Characterizing the Hemodynamic Response: Effects of Presentation Rate, Sampling...

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NeuroImage 11, 735–759 (2000)doi:10.1006/nimg.2000.0568, available online at http://www.idealibrary.com on

Characterizing the Hemodynamic Response: Effects of PresentationRate, Sampling Procedure, and the Possibility of Ordering

Brain Activity Based on Relative TimingF. M. Miezin, L. Maccotta, J. M. Ollinger, S. E. Petersen, and R. L. Buckner

Department of Psychology, Department of Radiology, Department of Anatomy and Neurobiology, and Departmentof Neurology and Neurological Surgery, Washington University, St. Louis, Missouri 63130

Received October 1, 1999

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Rapid-presentation event-related functional MRI(ER-fMRI) allows neuroimaging methods based on he-modynamics to employ behavioral task paradigmstypical of cognitive settings. However, the sluggish-ness of the hemodynamic response and its varianceprovide constraints on how ER-fMRI can be applied.In a series of two studies, estimates of the hemody-namic response in or near the primary visual and mo-tor cortices were compared across various paradigmsand sampling procedures to determine the limits ofER-fMRI procedures and, more generally, to describethe behavior of the hemodynamic response. The tem-poral profile of the hemodynamic response was esti-mated across overlapping events by solving a set oflinear equations within the general linear model. Noassumptions about the shape were made in solving theequations. Following estimation of the temporal pro-file, the amplitude and timing were modeled using a gfunction. Results indicated that (1) within a region, fora given subject, estimation of the hemodynamic re-sponse is extremely stable for both amplitude (r2 5.98) and time to peak (r2 5 0.95), from one series of

measurements to the next, and slightly less stable forestimation of time to onset (r2 5 0.60). (2) As the trial

resentation rate changed (from those spaced 20 spart to temporally overlapping trials), the hemody-amic response amplitude showed a small, but signif-

cant, decrease. Trial onsets spaced (on average) 5 spart showed a 17–25% reduction in amplitude com-ared to those spaced 20 s apart. Power analysis indi-ated that the increased number of trials at fast ratesutweighs this decrease in amplitude if statisticallyeliable response detection is the goal. (3) Knowledgef the amplitude and timing of the hemodynamic re-ponse in one region failed to predict those propertiesn another region, even for within-subject compari-ons. (4) Across subjects, the amplitude of the responsehowed no significant correlation with timing of theesponse, for either time-to-onset or time-to-peak esti-ates. (5) The within-region stability of the response
as sufficient to allow offsets in the timing of the
735

esponse to be detected that were under a second,lacing event-related fMRI methods in a position tonswer questions about the change in relative timingetween regions. © 2000 Academic Press

INTRODUCTION

Rapid-presentation event-related functional MRI(ER-fMRI) allows neuroimaging methods based onhemodynamics to employ behavioral task paradigmstypical of cognitive settings (Dale and Buckner,1997; Burock et al., 1998; Clark et al., 1998). Differ-nt trial types spaced a few seconds apart can beandomly intermixed and/or sorted post hoc based onubject performance (e.g., Buckner et al., 1998a;lark et al., 1998; Wagner et al., 1998). However,everal limitations and methodological issues placeonstraints on how rapid-presentation ER-fMRI para-igm can be applied including: (1) how the hemody-amic response summates over separate neuronalvents, (2) the variance associated with the hemody-amic response, (3) how the response is sampled inelation to trial presentation, and (4) the analyticrocedure by which the hemodynamic response isxtracted. In the following article, a review of thesessues is followed by presentation of two new empir-cal studies. The two studies provide constraints onhe design, analysis, and interpretation of rapid-resentation ER-fMRI. Results suggest that robuststimates of the hemodynamic response can be ob-ained for stimulus trials spaced as closely as 2.5 spart (mean spacing 5 5 s). These responses areoughly comparable to responses to trials spacedidely apart. Furthermore, the timing and shape of

he hemodynamic response can be estimated withccuracy sufficient to indicate temporal offsetsithin a region of less than 1 s, even for proceduressing whole-brain imaging with a repetition timeTR) of greater than 2.5 s.

1053-8119/00 $35.00Copyright © 2000 by Academic Press

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736 MIEZIN ET AL.

Hemodynamic Response Summation

The robust positive component of the blood-oxygen-ation level-dependent (BOLD) hemodynamic responseevolves over a 10- to 12-s period even for brief stimulusevents of a few seconds or less (Blamire et al., 1992;

andettini, 1993; Savoy et al., 1995; Boynton et al.,996; Buckner et al., 1996; Konishi et al., 1996). Subtleesidual components may persist for up to a minuteFransson et al., 1998a, 1999). On first appearance,hese findings would seem to negate the possibility ofeparating rapidly presented events. However, the ac-ual situation provides more hope than this first im-ression. While the temporally extended nature of theemodynamic response presents challenges to datanalysis, rapidly presented trials that overlap in timean be separated. The basis of separation is the findinghat sequential (or continuous) events summate in aoughly linear fashion (Boynton et al., 1996; Dale anduckner, 1997). That is, the effect of a neuronal eventill be to further increase the existing hemodynamic

esponses even if the hemodynamic responses fromreceding events have not completely decayed. Thisummation occurs in a nearly linear fashion underany circumstances: as a new distinct event is pre-

ented, the BOLD response increases by a similarmount regardless of the prior history of events. Dem-nstrating an extreme application of this principle,apid presentation of sequential events separated by50 ms has been shown to be sufficient for producingctivation maps (Burock et al., 1998). However, subtleonlinearities in the summation of the hemodynamicesponse have also been noted and present potentialhallenges to paradigm design and interpretation ofata.Boynton et al. (1996), in their seminal work describ-

ng the roughly linear summation of the hemodynamicesponse to stimuli of varied duration, noted that thehortest stimulus durations overestimated the re-ponse to longer durations—a form of nonlinear sum-ation. Their interpretation was that adaptation oc-

urred for the longer sustained stimuli. A similar formf nonlinearity as a function of visual stimulus dura-ion has also been noted by Vazquez and Noll (1998)nd also by Robson et al. (1998) in response to auditorytimuli. Dale and Buckner (1997) showed that the he-odynamic responses to temporally separated stimu-

us events summate in a nearly linear fashion, butubsequent events show a steeper decay and under-hoot of the baseline compared to isolated events. Thisatter paradigm presumably was not influenced bydaptation when between-event summation was con-idered, suggesting that subtle nonlinearities exist in aange of paradigm types.

The aforementioned studies suggest that cautionhould be exhibited in assuming a precisely linear
odel of hemodynamic response summation. Nonethe- r
less, the major component of the BOLD response doesappear to summate in a nearly linear fashion, and thenonlinear components appear to be either subtle orexhibited under extreme paradigm situations withvery high presentation rates (e.g., Friston et al., 1997).

hese findings collectively suggest that estimates ofesponses in the context of rapidly presented trialvents should be similar, but not necessarily identicalo, estimates obtained in the context of trials widelypaced in time. A goal of the present series of studiesas to address whether different estimates of the he-odynamic response would be obtained at different

rial presentation rates, at which varied degrees ofemodynamic response overlap occur.

Variance of the Hemodynamic Response

The hemodynamic response has been shown to varyn timing, amplitude, and shape across brain regionsnd cognitive task paradigms, and variance across sub-ects has been observed for nominally similar regionsnd tasks (Lee et al., 1995; Buckner et al., 1996, 1998b;im et al., 1997; Schacter et al., 1997; Aguirre et al.,998; Robson et al., 1998; D’Esposito et al., 1999). Suchariation is expected given that estimation of the he-odynamic response occurs in a real-world system

hat has many sources of measurement and biologicaloise. Several possible sources of variation can be con-idered including (1) variation across data sets withinn individual for a given region, (2) variation acrossndividuals for the same region, and (3) variationcross regions. The latter two sources may be particu-arly relevant in between-group comparisons involvingbnormal populations in which there is evidence foraseline differences in hemodynamic response proper-ies (Ross et al., 1997; Taoka et al., 1998). We considerach of the three possible sources of variation sepa-ately.Within an individual subject, for a fixed region, the

emodynamic response is highly reproducible in tim-ng, shape, and amplitude within the same experimen-al session (if many events are considered). Given twoeparate sets of data from the same subject, Dale anduckner (1997) showed that the hemodynamic re-ponse was nearly identical across separate measure-ents within visual cortex. Any individual event, of

ourse, can show considerable variation much in theame manner in which a behavioral estimate of perfor-ance may vary from one trial to the next (Kim et al.,

997). The extremely high level of stability within aubject for a given region’s response places event-re-ated fMRI in a strong position to contrast within-ubject conditions, even those that require detection ofiming offsets that are as brief as a few hundred mil-iseconds (e.g., Savoy et al., 1995; Menon et al., 1998).

When one moves beyond this reliability for a given
egion within a subject, the situation becomes more

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737ORDERING BRAIN ACTIVITY BASED ON RELATIVE TIMING

complicated. Across subjects, for nominally the sameregion, the hemodynamic response varies on the orderof a few seconds (in timing range) and the amplitudecan be doubled from one subject to the next (Kim et al.,1997; Buckner et al., 1998b). Across patient popula-ions, there is some evidence of systematic differencesn the timing of the response (Taoka et al., 1998).owever, when averaged groups of subjects from the

ame population are considered, the central tendencyf the hemodynamic response for a given region is suchhat—even for a relatively small group of subjects (N ;)—the mean amplitude and time to onset of the re-ponse can be specified and reproduced in a separateroup of subjects to within tenths of a percent andractions of a second (Buckner et al., 1998b). Thus,hile random variation exists across subjects, and sys-

ematic variation may further exist across differentopulations, strong central tendencies are present thatllow for meaningful averaging of the hemodynamicesponse across subjects and for modal properties to beharacterized.

