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Spatio-temporal information analysis of event-relatedBOLD responses

Galit Fuhrmann Alpert,a,⁎ Fellice T. Sun,a Daniel Handwerker,a

Mark D’Esposito,a,b and Robert T. Knighta,b

aHenry H. Wheeler Jr Brain Imaging Center, Helen Wills Neuroscience Institute, University of California at Berkeley, Berkeley, CA 94720-3190, USAbDepartment of Psychology, University of California at Berkeley, Berkeley, CA 94720-1650, USA

Received 1 March 2006; revised 27 September 2006; accepted 6 October 2006Available online 22 December 2006

A new approach for analysis of event-related fMRI (BOLD) signals isproposed. The technique is based on measures from information theoryand is used both for spatial localization of task-related activity, as wellas for extracting temporal information regarding the task-dependentpropagation of activation across different brain regions. This approachenables whole brain visualization of voxels (areas) most involved incoding of a specific task condition, the time at which they are mostinformative about the condition, as well as their average amplitude atthat preferred time. The approach does not require prior assumptionsabout the shape of the hemodynamic response function (HRF) norabout linear relations between BOLD response and presented stimuli(or task conditions). We show that relative delays between differentbrain regions can also be computed without prior knowledge of theexperimental design, suggesting a general method that could be appliedfor analysis of differential time delays that occur during natural,uncontrolled conditions. Here we analyze BOLD signals recordedduring performance of a motor learning task. We show that, duringmotor learning, the BOLD response of unimodal motor cortical areasprecedes the response in higher-order multimodal association areas,including posterior parietal cortex. Brain areas found to be associatedwith reduced activity during motor learning, predominantly inprefrontal brain regions, are informative about the task typically atsignificantly later times.© 2006 Elsevier Inc. All rights reserved.

Keywords: Information theory; Hemodynamic response function; Model-free analysis; fMRI; Motor learning

Introduction

Functional mapping is rapidly becoming a crucial tool forunderstanding principles of information representation and func-

tional organization of the human brain. In particular, thenoninvasive Functional Magnetic Resonance Imaging (fMRI)technique has been extensively used to identify functional areasand subdivisions in the human cortex.

The increasing popularity of using fMRI results in large datasets, which are usually analyzed in conventional ways. Theconventional approach for the statistical analysis of BloodOxygenation Level Dependent (BOLD) signals from fMRI isbased on the general linear model (Friston et al., 1995; Worsleyand Friston, 1995; Boynton et al., 1996).

According to the GLM, the signals can be represented as alinear combination of a set of model functions plus noise (Buxton,2002). The analysis consists of finding the set of amplitudes thatscale each model function to provide the best fit of the model in aleast-squares sense (minimizing the sum of squares of theresiduals after the estimated signal from the model is subtractedfrom the data). These sets of amplitudes are free parameters of themodel, however, the model functions are assumed to have a fixedshape.

Therefore, the first step in the GLM analysis is to predict theshape of the BOLD hemodynamic response to a given stimuluspattern. The hemodynamic response function (HRF) to a briefstimulus is assumed to be of a fixed shape (Henson et al., 2002),and the response to any other stimulus is modeled as a linearconvolution of the HRF with the stimulus pattern.

While this powerful approach has without a doubt proven to bea useful framework for the study of functional brain organization,mainly in terms of the spatial localization of statistically significanttask-related activity, the model is based on two fundamentalassumptions, both of which are questionable under certainconditions.

First, the assumption of a constant HRF is problematic. HRFshapes have actually been shown to vary across regions, subjectsand even cortical layers (Aguirre et al., 1998; Silva and Koretsky,2002; Handwerker et al., 2004). These findings have importantconsequences for the localization of task-related activated voxels.In fact, theoretically, localization could be so dependent on theHRF employed that by using different shaped HRFs, different

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⁎ Corresponding author.E-mail address: [email protected] (G. Fuhrmann Alpert).Available online on ScienceDirect (www.sciencedirect.com).

1053-8119/$ - see front matter © 2006 Elsevier Inc. All rights reserved.doi:10.1016/j.neuroimage.2006.10.020

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brain regions could be highlighted and determined to be“statistically significantly” activated (for experimental support,see for example Solbakk et al., 2005).

