- Email: [email protected]
Including prior knowledge for accurate and fast motor threshold estimation
Brain Stimulation (2011) 4, 60–1
www.brainstimjrnl.com
COMMENTARY
Including prior knowledge for accurate and fast motor threshold estimation Feng Qi, Nicolas Schweighofer Department of Biokinesiology and Physical Therapy, University of Southern California, Los Angeles, California
Accurately estimating motor threshold (MT) is important in transcranial magnetic stimulation (TMS), because the MT is used as a reference to adjust individual subject’s machine output intensity.1 MT is defined as the minimum TMS output intensity that can induce reliable motor evoked potentionals (MEPs) (usually . 100 mV), with a probability of 50%. The Parameter Estimation in Sequential Test (PEST) method, which is based on maximum likelihood regression, has previously been proposed to speed up MT estimation.2 We recently proposed a new Bayesian PEST method that modifies the previous PEST method in two ways.3 First, we used prior knowledge, in the form of a probabilistic model, to facilitate MT estimation. Second, we used the probability interval of the estimated MT distribution to control the estimation error. Specifically, the width of 95% of the area under the curve of MTs probability density function was taken as a measure of the estimation precision. We experimentally tested the accuracy, and hence safety, of our Bayesian method in 10 healthy subjects.3 According to Awiszus,4 our new method suffers from three potential problems. First, the new method translates prior knowledge into a probability distribution, which is difficult to validate. Second, the use of the probability interval stopping rule in conjunction with adaptive threshold estimation ‘‘is not justified.’’ Third, the simulation results of Awiszus showed that even if our new method had used accurate
Correspondence: Dr. Nicolas Schweighofer, Department of Biokinesiology and Physical Therapy, University of Southern California, 1540 E. Alcazar, Los Angeles, CA 90089. Submitted September 16, 2010. Accepted for publication September 16, 2010. 1935-861X/$ - see front matter Ó 2011 Elsevier Inc. All rights reserved. doi:10.1016/j.brs.2010.09.005
prior knowledge, more than 14 stimuli were still required to achieve safe MT estimation. The first concern is valid, but does not disprove that our new method is faster and safe. We chose Gaussian probability distributions of MTs for their simplicity, and our combined simulation and experimental results show satisfying accuracy and smaller number of pulses with these priors. In addition, our method can be extended to incorporate other type of distributions beside the Gaussian distribution. More generally, estimation with correct prior knowledge should be faster than without. Accordingly, Awiszus and Borckardt5 have provided options to incorporate prior knowledge in their new software. Therefore, both Awiszus and we agree that prior knowledge is potentially helpful to speed up MT determination. This consensus opens the door for improving previous MT estimation methods, though the best way to use the prior knowledge remains a subjective choice at this time. Regarding the second concern, Awiszus asserts that the probability interval stopping rule cannot control the estimation error. However, the cited article, by Alcala-Quintana and Garcia-Perez,6 showed that with an uniformly distributed prior (which can be interpreted as no prior information) the probability interval stopping rule has an error-controlling power that is no greater than many other tested stopping rules. Therefore, it is our belief that the study by Alcala-Quintana and Garcia-Perez.6 only indicates that the probability interval stopping rule alone cannot make the PEST method faster. Accordingly, we proposed the probability interval stopping rule to control the MT error, not to accelerate the determination of MT. The third concern was based on computer simulations, in which Awiszus showed that the Bayesian PEST required
Accurate and fast MT estimation only three pulses fewer than the ‘‘best-PEST.’’ Two factors influence the number of pulses: the safety criterion and the standard deviation of the prior. The safety criterion used by Awiszus is much stricter that that suggested by the current IFCN guidelines, which use a MT estimation with step size of 2% MSO.7,8 In our study, the error level of Bayesian PEST was not larger than the ‘‘best-PEST’’ implemented by Mishory et al.3 Second, the standard deviation of the prior is a crucial parameter that largely influences the speed of convergence. On one hand, if the prior knowledge is highly trustworthy, a small standard deviation of the prior can be chosen. In this case, the Bayesian-PEST method predicts that the MT is near the mean of the prior and that the convergence of the estimated MT to the true MT will be much faster than in the simulations by Awiszus. On the other hand, if the standard deviation is large, the prior’s accelerating effect will be small and a large number of pulses will be needed, as in the simulations by Awiszus. Inaccurate MT measurement and long stimulation procedure both increase the risk of TMS. When the prior knowledge of MT is accurate, our method will shorten the stimulation procedure and keep the level of accuracy of the best-PEST by Awiszus. Because the best-PEST is a special case of the Bayesian PEST when the prior is flat, if we know how to correctly set the prior, the Bayesian PEST should be at least as fast and accurate as the best-PEST. To enhance the
61 accuracy of our method, as in clinical studies for instance, a more stringent stopping criterion should be used. If the prior is unknown or not well defined, the final MT estimation should only be data driven and a flat prior should be used.