Finally, separate regions of cortex can exhibit widelyisparate hemodynamic response shapes and ampli-udes even within individual subjects (Lee et al., 1995;uckner et al., 1996, 1998b; Schacter et al., 1997; Rob-

son et al., 1998; Bandettini, 1999). Two levels of re-gional analysis have been examined. At the most locallevel, adjacent or nearby voxels have been shown tovary widely in their timing onset (up to 2 s) and am-plitude (1–5% in range). Because these differencesseem highly unlikely to be due to neuronal activity (Leeet al., 1995; Robson et al., 1998; Bandettini, 1999), theresults suggest separate influences of micro- and mac-rovasculature. At the level of larger regions, encom-passing 500–1000 cc, variations in amplitude and tim-ing that may reflect differential vascular sampling orperhaps differences in neural activity across regionshave also been noted (Schacter et al., 1997; Buckner etal., 1998b). The presence of regional variation presentsa serious challenge to using ER-fMRI as a means ofresolving the temporal cascade of neural activity acrossthe cortex. It seems possible, if not likely, that acrosscertain regions the absolute hemodynamic responselags will go in a direction opposite to the underlyingneuronal activity, making possible a serious interpre-tational error.

Another goal of the present series of studies was toexplore the variation of response magnitude and tim-ing within and between regions. Two separate issuesare considered. The first is the variation and predict-ability across regions. We ask this question: If oneknows the properties of the hemodynamic response inone region (e.g., the amplitude), can the behavior ofanother spatially separate region be predicted? Inother words, are there global response properties in anindividual subject that span regions? The second issue
relates to the stability of the hemodynamic response
within a region for a given subject, revisiting a ques-tion addressed by Menon et al. (1998; see also Savoy etal., 1995; Rosen et al., 1998; Dymond et al., 1999;Bandettini, 1999). Namely, can the stability of theresponse within a region be used to detect temporaloffsets of fractions of a second? These two issues areexplored in concert to ask if ER-fMRI is capable ofresolving relative offsets in timing across separate re-gions of cortex (see also Friston et al., 1998).

Hemodynamic Response Sampling

A potentially tricky issue surrounding estimation ofthe hemodynamic response is how the response is sam-pled. In many studies, there is a fixed relation betweenthe image acquisition and the presentation of a trialevent resulting in discrete sampling. If the TR is 3 s,the hemodynamic response will be sampled with aresolution of 3 s. It is easy to imagine that certaincomponents of the response, such as the peak, will bemissed and the response estimated inaccurately. Aclever alternative has been offered by Josephs et al.(1997), whereby the relation between the image acqui-sition and the trial presentation is systematically var-ied so that, across trials, numerous time points alongthe response are sampled. In many situations in whichbehavioral and analytical methods can handle theadded dimension of a varied sampling time, this ap-proach provides a useful means of oversampling thehemodynamic response in time. In situations in whicha fixed relation is desired between the image acquisi-tion and the hemodynamic response, there remainsopen the question of how much statistical power is lostand the degree to which parameter estimates of theresponse (e.g., the amplitude) are misestimated. Anal-ysis of blocked-design fMRI data suggests that errorsmay be significant (Price et al., 1999). A third goal ofthe present studies was to compare two effective ratesof sampling, in which the relation between the imageacquisition and the trial presentation is either heldconstant or systematically varied.

Hemodynamic Response Estimation

An issue related to sampling is the method by whichthe estimate of a hemodynamic response is derived. Inthe most extreme case, in which long intertrial inter-vals are present (.16 s apart), the estimate is themean signal change over time for an activated region,for which the mean is found by simply averaging acrosstrials. The assumption is that the robust positive de-flection from one trial has decayed before the occur-rence of another event (Blamire et al., 1992; Boynton etal., 1996; Buckner et al., 1996; Konishi et al., 1996;McCarthy et al., 1997; Bandettini, 1999; see alsoFransson et al., 1998 for discussion of potentially
longer components of the hemodynamic response).

738 MIEZIN ET AL.

As multiple trials in a sequence are moved closertogether in time, the underlying physiology and appro-priate analysis become more complicated. The evokedhemodynamic response to each trial may overlap withthe next, yielding a complex waveform that representsthe accumulated hemodynamic response to manyevents. A secondary procedure to solve for the estimatedcontribution of trial events becomes necessary. Severalapproaches to this problem have been effectively ap-plied, including a straightforward, linear methodbased on subtracting away prior and future histories ofoverlapping trials (Dale and Buckner, 1997) and mod-eling the temporally overlapping responses based onmultiple regression within the general linear model(Clark et al., 1998). Glover and colleagues (1999) haverecently suggested a promising method for responseestimation based on linear deconvolution.

Most directly relevant to the present article, theapproach of Clark et al. (1998), which shares similari-ties to the approach applied by Josephs et al. (1997),potentially allows for an estimate of the hemodynamicresponse to each kind of trial type within a rapidlypresented, randomly intermixed series. Critically, theestimate could be obtained with no assumption aboutthe specific shape of the response other than the as-sumption that responses, whatever their temporal pro-file, summate in a linear fashion. To the degree thatthey do linearly summate, the same response estimateshould be obtained whether the trial events are iso-lated and widely separated in time or whether they arerapidly presented, yielding overlapping hemodynamicresponses. A fourth goal of the present studies was toestimate the hemodynamic response for rapidly pre-sented trials using the general linear model while mak-ing no assumptions about the specific shape of theresponse.

The final issue addressed in the present paper is howthe hemodynamic response is described once its tem-poral evolution is estimated. That is, how does oneanswer the question of what the magnitude or timingof the response is? This issue is important for usingfMRI-based measurements as quantitative (in terms ofpercentage MR signal intensity) rather than just qual-itative measurements. Questions are beginning to beasked that require comparison of response levelswithin a region across conditions or populations, ratherthan simply the presence or absence of a response.Currently, while it is often difficult to equate a mean-ingful biological unit of measure to the level of theBOLD-contrast response, one can nonetheless describethe response in terms of percentage signal change. Tothe degree this estimate is reliable and valid, the rel-ative amplitude of the hemodynamic response can becompared across conditions and across different sub-ject populations.

However, there are tradeoffs in adopting a descrip-
tive estimate (or series of descriptive estimates) of the
hemodynamic response. For one, the temporal evolu-tion of the response is reduced to a set of values thatmay lose components of the response that are informa-tive. Furthermore, the estimate of the response is, inpractice, dependent on a model of the shape of thehemodynamic response, which may only partially ac-commodate the structure of the real response and mayalso have nonlinear components.

A final goal of the present studies was to employ amodel estimate of the hemodynamic response based ona g function (Boynton et al., 1996) to determine howstable quantitative estimates of the hemodynamic re-sponse are in terms of estimates of the peak percentagesignal change (amplitude), the time lag to responseonset (time to onset), and the time lag to response peak(time to peak). These quantities are offered as possiblemeasurements that can be used to make comparisonsacross conditions, studies, patient populations, andlaboratories to assess relative hemodynamic signalchange.

METHODS

Overview

The present series of studies provides an empiricalcharacterization of the hemodynamic response acrossparadigms that vary the intertrial interval (experi-ment 1) and sampling procedure (experiment 2). Twofeatures of the paradigms employed allowed questionsabout within- and between-region variation and thelimits of within-region response characterization to beanswered. First, both studies used a paradigm involv-ing sensory (visual) and motor response demands. Sub-jects viewed an 8-Hz large-field flickering checker-board for approximately 1.5 s and pressed a key uponstimulus onset (experiment 1) or upon its onset andoffset (experiment 2). In this manner, separate pri-mary sensory and motor responses could be comparedfor each subject, allowing analysis of how responseproperties in one region predict properties in anotherregion. For the motor variant in experiment 2, subjectspressed a key with one hand when the stimulus began(Onset) and with the other hand when the stimulusended (Offset), allowing us to ask whether event-re-lated fMRI can detect the temporal separation of se-quential responses in motor cortex that would occurabout 1 s apart. For both experiments, whole-brainimaging using a 1.5-T scanner was employed with a TRof about 2.5 s. General methods pertaining to bothstudies are discussed first, followed by specific descrip-tions of the two separate experiments.

Subjects

Eighteen subjects were recruited from the Washing-
ton University community in return for payment.

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Eight subjects served in experiment 1 (3 males, meanage 22.3, range 18–26 years) and 10 in experiment 2 (4males, mean age 23.1, range 20–27 years). All hadnormal or corrected-to-normal vision and reported nohistory of significant neurological problems. Subjectsprovided informed consent in accordance with theguidelines set by the Washington University HumanStudies Committee.

Imaging Procedures

Scans were conducted on a Siemens 1.5-T VisionSystem (Erlangen, Germany) with a standard circu-larly polarized head coil. A pillow and thermoplasticface mask were used to minimize head movement.Headphones dampened scanner noise and enabledcommunication with subjects.

Structural images were acquired using a high-reso-lution (1.25 3 1 3 1 mm) sagittal MP-RAGE T1-weighted sequence (TR 5 9.7 ms, TE 5 4 ms, flip angle12°, TI 5 300 ms, TD 5 0 ms). Functional images wereollected with an asymmetric spin-echo-planar se-uence sensitive to BOLD contrast [volume TR 5.50 s (experiment 1) or 2.68 s (experiment 2), 3.75 3.75-mm in-plane resolution; T2* evolution time 50 ms,5 90°]. In each functional run, 128 sets of 16 contig-

ous, 8-mm-thick axial images were acquired parallelo the anterior–posterior commissure plane; this pro-edure offered whole-brain coverage at a high signal-o-noise ratio (Conturo et al., 1996). Thus, each corticalegion was sampled 128 times per run, with 1 sampleccurring every 2.50 s (experiment 1) or 2.68 s (exper-ment 2). Throughout the paper, we refer to each 16-lice set of images covering the whole brain as animage acquisition” and its particular position in times a “time point.” The first 4 image acquisitions in eachun were discarded to allow stabilization of longitudi-al magnetization. Each run lasted approximately 51

2

min. A 2-min delay existed between runs, during whichtime subjects were permitted to rest.

