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ORIGINAL ARTICLE

Fast estimation of transcranial magnetic

stimulation motor threshold

Feng Qi,aAllan D. Wu,bNicolas Schweighofera,c

aNeuroscience, University of Southern California, Los Angeles, California

bDepartment of Neurology, University of California at Los Angeles, Los Angeles, California

cBiokinesiology and Physical Therapy, University of Southern California, Los Angeles, California

Background

In Transcranial Magnetic Stimulation (TMS), the Motor Threshold (MT) is the minimum intensity

required to evoke a liminal response in the target muscle. Because the MT reflects cortical excitability,

the TMS intensity needs to be adjusted according to the subject’s MT at the beginning of every TMS

session.

Objective

Shorten the MT estimation process compared to existing methods without compromising accuracy.

Methods

We propose a Bayesian adaptive method for MT determination that incorporates prior MT knowledge

and uses a stopping criterion based on estimation of MT precision. We compared the number of TMS

pulses required with this new method with existing MT determination methods.

Results

The proposed method achieved the accuracy of existing methods with as few as seven TMS pulses on

average when using a common prior and three TMS pulses on average when using subject-specific

priors.

Conclusions

Our adaptive Bayesian method is effective in reducing the number of pulses to estimate the MT.

? 2011 Elsevier Inc. All rights reserved.

Keywords

TMS; motor threshold; Bayesian method

Transcranialmagneticstimulation(TMS)isanoninvasive

neural stimulation technique that has broad applications.1

TMS generates an electromagnetic field that passes through

the scalp and induces an electrical current, which activates

neurons in the cortex.1In motor cortex studies, if TMS is

applied at an intensity above a threshold, the target muscle

contralateral to the stimulated cortical neurons responds

This work was in part supported by National Science Foundation grant

IIS 0535282 to NS.

Correspondence: Nicolas Schweighofer, Neuroscience, University of

Southern California, 1540 E. Alcazar, Los Angeles, CA 90089

E-mail address: schweigh@usc.edu

Submitted October 17, 2009; revised June 7, 2010. Accepted for

publication June 7, 2010.

1935-861X/$ - see front matter ? 2011 Elsevier Inc. All rights reserved.

doi:10.1016/j.brs.2010.06.002

Brain Stimulation (2011) 4, 50–7

www.brainstimjrnl.com

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with a distinguishable electrical waveform, called the motor

evoked potential (MEP). The International Committee of

Clinical Neurophysiology (IFCN) defined the motor

threshold (MT) as the minimum TMS machine output inten-

sity that can induce reliable MEPs (usually .100 mV), with

a probability of 50%.2

Most TMS studies require determining the MTaccurately

(i.e.,withsmalldifferencebetweenthemeasuredMTandthe

true MT value) and precisely (i.e., with little variance),

becausethechoiceofstimulatorintensityforeachparticipant

isadjustedaccordingtotheirMTs.EarlierMTdetermination

protocols were based on systematic search. According to the

protocol for MT determination proposed by the IFCN,2the

experimenter starts from a subthreshold intensity, then

increase the intensity in steps of 5% machine output until

50% of 10 to 20 consecutive pulses can induce MEPs. In

a revised IFCN protocol,3the experimenter starts from

a suprathreshold intensity, then decrease it in steps of 2%

or 5% until 50% MEP-induction can no longer be achieved

in 10 to 20 consecutive pulses. Mills and Nithi proposed

a protocol averaging an upper and lower threshold to deter-

mine MT. This protocol requires about 50 TMS pulses for

accurate MT determination.4,5

Shortening MT determination has the potential to both

save experimental time, discomfort to the subject, and

reduce the likelihood of inducing physiological changes

induced by multiple pulses. A breakthrough in MT

determination was the introduction of the ‘‘best PEST’’

