depolarization factor, which leads to motor evoked potentials (MEPs) with TMS are analytically computed and discussed. Then, an integrated model is developed which combines the neural membrane time constant and input--output curve. Identifiability of the proposed integrated model is discussed. A condition is derived, which assures estimation of the proposed integrated model. Finally, sequential parameter estimation (SPE) of the neural membrane time constant and IO curve is described through closed-loop optimal sampling and open-loop uniform sampling TMS. Without loss of generality, this paper focuses on a specific case of commercialized TMS pulse shapes. The proposed formalism and SPE method are directly applicable to other pulse shapes.

MAIN RESULTS

The results confirm satisfactory estimation of the membrane time constant and IO curve parameters. By defining a stopping rule based on five times consecutive convergence of the estimation parameters with a tolerances of 0.01, the membrane time constant and IO curve parameters are estimated with 82 TMS pulses with absolute relative estimation errors (AREs) of less than 4% with the optimal sampling SPE method. At this point, the uniform sampling SPE method leads to AREs up to 16%. The uniform sampling method does not satisfy the stopping rule due to the large estimation variations.

SIGNIFICANCE

This paper provides a tool for real-time closed-loop SPE of the neural time constant and IO curve, which can contribute novel insights in TMS studies. SPE of the membrane time constant enables selective stimulation, which can be used for advanced brain research, precision medicine and personalized medicine.