Behavioral Procedures

A Power Macintosh computer (Apple, Cupertino, CA)controlled by PsyScope software (Cohen et al., 1993)displayed the visual stimuli. Subjects responded bypushing a fiber-optic light-sensitive key press con-nected to a PsyScope button box (Carnegie Mellon Uni-versity, Pittsburgh, PA). Stimuli were rear projected(AmPro Model LCD-150) onto a screen placed at theback of the magnet bore. Subjects viewed the screen viaa mirror fastened to the head coil.

For both experiments the basic stimulus was a large-field 8-Hz counterphase flickering checkerboard (blackto white) subtending approximately 12° of visual angle(6° into each visual field). The Onset of the stimuluswas triggered by the scanner in relation to the begin-
ning of the image acquisition via the PsyScope button
box. Spatial frequency of the reversing checkerboardswithin the display decreased with visual angle to beapproximately constant in relation to acuity across thevisual field. The duration of the stimulus was approx-imately 1.5 s. Measuring the duration of the stimulusfrom the monitor revealed that the actual presentedduration varied by as much as 166 ms on a given trial,with most trials (;70%) being within 100 ms (mean1.53 s). For this reason we consider the timing approx-imately 1.5 s. Calculation of reaction times to the On-set or Offset of the stimulus are in relation to thepresentation duration of each trial.

Estimate of the Hemodynamic Response

For each functional MRI run, data were first prepro-cessed to remove several sources of noise and artifact.All functional image runs were corrected for odd/evenslice-intensity differences and motion artifact using arigid-body rotation and translation correction (Snyder,1996). Data were then analyzed within the generallinear model to estimate effects of stimulus presenta-tion. Each stimulus event was assumed to produce aresponse lasting 7 time points (;18-s response epoch)fter the start of the stimulus. No assumptions wereade about the shape of the response at this stage of

nalysis. Additionally, a mean and a linear drift com-onent for each run were included in the general linearodel. In this manner, estimates of the hemodynamic

esponse were made for trial events spaced a few sec-nds apart (Dale and Buckner, 1997; Burock et al.,

1998; Clark et al., 1998). The possibility of separatingthe BOLD responses to closely spaced stimuli can becounterintuitive and is influenced significantly by ex-actly how the trials are temporally spaced in relation toone another (Burock et al., 1998; Buckner and Braver,1999). For this reason, a more detailed account of theanalysis is provided.

The solution to estimating responses in a continualseries of trials can be thought of in terms of a set oflinear equations. A set of linear equations can beuniquely solved if there are as many equations as thereare unknowns. At each time point in the MRI timeseries, the measured value is equal to the sum of BOLDresponses plus noise, i.e., the measured value is alinear equation of the BOLD responses. Figure 1 illus-trates this point. These equations are repetitive foruniformly (fixed) spaced trials, such as when trials arepresented every 71

2 s (Fig. 1 left). In this example, thereare a total of three independent equations for the sevenunknown time points in the BOLD response. If theinterval is randomized (jittered) between stimuli as inFig. 1 (right), the number of unique equations morethan doubles. The underlying BOLD response can thenbe uniquely estimated. In situations in which there is arange of varied intervals between stimuli, the situation
further improves.

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740 MIEZIN ET AL.

Thus, in the presence of noise, it is desirable to haveconsiderably more equations than unknowns, so it isdesirable to jitter the stimuli by several unique valueseither explicitly (Buckner and Koutstaal, 1998) or byplacing gaps interspersed randomly throughout therun (Buckner et al., 1998a; Wagner et al., 1998). Inboth experiment 1 and experiment 2, we implementedthis procedure using gaps (fixation trials) that wererandomly interspersed with equal probability with thetrial events of interest (the visual checkerboards). Theordering of trials and gaps was random. On each trial,there was a 50% probability of a visual stimulus and50% probability of a gap. Sequential ordering was alsoensured so that gaps and trials followed each otherequally often (Buckner et al., 1998a). The resultingdistribution of gaps followed a near exponential distri-bution with long gaps underrepresented because of the

FIG. 1. The use of linear equations to estimate the hemodynamoints for the BOLD response are annotated as h1–h7. The first lineparate situations: for when the interval between stimulus events itimulus events is jittered in time [Randomized (Jittered) Interval; rows labeled Individual BOLD Responses. The Measured BOLD Resndividual BOLD responses. Analytically, when a fixed interval betwequations that confound the signal contribution by each event tontributions for each event cannot therefore be estimated. Howeaveform is produced that can be solved to estimate the separate c

inearly. Linear estimation based on the general linear model was u

sequential ordering constraint. In this manner, a high

degree of temporal jitter between stimulus trials wasachieved, providing a robust paradigm for analysiswithin the general linear model.

A further important aspect of our methods was to usean “interleaved” procedure to increase the effectivesampling rate of the hemodynamic response. Extend-ing from Josephs et al. (1997), the stimulus Onset wasvaried in relation to the timing of the image acquisi-tion. On every other run the stimulus was presentedeither at the beginning of image acquisition or 1.25 safter the onset of image acquisition. The response es-timates from the two runs were interleaved to samplethe averaged hemodynamic response across trials at ahigher temporal resolution than achieved with eitherrun alone. Specifically, each interleaved run pair wasconstructed to yield a hemodynamic response estimatethat effectively sampled the hemodynamic response at

response for overlapping events is illustrated. The estimated timebeled Stimulus Onset) plots the relative positions for trials in two

xed (Fixed Interval; left column) and for when the interval betweent column]. Each stimulus has its own signal change as shown by these will be a complex waveform that represents the summation overtrials is used (left), a constant MRI signal waveform results, yielding; fewer equations exist than unknowns. The independent signal, by varying the interval around the events (right) a modulatingributions of the events, to the degree the separate events summate

as the basis of response estimation in the present paper.

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experiment 1 and one sample every 1.34 s in experi-ment 2). This procedure is a variant of the procedureproposed by Josephs et al. (1997) in which the presen-tation of the trial occurs at multiple, systematicallyoffset time points in relation to the image acquisition.In our procedure, the effective sampling rate is doubledand the run pairs can be systematically combined toestimate the effect of sampling procedure (see descrip-tion of experiment 2).

In instances in which an interleaved procedure wasemployed, the two kinds of events (those occurring atthe beginning of the image acquisition and those oc-curring near the middle of the image acquisition) wereincorporated into the linear model as separate factors.These factors were recombined following linear re-sponse estimation to yield a continuous 14-time-pointestimate of the hemodynamic response (all 14 timepoints still being comprised within an ;18-s epoch).Importantly, estimation of the responses made no as-sumptions about the specific shape of the response.

The procedures described thus far result in an esti-mate of the temporally evolving response magnitudefor each time point related to the onset of the stimulus.The full estimate could be used in its entirety for cer-tain forms of data analysis procedures (e.g., explora-tion of an effect of time; Cohen et al., 1997). However,

FIG. 2. Illustrated are the three estimated parameters obtaineesponse profile for a single region estimated from the general lineasolid line. Amplitude, time to onset, and time to peak are estimate

ased on individual subject data or based on all estimates plotted a

s a simplified description of the response we adopted

n additional modeling procedure by which we assumegeneral shape of the response and then estimate the

eak amplitude, time to onset, and time to peak of theesponse based on this assumed shape. A three-param-ter g function was used as the generalized modelBoynton et al., 1996) with an additional parameterpecifying the time delay to response onset (Dale anduckner, 1997; Schacter et al., 1997; Buckner et al.,

1998a). Nonlinear least-squares fitting of the fMRI re-sponse using the Levenberg–Marquardt method (Presset al., 1992) provided estimates of the model parame-ters (see Fig. 2).

Statistical Map Generation

To construct statistical maps, the estimated time curveswere cross-correlated with a lagged g function (Boyntonet al., 1996; Dale and Buckner, 1997). Z-statistical mapswere then computed based on this cross-correlation.

Regional Analyses

Regions were defined on multiple functionally dis-tinct areas across the brain. Two separate regions weredefined for experiment 1 (visual cortex and left motorcortex) and three separate regions for experiment 2(visual cortex, right motor cortex, and left motor cor-

based on the least mean square g function fit. The hemodynamicodel is plotted as filled diamonds. The model fit is superimposed asas shown, based on the model fit. This model estimate can be madess subjects.

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742 MIEZIN ET AL.

those voxels most active within the general region ofprimary visual cortex and primary motor cortex. Forthe visual region, a threshold value that isolated theregion to the medial wall of each hemisphere includingstriate cortex was selected for each subject. The thresh-old Z ranged from 7 to 10 except for one subject for

hom a threshold of Z 5 19 was used. These valuesproduced region sizes varying from 10 to 58 voxelsacross subjects (mean 37.4 voxels). For motor cortex,the threshold Z ranged from 5.6 to 10, producing regionsizes varying from 4 to 23 voxels (right motor cortexmean 9.0 voxels, left motor cortex mean 7.3 voxels).

Two additional features were considered in con-structing regions. First, regions were confined to asingle slice and the time of acquisition of that slice wasprecisely specified based on when, in the slice acquisi-tion order, the slice was acquired. Such a procedureeliminated artifacts associated with acquisition timingwhich vary from slice to slice for planar scanning.Estimates derived from the general linear model weretime shifted to the precise timing relative to the onsetof the visual stimulus of each selected slice for eachsubject. Second, so as not to bias definition of the regionin relation to any of the comparisons of interest, theregions were defined using all conditions (runs) from agiven subject. This pooling produced equal contribu-tions from each condition and allowed for significantpower in defining the regions. Subsequent effects be-tween conditions would reflect genuine differences andnot artifacts of the regional selection method.

Time course estimates were obtained for each regionby extracting the mean signal intensity for each timepoint within the ;18-s epoch.

Experiment 1: Effect of Trial Presentation Rate

Experiment 1 manipulated the mean intertrial inter-val (ITI) to determine the comparability of hemody-namic response estimates at different rates of trialpresentation. The basic trial consisted of a 1.5-s 8-Hzflickering checkerboard. Subjects were instructed topress a key, with their right hand, each time the check-erboard appeared. In this manner, hemodynamic re-sponses in visual and motor cortex would be elicitedand would provide a basis for estimation and compar-ison of the hemodynamic response in two separatebrain regions.