The second questionable assumption is that of a linear relationbetween a given stimulus and the corresponding BOLD response.In fact, it has been shown that for sustained stimuli, the response isactually a sub-linear function of the stimulus duration (Boyntonet al., 1996; Friston et al., 1998).

Moreover, even though the linearity assumption has proven tobe a good approximation in many cases (Boynton et al., 1996; Daleand Buckner, 1997), mainly for long inter-trial intervals (ITI)between stimuli and for stimuli of relatively long duration (>4 s),this may not be the case for other paradigms including short ITIs(<4 s) or short stimuli (<3–4 s) (Friston et al., 1998; Vazquez andNoll, 1998; Glover, 1999; Huettel and McCarthy, 2000; Liu andGao, 2000).

The approach suggested in this study for the analysis of BOLDsignals is a model-free one, thus no assumptions about the shape ofthe HRF for localization of task-related activity are required, andtherefore it could account in theory for each voxel in the brainhaving its own pattern of response. Furthermore, this approachdoes not make any assumptions of linearity between the stimulusand BOLD response and thus could be generalized for the analysisof sustained stimuli or short ITIs.

A further advantage of this approach is its ability to extracttemporal information about the dynamics of brain activations.Temporal information regarding brain activations during taskperformance is crucial for our understanding of network interac-tions and functional connectivity between different brain regions.While spatial localization of task-related BOLD responses has beenextensively explored for many task conditions, few studies onlyhave addressed temporal aspects of neuronal circuitry engaged intask performance. Despite the challenges in mapping of BOLDresponses to underlying neural responses, several attempts havebeen made to address temporal aspects of BOLD responses, mostwithin the framework of the GLM analysis (Menon et al., 1998;Menon and Kim, 1999; Miezin et al., 2000; Weilke et al., 2001;Formisano et al., 2002; Henson et al., 2002; Hernandez et al.,2002; Liao et al., 2002; Bellgowan et al., 2003; Mohamed et al.,2003; Saad et al., 2003; Sun et al., 2005; see Formisano andGoebel, 2003 for review). Some studies have used non-linearapproaches for fitting the HRF (Calhoun et al., 2000; Richteret al., 2000). Nevertheless, all these studies, excluding Sun et al.(2005), assume a known shape of the HRF. However, it has beenshown that latency analysis in particular is sensitive to the exactshape of the HRF in use (Hernandez et al., 2002; Handwerkeret al., 2004).

Here we apply information theory for the analysis of fMRIdata. In the past decade, there has been an increasing interest in theapplication of information theory to various questions inneuroscience. Some examples include the study of single cellinformation coding in the fly (de Ruyter van Steveninck et al.,1997) and primate visual systems (Victor, 2000; Reich et al., 2001;Simoncelli and Olshausen, 2001; Kang et al., 2004), in the primarymotor cortex (Paz et al., 2003), neural and population coding ingeneral (Borst and Theunissen, 1999; Panzeri et al., 2003;Schneidman et al., 2003), as well as the study of cortical synapticcommunication (Fuhrmann et al., 2002; Goldman et al., 2002).However, to our knowledge, except for a few applications usingICA (McKeown et al., 1998; Arfanakis et al., 2000; Calhoun et al.,2000; Moritz et al., 2000) for cluster analysis, only one study has

made an attempt to apply information theory for the analysis offMRI time series by breaking the event-related responses intotwo epochs and computing the entropy at each half (de Araujo etal., 2003). This analysis does not assume a constant shape of anHRF, but nevertheless assumes a general structure of signal witha maximal change at the first half of the event-related response.Moreover, only spatial localization of task-related activity is ex-tracted. We propose a method to extract both spatial localizationof task-related activity in the brain, as well as temporalinformation about the sequence of activation of different brainregions.