References 1. Hallett M. Transcranial magnetic stimulation: a primer. Neuron 2007; 55:187-199. 2. Awiszus F. TMS and threshold hunting. Suppl Clin Neurophysiol 2003; 56:13-23. 3. Qi F, Wu AD, Schweighofer N. Fast estimation of transcranial magnetic stimulation motor threshold. Brain Stimulation. [Epub ahead of print]. 4. Awiszus F. Fast estimation of transcranial magnetic stimulation motor threshold: is it safe? Brain Stimulation. [Epub ahead of print]. 5. Awiszus F, Borckardt JJ. TMS Motor Threshold Assessment Tool (MTAT 2.0). Brain Stimulation Laboratory, Medical University of South Carolina, USA. Available at: http://www.clinicalresearcher.org/ software.htm. Accessed on: January 6, 2011. 6. Alcala-Quintana R, Garcia-Perez MA. Stopping rules in Bayesian adaptive threshold estimation. Spat Vis 2005;18:347-374. 7. Rossini PM, Barker AT, Berardelli A, et al. Non-invasive electrical and magnetic stimulation of the brain, spinal cord and roots: basic principles and procedures for routine clinical application. Report of an IFCN committee. Electroencephalogr Clin Neurophysiol 1994;91:79-92. 8. Rothwell JC, Hallett M, Berardelli A, et al. Magnetic stimulation: motor evoked potentials. The International Federation of Clinical Neurophysiology. Electroencephalogr Clin Neurophysiol Suppl 1999; 52:97-103.
www.brainstimjrnl.com
COMMENTARY
Including prior knowledge for accurate and fast motor threshold estimation Feng Qi, Nicolas Schweighofer Department of Biokinesiology and Physical Therapy, University of Southern California, Los Angeles, California
Accurately estimating motor threshold (MT) is important in transcranial magnetic stimulation (TMS), because the MT is used as a reference to adjust individual subject’s machine output intensity.1 MT is defined as the minimum TMS output intensity that can induce reliable motor evoked potentionals (MEPs) (usually . 100 mV), with a probability of 50%. The Parameter Estimation in Sequential Test (PEST) method, which is based on maximum likelihood regression, has previously been proposed to speed up MT estimation.2 We recently proposed a new Bayesian PEST method that modifies the previous PEST method in two ways.3 First, we used prior knowledge, in the form of a probabilistic model, to facilitate MT estimation. Second, we used the probability interval of the estimated MT distribution to control the estimation error. Specifically, the width of 95% of the area under the curve of MTs probability density function was taken as a measure of the estimation precision. We experimentally tested the accuracy, and hence safety, of our Bayesian method in 10 healthy subjects.3 According to Awiszus,4 our new method suffers from three potential problems. First, the new method translates prior knowledge into a probability distribution, which is difficult to validate. Second, the use of the probability interval stopping rule in conjunction with adaptive threshold estimation ‘‘is not justified.’’ Third, the simulation results of Awiszus showed that even if our new method had used accurate
Correspondence: Dr. Nicolas Schweighofer, Department of Biokinesiology and Physical Therapy, University of Southern California, 1540 E. Alcazar, Los Angeles, CA 90089. Submitted September 16, 2010. Accepted for publication September 16, 2010. 1935-861X/$ - see front matter Ó 2011 Elsevier Inc. All rights reserved. doi:10.1016/j.brs.2010.09.005
prior knowledge, more than 14 stimuli were still required to achieve safe MT estimation. The first concern is valid, but does not disprove that our new method is faster and safe. We chose Gaussian probability distributions of MTs for their simplicity, and our combined simulation and experimental results show satisfying accuracy and smaller number of pulses with these priors. In addition, our method can be extended to incorporate other type of distributions beside the Gaussian distribution. More generally, estimation with correct prior knowledge should be faster than without. Accordingly, Awiszus and Borckardt5 have provided options to incorporate prior knowledge in their new software. Therefore, both Awiszus and we agree that prior knowledge is