Correlating active and resting motor thresholds for transcranial magnetic stimulation through a matching model

Abstract

Dear Editor, Transcranial magnetic stimulation (TMS) can relatively focally elicit action potentials in cortical neurons in the brain. Sufficiently strong pulses over the primary motor cortex can trigger cortico-spinal output signals leading to measurable motor-evoked potentials (MEPs) and even visually detectable muscle twitches [[1]Goetz SM, Alavi SMM, Deng ZD, and Peterchev AV. Statistical Model of Motor-Evoked Potentials. IEEE Transactions on Neural Systems and Rehabilitation Engineering 2019; 27:1539–1545.Google Scholar]. The motor threshold (i.e., expressed as a percentage of the maximum stimulator output) as an indirect indicator of the motor cortex excitability represents the lowest stimulus strength that evokes a MEP with an amplitude around 50 μV at rest (resting motor threshold, RMT) and of around 200 μV during voluntary contraction of the tested muscle (active motor threshold, AMT) [2Rossini PM, Burke D, Chen R, Cohen L, Daskalakis Z, Di Iorio R, et al. Non-invasive electrical and magnetic stimulation of the brain, spinal cord, roots and peripheral nerves: Basic principles and procedures for routine clinical and research application. An updated report from an IFCN Committee. Clinical neurophysiology 2015; 126:1071–1107.Google Scholar, 3Wang B, Peterchev AV, and Goetz SM. Three novel methods for determining motor threshold with transcranial magnetic stimulation outperform conventional procedures. Journal of Neural Engineering 2023; 20:056002.Google Scholar]. The AMT enhances both spinal and cortical excitability in the primary motor cortex through voluntary muscle contraction for higher sensitivity of the neural circuits and therefore typically leads to lower values than the RMT [[4]Lazzaro VD, Restuccia D, Oliviero A, Profice P, Ferrara L, Insola A, et al. Effects of voluntary contraction on descending volleys evoked by transcranial stimulation in conscious humans. The Journal of physiology 1998; 508:625–633.Google Scholar]. The motor threshold serves as the main metric for individualising the pulse strength in neuromodulation for both experimental brain research and clinical trails [2Rossini PM, Burke D, Chen R, Cohen L, Daskalakis Z, Di Iorio R, et al. Non-invasive electrical and magnetic stimulation of the brain, spinal cord, roots and peripheral nerves: Basic principles and procedures for routine clinical and research application. An updated report from an IFCN Committee. Clinical neurophysiology 2015; 126:1071–1107.Google Scholar, 5Pridmore S, Fernandes Filho JA, Nahas Z, Liberatos C, and George MS. Motor threshold in transcranial magnetic stimulation: a comparison of a neurophysiological method and a visualization of movement method. The journal of ECT 1998; 14:25–27.Google Scholar]. Additionally, the motor threshold is the reference pulse strength for practically all safety recommendations and limits [[6]Rossi S, Antal A, Bestmann S, Bikson M, Brewer C, Brockmöller J, et al. Safety and recommendations for TMS use in healthy subjects and patient populations, with updates on training, ethical and regulatory issues: Expert Guidelines. Clinical Neurophysiology 2021; 132:269–306.Google Scholar]. Whereas repetitive TMS with fixed pulse rhythms is typically based on the RMT, patterned pulse protocols, such as theta-burst stimulation, preferably use the lower AMT as a reference stimulation strength [[7]Turi Z, Lenz M, Paulus W, Mittner M, and Vlachos A. Selecting stimulation intensity in repetitive transcranial magnetic stimulation studies: A systematic review between 1991 and 2020. European Journal of Neuroscience 2021; 53:3404–3415.Google Scholar]. However, it was found that the outcome of theta-burst stimulation does not only depend on the TMS pulse strength but also muscle pre-activation before the neuromodulatory intervention—which obviously is an inherent part of the AMT detection procedure [8Gentner R, Wankerl K, Reinsberger C, Zeller D, and Classen J. Depression of human corticospinal excitability induced by magnetic theta-burst stimulation: evidence of rapid polarity-reversing metaplasticity. Cerebral cortex 2008; 18:2046–2053.Google Scholar, 9Wankerl K, Weise D, Gentner R, Rumpf JJ, and Classen J. L-type voltage-gated Ca2+ channels: a single molecular switch for long-term potentiation/long-term depression-like plasticity and activity-dependent metaplasticity in humans. Journal of Neuroscience 2010; 30:6197–6204.Google Scholar]. Furthermore, the detection of the AMT