Original Research

BOLD-fMRI Response Vs. Transcranial MagneticStimulation (TMS) Pulse-Train Length: Testing forLinearity

Daryl E. Bohning, PhD,1* Ananda Shastri, PhD,1 Mikhail P. Lomarev, MD, PhD,1,2

Jeffrey P. Lorberbaum, MD,3 Ziad Nahas, MD,3 and Mark S. George, MD1,3–5

Purpose: To measure motor and auditory cortex blood ox-ygenation level-dependent (BOLD) functional magnetic res-onance imaging (fMRI) response to impulse-like transcra-nial magnetic stimulation (TMS) pulses as a function oftrain length.

Materials and Methods: Interleaved with fMRI at 1.5 T,TMS pulses 0.3-msec long were applied at 1 Hz to the motorcortex area for thumb. Six subjects were studied in a TR �1 second session administering trains of 1, 2, 4, 8, and 16pulses, and a TR � 3 seconds session administering trainsof 1, 2, 4, 8, 16, and 24 pulses. A simple hemodynamicmodel with finite recovery and saturation was used toquantitatively characterize the BOLD-fMRI response as afunction of train length.

Results: In both the activations directly induced in motorcortex by TMS and the indirect activations in auditory cor-tex caused by the sound of the TMS coil firing, the BOLD-fMRI responses to multiple pulses were well described by asummation of single-pulse impulse functions.

Conclusion: Up to 24 discrete pulses, BOLD-fMRI re-sponse to 1 Hz TMS in both motor cortex and auditorycortex were consistent with a linear increase in amplitudeand length with train length, possibly suggesting that stim-uli of 1 to 2 seconds may be too long to represent impulses.

Key Words: transcranial magnetic stimulation (TMS);fMRI; train length; BOLD response linearity; motor cortexJ. Magn. Reson. Imaging 2003;17:279–290.© 2003 Wiley-Liss, Inc.

FUNCTIONAL MAGNETIC RESONANCE imaging (fMRI)using blood oxygenation level-dependent (BOLD) con-trast (1–3) is well established as a tool for studyingbrain function. Although it is also well known that theBOLD response is highly correlated with blood flow(4–6), and, in turn with neuronal activity in the brain(7), despite intensive study, the exact relations betweenthe BOLD response and neuronal activity is still notclearly defined. Ideally, one would like to have a quan-titative relation describing the BOLD signal in terms ofthe entire chain of underlying processes that are initi-ated by the discharge of neurons in the cerebral cortexand that make up the brain’s response to a particularstimulus.

Originally, because it was the simplest thing to do,because the technology was less sophisticated and be-cause early data were reported to be consistent with alinear response (8–11), it was first assumed that a lin-ear model described the relation (10,12,13). That is, itwas assumed that the response to a single, very shortstimulus, a so-called impulse response function, couldbe determined, and that the behavior of the system foran arbitrary pattern of stimuli could be described bysuperimposing the individual impulse response func-tions of the series of short stimuli making up the stim-ulus pattern. Mathematically, this is equivalent to say-ing that the output function can be found by convolvingthe stimulus input function with the impulse responsefunction. Alternatively, if the impulse response functionis known, the neuronal activation pattern can be esti-mated from the fMRI response by deconvolving the im-pulse response function (14). Most fMRI analysis tech-niques have been based on the assumption that thesystem is linear (15).

Even early on, however, Binder, et al (16) reportedthat auditory response was nonlinear at shorter stim-uli, and Boynton, et al (8) noted that visual cortex (V1)responses to the shortest (3 seconds) stimulus tended

1Department of Radiology, Medical University of South Carolina,Charleston, South Carolina.2The Institute of the Human Brain, St. Petersburg, Russia.3Department of Psychiatry, Medical University of South Carolina,Charleston, South Carolina.4Department of Neurology, Medical University of South Carolina,Charleston, South Carolina.5The Ralph H. Johnson Veterans Hospital, Charleston, South Carolina.Contract grant sponsor: National Alliance for Research in Schizophre-nia and Depression (NARSAD); Contract grant sponsor: Ted and VadaStanley Foundation; Contract grant sponsor: Borderline PersonalityDisorder Research Foundation; Contract grant sponsor: NIMH R21.Presented as a poster at ISMRM 2000.*Address reprint requests to: D.E.B., Radiology Department, MedicalUniversity of South Carolina, 169 Ashley Avenue, Charleston, SouthCarolina 29425. E-mail: bohninde@musc.eduReceived May 9, 2002; Accepted October 30, 2002.DOI 10.1002/jmri.10271Published online in Wiley InterScience (www.interscience.wiley.com).