During each of eight functional runs (four sets of“interleaved run pairs”), one of four mean trial rateswas employed as described in Table 1. The trial ratewas varied between a mean rate of one trial every 5 s(minimum 2.5 s) to one trial every 20 s. For the threefastest rates, the spacing between individual trials wasjittered in time to allow linear estimation of the hemo-dynamic response as previously described by Dale andBuckner (1997) and Burock et al. (1998) and applied in
Buckner et al. (1998a) and Wagner et al. (1998). From
the subject’s perspective, this kind of trial spacing ap-pears as one continuous task block in which the onsetsof trials are unpredictable. For the most widely spacedtrials, the trials were presented at a fixed interval of20 s apart. Responses during these widely spaced trialsserved as the “gold standard” and were assumed to beessentially unaffected by response overlap. At the endof the eight functional runs, which were counterbal-anced for order of presentation rate across subjects, afinal set of widely spaced (20 s) trial runs was con-ducted. This last set was included for two reasons. Thefirst reason was to boost the number of trials contrib-uting to the gold standard estimate of the response.The second was to explore the effect of run order sincethe final set of widely spaced runs could be compared tothe identical set of runs occurring earlier in the ses-sion. For analyses in which effect of rate was the focus,only the counterbalanced interleaved run pairs fromthe first eight runs were considered. Thus, effects ofrate were explored in the context of fully counterbal-anced data.

Experiment 2: Effect of Sampling Rate and EstimatingBrief Temporal Offsets

Experiment 2 held constant the mean ITI at a ratenear the fastest rate considered in experiment 1 (5.36 smean, minimum 2.68 s). The basic trial was a slightlymodified variant of experiment 1. Subjects were againpresented with a 1.5-s 8-Hz flickering checkerboard oneach trial. However, subjects now made two separatemotor responses. With one hand, they pressed a keywhen the checkerboard appeared (Onset). With theother hand, they pressed a second key when the check-erboard disappeared (Offset). Across four runs (twointerleaved run pairs), subjects alternated which hand(right or left) was used to indicate Onset or Offset. In

TABLE 1

Trial Presentation Rates and Numbers of Trialsfor Experiment 1

Cond Trial spacing Min interval Mean interval No. of trials

TR1 Randomized 2.5 s 5.0 s 120TR2 Randomized 5.0 s 10.0 s 60TR3 Randomized 7.5 s 15.0 s 40TR8 Fixed 20.0 s 20.0 s 30TR8a Fixed 20.0 s 20.0 s 30

Note. Cond is the condition name based on the minimum numberof TR intervals that separate presentation of unique trials (eachTR 5 2.5 s). No. of trials is the number of trials per subject whichwere divided across two separate functional runs that constitute an“interleaved” run pair. For analysis of effects of rate, only the initialfour counterbalanced conditions were used.

a The last TR8 condition (Cond) always occurred in the last twoun positions, whereas the order of all other conditions was counter-alanced across subjects.

this manner, comparing trials across runs, the same

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motor region could be examined for a response to theOnset of the checkerboard and separately to the Offsetof the checkerboard. The two motor responses wouldoccur approximately 1 s apart. Note that this is not thesame as comparing responses across motor regions(which was also possible). In the present comparison,the motor region was held constant and the responsecondition (right hand, then left hand, or left hand, thenright hand) varied across runs. Moreover, for each sub-ject, two separate estimates of the Onset and Offsetresponses could be made (one for left motor cortex andone for right motor cortex) enabling generalization ofany within-region findings.

A further modification of experiment 2 was that twoseparate interleaved run pairs at the same fast ratewere acquired (four runs total). Having two run pairsallowed the data to be combined in two separate man-ners (Fig. 3). Each interleaved pair could be combinedto provide an estimate of the hemodynamic response inwhich the effective sampling rate is twice that of theTR, such as was done for experiment 1. In addition, bycombining the runs across interleaved pairs, the hemo-dynamic response could also be estimated for the moreconventional case in which the stimulus presentationwas fixed in relation to the image acquisition. More-over, this estimate could be obtained when the fixedrelation involved a trial occurring at the onset of theimage acquisition (Immediate) or delayed 1.25 s fromthe onset (Delay). Thus, by combining the runs in twoseparate manners, hemodynamic response estimates

FIG. 3. The interleaved procedure for data acquisition is illus-rated. The runs differ as to when the stimulus occurs in relation tohe image acquisition (represented by vertical broken lines), eitherccurring at the onset of the image acquisition (referred to as themmediate condition; top) or delayed by 1.25 s from the onset (re-erred to as the Delay condition; bottom). By obtaining separate runsf each of the Immediate and Delay acquisitions, the two runs can beombined (interleaved) to yield a temporal sampling rate twice thatf either run alone (middle).

could be obtained for the same amount of data for

which: (1) an interleaved sampling procedure wasused, providing an effective sampling rate of 1.34 s,and (2) a conventional Sparse sampling procedure(fixed relation between image acquisition and trial pre-sentation) was used yielding a sampling rate of 2.68 s.In this manner, the effect of sampling procedure couldbe determined. As a gold standard for comparison, thecombined data from all four runs were used.

Finally, because the interleaved run pairs were re-peated in each subject, the test–retest reliability ofhemodynamic response estimates could be explored.That is, one interleaved run pair could be used todetermine hemodynamic response estimates and thesecond interleaved run pair could be used to assesswhether those estimates could be reproduced.

RESULTS

Trial Presentation Rate Modestly Affects ResponseEstimation for Visual Cortex and Motor Cortex

Analyses were conducted on the data from experi-ment 1 to characterize properties of the hemodynamicresponse as a function of trial presentation rate. First,several analyses were conducted to check the validityof the procedures. In order to check the validity of themethods for characterizing the hemodynamic re-sponse, the fitted g function was plotted on top of eachsubject’s visual and motor cortex data based on thegold standard responses from the widely spaced trials(all four widely spaced trial runs were included). Qual-itatively, the model fit predicted the empirically de-rived visual cortex data (Fig. 4) yielding a mean esti-mate of amplitude of 2.30%, a mean estimate of time toonset of 1.82 s, and a mean estimate of time to peak of4.88 s. Motor cortex data were also modeled well by a gfunction, yielding mean estimates of amplitude of1.93%, of time to onset of 2.54 s, and of time to peak of4.44 s. It should be noted that although the assumed gunction model described the response for most types ofrials well, certain components appeared to be misseduch as the presence of a poststimulus undershoot,endering the fits less optimal than might be achievedith an increased number of model parameters or withdifferent model function (Fig. 4).Furthermore, the amplitude, time-to-onset, and

ime-to-peak estimates in visual cortex did not show anffect of run order as determined by comparing earlybeginning of session) and late (end of session) widelypaced trial runs (P . 0.15). Qualitatively, the three

estimates were quite similar (amplitude 2.35% forearly runs and 2.27% for late runs, time to onset 1.68 sfor early runs and 1.85 s for late runs, time to peak4.91 s for early runs and 4.85 s for late runs). Similarly,no effect of run order was observed in time-to-onset andtime-to-peak estimates for the motor cortex data (time
to onset 2.53 s for early runs and 2.54 s for late runs,

744 MIEZIN ET AL.

time to peak 4.43 s for early runs and 4.42 s for lateruns). Run order did significantly affect the motor cor-tex amplitude estimate [ANOVA F(7,1) 5 9.13, P ,0.05; amplitude 2.09% for early runs and 1.81% for lateruns].

The presence of an order effect in motor cortex andnot visual cortex may be attributed to the fact thatvisual cortex ability coincides with a relatively “pas-sive” response (not requiring voluntary control), whilemotor cortex activity is related to an “active” response(a finger press) which requires voluntary control andthus may become more efficient during the experiment.Thus, order effects can be significant, even in thissimple sensory/motor paradigm, reinforcing the needto counterbalance order across conditions.

Turning to the specific question of trial presentationrate, the basic shape of the hemodynamic response wassimilar, but not identical, across presentation rates.Considering only the first eight runs in which rate wasfully counterbalanced, the fastest presentation rate(mean ITI of 5 s) tended to show a smaller amplitude

FIG. 4. Visual cortex hemodynamic response estimates are showand the y axis amplitude (in percentage signal change). Hemodynamdiamonds. The curves represent the best fit model based on a g fun

hemodynamic response and the second fastest rate

(mean ITI of 10 s) tended to show a larger hemody-namic response for visual cortex. Using the model es-timate of amplitude, for visual cortex this effect ofpresentation rate was found to be significant [ANOVAF(7,3) 5 29.65, P , 0.0001] (Fig. 5A). Consistent withthe qualitative observation mentioned above, the fast-est rate was associated with the smallest hemody-namic response amplitude, although the quantitativeestimate of the amplitude reduction was modest (17%below the estimate for the widely spaced trials). Thegreatest amplitude was found for the second fastestrate (11% above the estimate for the widely spacedtrials). Both of these deviations in amplitude estimatefrom the widely spaced trials were significant in posthoc statistical tests: the fastest rate was associatedwith a significantly reduced amplitude [two-tailed t-test; t(7) 5 4.03, P , 0.005] and the second fastest ratewas associated with a significantly increased ampli-tude [two-tailed t-test; t(7) 5 5.27, P , 0.005]. Thus,the overall effect of rate on response amplitude wassignificant with a nonlinear pattern (Fig. 5A). Trial

r each subject in experiment 1. The x axis displays time (in seconds)esponse estimates from the general linear model are plotted as filledn.