method, an adaptive method based on Parameter Estimation

by Sequential Testing (PEST) and Maximum Likelihood

(ML) regression.6Unlike other systematic methods, the

‘‘best PEST’’ is model based, in that it uses an S-shaped

metric function to model the relationship between the prob-

ability of eliciting an MEP and the TMS intensity. At each

trial, the intensity that is predicted to yield a 50% proba-

bility of generating an MEP according to the model is

selected as the intensity for the next TMS pulse. This

method is effective because at each trial the stimulation

intensity is set to yield the highest (predicted) information

gain.7,8Compared with the Mills and Nithi protocol, the

‘‘best PEST’’ has been shown to determine the MT with

24 TMS pulses on average in computer simulations,6and

with 16 TMS pulses on average in experiment that used

MEP to detect MT.5

Although prior knowledge of MT is often available

before experiments and has the potential to speed up MT

determination, it has not been thoroughly used in previous

studies. Awiszus used two data points (MEP induction at

100% machine output and no MEP induction at 0%

machine output) to initialize the ‘‘best PEST,’’ which

reflects the belief about MEP induction under extreme

machine output conditions.6Borckardt et al.9found that if

an experimenter has ‘‘a reasonably accurate guess’’ of MT

and starts the PEST procedure with this guess, a nonpara-

metric version of PEST required fewer trials, although the

‘‘best PEST’’ suffered a loss of accuracy.

Knowing when to stop the procedure can furthermore

potentially speed up MT determination; care must be taken,

however, to ensure that accuracy is not jeopardized by (too)

early stopping. Mishory et al.5used a repeat-once stopping

criterion that requires two consecutive estimations with the

sameMTprediction.Borckardtetal.9requiredthatthediffer-

ence between two consecutive estimations be lower than

a threshold. In their freely distributed software, Borckardt

et al.9used a progress bar to give ‘‘a rough visual estimate

of how close the user is to reaching the rMT estimate’’; no

mathematical details were provided, however.

In this study, we propose to use Bayesian regression for

PESTtoaddtwomodificationstothe‘‘bestPEST’’methodto

determinetheMTquickly,accurately,andprecisely.Thefirst

modification is to integrate prior MT data. The second

modification is to determine a systematic and theoretically

sound stopping criterion. The use of Bayesian regression in

PEST is an established method in psychophysics,10but has

not yet been applied to TMS in general, and MT determina-

tion in particular. The Bayesianframework hastwo potential

advantages: The first advantage is that it is ideal for the

systematic incorporation of prior knowledge.11After each

trial, the likelihood that the MEP is generated by the model

is combined with the prior probability distribution of MT

probability to generate a posterior probability distribution

of MT. This ‘‘posterior’’ can then be used to determine the

thresholdandtodeterminetheintensityofthenextpulse.12,13

In this study, we leveraged two kinds of prior information

separately: (1) A distribution of MTs is often available for

the subject pool of the laboratory or the institution. We call

this the common prior. (2) In multisession experiments, the

MT determined in a previous session can be used to estimate

theMTofthecurrentsession,becausetheMTmeasuredfrom

asamesubjectisrelativelystableovertime.14Wecallthisthe

subject-specific prior. The second advantage of Bayesian

regression is that it naturally lends itself to derive a stopping

criterionbasedontheposteriorprobabilitytoensureaprede-

terminedlevelofprecision.10,15Inthisstudy,wethushypoth-

esized that combining prior knowledge with a posterior

probability-based stopping criterion in the Bayesian PEST

allows MT determination with fewer pulses than both the

IFCN protocol and the ‘‘best PEST.’’

Materials and Methods

Experimental comparison

of MT estimation methods

Ten right-handed subjects (five male and five female, age

27.7 6 3.0 SD years) gave their informed consent for study

procedures approved by the local institutional review board.

WedeterminedtherestingMToftherightFDIineachsubject

with four methods: (1) IFCN protocol; (2) ‘‘best PEST’’; (3)

Bayesian PESTwith common prior; and (4) Bayesian PEST

with subject-specific prior. Because the true MT of the

Fast estimation of TMS MT 51

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subjectsisunknown,wechosetousetheMTestimatedbythe

IFCNprotocolasthestandardforMTestimation.Allsubjects

hadtheirFDIrestingMTpreviouslymeasuredwiththeIFCN

protocol, at least 1 week before the experiment. For each

subject, all four methods were tested in a pseudo random

order, and a 10-mintue interval separated two consecutive

methods within the session.