Information analysis is applied for studying spatio-temporaltask-related activations during performance of a motor learningtask. Localized BOLD signal in cortical regions was measuredwhile subjects performed a bimanual serial reaction-time taskwhile learning a novel sequence. Spatial localization of a task-related activity is compared to maps calculated using the standardGLM analysis and is shown to involve a motor cortical network,as well as more prefrontal regions than those revealed by the GLManalysis. Temporal analysis is performed for single subjects aswell as for the grand average of all subjects, and compared tolatency analysis performed according to peak of event-relatedresponses as well as according to the time of minimal variance inresponses. Finally, sequential activation of specific regions ofinterest (ROIs) is performed by computing mutual informationbetween pairs of ROIs, without using knowledge of the experi-mental design. The principal regions of interest in this study includethe primary sensorimotor cortex (S1/M1), premotor cortex (PM),supplementary motor area (SMA) and posterior parietal cortex(PPC).

Materials and methods

Experimental methods

Subjects and behavioral taskData from fourteen right-handed subjects (4 female; ages 19–

29 years; mean age=23.5) from an existing data set (Sun et al.,2005) were analyzed for the purpose of this study. The originaldata set consists of fourteen subjects that participated after givinginformed consent according to procedures approved by theUniversity of California. The subjects reported no history ofneurological or psychiatric disorders and were taking no medica-tions at the time of the study.

Training. Prior to scanning, subjects were trained on one of twobimanual sequences; sequence A, denoted by L4–R2–L3–R4–L5–R5–L2–R3, or sequence B, denoted by L5–R3–L2–R5–L4–R2–L3–R4. Here, the letter signifies the hand (R=right, L= left)and the number signifies the finger (2= index finger, 3=middlefinger, 4=ring finger, 5=fifth finger). During training, thesubjects were seated comfortably in a dimly lit room. Each handwas positioned on a 5-fingered response box such that eachfinger aligned with a single key. The training sequence waspresented to the subject as a series of visual cues indicating thekey to press. The response window for each cue was 725 ms, andsubjects were instructed to respond as quickly and accurately aspossible upon seeing each cue. A sequence was consideredcorrect only when all eight key presses were performed correctly.The same sequence was repeated 20 times within a set, with a 2 sinterval between each sequence. Subjects were trained until they

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were able to complete a set of sequences with an accuracy of atleast 85%. Training sessions consisted of an average of 4 sets (80sequence trials).

MRI scanning. In the MRI scanner, five 8-minute functional runswere acquired for each subject using a mixed block/event-relatedparadigm (Visscher et al., 2003). The runs were composed of 4condition blocks (LEARN, PLAY, RANDOM, and FIXATION),each presented twice in a pseudo-random order, counter-balancedacross subjects. Each block began with an instructional cue,indicating the type of block. Within each of the PLAY, LEARN,and RANDOM condition blocks, sequences were presented withvisual cues as in training (725 ms/key press, 5800 ms/sequence),but with a pseudo-randomized inter-trial interval (ITI) of 2.2, 4.4,or 6.6 s (Fig. 1). During the PLAY condition, subjects werepresented with the same sequence that they learned during thetraining session (e.g., Sequence A). During the LEARN condition,subjects were presented with the alternate sequence (e.g., SequenceB), which was novel to them at the beginning of the scan session.Subjects were instructed to learn the sequence across the blocks.During the RANDOM condition, subjects were presented with anew sequence for each trial. Subjects were instructed to play allsequences as accurately as possible. Five sequences were presentedin each block for a total block length of 58 s. During theFIXATION block, also of length 58 s, subjects were presented witha centered fixation cross. For this condition, subjects wereinstructed not to perform or rehearse any of the sequences.Subjects received accuracy and timing information at theconclusion of each condition block. The results from the LEARNcondition are presented in this paper.

The stimuli were designed and presented using Eprimepresentation software (www.pstnet.com). They were then back-

projected onto a custom-designed, non-magnetic projection screenthat the subject viewed via a mirror. Responses were collectedusing a pair of five-fingered MR-compatible keyboards.