JOURNAL OF MAGNETIC RESONANCE IMAGING 17:279–290 (2003)

© 2003 Wiley-Liss, Inc. 279

to overestimate the response to the longer stimuli. Theyattributed this to neural adaptation. With the increas-ing use of event-related designs (12,13) and carefulscrutiny of the response as a function of stimulusstrength, duration, and interstimulus intervals, evi-dence began accumulating that the response is nonlin-ear, with the most consistent finding being that shortduration stimuli produced responses larger than ex-pected from a linear system (16–18). Aside from theimportance this has for fMRI data analysis (14,19,20),this nonlinear behavior has drawn increasing attentionas a means to explore and better define the relationshipbetween neuronal output and the BOLD-fMRI signal,and, ultimately, to find a mathematical relation relatingthe two (5,14,20). For example, this nonlinearity mightbe a result of an overshoot in the neuron activity inresponse to the stimulus onset, response saturation, ornonlinearities within the hemodynamics, such asslower blood volume changes or the nonlinear depen-dence of oxygen extraction on flow, which translate theneuronal activity into the BOLD signal (5,21).

Common to the majority of these investigations is theuse of very short stimuli, first alone, to define the im-pulse function, and then in series, varying the inter-stimulus intervals and number of stimuli to explore therelationship (14,19,22). The first step being to demon-strate the nonlinearity, and the next step to quantify it.

Transcranial magnetic stimulation is a technique inwhich a pulsed magnetic field from a small coil is usedto create localized neuron depolarizing currents in thecerebral cortex (23). It has been used to investigatenerve function for over a decade (24), and is finding avariety of applications in neuropsychiatry (25). It is alsopossible to combine transcranial magnetic stimulation(TMS) with fMRI to visualize regional brain activity inresponse to direct non-invasive stimulation (26–30). Asa noninvasive way of applying an extremely short (0.2–0.3 msec) stimulus directly to the cerebral cortex, itprovides a unique means for testing the linearity of theBOLD-fMRI neuronal discharge relationship.

Because TMS directly induces neuronal depolariza-tion, it is believed that the associated BOLD fMRI re-sponse does not depend on any intervening sensory orcognitive processing, which may itself affect the form ofthe response. Though artificial, it uniquely and nonin-vasively provides what might be called a true impulsefor testing the form of the BOLD-fMRI response and itslinearity with both pulse frequency and train length. Atthe same time, the auditory response caused by theaccompanying short “snap” of the TMS coil as it is firedprovides a good physiologic reference because it mustbe processed in the same way as other auditory chal-lenges. Figure 1b diagrams a conceptualization distin-guishing the direct and indirect activations, and pro-vides an idea of the relative routes that might beinvolved. The separation into input and output neuronsfollows the suggestion of Logothetis, et al (7) that BOLDactivation may actually reflect more the neural activityrelated to the input and the local processing in anygiven area, rather than the spiking activity commonlythought of as the output of the area. To give an idea ofthe approximate magnitude of the cross-collosal delay,dcc, measurements with an electroencephalogram

(EEG) (31) immediately after TMS over the motor cortexhave shown the response in the contralateral motorcortex lags that in the ipsilateral motor cortex by 5–10msec. If the response functions at every step are linear,it would be possible to treat them as a series of convo-lutions and, ultimately, lump them into a single convo-lution with a cumulative delay.

A cautionary note is important here. A direct neuro-nal discharge stimulated by TMS is artificial and de-pends on the TMS coil’s field distribution, as well as thenatural neuronal functional organization of the cortex,so the associated BOLD response may well arise from adifferent neuronal discharge pattern than that under-lying strictly physiologic stimulations. Although thismeans that the BOLD response to TMS may not bedirectly comparable to that for physiologic stimula-tions, it also means that that difference might be usedto explore the underlying neuronal discharge.

Typically applied in trains, electrophysiologic studieswith TMS have reported inhibition when applied at fre-quencies of � 1 Hz (32) and facilitation when applied atfrequencies � 1 Hz (33). This implies nonlinearity, butwith respect to inter-stimulus interval (ISI) rather thanstimulus train length.

Though interleaved TMS/fMRI has been successfullyused to detect the BOLD-fMRI response to TMS, theTMS applications were limited to a single pulse (28),fixed length trains of 18–21 pulses delivered at 1 Hz(26,29), or a series of 1-second-long, 10-pulse trains(30). None of these studies were able to address thequestion of the linearity of the BOLD response.

The objective of this work was to use 1-Hz TMS inter-leaved with fMRI to measure the amplitude and dura-tion of the BOLD-fMRI response in motor and auditorycortex as a function of TMS pulse-train length. A fur-ther objective was to fit the unique direct (artificial)motor cortex response induced by TMS, and the indi-rect (physiologic) auditory cortex response accompany-ing it, to a nonlinear hemodynamic model with finiterecover and saturation to determine if the two re-sponses differ, to what degree they show nonlinearity,and if there is any sign of the negative correlation ofTMS response with train length observed with TMS/PET (34) or the inhibition or facilitation observed withelectrophysiologic techniques.

MATERIALS AND METHODS

General Experimental Design

Using interleaved TMS/fMRI (26,27) in a 1.5-T clinicalMRI scanner (EDGE, Rel.9.4, Picker International, Inc.,Highland Heights, OH), BOLD sensitive single-shotecho-planar imaging (EPI)-fMRI images were acquiredcontinuously while individual TMS pulses, at a fre-quency of 1 Hz and 120% of motor threshold (MT), wasapplied over the left motor cortex for the thumb indifferent length trains. The in-magnet stimulation wasperformed using a Dantec MagPro� (Dantec MedicalA/S, Skovlunde, Denmark) with special non-ferromag-netic TMS coil of figure-of-eight design. The details ofthe method have been published elsewhere (26,27).TMS stimulation of thumb motor cortex was chosen

280 Bohning et al.

because it allowed independent verification of properfunctional location of the TMS coil in the form of thumbmovement and is the standard area used to obtain MT.