Single-pulse TMS

Focal single-pulse TMS was delivered with a figure-of-eight

coil connected to a commercially available magnetic stim-

ulator (Magstim200).Thecoilwas placed onthe scalpat the

optimal position for stimulation of the right first dorsal

interosseus (FDI), and at a 45-degree with respect to the

posterior-anterior direction toward the right. Surface elec-

tromyographic (EMG) electrodes were attached to the skin

overthe FDImuscle usingelectrodegel andtape.Signalwas

sampled at 2 kHz with differential amplifiers (Grass Instru-

ments IP511) with a bandwidth of 1 Hz-1 kHz. Electrophys-

iologic signals from the musclewere amplified and recorded

for analysis. Participants, who sat in a chair adjusted to

a comfortable height, put their right hands on a soft pillow,

andwereinstructedtorelaxduringthestimulationsession.A

Lycra swim cap was worn over the head er to mark locations

ontheheadsothattheTMScoilcouldbereliablyplacedover

same scalp regions during the course of the test session. The

hotspotforFDIwasdeterminedwithastandardprotocol16at

the beginning of each experimental session before MT esti-

mation. A computer software displayed the EMG baseline

activity, for which good resting condition was considered

qualified if the amplitude remains within 6 20 mV. We

used the criterion that any MEP peak-to-peak amplitude

should be larger than 50 mV.

Description of MT estimation protocols

The

described.3We started from a suprathreshold intensity

determined during hotspot hunting, and decreased it by

steps of 2 % maximal stimulator output (MSO), until 5 of

10 consecutive TMS pulses can induce MEPs. If fewer

than 10 pulses were delivered but more than five induced

MEPs, the next lower intensity was tested.

The ‘‘best PEST’’ protocol was performed as previously

described.5At first, two artificial data points, MEP induc-

tion at 100% MSO and no MEP induction at 0% MSO,

were used to initialize the ‘‘best PEST.’’ Accordingly, the

first TMS trial intensity was set at 50% MSO. After each

trial, all available data were used for ML regression to

find the probit function of the MEP probability-TMS inten-

sity relationship (the probit function is S-shaped function

obtained with the cumulative distribution function associ-

ated with the normal distribution; see Supplementary

Material). The threshold parameter of this function equals

the estimated MT. The next TMS pulse intensity was set

IFCN protocolwas performedas previously

to this estimated MT and the procedure continued until

the repeat-once criterion was met. The experimenter manu-

ally entered the TMS intensity and the resulting MEP

observation (0 or 1) for each trial, as prompted by inhouse

developed software. After the stopping criterion had been

reached, a visual display on the computer screen indicated

that the procedure should be stopped.

The Bayesian PEST protocol was tested with both

common and subject-specific priors. In both cases, and as

illustratedinFigure1,thismethod started fromapriordistri-

butionofMT,modeled byaGaussian distributionwith mean

MT0and standard deviation s0. These parameters will be

determined in computer simulations (see below). Bayesian

probit regression was performed on all available data before

the delivery of each TMS pulse. The intensity of the next

TMSpulsewasthensettobetheMTpredictedbytheregres-

sion.Afterthisnextpulse,boththeindependentvariable(the

intensity)andthebinarydependentvariable(whetherMEPis

observed or not) were added to the entire dataset, and a new

regression was carried out on the increased dataset to update

the MT distribution probability (Figure 1). The procedure

was iterated until the stopping criterion was met.

ThestoppingcriterionusedintheBayesianPESTisbased

on the width of the MT posterior probability distribution.15

Specifically, the (1-a)% probability interval of MT, the

(12 a)PI, is the range of MT [ql, qu] corresponding to

Zqu

ZN

where ‘‘Posterior(MT)’’ is the posterior distribution of

MT, and ql and qu are the lower and upper bounds of

MT(12 a)PI. When qu-qlwas less than a specific value,

that we called ‘‘maximal(12 a)PI width,’’ the MTestimation

procedure was stopped.10The maximal(12 a)PI width will

be determined in computer simulations, as we now discuss.