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presentation rate showed a trend for an effect on am-

FIG. 5. Mean parameter estimates for the hemodynamic response are shown for both visual and motor cortex, across stimuluspresentation rates. For each graph, a different parameter is plotted on the y axis (A, amplitude in percentage signal change; B, time to onsetin seconds; and C, time to peak in seconds). The four presentation rates, in terms of their intertrial interval, are graphed separately on thex axis. Error bars represent standard errors of the mean. The bottom, D, graphs all of the data from all subjects together and shows the bestfit to each stimulus presentation rate using a solid line. This graph may differ slightly from the mean estimates in A, B, and C, as those are
obtained for each subject and then averaged.
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746 MIEZIN ET AL.

plitude in motor cortex regions [ANOVA F(7,3) 5 2.42,5 0.09]. Similarly to the visual cortex regions, the

astest trial presentation rate qualitatively showed aecreased amplitude with respect to the slowest trialresentation rate (25% below the estimate for theidely spaced trials; Fig. 5A).No consistent effects of rate for the estimates of

esponse timing (time to onset, time to peak) werebserved. An effect on time-to-onset estimate was ob-

served in the visual cortex data [ANOVA F(7,3) 5 3.48,P , 0.05] (Fig. 5B). Post hoc comparisons showed thathe mean time to onset of 2.05 s at the second fastestresentation rate (mean ITI 10 s) was significantlyonger than the mean time to onset of 1.74 s at the rateith a mean ITI of 15 s [two-tailed t-test; t(7) 5 2.61,

P , 0.05] and than the mean time to onset of 1.68 s atthe slowest rate (mean ITI 20 s) [two-tailed t-test;t(7) 5 2.54, P , 0.05]. No such significant effect on timeto onset was observed in motor cortex [ANOVAF(7,3) 5 0.25, P . 0.85]. No effect on time to peak wasbserved for either region. The estimated time to peakas similar across all rates; there was no effect of rate

n visual cortex [ANOVA F(7,3) 5 1.39, P . 0.25] nor inotor cortex [ANOVA F(7,3) 5 0.39, P . 0.75] and no

ost hoc comparison reached significance (Fig. 5C).As can be observed in Fig. 5A, the influence of trial

resentation rate on amplitude was quantitativelyodest despite its significance. Comparing the most

xtreme cases in visual cortex (the second fastest ratend the fastest rate), the amplitude decreased by 25%2.61 to 1.95%); comparing the fastest rate to the slow-st rate showed an amplitude reduction of 17% (2.35 to.95%). In terms of statistical significance associatedith detecting a response (used here as an estimate ofower), the increased number of events during theastest rate well outweighed the modest reduction inmplitude. In every subject, the Z score obtained foruns including data collected at the fastest rate wasigher than for any other rate (Fig. 6). Thus, for a fixed

FIG. 6. Power as estimated by mean Z score is plotted across thebars indicate standard errors of the mean.

un length, among the trial presentation rates tested f

ere, there was a clear power advantage for the fastestate. If the experimental goal is response detection,hese results would suggest faster is better (as theoret-cally suggested by Burock et al., 1998, and Bucknernd Braver, 1999). However, at the fastest rates thereay be a modest loss of signal amplitude (Fig. 5A).

Sampling Procedure Modestly Affects ResponseEstimation for Visual Cortex

Analyses were conducted on the data from experi-ent 2 to characterize hemodynamic response proper-

ies as a function of sampling procedure. Again, inrder to check the validity of the methods for charac-erizing the hemodynamic response, the model esti-ate based on the g function was applied to each

ubject’s visual cortex gold standard response. As cane seen visually, the model fit predicted the empiricallyerived data well (Fig. 7), yielding a mean amplitudestimate of 2.52%, a mean time to onset estimate of.06 s, and a mean time-to-peak estimate of 4.94 s.The effect of sampling procedure was examined by

omparing runs in which there was Sparse sampling2.68 s) to runs in which there was Interleaved sam-ling (effective sampling rate of 1.34 s). Two possiblestimates for each of the Sparse and the Interleavedampling procedures were available for each subject,wing to the crossing of four separate runs (see Fig. 3).hese estimates are referred to as Sparse–Immediate,parse–Delay, Interleaved–One, and Interleaved–wo. “Immediate” and “Delay” refer to when, after thetart of image acquisition, the stimulus occurred;One” and “Two” are arbitrary terms that refer to thewo separate but nominally identical estimates. Criti-ally, all estimates were based on the same amount ofata, allowing effects of sampling procedure to be de-ermined while holding constant the amount of dataontributing to each estimate.Sampling procedure modestly, but significantly, af-

r presentation rates for visual (left) and motor (right) cortex. Error
fou
ected the estimate of response amplitude [ANOVA


F(9,3) 5 4.79, P , 0.01] (Fig. 8). The effect, however,was counterintuitive: Sparse sampling produced over-estimates of the response amplitude regardless of whenthe stimulus occurred during the image acquisition. Inboth instances (Sparse–Immediate and Sparse–Delay),the amplitude of the hemodynamic response was over-estimated by at least 8% of its value. In contrast, inboth instances of interleaved sampling, the amplitudeestimate was 61% of the gold standard estimate value.Post hoc statistical tests supported all of these conclu-sions. Both Sparse sampling procedures yielded signif-icantly increased estimates compared to either of theInterleaved estimates (all P , 0.05, except Sparse–Immediate versus Interleaved–Two was P 5 0.06). Incontrast, Sparse–Delay was not significantly different

FIG. 7. Visual cortex hemodynamic response estimates are showand the y axis displays amplitude (in percentage signal change).displayed as solid diamonds. The lines represent the best fit model

from Sparse–Immediate and Interleaved–One was not

significantly different from Interleaved–Two (both P .0.15).

No significant effect of sampling procedure on re-sponse timing was observed [ANOVA F(9,3) 5 2.27,P . 0.10 for time-to-onset estimates and ANOVAF(9,3) 5 0.70, P . 0.55 for time-to-peak estimates) andno post hoc comparison reached significance. Nonethe-less, a qualitative analysis suggested a common trendof overestimation of the time-to-onset estimate in thetwo Sparse conditions, while no such trend was seen ineither of the two interleaved conditions (Fig. 8B).Quantitatively, the greatest difference in time-to-onsetestimates was between the gold standard estimate andthe Sparse–Immediate estimate (0.47 s). Conversely,no such qualitative trend could be discerned for the

r each subject in experiment 2. The x axis displays time (in seconds)odynamic response estimates from the general linear model are

ed on a g function.

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time-to-peak estimates.

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748 MIEZIN ET AL.

In terms of statistical significance associated withdetecting a response (used here as an estimate ofpower), the mean Z scores were very similar for allsampling procedures, suggesting that, within the pa-rameter constraints of this study, all forms of samplingwould be equally likely to detect a response (Fig. 9).

Amplitude Estimates Are Unrelated to Timing Estimatesfor Visual Cortex

A natural question to ask about the hemodynamicesponse is the relation between the amplitude of theesponse and the timing of the response. One possibil-ty is that the two are related: a larger hemodynamicesponse takes longer to build and is slower to decay,hile smaller responses might evolve more rapidly.nother possibility is that the two are unrelated andeflect independent quantities that vary across sub-ects. Both experiments 1 and 2 provide data that coulde used to answer this question. For both experiments,he visual cortex gold standard estimates of response

FIG. 8. Mean parameter estimates for the hemodynamic re-sponse are shown for visual cortex, across the different samplingprocedures. For each graph, a different parameter is plotted on the yaxis (A, amplitude in percentage signal change; B, time to onset inseconds; and C, time to peak in seconds). The different samplingprocedures are graphed separately on the x axis. Error bars repre-sent standard errors of the mean. The first two columns in eachgraph come from the Sparse sampling procedures, the next two fromthe Interleaved sampling procedures. The rightmost, darkly filledbar represents data from the gold standard estimate using all data.The dotted line in each graph represents the mean as determined bythe gold standard estimate. The bottom, D, graphs all of the esti-mates from all subjects together and shows the best fit to the esti-mates using a solid line. These solid lines thus represent that shapeof the hemodynamic response that would be estimated for eachsampling procedure if all of the data, across subjects, were pooled.This graph may differ slightly from the mean estimates in A, B, and

FIG. 9. Power as estimated by mean Z score is plotted across thefour sampling procedures. Error bars indicate standard errors of themean.

C as those are obtained for each subject and then averaged.

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amplitude, time to onset, and time to peak were exam-ined to determine the degree of correlation across sub-jects. For experiment 1, the data came from the fourruns (two interleaved run pairs) that contained trialsspaced widely apart. For experiment 2 the data camefrom the four runs that all contained rapidly presentedtrials (again two interleaved run pairs). Results areshown in Fig. 10.

As can be seen visually there was negligible relationbetween response amplitude and timing (time to onsetand time to peak). Larger amplitude responses did notsignificantly predict slower time to onset of the hemo-dynamic response, in either experiment 1 or experi-ment 2 (r2 5 0.30 and 0.00, respectively; both P . 0.15).

he modest, nonsignificant, correlation in experimentappears to be carried largely by a single subject.

imilarly, larger amplitude responses did not signifi-antly correspond to slower time to peak of the hemo-ynamic response. For experiments 1 and 2, r2 5 0.14

and 0.00, respectively (both P . 0.35). The lack of

FIG. 10. The relations between separate parameter estimates arepresents data from a single subject. The graphs labeled A plot the rlabeled B plot the relation between estimated amplitude and time toeach) are also displayed. Note that there is little consistent relation

predictive power was not due to the instability of the

estimates themselves as is shown in the next section.Rather, the lack of significant correlation between re-sponse amplitude and timing appears more likely to bedue to the fact that the two are unrelated when re-gional hemodynamic responses are estimated. As afurther illustration of this point, Fig. 11 shows thehemodynamic response for each individual subject inexperiments 1 and 2. In these data sets, the largestamplitude response (indicated as A) occurred in thepresence of a response evolving within the averagetime frame, while the slowest evolving response (indi-cated as B) occurred within a response of average am-plitude.

