Department of Psychiatry and Behavioral Sciences, School of Medicine, Duke University, Durham, NC, United States of America.
Department of Electrical and Computer Engineering, School of Engineering, Duke University, Durham, NC, United States of America.
J Neural Eng. 2023 Sep 13;20(5). doi: 10.1088/1741-2552/acf1cc.
. 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.. 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 maximum(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.. 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.. 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.
. 神经元反应的阈值化是经颅磁刺激 (TMS) 许多应用的核心，但神经元活动和运动诱发电位 (MEPs) 的随机性给阈值化技术带来了挑战。我们分析了获得 TMS 运动阈值的现有方法及其变化，从其他领域引入了新的方法，并比较了它们的准确性和速度。除了现有的相对频率方法，如五分之法，我们还研究了基于最大似然 (ML) 或最大 (MAP) 估计的概率运动阈值模型的自适应方法。为了提高这些自适应估计方法的性能，我们探讨了估计过程的变化和群体水平先验信息的纳入。我们采用了一种贝叶斯估计方法，该方法迭代地将 TMS 响应信息纳入概率密度函数。还探索了具有不同收敛标准和步长规则的一组非参数随机求根方法。使用独立的随机 MEP 模型评估了阈值方法的性能。传统的相对频率方法需要大量刺激，在群体水平上固有偏差，并且个体受试者的误差分布很宽。参数估计方法获得阈值的速度要快得多，其准确性取决于估计方法，当纳入群体水平先验信息时，性能会显著提高。随机求根方法与自适应估计方法相当，但实现起来要简单得多，并且不依赖于潜在不准确的基础估计模型。与传统的单参数 ML 估计相比，双参数 MAP 估计、贝叶斯估计和随机求根方法具有更好的误差收敛性，所有这些方法都比传统的相对频率方法需要更少的 TMS 脉冲来进行准确估计。由于计算要求低、算法实现简单以及与参数估计器中的潜在模型缺陷无关，随机求根方法特别有吸引力。