2N

PosteriorðMTÞdMT5

PosteriorðMTÞdMT512a

ql

2;

ð1Þ

Computer simulations to determine

MT prior distributions and maximal95PI width

We generated synthetic TMS data with Monte Carlo simula-

tions, by building 10 data generators with probit regression

based on 10 datasets previously collected in TMS MT

estimation, as previously described.6,9Each data generator

was associated with one probit function determined by the

data fromonesubject. Givena TMSintensity, thedatagener-

ator stochastically generated 1 or 0 (MEP or no MEP) with

probability calculated according to the probit function. The

true MT of a data generator was equal to the value of the

threshold parameter of the probit function.

Gaussian distributions were used to model the priors. The

common prior mean MT0and standard deviation s0were

determined with the mean and standard deviation of the

true MTs of the data generators. We found MT05 40%

52F. Qi et al

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MSO and s05 8% MSO. To determine the maximal95PI

width for Bayesian PEST with the common prior, we

selected the largest maximal95PI width that enabled the

Bayesian PEST to yield an average estimation error not

significantly different from that of the simulated ‘‘best

PEST’’ with the repeat-once criterion.5We tested maximal

95PI widths of 21, 11, 9, 7, 6, and 5% MSO.

Because the mean MT0of the individual subjects was not

available, we assumed that the prior mean MT0was in the

range defined by MT 6 10% MSO for each data generator,

where MT was the true MT of the corresponding data

generator. The standard deviation s0of the subject-specific

prior was taken as 3% MSO (see Supplementary Material

for rationale). To determine the maximal95PI width for

Bayesian PEST with the subject-specific prior, we tested

maximal95PI widths of 5, 7, and 9% MSO. We selected the

maximal95PI width that enabled the Bayesian PEST to yield

anaveragestoppingerrornotsignificantlydifferentfromthat

given by the ‘‘best PEST’’ with the repeat-once criterion5

when MT0was in the range of MT 6 5% MSO. This range

of true MT 6 5% MSO for MT0was chosen based on our

observations in the laboratory that the difference of

between-session MT in healthy subjects is less than 5%

MSO. This observation is consistent with the data shown in

Figure 2,14in which six of seven healthy subjects had

between-session MT differences less than 5% MSO.

To evaluate the stopping error, we compared the

estimated MT against the true MT of the corresponding

data generator, and used the relative error as stopping error:

Relative Error 5jTrue MT2Model Estimated MTj

True MT

ð2Þ

We repeated 50 simulation runs to evaluate the relative

error for each condition. Further details and rationale of the

computer simulation can be found in the Supplementary

Material.

Data analysis

We compared the MTs determined with each method with

those measured by the IFCN protocol by paired t test and

Pearson’s correlation, taking the IFCN protocol has the

published standard recommendation for MT estimation.

Figure 1

after different number of trials in the Bayesian PEST procedure.

The true MT in this simulated subject was 40% MSO. In each

panel, the x-axis represents MT in % MSO, and the y-axis repre-

sents probability. A, The prior is a Gaussian distribution with

mean 50% MSO and standard deviation 4.5% MSO. B, Posterior

MT distribution after three trials. C, Posterior MT distribution

after 14 trials. D, Posterior MT distribution after 20 trials.

Illustration of the probability distributions of MTs

Figure 2

‘‘best PEST’’ (ML) and Bayesian PEST. Mean relative errors of

10 data generators as a function of stopping trials, for the ‘‘best

PEST’’ (square) and for different maximal95PI width (21, 11, 9,

7, 6, and 5 from left to right) for the Bayesian PEST (triangles).

The maximal95PI width tested is labeled as a number next to

each triangle data point. Horizontal bars represent 6 1 standard

deviation for stopping trials; vertical bars represent 6 1 standard

deviation for the relative error.

Comparison of stopping trial and relative error of

Fast estimation of TMS MT53

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We also examined the individual differences among the

MTs measured by all methods. We considered a difference

of 5% MSO from the IFCN estimation a large deviation

because the IFCN protocol recommended TMS intensity

steps of 2-5% MSO.3To evaluate the speed of each method,

we compared the numbers of trials with paired t tests. The

significance level for all statistical tests was P , .05.