is more complicated for both the subject and the operator, while the extra degrees of freedom and additional error sources may increase variability. Based on these issues, it would appear reasonable to use a measure that allows isolating and independently controlling such pre-activation and exclusively use RMT as a reference instead of AMT for necessary applications. However, a translation or matching of procedures to an RMT reference would need knowledge of the quantitative relationship between AMT and RMT, which is yet poorly established [10Wassermann EM. Variation in the response to transcranial magnetic brain stimulation in the general population. Clinical neurophysiology 2002; 113:1165–1171.Google Scholar, 11Ngomo S, Leonard G, Moffet H, and Mercier C. Comparison of transcranial magnetic stimulation measures obtained at rest and under active conditions and their reliability. Journal of neuroscience methods 2012; 205:65–71.Google Scholar]. To fill this research gap, we collected individual motor threshold data from previous studies that collected both RMT and AMT in the first dorsal interosseuous muscle (see Supplementary material). As the statistical distribution of the (after all purely positive and therefore unlikely gaussian-distributed 1When random variables are purely positive, normal distributions are in general rarely mathematically correct as they have long-ranging tails and would, in contrast to a log-normal distribution, suggest a certain nonnegligible portion of negative values. For narrow distributions, i.e., low variability, normal and log-normal distributions practically converge into each other, though. However, the high variability in brain stimulation does not appear to be such case, as the different skewness levels indicate.) motor threshold values was strongly right-skewed (skewness γ(RMT)=0.973 and γ(AMT)=0.843), we normalised all motor threshold measurements using natural logarithmic transformation, resulting in γ(ln⁡(RMT))=0.380 and γ(ln⁡(AMT))=0.184 (Figure 1 (A)). We selected AMT as the dependent variable and the remaining variables as independent predictors including both categorical and continuous types. We employed a mixed-effect model to analyse the data and derive a functional relationship between AMT and RMT, taking into account biological differences among individuals and random sources in different experiment techniques, since it contains both fixed and random effects that can describe the hierarchical database in terms of multi-levels of interest (see Supplementary material). Overall, we selected RMT (continuous), AGE (continuous), SEX (categorical), STIMULATED HEMISPHERE (categorical), and PULSE SHAPE (monophasic vs. biphasic, categorical) as fixed-effect variables. In addition, this study considered two random-effect sources: STUDY and SUBJECT nested within STUDY, which is termed SUBJECT(STUDY). Package lme4 (version 1.1–31) was used to calibrate the mixed-effect model in R. The restricted maximum likelihood technique served for estimating the variance components in the hierarchical database since it can be applied to unbalanced data and avoid the problem of biased variance estimation by maximum likelihood estimation [[12]Bates D, Mächler M, Bolker B, and Walker S. Fitting linear mixed-effects models using lme4. arXiv preprint arXiv:1406.5823 2014.Google Scholar]. We tested the significance of the fixed-effect variables with a type-III ANOVA with Satterwaite's method. Moreover, package emmeans (1.8.3) in R served for post-hoc analysis with Bonferroni correction. This study calls a p-value of less than 0.05 significant. We calibrated the mixed-effect model with the database with in total 515 observations and 237 subjects coming from eight studies (see Supplementary material). Therefore, this mixed-effects model can be written asyijk=β0+∑h=1pβhxhijk+γk+αjk+ϵijkγk∼N(0,σγ2),αjk∼N(0,σα2),ϵijk∼N(0,σϵ2)(1) where yijk is the i-th response of the j-th individual in the k-th study; xhijk the explanatory value of the j-th individual in the k-th study for the h-th predictor βh (i.e., the fixed-effect variable); γk is the study-specific random-effect variable with a mean of zero and variance of σγ2; αjk is the subject-specific random-effect variable in the k-th study with mean of zero and variance of σα2; ϵijk is the residual with mean of zero and variance of σϵ2 for each yijk; β0 is the constant intercept for all responses yijk. The model has a constant level (β0=0.41) and demonstrates a significant dependence of the AMT on the RMT (βRMT=0.84, F(1,468.38)=1339.89, p<2⋅10−16) and