potentially helpful to speed up MT determination. This consensus opens the door for improving previous MT estimation methods, though the best way to use the prior knowledge remains a subjective choice at this time. Regarding the second concern, Awiszus asserts that the probability interval stopping rule cannot control the estimation error. However, the cited article, by Alcala-Quintana and Garcia-Perez,6 showed that with an uniformly distributed prior (which can be interpreted as no prior information) the probability interval stopping rule has an error-controlling power that is no greater than many other tested stopping rules. Therefore, it is our belief that the study by Alcala-Quintana and Garcia-Perez.6 only indicates that the probability interval stopping rule alone cannot make the PEST method faster. Accordingly, we proposed the probability interval stopping rule to control the MT error, not to accelerate the determination of MT. The third concern was based on computer simulations, in which Awiszus showed that the Bayesian PEST required
Accurate and fast MT estimation only three pulses fewer than the ‘‘best-PEST.’’ Two factors influence the number of pulses: the safety criterion and the standard deviation of the prior. The safety criterion used by Awiszus is much stricter that that suggested by the current IFCN guidelines, which use a MT estimation with step size of 2% MSO.7,8 In our study, the error level of Bayesian PEST was not larger than the ‘‘best-PEST’’ implemented by Mishory et al.3 Second, the standard deviation of the prior is a crucial parameter that largely influences the speed of convergence. On one hand, if the prior knowledge is highly trustworthy, a small standard deviation of the prior can be chosen. In this case, the Bayesian-PEST method predicts that the MT is near the mean of the prior and that the convergence of the estimated MT to the true MT will be much faster than in the simulations by Awiszus. On the other hand, if the standard deviation is large, the prior’s accelerating effect will be small and a large number of pulses will be needed, as in the simulations by Awiszus. Inaccurate MT measurement and long stimulation procedure both increase the risk of TMS. When the prior knowledge of MT is accurate, our method will shorten the stimulation procedure and keep the level of accuracy of the best-PEST by Awiszus. Because the best-PEST is a special case of the Bayesian PEST when the prior is flat, if we know how to correctly set the prior, the Bayesian PEST should be at least as fast and accurate as the best-PEST. To enhance the
61 accuracy of our method, as in clinical studies for instance, a more stringent stopping criterion should be used. If the prior is unknown or not well defined, the final MT estimation should only be data driven and a flat prior should be used.
References 1. Hallett M. Transcranial magnetic stimulation: a primer. Neuron 2007; 55:187-199. 2. Awiszus F. TMS and threshold hunting. Suppl Clin Neurophysiol 2003; 56:13-23. 3. Qi F, Wu AD, Schweighofer N. Fast estimation of transcranial magnetic stimulation motor threshold. Brain Stimulation. [Epub ahead of print]. 4. Awiszus F. Fast estimation of transcranial magnetic stimulation motor threshold: is it safe? Brain Stimulation. [Epub ahead of print]. 5. Awiszus F, Borckardt JJ. TMS Motor Threshold Assessment Tool (MTAT 2.0). Brain Stimulation Laboratory, Medical University of South Carolina, USA. Available at: http://www.clinicalresearcher.org/ software.htm. Accessed on: January 6, 2011. 6. Alcala-Quintana R, Garcia-Perez MA. Stopping rules in Bayesian adaptive threshold estimation. Spat Vis 2005;18:347-374. 7. Rossini PM, Barker AT, Berardelli A, et al. Non-invasive electrical and magnetic stimulation of the brain, spinal cord and roots: basic principles and procedures for routine clinical application. Report of an IFCN committee. Electroencephalogr Clin Neurophysiol 1994;91:79-92. 8. Rothwell JC, Hallett M, Berardelli A, et al. Magnetic stimulation: motor evoked potentials. The International Federation of Clinical Neurophysiology. Electroencephalogr Clin Neurophysiol Suppl 1999; 52:97-103.