Results

Demonstration of MT distribution

change in Bayesian PEST

A Bayesian PEST simulation that demonstrates the change

in MT distribution after incoming data is available is shown

in Figure 1. The true MT of the artificial data generator is

40% MSO. The prior is a broad Gaussian distribution

with mean at 50% MSO and standard deviation at 4.5%

MSO (Figure 1A). As the number of pulses available

increases, two changes happen to the estimated distribution

of MT (Figure 1B-D): (1) the mean shifts towards the true

MT (the accuracy increases), and (2) the standard deviation

of the estimator decreases (the precision increases). The

second change will eventually allow the posterior distribu-

tion to satisfy the(12 a)PI criterion.

Using computer simulations

to determine maximal95PI width

To determine the maximal95PI width for the Bayesian PEST

with common prior, we compared the ‘‘best PEST’’ and the

Bayesian PEST in simulation. The ‘‘best PEST’’ stopped,

on average, at 10.7 6 0.6 (mean 6 standard deviation) trials

with a relative error of 0.027 (Figure 2, squares). As the

maximal

95PI width decreased, the stopping error of

Bayesian PEST decreased, but the number of TMS trials

required increased. Bayesian PEST was as accurate as the

‘‘best PEST’’ (paired t test, P 5 .605, relative error 0.027)

formaximal95PIwidthequalto7%MSO.Forthiscondition,

theBayesianPESTstoppedafter6.362.1(mean6standard

deviation) trials, which is significantly lower than that of

‘‘best PEST’’ (paired t test, P , .0001). The maximal95PI

width was thus determined as 7% MSO for the Bayesian

PESTwith common prior.

To determine maximal95PI width for the Bayesian PEST

with subject-specific prior, we considered maximal 95PI

widths of 5, 7, and 9% MSO with MT0within the range

MT610%MSO.ThetoprowofFigure3showsthestopping

error (Figure 3A) and the number of trials (Figure 3B) when

the maximal95PI width was 5% MSO. In the range of true

MT 6 5% MSO, the average stopping relative error was

below 0.021 (Figure 3A), and the average number of trials

was less than 15 (Figure 3B). The middle row of Figure 3

showsthestoppingerror(Figure3C)andthenumberoftrials

(Figure 3D) when the maximal95PI width was 7% MSO.

In the range of true MT 6 5% MSO, the average stopping

relativeerror was below 0.027 (Figure 3C), which was equal

to the stopping error of the ‘‘best PEST’’ (Figure 2 square),

and the average number of trials was less than 6

(Figure 3D). The lower row of Figure 3 shows the stopping

error (Figure 3E) and the number of trials (Figure 3F)

when the maximal95PI width was 9%. In the range of true

MT 6 5% MSO, the average stopping relative error was

notlowerthan0.027(Figure3E).Inlightofthesesimulations

results, the maximal95PI width was determined as 7% MSO

for the Bayesian PESTwith subject-specific prior.

Experimental comparison

of MT estimation methods

Our experiment results showed the Bayesian PEST with

subject-specific prior required the fewest number of TMS

pulses (Figure 4A). Specifically, the number of pulses are

29.9 611.6 (mean 6 SD) for the IFCN method, 12.2 65.5

for the ‘‘best PEST’’ method, 6.6 6 2.6 for the Bayesian

PEST with common prior, and 2.7 6 0.5 for the Bayesian

PEST with subject-specific prior. The subject-specific prior

required fewer pulses than the common prior (paired t test,

P, .001), which itself required fewer trials than the no prior

‘‘best PEST’’ (paired t test, P 5 .016). Finally, the ‘‘best

PEST’’ required fewer pulses than the IFCN method (paired

t test; P 50.0046), as previously reported5(Figure 4A).