Six healthy male volunteers (mean age 42.7 � 10.0years) were studied, in two different scan sessions per-formed several months apart, under a protocol ap-proved by the Medical University of South Carolina’sInstitutional Review Board for Human Research.

In the first scan session, using a TR of 1 second forhigh temporal resolution, pulse trains of 1, 2, 4, 8, and16 pulses were given in pseudo-random order in fiveconsecutive 39-second epochs, with the entire cycle

being repeated five times for a total scan length of 16.25minutes. In the second scan session, using a TR of 3seconds to allow a longer recovery period and extendedpulse train, pulse trains of 1, 2, 4, 8, 16, and 24 pulses,again in pseudo-random order, were given in six 60-second epochs, with the cycle being repeated four timesfor a total scan length of 24.00 minutes. Coronal sec-tions (102 � 64 matrix reconstructed to 128 � 128images, field of view [FOV] � 270 mm, TR � 1 second,and � � 72° [or TR � 3 seconds and � � 88°], TE � 40.0msec, slice thickness � 5 mm, slice gap � 1.5 mm, withfrequency-selective fat saturation), positioned to bilat-

Figure 1. a: Z-map for individual showing M1 activations directly induced in the motor cortex by TMS (ipsimotor) and auditoryactivations induced indirectly by its sound. b: Conceptual diagram for TMS action, the n functions representing input andoutput neuron activity in each area; h, the hemodynamic response function; d, the various within-area and between-area delaysin the circuit; and s functions, the BOLD-fMRI signals.

Linearity of BOLD-fMRI Response to TMS 281

erally include motor and auditory cortex, were acquiredevery second (or three seconds).

In the TR � 1 second session, the TMS pulses weregiven 20 msec after the beginning of each volume (eightslices) acquisition. This avoided the radiofrequency (RF)fat saturation and excitation pulses for the acquisitionof the first slice, and gave 105 seconds for the effects ofTMS pulse to dissipate. As will be described in theresults section, this proved inadequate, and resulted insubstantial artifact. In the TR � 3 second session, TMSpulses were applied 20 msec after the beginning ofevery fourth slice of the volume (12 slices) acquisition.This again avoided the RF fat saturation and excitationpulse, but this time gave 230 msec for the effects of theTMS pulses to dissipate.

TMS Coil Placement

Before the subject was moved into the scanner, the TMScoil, padded with a napkin and with vitamin E capsulesplaced at its ends to help locate it in the structuralimages, was rigidly mounted in the MRI head coil in theapproximate position required to activate the individu-al’s motor cortex for right thumb. Then, while the TMScoil was intermittently pulsed, initially at high intensity(90% machine output when MT was unknown, lower forsubjects whose approximate MT was known from pre-vious studies), the subjects adjusted their head posi-tion until visible movement of the contralateral (right)hand abductor pollicis brevis (thumb) was consistentlyinduced. Although formal electromyogram (EMG) deter-mination of position and MT were not performed, aclose concordance has been found between EMG-deter-mined MT and visually-determined MT using this Dan-tec system (35). The subject’s head was then stabilizedwith foam-padded inflatable restraints. Finally, MT wasdetermined by gradually decreasing stimulation inten-sity until movement (slight thumb twitch) was observedapproximately 50% of the time. The stimulator wasthen set to 120% of the subject’s MT. After scannertuning and acquisition of T1-weighted reference images,and before the TMS/fMRI acquisition was started, theTMS coil-to-head relation was rechecked with one ormore individual manual TMS pulses. Subjects woreearplugs and were told to lie quietly with their eyesclosed during the scan.

Data Processing

After acquisition, the raw image data were transferredto a remote workstation for offline reconstruction, andthen processed as described below.

Motion Check

A check to be certain that subject movement was lessthan 3 mm along all three major axes was performed oneach image set using MEDx 3.0 (Sensor Systems, Inc.,Sterling, VA), eliminating two of the six data sets fromeach of the sessions. The images in the remaining datasets were then coregistered to a common mean imageand the motion check performed again to be certainthat movement was reduced to less than 1.5 mm (lessthan half a pixel).

T-Test for Areas of Activation

Paired t-tests compared the images acquired during theinterval 3–15 seconds after the first TMS pulse in eachepoch (TMS) to the images acquired in an interval of thesame length close to the end of the epoch (REST) togenerate Z-maps, images representing the pixel-by-pixel Z-values for the comparison between the two con-ditions, TMS, and REST.