Amplitude and Timing Estimates Are Extremely Reliablefor Visual Cortex

Centrally important to estimates of response ampli-tude and timing is the reliability of such estimates. Forexample, it is possible that the lack of predictive power

plotted for visual cortex for both experiments. Each solid diamondtion between estimated amplitude and time to onset and the graphsak. The regression line (dotted line) and correlation (bottom right oftween the amplitude estimates and either estimate of timing.

reelape

between response amplitude and timing observed in

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750 MIEZIN ET AL.

the preceding section was due to the instability of theestimates. Data from experiment 2 were analyzed toaddress this issue. Experiment 2 contained two sepa-rate interleaved run pairs (Interleaved–One and Inter-leaved–Two), which were each collected identicallywithin the same subjects. These two run pairs couldthus be used to determine the reliability of the hemo-dynamic response estimates. Results are shown in Fig.12.

For all estimates high reproducibility was obtained:for response amplitude r2 5 0.98, for response time toonset r2 5 0.60, and for response time to peak r2 5 0.95(all P , 0.001). These strikingly high correlations (es-

ecially for amplitude and time to peak) stand in starkontrast to the lack of significant correlation betweenmplitude and time-to-onset estimates and betweenmplitude and time-to-peak estimates. Thus, while thestimates of amplitude and timing (time to onset andime to peak) are highly reliable, they appear to beompletely uncorrelated with each other in the contextf the present study. Of the three forms of estimate,mplitude and time to peak were the most stable.

Response Properties in Visual Cortex Failed to PredictProperties in Motor Cortex

A further question that can be asked is how wellesponses estimated in one region can predict responseharacteristics in another region. That is, does an in-ividual with a high-magnitude response in visual cor-ex tend to have a high-magnitude response in motorortex? To answer this question the amplitude, time-o-onset, and time-to-peak estimates from experimentwere correlated across regions (using the gold stan-

FIG. 11. The across-subject variability of the hemodynamic respoThe left plots the 8 subjects from experiment 1 and the right plots tamplitude and time to peak (averaged across subjects) for each experibetween amplitude and timing estimates. Larger amplitude responseby two subjects in experiment 2. The subject labeled A has an extremthe mean. In contrast, the subject labeled B has the longest time tosimilar to the mean.

ard estimate from the conditions with a mean ITI of

20 s). No correlations were significant (Fig. 13). Therewas a modest magnitude of correlation in amplitude(r2 5 0.39; not significant P 5 0.1) but it was in theopposite direction as would be expected: increased vi-sual cortex amplitudes predicted lower motor cortexamplitudes. The lack of significance and odd directionof correlation cast doubt on the existence of an actualrelation between responses in different regions in thepresent data. The r2 for time to onset and time to peakwere 0.01 and 0.02, respectively. Thus, knowing theamplitude and delay of a hemodynamic response invisual cortex for a subject tells the experimenter littleabout the characteristics of the response in motor cor-tex, at least insofar as the analysis is applied tohealthy young adults.

Relative Estimates of Response Timing Can Be Used toInfer Relative Offsets in the Timing of Neural Activity

Absolute estimates of hemodynamic response timingmay not always be sufficient for making inferencesabout the timing of neural activity between brain re-gions. Variance in the timing of the response acrossregions can be considerable, even when nearly adjacentvoxels are considered. However, the extreme stabilityof the timing of the hemodynamic response within aregion still leaves open the possibility of making infer-ences about relative changes in the timing of neuralactivity within a region. That is, for a given region, thehemodynamic response (whatever its temporal profile)may shift in time to reflect changes in the timing of anunderlying neuronal response. Experiment 2 providesdata to test this possibility.

Experiment 2 counterbalanced two separate motor

is illustrated by plotting each subject’s estimate on the same graph.0 subjects from experiment 2. The dotted lines represent the mean

nt. Of particular interest is the visualization of the lack of correlationo not necessarily lead to longer temporal evolution, as shown clearlyhigh amplitude response, yet evolves with a temporal evolution neark and second longest time to onset, yet has an amplitude estimate

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response to the Onset or Offset of the visual stimuluscausing the motor response for a given hand to betemporally offset across runs. Two separate conditionswere used, in which the subjects were instructed topress with their right hand at stimulus Onset and withtheir left hand at stimulus Offset or vice versa. Inrelation to the question of timing differences betweenOnset and Offset responses, it should be noted that,behaviorally, the Offset responses were significantly

FIG. 13. The relation of the parameter estimates across brainregions (visual and motor) is plotted for the second experiment (A,amplitude in percentage signal change; B, time to onset in seconds;and C, time to peak in seconds).

faster for both the right-hand-first and the left-hand-

FIG. 12. The reliability of the parameter estimates is plottedfor the second experiment, in which two independent Interleaveddata sets were acquired for each subject. Each filled diamondrepresented data from a single subject. Each graph represents thereliability of a separate parameter estimate, plotting the estimatefor the first data set in a given subject against the value for thesecond data set. (A) Amplitude in percentage signal change, (B)time to onset in seconds, and (C) time to peak in seconds. Ideally,the correlation would be 1.00 and all data points would fallalong the diagonal; movement along the diagonal reflects be-tween-subject variance. For amplitude (A) and time to peak (C)estimates, this ideal is nearly achieved. The time to onset (B) isless stable, but still highly correlated from one measurement tothe next.

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752 MIEZIN ET AL.

first conditions, likely indicating preparation or antic-ipation of the Offset responses [t(9) 5 3.30 and 4.12,respectively; both P , 0.01]. For the right-hand-first(left motor cortex) condition, the “Onset” response oc-curred 310 ms after stimulus Onset and the “Offset”response 285 ms after stimulus Offset; for the left-hand-first (right motor cortex) condition, these re-sponse times were 344 and 292 ms, respectively.

To answer the question of whether hemodynamicresponse estimates can reflect changes in underlyingneuronal activity, timing (time-to-onset and time-to-peak) estimates were made for both the left and theright motor cortex regions comparing directly thoseestimates based on Onset responses to those estimatesbased on Offset responses. Estimates of timing withineach motor region showed a significant change in tim-ing between Onset and Offset conditions. For the rightmotor cortex, the estimated time to onset shifted from2.23 to 3.10 s [t(9) 5 4.09, P , 0.005], while the esti-mated time to peak shifted from 4.25 to 4.98 s [t(9) 59.33, P , 0.0001]. Similarly, for the left motor cortex,he estimated time to onset shifted from 2.08 to 3.15 st(9) 5 6.15, P , 0.0005] while the estimated time toeak shifted from 4.08 to 4.79 s [t(9) 5 5.24, P ,

0.0005]. Thus, the estimated hemodynamic responsewithin motor cortex shifted significantly by 0.75 s to 1 swhen the response occurred to Offset as opposed toOnset of the visual stimulus. This value is quite plau-sible given the paradigm constraint that the Offsetresponses could be prepared in advance of their execu-tion (and the finding that Offset responses were signif-

FIG. 14. Timing offsets in motor cortex for experiment 2 are distime (in seconds) and the y axis represents signal change (in percentathose conditions in which the contralateral motor response was mrepresents the analogous estimate for when the contralateral motor rpositions of the responses are shown schematically by solid bars at tevident in both right and left motor cortex, consistent with the orde

icantly speeded). While providing only a rough esti-

mate, these results when submitted to a poweranalysis imply that a relative offset in hemodynamicresponse timing of as little as 100 ms could be detectedin conditions similar to the present study 50% of thetime at a 5 0.05. Figure 14 shows the averaged hemo-dynamic response across subjects with the temporalshift between the Onset and the Offset response clearlyvisible.

A further extension of this kind of analysis that mayprovide information about relative timing offsets be-tween regions is possible (Friston et al., 1998). Forexample, motor cortex may change the timing of itsactivity more than visual cortex (each relative to theirown timing baseline). Relative timing offsets may al-low inferences about which regions are involved in acognitive or behavioral operation and in what order.

To illustrate this possibility, estimates of the time toonset and time to peak from the present data set weresubjected to a region (visual cortex, left motor cortex,right motor cortex) 3 condition (right hand first, lefthand first) ANOVA. The logic was as follows. Regionswhose hemodynamic response timing is affected by thecondition manipulation likely reflect those regions par-ticipating in the process that differed across conditions(in this instance motor programming and execution)and/or are downstream from regions affected by theprocess. Regions that are unaffected by the conditionmanipulation would be those earlier in the processinghierarchy and/or unrelated to the process being manip-ulated. In the present example, the prediction would bea region 3 condition interaction, with post hoc analy-

ed separately for right and left motor cortex. The x axis represents). In each graph, the earlier curve represents the pooled estimate forfirst (at the Onset of the visual stimulus), while the latter curveonse came second (at the Offset of the visual stimulus). The relativebottom. A significant offset in the hemodynamic response is clearlyg of the motor responses.

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manipulation (whether a right or a left key press wasmade first) and visual cortex unaffected. The maineffect of region would be uninteresting and involve themultiple possible influences for baseline differences inhemodynamic delay. Critically, the interaction of re-gion 3 condition would be significant only if the condi-tion manipulation influenced response timing aboveand beyond the baseline differences in regional timing.

Figure 15 illustrates the interaction graph. A clear,significant interaction of region 3 condition existed foroth time-to-onset and time-to-peak estimatesF(2,27) 5 35.32, P , 0.0001 for time to onset and

F(2,27) 5 58.50, P , 0.0001 for time to peak]. Thepattern lends itself to a straightforward interpretation.Visual cortex is unaffected by whether the first keypress is made with the right or left hand. In contrastmotor cortex is directly affected by which hand makesthe first key press. Left motor cortex is fastest whenthe right hand presses first; right motor cortex is fast-est when the left hand presses first. The inferencewould be that motor cortex is involved in the processand its involvement comes after that of visual cortex,which is completely unaffected by the condition manip-ulation.