There was no difference in average in the estimated MTs

betweentheIFCN,the‘‘bestPEST,’’theBayesianPESTwith

common prior, and the Bayesian PESTwith subject-specific

prior (Figure 4B). Specifically, for paired t test on the null

hypothesis that the estimated MTs of two methods are the

same, the P value for the ‘‘best PEST’’ and the IFCN method

was .31, the P value for the Bayesian PEST with common

prior and the IFCN method was .84, the P value for the

Bayesian PEST with subject-specific prior and the IFCN

method was ..99. The difference was 0.7 6 2.1% MSO

between the ‘‘best PEST’’ and the IFCN method, 0.2 6

3.1% MSO between the Bayesian PESTwith common prior

and the IFCN method, and 0.0 6 1.6% MSO between the

Bayesian PEST with subject-specific prior and the IFCN

method. The MT estimated by the IFCN method and by the

‘‘best PEST’’ were significantly correlated with coefficient

0.95 (P , .001), the MT estimated by the IFCN method

and by the Bayesian PESTwith common prior were signifi-

cantly correlated with coefficient 0.879 (P , .001), and the

MT estimated by the IFCN method and by the Bayesian

PEST with subject-specific prior were significantly corre-

lated with coefficient 0.986 (P , .001).

The MTs estimated by each method for individual

subjects are shown in Figure 4C. The estimation difference

between IFCN method and ‘‘best PEST’’ for all subjects

was below 4% MSO. The estimation difference between

Bayesian PEST with common prior and IFCN method for

one subject was 6% MSO (‘‘1’’ marker in Figure 4C), and

for the other of nine subjects was below 5% MSO. The

54F. Qi et al

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estimation difference between Bayesian PESTwith subject-

specific prior and the IFCN method was below 3% MSO for

allsubjects.Weconsideredadifferenceof5%MSOfromthe

IFCN estimation a large deviation because the IFCN recom-

mended using 2-5% MSO as step size for MT estimation.

Thus, except for one subject in the Bayesian PEST with

common prior, all deviations are acceptable.

Discussion

Our results showed that the Bayesian PEST with posterior

95PI stopping criterion is a fast, precise, and accurate MT

determination method. Our experiment showed that, on

average, the common prior requires seven TMS trials and

the subject-specific prior requires as few as three TMS trials

(Figure 4A). The MT determined by the Bayesian PEST

methods were not different from that estimated by the IFCN

method (Figure 4B), except for one subject, for which a 6%

MSO difference was found between the MT estimated by

IFCN method and the MT estimated by Bayesian PEST

with common prior (Figure 4C).

Introduction of prior knowledge in the Bayesian frame-

work can largely speed up the determination of the MT. It

may seem surprising that MT can be estimated in as few as

three trials when a subject-specific prior is available. This

can be understood as the prior information accounts for the

information provided by multiple trials. Indeed, a posterior

Figure 3

(C, D), and 9 (E, F) % MSO. In each subplot, the MT0changes from true MT 210% MSO to true MT 110% MSO. Bars represent

average 6 1 standard deviation across results of 10 data generators. When the maximal95PI width was 7% MSO and MT0was in the range

of true MT 6 5% MSO, Bayesian PEST stopping relative error was less than the ‘‘best PEST’’ stopping relative error 0.027, therefore we

selected the maximal95PI width of 7% MSO.

The stopping relative error and the number of trials of Bayesian PEST when the maximal95PI widths were equal to 5 (A, B), 7

Fast estimation of TMS MT 55

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after N trials can be viewed as the prior before the N 1 first

trial, and having a prior at the beginning is equivalent to

starting with multiple trials.

Previous psychophysics studies suggested that Bayesian

PEST requires at least 20 samples to be collected because

of the concern that too few samples may not be sufficient

for threshold estimation.10,12In this study, fewer samples

are adequate because there are two major differences

between our study and these studies: (1) We focused on

the field of TMS and used sound domain-specific prior,

whereas other studies usually examined the algorithm in

general and used uniform prior.12(2) TMS has a minimal

tunable intensity unit that is 1% MSO. Our estimates based

on the results of Alcala-Quintana and Garcia-Perez12indi-

cate that after 10 trials, the error of MTestimation can be as

small as 0.2% MSO, which is lower than the possible 1%

MSO tunable in TMS experiments.

Our current Bayesian method has three possible limita-

tions. First, we used Gaussian distribution to model the

prior for MT. Because true MT cannot be less than 0%

MSO in experiment, the Gaussian prior is in theory only

suitable for modeling the prior knowledge when its tail is

small below zero. However, even if a Gaussian prior has

a relatively large tails outside the range 0 and 100% MSO,

subsequent Bayesian PEST sampling will reduce the tail.