BOLD Activity Time Course

Clusters of pixels, distinguished by relatively high locallevels of activation, were identified in the Z-maps in theareas of motor and auditory cortex. First, the Z-valuewas set at a relatively low level where activations couldbe seen scattered throughout the brain to gain an im-pression of the noise level. Then, the Z-value thresholdwas systematically raised until the scattered activa-tions were excluded, but, if possible, activations in mo-tor and auditory cortex remained. The time course ofthe BOLD signal in each cluster was obtained by ex-tracting the mean intensity of the voxels in the clusterfrom the functional images acquisition by acquisition,and averaging over the cycles. Time courses for eachsubject were then averaged point-by-point across sub-jects to obtain a subject and cycle averaged time course,normalized by the mean signal during the REST inter-val in the single-pulse epoch. The error bars representthe standard error (SE) of the subject average.

Hemodynamic Response Model

To quantify the dependence of the BOLD response onTMS pulse interval (i.e., rate of delivery), as well asnumbers of pulses delivered, a parameterized modelwas created. This model (Eq. [1]) consisted of a productof three functions separately dependent on the threevariables: t, the time after the pulse; �, the time sincethe previous pulse; and, n, the position of the pulse inthe train, along with five parameters:

f(n,�,t)�s(n)�r(�)�h(t) (1)

h(t) is a hemodynamic response function similar to thatgiven by Kruggel and von Cramon (20):

h(t) � �b1

b3�e�

(t�b2)2

2b32

with the parameters: b1, b2, and b3, representing re-sponse amplitude, lag, and duration, respectively. r(�) isa simple exponential interstimulus interval recoveryfunction given by:

r(�) � 1�e��/�1

with the parameter, �1, representing a recovery time,and s(n) is a simple exponential saturation function notunlike that used by Robson, et al (17):

s(n) � e�(n�1)s1

282 Bohning et al.

with the parameter s1 representing a response satura-tion (habituation) or enhancement (facilitation). The re-covery function, r(�), relates to the degree to which theBOLD response to a TMS pulse recovers in the time, �,since the previous TMS pulse in the train; the timebetween trains is long enough that there is full recovery.The saturation function, s(n), relates to the progressivesaturation or facilitation (in the general sense of thewords) of the BOLD response to a TMS pulse as a func-tion of the pulse’s position in the train. That is, is theresponse progressively decreasing or increasing withthe length of the train.

Figure 2a shows a plot of the hemodynamic responsefunction, and Figure 2b shows the simulated responsefor the first and fifth pulses in a train of five pulses,delivered at the rate of 0.2 Hz, to indicate the combinedeffects of recovery and saturation on pulse size.

The complete model function was computed by pro-gressively summing the function, f(n,�,t), representingthe individual TMS pulses, taking into account the ap-propriate recovery delay since the previous pulse, �, andposition in the train, n, of each pulse. This gave a totalof five parameters, excluding the baseline normaliza-tion. A nonlinear fit (Levenberg-Marquardt) was thenperformed to find the combination of parameters thatgave the best fit to the BOLD response curves.

An attempt was also made to fit the undershoot andrecovery part of the curve by adding to the hemody-namic response model function, f(n,�,t), its negative,scaled and with a lag relative to the positive response.

This gave three additional parameters to fit: undershootamplitude, lag, and dispersion.

RESULTS

TR � 1 Second, 1-, 2-, 4-, 8-, 16-Pulse Train Data

The data for four of the six subjects met the motioncriterion for complete analysis. Figure 1a shows a sam-ple Z-map for a slice with bilateral activations in motorand auditory cortex areas. Figure 3 shows the cycle-averaged time course plots of BOLD response vs. TMStrain length for ipsilateral motor cortex (a), contralat-eral motor cortex (b), ipsilateral auditory cortex (c), andcontralateral auditory cortex (d) activations, averagedover the five subjects. There is a progressive increase inthe amplitude of the responses with pulse-train lengthsfrom 1 to 8, and then there appears to be a leveling off,or even a decrease, with the 16-pulse train. This is anartifact, obvious in the 16-pulse trains, but present forthe other trains as well. It was found that, due to theshort TR, the lingering affects of firing the TMS coil inthe MRI magnet was disrupting the acquisition of thefMRI images acquired immediately after. An explana-tion of this phenomenon can be found in Shastri, et al(27). As one can see in the plots, the affected time pointsduring the application of the TMS pulses have beendiscarded and are not used in the model fits.

Figure 2. BOLD-fMRI response model for 1 Hz TMS trains. a: h(t), the response to a single TMS pulse; b: r(�) and s(n), therecovery and saturation functions, respectively; and, for reference, c: the simulated response to the first and fifth TMS pulsesfor a 0.2-Hz TMS train.

Linearity of BOLD-fMRI Response to TMS 283

Figure 3. BOLD-fMRI response (TR � 1 second) to 1-, 2-, 4-, 8-, and 16-pulse trains of TMS pulses compared with nonlinear fitto model, allowing all five parameters to vary: ipsilateral motor (a), contralateral motor (b), ipsilateral auditory (c), andcontralateral auditory (d) areas.

Figure 4. BOLD-fMRI response (TR � 3 seconds) to 1-, 2-, 4-, 8-, 16-, and 24-pulse trains of TMS pulses compared withnonlinear fit to model, allowing all five parameters to vary: ipsilateral motor (a), contralateral motor (b), ipsilateral auditory (c),and contralateral auditory (d) areas.