less so of the AGE (βAGE=1.8⋅10−3, F(1,227.67)=6.01, p=0.015), while other fixed-effect variables did not show significant effects. In addition, this model has high marginal and conditional coefficients of determination, which are respectively equal to RM2=0.813 and RC2=0.948. Among the random-effect variables, STUDY obeys the distribution of γk∼N(0,2⋅10−3) and SUBJECT(STUDY) obeys the distribution of αjk∼N(0,4⋅10−3). As shown in Figure 1 (B), the distribution of the residuals appears to be Gaussian (ϵijk∼N(0,2.5⋅10−3)) satisfying the residual distribution assumptions, since the Chi–square normality test and Levene's test show that the model (with properly log-transformed RMT and AMT) does not violate the mixed-effect model assumptions of residual normality (P=26.214, p=0.243) and homogeneity of variance (F(234,278)=0.575, p=1). Our findings suggest that the relationship between AMT and RMT does not depend on the pulse shape (for the included monophasic and biphasic pulses), sex, and stimulated hemisphere, but is at most influenced by a subject's age. This observation implies that the RMT and AGE explain most of the variability of AMT and allow a good prediction of the AMT. We calibrated an linear regression model including both RMT and AGE. However, RMT explains the 84.06% of the total variance of the measurements, while AGE only explains 2.4⋅10−3%. Therefore, we further calibrated the model with RMT only and the prediction equation would beln⁡(AMT)=0.06+0.92⋅ln⁡(RMT)±0.089,(2) where ±0.089 is the standard uncertainty. This matching model would allow estimating AMTs and the necessary pulse strength in repetitive and accelerated stimulation paradigms down to a root-mean square error of less than 8.93⋅10−2 without the need to measure the AMT with muscle contraction. In addition, RMT explains 84.06% of the total variance of the measurements. Left panel of Figure 1 (C) shows the logarithmic AMT prediction based on logarithmic RMT for this linear model. Not only is the determination of RMT usually technically less challenging and variable but also avoids influencing the brain or circuit state of the motor system with the muscle pre-activation needed for AMT determination. In conclusion, this study derives a quantitative functional relationship between AMT and RMT based on threshold data of 237 subjects. Taking exponential on both sides and simplifying Equation (2), the relationship becomesAMT=(1.062⋅RMT0.92)×/÷1.093.(3) Equation (3) predicts AMT over RMT in normal scale as shown in the right panel of Figure 1 (C). This relationship can provide a reliable link to reference all necessary stimulation strength values to the RMT for an easier procedure and separate any influence of muscle pre-activation before the neuromodulatory intervention. In some previous research, ethnicity appeared to influence the RMT but not AMT, thus potentially also impacting the relationship between both [[13]Yi X, Fisher KM, Lai M, Mansoor K, Bicker R, and Baker SN. Differences between Han Chinese and Caucasians in transcranial magnetic stimulation parameters. Experimental brain research 2014; 232:545–553.Google Scholar]. However, other research disagrees with these reports and considers methodological reasons leading to such apparent influences [[14]Suzuki YI, Ma Y, Shibuya K, Misawa S, Suichi T, Tsuneyama A, et al. Effect of racial background on motor cortical function as measured by threshold tracking transcranial magnetic stimulation. Journal of Neurophysiology 2021; 126:840–844.Google Scholar]. Our dataset with parts from Japan, Australia, and Europe with local subject populations did not indicate any such influence on the relationship between RMT and AMT (see Supplementary material). In addition, the dataset only used voluntary muscle contraction levels of 5−20% during the AMT measurement. By isolating muscle pre-activation and exclusively using RMT as the reference, our approach facilitates the accurate estimation of AMT, advancing standardised and effective neuromodulatory interventions using TMS. SMG and KM designed the research. KM derived the mathematical model and initial method as well as code for the mixed-effect model. SMG helped supervise the project. KM, MH, VDL, BH, AG, and GMO collected the TMS data. KM and SMG wrote the text. All authors proof-read, polished and approved the text. None of the authors has potential conflicts of interest to be disclosed. Supplementary document to this article can be found online (https://github.com/BIOMAKE/CorrelatingAMTandRMT).

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