A further point is worth making with regard to theabsolute timing of the response across regions. Whilethe time-to-onset estimates behaved in a manner gen-erally consistent with the expected time course of brainactivity (visual cortex preceding motor cortex), it didnot do so consistently. A clear violation of the expected

FIG. 15. Parameter estimates of time to onset (left) and time toresponse conditions. The two conditions (plotted on the x axis) indicatresponse (left3 right) or vice versa (right3 left). A clear and significcortex does not change timing in relation to motor response conditioin that right motor cortex responds fastest when a left key press is mis made first. Error bars indicate standard errors of the mean.

pattern was observed: visual cortex appeared to onset

after left motor cortex in one condition. This seemsunlikely to reflect a true assessment of neuronal activ-ity. Thus, the absolute estimate of the time to onsetshould be interpreted cautiously. Absolute estimates ofthe time to peak are even more difficult to interpret.While the motor response is presumably brief in time,the visual response used here evolves over a longerperiod of time so that the peak response can occur laterin visual cortex than in motor cortex.

DISCUSSION

The hemodynamic response was extracted from rap-idly presented trials across two separate ER-fMRIstudies using linear estimation. A number of clear ob-servations emerged that can be summarized as follows:

(1) The hemodynamic response can be estimatedduring rapid-presentation ER-fMRI paradigms usinglinear estimation methods without making assump-tions about the shape of the response. Moreover, theseestimates are possible in the context of whole-brainimaging and MR sampling rates as sparse as one ac-quisition every 2.68 s.

(2) For experiment 1, the visual cortex response inthe context of rapidly presented trial events began at1.90 s (time to onset), peaked at 4.75 s (time to peak),and reached an amplitude of 1.95%. For experiment 2,these estimates were 2.06 s (time to onset), 4.94 s (time

k (right) are plotted for each region, for each of the separate motorhether a left-hand response was made first, followed by a right-handinteraction is observed for both forms of parameter estimate. Visualhile motor cortex does. Motor cortex shows a crossover interaction

e first and left motor cortex responds fastest when a right key press

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similar, but not identical to, estimates based on widelyspaced trials.

(3) Trial presentation rate had a modest, but signif-icant, effect on the estimated response amplitude forvisual and motor cortex. In particular, rapidly pre-sented trials (;5 s apart on average) showed a 17%visual cortex) and 25% (motor cortex) reduction instimated amplitude compared to trials spaced in time.t is unclear whether the reduction is due to hemody-amic response saturation or to differences in under-

ying neuronal activity across rates.(4) Despite the modest amplitude reduction at fast

rial-presentation rates, the power for detecting a re-ponse was significantly greater at fast rates owing tohe increased number of trials possible. In other words,he increased number of trials outweighs the reductionn response amplitude, insofar as power in detecting aesponse is the goal.

(5) Sampling procedure had a modest, but signifi-ant, effect on the estimated response amplitude forisual cortex. Sparse sampling, where measurementsere made every 2.68 s, showed an 8% overestimate

ompared to denser sampling (effective sampling rate.34 s). In terms of statistical power, both sparse andense sampling procedures were equivalent.(6) The estimated amplitude and timing (time to

nset and time to peak) of the hemodynamic responseere stable across separate data sets collected in the

ame subject, for the same region (r2 5 0.98, 0.60, and0.95 for amplitude, time to onset, and time to peak,respectively). Thus, the amplitude and time-to-peakestimates were nearly perfectly correlated from onedata set to the next, positioning them as extremelyreliable measures of the hemodynamic response, atleast insofar as good signal-to-noise properties exist inthe data.

(7) The estimated timing (time to onset and time topeak) of a region’s hemodynamic response could not be

sed to predict its amplitude. The two components ofhe response appeared unrelated on the spatial scale ofrain regions.(8) Estimates of response properties in visual cortex

id not predict response properties in motor cortex,uggesting that, across subjects, the regional variationn response is substantially greater than any globalactors influencing response properties that varycross young, normal subjects. That is, if there is ten-ency for one subject to have globally larger and/orlower hemodynamic responses than another subject,uch a tendency could not be detected in the presentata.(9) Estimates of relative change in timing of the

emodynamic response within a region could be de-ected for a temporal difference of under a second.

hen motor response was delayed, a clear temporalhift of the hemodynamic response in motor cortex was
bserved. Preliminary power analysis suggests the
limit for detecting a temporal offset within a region,using our procedures involving whole-brain data acqui-sition and a TR of 2.68 s, may be as little as 100 ms.

(10) Relative timing changes between regions couldbe used to make inferences about which regions con-tributed to motor response programming. Specifically,in the present study, an interaction between visual andmotor cortex was found in relation to motor responsedelay, with a significant effect of timing identified onlyfor motor cortex. This analysis empirically suggeststhat motor cortex predicts the delay in response; visualcortex does not. Moreover the presence of a delay inmotor cortex and not in visual cortex suggests that theprogression of processing goes from visual to motorcortex hierarchically in this paradigm. While such afinding is easily predicted based on known roles forvisual and motor cortex, the empirical finding wasdriven by the timing estimates across regions and theirrelation to behavioral data, not preexisting knowledge.Thus, analysis of relative timing across regions may bea powerful method for determining the processing con-tributions of brain regions where their role in a cogni-tive or behavioral process is less well understood.

Implications

The present observations have a number of practicaland conceptual implications. These relate to the fourareas outlined in the Introduction: hemodynamic re-sponse summation, variance of the hemodynamic re-sponse, hemodynamic response sampling, and hemo-dynamic response estimation. In addition, the resultshave important implications for a possible new use offunctional MRI involving the ordering of processes be-tween brain regions based on relative timing effects.Each of these areas is discussed separately.

Hemodynamic Response Summation

Consistent with the near-linear summation proper-ties previously observed in fMRI studies using BOLDcontrast (e.g., Boynton et al., 1996; Dale et al., 1997),the shape and properties of the hemodynamic responseremained roughly the same across presentation rates(see Fig. 5D). In the fastest presentation conditions inthis study (minimum ITI 2.5. s; mean ITI 5.0 s), inwhich there was maximum overlap across trials, theestimates of the hemodynamic response were similarto those for trials spaced widely apart. Such a findingreinforces the empirical observation that fast presen-tation rates can be used in cognitive neuroimagingstudies (Buckner et al., 1998a; Clark et al., 1998; Wag-ner et al., 1998).

There was evidence for saturation of the response inthat the amplitude of the response at the fastest ratewas between 17% (visual cortex) and 25% (motor cor-tex) reduced relative to the slowest rate (see Fig. 5A).
This reduction in amplitude was present after the he-

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modynamic response was estimated within the generallinear model to remove overlap across trials. Thepresent data do not distinguish between the possibilitythat the observed reduction in response amplitude rep-resents a change in the underlying neural response(e.g., a form of habituation or interaction across adja-cent events) or whether the neuronal response is con-stant and the hemodynamic response itself saturated.

Almost all previous studies of hemodynamic re-sponse summation have noted some form of nonlinear-ity when temporally extended or overlapping eventswere considered. Nonlinear summation has sometimesbeen quite pronounced at extremely fast trial presen-tation rates (e.g., Friston et al., 1997). The finding ofmodest amplitude reduction in the present study isconsistent with the observation that some amount ofsaturation can occur at rates in the range of one trialevery few seconds. However, the consequence of ampli-tude reduction was marginal in the present data set,and the data suggest that response summation is suf-ficiently linear to use rapid presentation paradigms.Robust responses were detected at all rates and, due tothe fact that considerably more trials are available atfaster rates, the power to detect a response was great-est at the fastest rate. The timing of the hemodynamicresponse remained largely stable across presentationrates, in terms of both time to onset and time to peak.

Variance of the Hemodynamic Response

Three kinds of variance related to the hemodynamicresponse were explored: variance across data sets forthe same region within a subject, variance across sub-jects for a given region, and variance across regions.The first kind of variance (pertaining to the same re-gion within a subject) presented the most optimisticfinding: for a given region, the hemodynamic responsewas nearly identical from one data set to the next.Figure 12 illustrates this point most directly. Esti-mates of amplitude and time to peak were nearly per-fectly correlated between separate data sets (r2 5 0.98,r2 5 0.95). The statistically significant correlation forime to onset was lower, but nonetheless quite highr2 5 0.60). Another place where this extreme stability

could be seen was when separate estimates were com-pared for data averaged over subjects, in which everysubject contributes to each estimate. Figure 8D illus-trates such a comparison. When the Interleaved sam-pling procedure was used, the two separate estimatesproduced hemodynamic responses that overlappednearly completely. The extreme stability of the hemo-dynamic response within a region, for a given subject,was exploited in estimating temporal offsets acrossregions, as will be discussed below.

The second kind of variance—between subjects for agiven region—showed more variation but still revealed
considerable central tendencies across subjects. Figure
11 shows the hemodynamic response for a region invisual cortex for each subject. As can be seen visually,the amplitude of the visual response tended to bearound 2% and varied with a range of 1.95 to 3.15% inexperiment 1 (widely spaced trials) and between 1.57and 4.28% in experiment 2; the standard deviationswere 0.40 and 0.73%, respectively. Time to onset andtime to peak also showed strong central tendencies.This range of variation suggests that it is reasonable toaverage across subjects with the assumption that agroup of 10 or more subjects would closely approximatea modal response for a given region (such as is donewith many event-related data analysis procedures).The error induced would be relatively small, on aver-age. However, there is sufficient variance that for pre-cise estimates either large samples of subjects would berequired to make comparisons across groups or within-subject designs should be adopted.

Variance across regions, even within the same sub-jects, was found to be sufficient to present a formidablechallenge to interpretation of absolute timing parame-ters across regions. Considering regions in visual andmotor cortex, there was almost no relation betweenamplitude or timing estimates between regions (Fig.13). That is, knowing the amplitude and delay of asubject’s response in visual cortex did little to informone about those parameters of the response in motorcortex. Moreover, the absolute estimates themselvesappeared to have only a rough relation to the likelyordering of activity within the regions. For example, inone condition, motor cortex appears to onset (in termsof estimated hemodynamic response parameters) ear-lier than visual cortex (Fig. 15, left, right3 left condi-ion). This inability to make predictions across regions,r to reveal consistently interpretable relations be-ween absolute measurements across regions, may beue to the underlying differences in vasculature (Lee etl., 1995; Robson et al., 1998) or to as yet undetermined

factors.The practical upshot of these findings is that the

present data do not support the possibility of usingabsolute measurements of the hemodynamic responsein one region to predict or interpret measurements inanother region (in healthy young adults).