284 Bohning et al.

TR � 3 Seconds, 1-, 2-, 4-, 8-, 16-, 24-Pulse TrainData

Again, the data for four of the six subjects met themotion criterion for analysis, although only three indi-viduals were common to both the TR � 1 and the TR �3 final groups of four. Figure 4 shows the cycle- andsubject-averaged BOLD response time course plots inthe ipsilateral motor cortex (a), contralateral motor cor-tex (b), ipsilateral auditory cortex (c), and contralateralauditory cortex (d). Again the data show a clear mono-tonic increase with train length for trains from 1 to 8pulses long, but, in these data, the trend obviouslycontinues through the 16- and 24-pulse trains.

BOLD Response Nonlinear Model

The data were compared with the model in two differentways to check for nonlinearities. In the first compari-son, the data for all train lengths were fit to the com-plete model, f(n,�,t; b1,b2,b3,r1,h1), allowing all five pa-rameters to vary in the nonlinear fitting procedure. Thefitted parameters, averaged over the four subjects ineach group for ipsilateral and contralateral motor andipsilateral and contralateral auditory, are given in Table1 for both the TR � 1 and TR � 3 data. The best fitfunctions were also plotted and superimposed on thetime curve plots for the TR � 1 and TR � 3 seconds

session data in Figures 3 and 4 (heavy solid red lines),respectively.

In the second comparison, the single-pulse responsewas used to predict the response to the longer trains ina manner similar to Vazquez and Noll (18) and Glover(14). The single-pulse response was fit to the hemody-namic response function, h(t; b1,b2,b3), by itself, deter-mining best-fit values for the three parameters (b1, b2,and b3) to obtain the single-pulse response impulsefunction. Then this fixed impulse function was multi-plied by the finite recovery, r(�), and saturation func-tions, s(n), to obtain a two-parameter model f(n,�,t;r1,h1), which was then fit to the data using the samenonlinear regression fitting routine. The fitted parame-ters for these fits are given in Table 2 and the corre-sponding best fit functions plotted and superimposedon the time curves for the two sessions in Figures 5 and6 (heavy solid red lines), respectively. Originally, we hadhoped to use the hemodynamic response determined byeach individual’s 1-pulse train from the TR � 1 sessionas the impulse function for the longer trains followingobservations by Aguirre (22), and as Glover (14) andVazquez and Noll (18) modeled their data, but we wereunable to successfully fit the individual 1-pulse data.

As can be seen from the full-fit parameters in Table 1,the lags and recoveries are approximately the same forboth TR � 1 and TR � 3 seconds data. The absolute

Table 1Hemodynamic Response � Finite Recovery � Saturation Model Parameter Fits Over All Train Lengths (Mean � SD)

Variable interpretationunits

b1

amplitude%

b2 lagsec

b3

durationsec

�1

recoverysec

s1 saturationfraction

TR � 1 sec 1-2-4-8-16-Pulse TrainsIpsilateral motor 4.3 � 2.8 6.2 � 1.6 3.0 � 1.0 4.8 � 4.9 0.08 � 0.17Contralateral motor 3.4 � 0.8 6.2 � 0.8 3.4 � 0.6 4.4 � 2.4 0.06 � 0.05Ipsilateral auditory 4.0 � 1.2 6.1 � 0.8 3.2 � 0.9 2.9 � 1.5 0.09 � 0.04Contralateral auditory 4.2 � 2.5 5.9 � 0.8 2.9 � 0.1 3.3 � 1.7 0.04 � 0.04

TR � 3 sec 1-2-4-8-16-24-Pulse TrainsIpsilateral motor 5.1 � 2.9 8.2 � 4.4 6.6 � 6.0 4.2 � 2.1 �0.01 � 0.02Contralateral motor 3.2 � 2.6 5.8 � 2.8 4.9 � 3.3 4.2 � 4.3 �0.03 � 0.03Ipsilateral auditory 5.5 � 4.5 4.2 � 1.1 4.0 � 0.7 8.9 � 8.9 �0.03 � 0.03Contralateral auditory 4.4 � 3.5 5.8 � 2.2 3.9 � 2.7 4.2 � 1.5 �0.02 � 0.01

Table 2Hemodynamic Response � Finite Recovery � Saturation Model Parameter Fits for Single Pulse Followed by Fit to Longer Trains(Mean � SD)

Variableinterpretation

units

b1

amplitude%

b2 lagsec

b3

durationsec

�1

recoverysec

s1 saturationfraction

TR � 1 sec 1-2-4-8-16-Pulse TrainsIpsilateral motor 6.1 � 3.9 6.9 � 2.2 3.2 � 0.9 9.9 � 5.7 0.01 � 0.13Contralateral motor 4.1 � 1.7 5.1 � 1.6 2.9 � 0.4 12.3 � 9.7 0.01 � 0.10Ipsilateral auditory 4.9 � 2.3 5.1 � 1.1 3.1 � 0.8 3.7 � 1.4 0.07 � 0.06Contralateral auditory 4.8 � 3.2 5.3 � 0.8 3.0 � 0.4 3.3 � 1.7 0.05 � 0.05