Furthermore, as our results show, and at least for healthy

subjects, the prior distributions are largely contained within

the 0-100% MSO range. If the MTs are expected to be near

the 0% MSO boundary (which would generate very large

tails with a Gaussian prior), bounded prior distributions

such as the Gamma distribution can be used.

Second, if the mean of the prior is different from the true

MT, both the number of trials and error increase (Figure 3).

When the prior is neither a uniform distribution nor the

same as the true distribution, a bias is introduced into the

MTestimation. However, the stopping criterion can mitigate

effect of the prior bias: As the number of pulses increases,

precision improves together with accuracy (Figure 1), the

95PI stopping criterion controls the stopping accuracy

(Figures 2 and 3). With our assumption that the difference

between the MT0and true MT is within 5% MSO, this

amount of prior bias can be well controlled by 7% MSO

maximal95PI width; the relative error is then lower than

therelativeerrorofthe‘‘bestPEST’’(0.027).Ifinaparticular

clinical or experimental setting, it isimportant thatthe MTis

determined with a very high accuracy (for safety reasons for

instance), then the assumption can be made that the differ-

encebetweenthepriormeanMT0andtrueMTcanbeaslarge

as 10% MSO; in this case, a stopping criterion of 5% MSO

maximal95PIwidthshouldbechosen.Asaresult,therelative

error will decrease (Figure 3A) and the number of trials will

increase(Figure3B).Ifasafer(althoughpresumablylonger)

Figure 4

MTs measured. For one subject there was a 6% MSO difference between MT measured by the IFCN method and the Bayesian PEST

with common prior (filled circle); for all other subjects, this difference was less than 5% MSO. All error bars represent 6 1 standard devi-

ation. ‘‘ML,’’ ‘‘best PEST’’ with the stopping-once criterion; ‘‘Common,’’ Bayesian PEST with common prior; ‘‘Subject,’’ Bayesian PEST

with subject-specific prior. The marks ‘‘*’’ indicate statistically significant differences. The mark ‘‘1’’ indicates the MT measured by

Bayesian PEST was 6% MSO lower than the MT measured by IFCN method, for the subject.

Comparison of MT determination methods. A, Average number of pulses used. B, Average MT estimated. C, Single subject

56 F. Qi et al

Page 8

approach is required, ML regression can be used for the final

MT estimation based on all collected data. In such case,

Bayesian regression could then only be used for determina-

tion of the next sampling intensity. The effect of prior with

this ‘‘hybrid’’ method would thus only bias which intensities

are sampled, but would not affect the final MTestimation.

Third, because the Bayesian PESTuses all previous data,

erroneous data are a potential problem for both ‘‘bestPEST’’

and Bayesian PEST. During MT estimation process, MEP

identification may be inaccurate because of the volitional

muscle twitch or simply wrong data entry. Nonparametric

PEST9does not explicitly uses all data and is robust against

erroneous data. Besides careful experimental operation,

a systematic evaluation of the robustness of these techniques

or the development of robust Bayesian regression for PEST

may be necessary in future studies.

In our study, as in Awiszus,6we assumed that the hot-

spot, defined as the optimal position that has the lowest

MT on the scalp for placing the TMS coil, had already

been found before MT estimation. In actual TMS experi-

ments, however, locating the hotspot is not a trivial task.

Further, hotspot location and MT determination are often

carried out simultaneously. TMS studies would thus greatly

benefit from adaptive methods that extend our proposed

Bayesian adaptive MT determination method with the addi-

tion of priors in two-dimensional space to concurrently

optimize the sampling location and the sampling intensity.

Acknowledgments

We thank Dr. Beth Fisher director of the NAIL TMS

laboratory at USC for her help and support during this

work; Erica Pitsch (PT, MPT, Division of Biokinesiology,

University of Southern California) for sharing TMS

threshold data; and Dr. Zhong-Lin Lu for his comments

on a previous draft (Department of Psychology, University

of Southern California).

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Supplementary data

Supplementarydataassociatedwiththisarticlecanbefound,

in the online version, at doi:10.1016/j.brs.2010.06.002

Fast estimation of TMS MT57