Hemodynamic Response Sampling

Experiment 2 allowed a direct comparison of twosampling procedures. In the first procedure, hemody-namic response estimates were obtained for data ac-quired with systematically varied delays between theimage acquisition and the trial presentation (Josephset al., 1997). Varying the delay allows one to increasethe effective sampling rate by systematically acquiringthe data at different points during the hemodynamicresponse. In our implementation, the stimulus was
either presented at the beginning of the whole-brain

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image acquisition or delayed by 1.25 s. We call this“interleaved” because the resulting hemodynamic re-sponse estimates can be interleaved to reconstruct acontinuous estimate (Fig. 3). In the second samplingprocedure the stimulus always appeared at the sametime relative to the image acquisition.

The theoretical reason for employing an interleavedprocedure is the desire to estimate the true shape ofthe response with as high temporal sampling resolu-tion as is practically possible (Josephs et al., 1997;

rice et al., 1999). The present study allowed a directxamination of the utility of such a procedure by hold-ng constant the amount of data contributing to a givenemodynamic response estimate and manipulatinghether or not the sampling used an interleaved pro-

edure. What advantage, if any, does a procedure withnterleaved sampling have over fixed sampling?

For the most commonly used forms of analysis inhich response detection is the goal, the benefit of

nterleaved sampling appears minimal. All proceduresielded estimates of the hemodynamic response thatere roughly similar (Fig. 8). However, this finding

hould not be generalized to instances of sparser sam-ling (e.g., 4–5 s or more), which have been shown toave marked effects even in blocked-task paradigmsPrice et al., 1999). Nonetheless, in the present study, aampling rate of 2.68 s was found to consistently esti-ate the response to within several tenths of a per-

entage of its amplitude, and within about one-halfecond for all timing estimates.However, the interleaved sampling procedure was

onsistently better at estimating the exact value foresponse amplitude and timing (specifically the time tonset). Two separate measures indicated this improve-ent. The first relates to how close the estimates for

ach sampling procedure were to the gold-standardstimates obtained from the pooled data with optimalemporal sampling. The interleaved estimates wereoth within one-tenth of a second for time to onset andime to peak and within one-tenth of one percent formplitude (e.g., see Figs. 8A and 8B). In contrast, theparse sampling estimates, which did not involve in-erleaved sampling, were nearly one-half of a percentnd one-half of a second different from the gold stan-ard estimates. While it is impossible in the presentontext to know whether the gold standard estimateruly represents the most valid estimate of the under-ying response, it is our best guess and, holding themount of data contributing to an estimate equal, in-erleaved sampling provided estimates closer to thisold standard.The second measure that indicated an improvement

or the interleaved sampling procedure was its reliabil-ty across separate data sets. As noted, two indepen-ent interleaved data sets were acquired in each sub-ect, allowing two independent estimates of the
esponse for an averaged group of subjects. The mean
isual cortex estimates for amplitude, time to onset,nd time to peak for the first data set were 2.49%,.03 s, and 4.98 s, respectively. These estimates for theecond independent data set were 2.54%, 2.13 s, and.90 s, respectively. The largest difference was for thestimated time to onset, which was less than one-tenthf one second. Furthermore, the estimated shapes ofhe hemodynamic responses nearly overlapped acrosshe two separate data sets (Fig. 8D). Thus, a benefit ofhe interleaved sampling procedure is conveyed to theegree that an application requires the extra level ofrecision in the hemodynamic response estimate. Oneossible application will be discussed below under Or-ering of Processes between Brain Regions Based onelative Timing Offsets. Other applications also exist

e.g., characterization of temporally fine aspects of theemodynamic response such as the “pre-dip,” Hu et al.,999, or the “post-undershoot,” Buxton et al., 1999). Ifrecise amplitude and timing estimations are not re-uired, a sampling rate of about 21

2 s would appearsufficient for most rapid presentation ER-fMRI appli-cations that attempt to detect the robust positive de-flection of the BOLD hemodynamic response.

Hemodynamic Response Estimation

A central component of the procedures employed inthe present studies was automatically estimating theamplitude and timing of the hemodynamic responses.The basic model was a three-parameter g function withan added delay (time to onset) parameter (Dale andBuckner, 1997; extended from Boynton et al., 1996).The raw estimates of the hemodynamic response werefit to this function using a least-squares procedure.Estimates of amplitude, time to onset, and time to peakwere then derived (see Fig. 2). Because of the impor-tance of these estimates to the present paper, and thebroad need for developing stable methods for quantify-ing event-related fMRI data, it is worth discussing thesuccesses and failures associated with this procedure.

Overall, the data were well fit by a simple g function.Figures 4 and 7, for example, show the raw data su-perimposed on the best fit model for each of the sub-jects. Most of the variance is accounted for and the fitappears face valid, as the model’s peak approximatesthe data peak, and the model’s timing estimate approx-imates the temporal changes in the data. However, twodeviations from the model can also be observed, al-though these would not be expected to affect the am-plitude or time-to-peak estimates.

First, the model failed to account for a poststimulusundershoot that was present in many data sets (e.g.,the first three subjects, vc734, vc750, and vc751, in Fig.4). This undershoot has been observed in event-relatedfMRI data previously (Boynton et al., 1996; Dale andBuckner, 1997; Buckner et al., 1998a) and may reflect
a temporally lagged component of the hemodynamic

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response relating to blood volume change (Mandevilleet al., 1996; Buxton et al., 1998). Regardless of theorigin, the model based on a single g function did notaccount for the poststimulus undershoot. Indeed, giventhe basic form of a g function, there is no way that itcan model a second inflection in the data, such as isobserved for the extended components of the responseundershoot (Fransson et al., 1998a,b). Second, on therising portion of the response, the raw data showed anincrease in signal intensity that was more spread outthan provided for by the model. This could often beseen at about 2 s after the stimulus onset (e.g., vc750and vc751 in Fig. 4 or vc518 and vc519 in Fig. 7). Thislatter component relating to the rise of the curve mayhave influenced the time-to-onset estimate, which wasthe least stable of the quantified variables, as dis-cussed above in the context of variability.

One caveat about the fitting procedures employed isthat, although the response estimates were initiallycomputed in an assumption-free manner, regions foranalysis were selected based on statistical maps gen-erated by cross-correlation to a g function. In this re-ard, voxels showing responses of significantly differ-nt shape—that deviate from a single peaked,elatively transient form—would be missed by theresent analyses. Thus, the description and appropri-teness of the fitting procedure employed may not gen-ralize to all circumstances and responses. In theresent study, there was a bias toward identifying aertain class of hemodynamic response shapes which,o our knowledge, is appropriate to visual and motorortex and likely appropriate for many cortical regions.

Ordering of Processes between Brain Regions Basedon Relative Timing Offsets

Perhaps the most significant implication of the afore-entioned observations is the possibility of ordering

he temporal cascade of processing across brain re-ions, a possibility raised previously by Menon andolleagues (1998). The present study was able to detectsignificant interaction across the timing of regions

visual and motor cortex) in relation to whether a re-ponse was made first with one hand, then with thether. Specifically, as would be expected, the analyseshowed an interaction between visual and motor cor-ex. Visual cortex showed no effect of response orderinghile motor cortex was significantly influenced by therder of response, showing an increased delay whenhe contralateral response took longer. This result isot surprising but has potentially broad implications.vent-related fMRI is able to detect temporal offsetsithin regions and to further contrast relative tempo-

ral offsets across regions.The emphasis on “relative” is important here be-

cause the absolute timing estimates seemed to vary in
a sometimes unpredictable manner that may reflect
differences in underlying vasculature. Thus, while thepresent results show how powerful evaluation of rela-tive timing changes across regions may be, the resultsalso cast doubt on always using the absolute measuresof timing as reliable indices (see Friston et al., 1998, fora similar point). Caution is suggested since some abso-lute timing estimates revealed delay ordering thatseemed implausible in the present paradigm (e.g., mo-tor cortex activating earlier than visual cortex). Fur-thermore, using relative timing estimates makes sev-eral implicit assumptions about the regions active in atask, namely, that the regions are hierarchically re-lated to one another and that they directly participatein task completion. Examination of relative timing islikely to be a powerful tool but only for those circum-stances in which reasonable assumptions can be madeabout the underlying functional anatomy.

The present study employed whole-brain functionalimaging in the context of routinely used imaging pa-rameters (a low-field 1.5-T scanner and 16-slice whole-brain acquisition across a TR of 2.50 or 2.68 s). Theresults obtained with these imaging parameters, whichare similar to parameters used by many laboratoriesemploying fMRI, suggest that examining temporal re-lations across brain regions should be possible by mod-ifying the behavioral paradigms and image analysisprocedures. Specifically, using some form of procedureto effectively increase the sampling rate (our inter-leaved procedure or that of Josephs et al., 1997) cou-pled with a model fitting approach to estimate responsetimes, appears sufficient to estimate relative delays ofless than a second. There is a wide range of cognitiveneuroscience questions that would benefit from thisform of analysis. In addition, such procedures mayserve as an anchor point for making between-modalitycomparisons between fMRI and MEG/EEG or fMRIand optical imaging methods.

ACKNOWLEDGMENTS

We thank Amy Sanders for help with data collection, Bill Kelleyfor help with implementation of the behavioral component of thestudy, and Erbil Akbudak, Abraham Snyder, and Thomas Conturofor support and development of the MRI procedures. Todd Braverprovided valuable comments on an early draft of the manuscript.R.L.B. thanks Bruce Rosen and Robert Savoy for discussion thatmade this work possible. This work was supported by grants fromthe McDonnell Center for Higher Brain Function (to R.L.B.), NIHGrants MH57506 (to R.L.B.) and NS32979 (to S.E.P.), and a contractfrom the government (to Henry Roediger).

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