TR � 3 sec 1-2-4-8-16-24-Pulse TrainsIpsilateral motor 3.6 � 1.9 6.0 � 2.3 1.6 � 0.5 11.5 � 14.6 �0.04 � 0.05Contralateral motor 3.7 � 2.3 4.1 � 2.9 2.6 � 0.7 5.8 � 4.2 �0.03 � 0.02Ipsilateral auditory 3.7 � 2.0 5.6 � 1.7 2.3 � 1.0 4.6 � 2.3 �0.02 � 0.02Contralateral auditory 3.0 � 2.8 4.2 � 1.5 1.8 � 1.6 6.4 � 9.9 �0.05 � 0.04

Linearity of BOLD-fMRI Response to TMS 285

amplitude and duration parameters seem to be slightlysmaller in the TR � 1 data compared with the TR � 3data. The main difference, however, is that the increasein pulse amplitude with train length is marginally sub-linear in the TR � 1 data and marginally supralinear inthe TR � 3 data. That is, in the TR � 1 data, there seemsto be a small progressive inhibition, and in the TR � 3data, there seems to be a small progressive facilitation.

From Table 2, it can be seen that the single-pulseamplitudes are larger in the TR � 1 data than in theTR � 3 data; in addition, the lags are shorter and thedurations are greater.

It should be noted that the model, including under-shoots, was not successfully fit to either set of data.Those fits either did not converge or resulted in highlydistorted curves that poorly matched the data. In par-ticular, the recovery was pushed up against the end ofthe epoch. This can be understood by observing howthe data sometimes falls right up to the beginning of thenext epoch rather than reaching a minimum and thenrecovering. It is possible that this indicates a vascularrebound effect from the TMS trains, but it was notclearly associated with the longer trains as one wouldexpect if this were the case (11,17).

Although only the parameter values averaged oversubjects are shown, there was no appreciable differencebetween subjects in any of the parameter values. Also,with the limited number of replications and the noisi-ness of the data, no effort was made to try to extract thearea of response vs. train length.

DISCUSSION

Despite subject head restraint and rigid mounting ofthe coil, motion was still a problem because of thefrequent, fairly high level (120% MT) TMS, causing fourof the 12 data sets to be lost as unsuitable for analysis.In the remaining fMRI data sets, activations were ob-served bilaterally in both motor and auditory cortex,and the amplitudes of the BOLD response observed inthose activations were consistent with those reportedearlier (26,28–30). For 120% MT TMS over motor cortexat 1 Hz in trains of up to 24 pulses, the time courses ofBOLD response, presumably (see 30) directly inducedin motor cortex by TMS and indirectly induced in audi-tory cortex by the sound of the TMS coil, are both welldescribed by a nonlinear model combining hemody-namic response with finite recovery and saturation/facilitation (in the general sense of the words). Bothmotor and auditory cortex show incomplete recovery forsuccessive pulses at this delivery rate of 1 Hz, and aprogressive saturation/habituation (17) consistentwith zero, that is, a linear response. Because the arti-ficial TMS-induced neuronal discharge would be ex-pected to depend more on the TMS coil’s field distribu-tion than on the natural pattern of the motor neurons,this may mean that the TMS BOLD response associatedwith TMS is dominated by physiologic feedback, as sug-gested by Baudewig, et al (30), and both responses arephysiologic.

Although measuring blood flow rather than the BOLDresponse, a combined TMS/PET (36) study in whichsubthreshold TMS was applied to the left frontal eye

field at an effective rate of 10 Hz with five-pulse trains1500 msec apart found a positive correlation betweencerebral blood flow (CBF) and the number of pulsetrains in the region under the coil, as well as in severalareas of the visual cortex and the right supplementaryeye field. However, because CBF as a function of thenumber of pulses was not reported, one could not esti-mate the effect of a minimal response.

In another study (34), the same group provided a plotof CBF vs. the number of pulse trains for response inthe left central sulcus for stimulation over left primarysensorimotor cortex, again delivered at subthresholdintensity. In this study, CBF in M1/S1 under the coilcorrelated negatively with the number of pulse trains,falling almost linearly from a value of 5% at five trainsto –3% at 20 trains, where it stayed out to 30 trains.

Because of their low time resolution, positron emis-sion tomography (PET) images necessarily represent anintegrated blood flow response rather than the bloodflow increase associated with a single event, and are notsuitable for investigating the linearity of response toshort stimuli. Nevertheless, these studies are relevantbecause they show train-length-dependent changes inthe response to TMS.

We did not find the negative correlation of blood flowwith train length, as reported by Paus, et al (34). This isnot, however, a contradiction, because the TMS appliedby Paus, et al, although subthreshold, was at 10 Hzrather than the 1 Hz used in the current fMRI study,and a far greater number of pulses were applied. Intheir study, a minimum of five 400-msec long trains offive pulses (equivalent to 10 Hz) 1600 msec apart, or 25pulses, were delivered over a total period of about 8400msec, compared with a maximum of 24 pulses in24,000 msec in the present study.

The data were well fit with the model both in ampli-tude and width. Although Kruggel and von Cramon (20)applied their nonlinear regression model for BOLD re-sponse to sample data from a single-trial fMRI study oflanguage comprehension, an auditory presentation ap-proximately 6 seconds long followed by a pause 18seconds long, the lag and duration model parametervalues we obtained for motor and auditory cortex weresimilar to those they obtained for a number of differentareas of cerebral cortex. The duration values found herewere slightly lower than their values in our TR � 1second session (� 3) and slightly higher in our TR � 3seconds session (� 5), possibly a reflection of the TR,because their data had a TR of 2 seconds, giving � 5.

Examining BOLD-fMRI response of the visual cortex,Janz, et al (9) found that it behaved in a manner con-sistent with a linear model when using stimuli from 2 to8 seconds. Also in the visual system, Hu, et al (11) useda 4-T magnet to gather data in response to stimuli of2.4- to 4.8-second duration consistent with a linearmodel for the hemodynamic response. Boynton, et al (8)also found that the response of the visual cortex be-haved in a manner consistent with a linear model whenusing stimuli from 6 to 24 seconds, but noticed a de-parture from linearity in V1 with stimuli of � 3 seconds.Vazquez and Noll (18), working at even shorter stimulilengths (1 and 2 seconds), also reported nonlinear be-havior in the visual cortex. Using stimulus OFF rather

286 Bohning et al.

Figure 5. BOLD-fMRI response (TR � 1 second) to 1-, 2-, 4-, 8-, and 16-pulse trains of TMS pulses compared with nonlinear fitto model, with fixed single-pulse impulse function allowing only recovery and saturation parameters to vary: ipsilateral motor (a),contralateral motor (b), ipsilateral auditory (c), and contralateral auditory (d) areas.

Figure 6. BOLD-fMRI response (TR � 3 seconds) to 1-, 2-, 4-, 8-, 16-, and 24-pulse trains of TMS pulses compared withnonlinear fit to model, with fixed single-pulse impulse function allowing only recovery and saturation parameters to vary:ipsilateral motor (a), contralateral motor (b), ipsilateral auditory (c), and contralateral auditory (d) areas.

Linearity of BOLD-fMRI Response to TMS 287

than ON durations, Birn and Bandettini (37) reportedthat BOLD response to visual stimulation is nonlinearfor OFF periods shorter than 4 seconds, with signaldecreases smaller than expected. Pfeuffer, et al (38),using visual stimuli as short as 100 msec, reportedstrong nonlinearity appearing at 2 seconds.

In the auditory system, Robson, et al (17) looked atthe response to trains of 100-msec tone bursts between100 msec and 25.5 seconds long, and concluded thatthe fMRI response to auditory stimuli is approximatelylinear for trains of 6 seconds and longer, but shorterstimuli produced signals that are longer than might beexpected from the response to the longer stimuli.Binder, et al (16) also reported a departure from linear-ity in auditory response at shorter stimulus times. Fris-ton, et al (19) used an extension of convolution methodswith nonlinear basis functions to account for nonlin-earites in auditory responses to words spoken at differ-ent rates. This modeling approach requires a priori as-sumptions about the impulse response in the form ofpreselection of basis functions, and is explicitly nonlin-ear.

Studying both auditory and sensorimotor systems asin the present work, Glover (14) found both corticalsystems to be nonlinear in that the response to a longstimulus could not be predicted by convolving the1-second response with a rectangular function. In theshort-time regime, the amplitude of the response variedonly slowly with stimulus duration. He found that thischaracter could be predicted with a modification to theBuxton, et al balloon model (5). It was concluded thatlinear deconvolution is effective when the stimuli areseparated by at least 4 seconds and if the deconvolutionfilter is measured for each subject using a short-stim-ulus paradigm.

In all reports of nonlinearity, shorter stimuli exhibitenhanced fMRI responses relative to those predictedfrom longer stimuli and the linear model, and the stim-ulation duration at which the nonlinearity appears isabout 2–3 seconds. Hence, if our pulse separation iscomparable to the stimulus duration for BOLD re-sponse, with a 1-second pulse separation, the presentdata should demonstrate nonlinear effects. Whetherthey do or not is open to interpretation.

In many of the previous studies, the observations oflinearity were qualitative, and the studies that didquantify the nonlinearity used different models. In ad-dition, a train of discrete TMS or auditory stimuli ismost likely not the same as a continuous stimulus ofsimilar total duration. Therefore, it is difficult to com-pare their results with the degree of nonlinearity, orlack of it, observed in the present data. The data fromthe TR � 1 second session would indicate a smallamount (5%–10%) of nonlinearity, in the form of satu-ration, or, by other names, adaptation (8) or habitua-tion (17). The data from the TR � 3 seconds sessionshow even less nonlinearity (only 1%–3%) but it is in theopposite direction, i.e., the amplitudes increase withtrain length (facilitation). To be certain that there wasnot some change of response behavior between trains of16 and 24 pulses, the data for the 1-, 2-, 4-, 8-, and16-pulse trains were refit, excluding the 24-pulse train.The parameter values did not change significantly.

Although we used the Gaussian form suggested byKruggel and von Cramon (20) for the hemodynamicresponse function, it is unlikely that our results wouldhave been different if we had used one of the otherhemodynamic response impulse functions that havebeen used, e.g., a Poisson function (15), gamma func-tions (12,14,19,39), or, although only the LaplaceTransform was given, what amounts in the time domainto a difference of two decaying exponentials multipliedby a rectangular filter function (18).

Neither the data for the T � 1 second session nor thedata for the T � 3 seconds session supported the pulsebroadening with stimulus duration reported by others(38) as a mark of nonlinearity. The model was quitesuccessful in fitting the data, both overall (Figs. 3 and 4)and in its single-pulse form (Figs. 5 and 6) with a single-duration parameter and no train-length-dependentbroadening. This may well be due to the difference be-tween stimuli of different duration and the length of atrain of discrete stimuli. There is clearly a differencebetween a stimulus 3 seconds long and three discrete0.3-msec stimuli separated by 1 second, though, inboth cases, the total duration of the stimulation is 3seconds. Also, most impulse stimuli used elsewherewere far longer than here; for example, Glover (14) useda discrete set of 1-second duration stimuli, each pulsebeing 3000 times as long as our TMS pulse.

Rather subjectively, considering the problems withthe TMS pulse artifact in the TR � 1 second session,and the additional longer train length in the TR � 3seconds session, one would have to conclude that inexamining the response to TMS pulse trains up to 24pulses, delivered at the rate of 1 Hz, we were unable toclearly demonstrate nonlinearity.

With the low temporal resolution of the present data,there was no thought of being able to observe a differ-ence in delay times between the response to, presum-ably, direct TMS stimulation and the indirect responseof auditory cortex, or ipsilateral vs. contralateral motor(Fig. 1b), but the errors of the lag times were of interestfor planning future studies. They are approximately 10times the 10–20-msec time resolution likely to be re-quired (31), though Buckner, et al (10) and Robson, etal (17) implied that processing lags between differentareas could be detected with AST studies.

Significantly, Baudewig, et al (30), using 23 trains(separation, 12–20 seconds) of 10 stimuli delivered at10 Hz, similar to the PET study of Paus, et al (34), havequestioned whether TMS actually causes a direct BOLDresponse, proposing that the observed BOLD responseis actually sensory feedback from the moving fingers.Because primary motor, premotor, and sensory cortexare quite close, the present data cannot rule out thatinterpretation. We are currently analyzing data from astudy with 11 subjects, each repeated three times, totry to measure more precisely the position and ampli-tude of the artificial BOLD response associated withTMS-induced movement relative to the physiologicBOLD response caused by a similar volitional move-ment to better understand the similarities and differ-ence.

In a study that might be considered to create veryshort stimulations like those of TMS (40), square elec-

288 Bohning et al.

trical pulses with duration 0.2 msec were deliveredthrough two ring electrodes to the left index fingers atan intensity of 8 mA. The number of activated pixelsand the percent signal increases at 4, 8, and 16 Hz wereobserved to be significantly greater than at 1 Hz. Thepercent signal increases at 4, 8, and 16 Hz were alsosignificantly greater than at 32 Hz. Though not signifi-cant, they also reported a tendency for the number ofactivated pixels at 32 Hz to be smaller than those at 4,8, and 16 Hz. This is very much in line with the neuro-physiologic studies that have shown that TMS inhibitswhen applied at frequencies � 1 Hz (32) and facilitatedwhen applied at frequencies � 1 Hz (33). The reductionat 32 Hz may be showing a limit to the facilitation effect.

In conclusion, for 120% MT TMS over motor cortex at1 Hz in trains of up to 24 pulses, the time courses ofBOLD response, presumably directly induced in motorcortex by TMS and indirectly induced in auditory cortexby the sound of the TMS coil, are both well described bya nonlinear model combining hemodynamic responsewith finite recovery and saturation/facilitation. Bothmotor and auditory cortex show incomplete recovery forsuccessive pulses at this delivery rate of 1 Hz, and aprogressive saturation/facilitation consistent withzero, that is, a linear response with train length. Thereis no sign of the negative correlation of response withtrain length reported by Paus, et al (34) for a longerseries of short trains at 10 Hz.

Responses to even very short stimuli of 1–2 secondsmay still not be sufficiently short to be considered im-pulses. Consequently, stimulus amplitude, duration,frequency, and train length, as well as the cortex in-volved, will all have to be taken into account to predictresponse.

Although these data could not distinguish the artifi-cial TMS-induced BOLD response in motor cortex fromthe more physiologic BOLD response observed in audi-tory cortex, implying similarity, there are likely funda-mental differences in the underlying neuronal activitythat produce them. Interleaved TMS/fMRI could be auseful technique for studying those differences.

ACKNOWLEDGMENTS

Partial equipment and salary support was receivedfrom the National Alliance for Research in Schizophre-nia and Depression (NARSAD; Young Investigator andIndependent Investigator Award, Dr. George), the Tedand Vada Stanley Foundation (Drs. George andBohning), the Borderline Personality Disorder ResearchFoundation (Drs. George and Bohning), and an NIMHR21 award (Dr. Bohning).

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