MRI data acquisitionAll images were acquired with a 4 Tesla Varian INOVA MR

scanner (www.varianinc.com) and a TEM-send and receive RFhead coil (www.mrinstruments.com). Functional images wereacquired using a 2-shot gradient-echo echo-planar image (EPI)sequence with a repetition time (TR) of 543 ms per shot, with anecho time of 28 ms and flip angle of 20°, resulting in 432 totalvolumes acquired per run (864 after time-interpolation). Eachvolume, covering the top of the brain, consisted of ten 5 mmthick axial slices with a 0.5 mm inter-slice gap. Each slice wasacquired with a 22.4 cm2 field of view with a 64×64 matrix size,resulting in an in-plane resolution of 3.5×3.5 mm. Highresolution (0.875×0.875 mm) in-plane T1-weighted anatomicalimages were also acquired using a gradient-echo multi-slice(GEMS) sequence for anatomical localization. Finally, MPFLASH3D T1-weighted scans were acquired so that functional data couldbe normalized to the Montreal Neurological Institute (MNI) atlasspace.

Methods of data analysis

PreprocessingFunctional images acquired from the MR scanner were recon-

structed from k-space using a linear time-interpolation algorithm(Noll et al., 2000) to double the effective sampling rate and correctedfor slice-timing skew using temporal sinc-interpolation. Images werethen corrected for movement using rigid-body transformationparameters and smoothed with an 8 mm full width at half maximum

Fig. 1. Experimental design.

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(FWHM) Gaussian kernel using the software package SPM2 (www.fil.ion.ucl.ac.uk/spm).

Information-theoretic analysisData analysis is based on concepts from information theory. In

particular, we quantify the information contained in the BOLDsignals of a voxel about a preceding task condition. To computethis information, we use two information-theoretic measures(Cover and Thomas, 1991).

The first measure is the entropy of a random variable thatquantifies the amount of uncertainty one has about its value. For adiscrete random variable X, which can take any value x from aparticular set χ with probability p(x), the entropy H(X) in bits iscalculated as follows:

HðX Þ ¼ �X

xavpðxÞlog2 pðxÞ ð1Þ

Generally, the wider the probability distribution of the possiblevalues of X, the harder it is to guess the exact value of the variableat a given instance, and thus the entropy is larger. Relevant randomvariables for the present study are the magnitude of the BOLDsignal of a voxel and the stimulus, or a code representing a taskcondition.

The second information-theoretic measure is the mutualinformation, I(X;Y), between a pair of random variables X, Y. Itis defined using the conditional entropy of X given Y, H(X|Y):

HðX jY Þ ¼X

yag

pðyÞHðX jY ¼ yÞ

¼ �X

yag

pðyÞX

xav

pðxjY ¼ yÞlog2 pðxjY ¼ yÞ ð2Þ

where p(x|Y=y) is the conditional probability of X=x given thevalue y of Y. If X (e.g., the BOLD response) is statisticallycorrelated to Y (e.g., the preceding stimulus), then knowledge of Yreduces the uncertainty about the value of X. In this case, H(X|Y)will be less than H(X), which we refer to as the unconditionalentropy. This reduction in uncertainty about a single randomvariable X, due to the knowledge of another variable, is quantifiedby the mutual information and is given by the difference betweenthe unconditional and conditional entropies of X,

IðX ; Y Þ ¼ HðX Þ � HðX jY Þ ð3ÞThis measure is symmetric: I(X;Y)= I(Y;X), i.e., the information

that a stimulus has about the BOLD response to follow is equal tothe information that the response has about the preceding stimulus.

The entropy of a continuous random variable (as are the BOLDresponses) is computed, in practice, by dividing the range of X intofinite bins of a chosen precision (Δ) and evaluating the resultingprobability distribution of the corresponding discrete variable. Thecomputed entropy will therefore depend on the precise choice of thebin size:

HðXΔÞ ¼ �X

Δf ðxiÞlog f ðxiÞ � logΔ ð4Þwhere f (xi) is the X’s density function.

However, it has been shown that as the bin size (Δ) approacheszero

HðXΔÞYhðX Þ � logΔ ð5ÞTherefore, if the bin size is sufficiently small and set constant

for both conditional and unconditional entropies, then the

computed mutual information I(X; Y) is independent of the binsize:

IðXΔ; YΔÞ ¼ HðXΔÞ � HðXΔjYΔÞchðX Þ � logΔ� ðhðX jY Þ � logΔÞ¼ IðX ; Y Þ ð6Þ

where h(X) is the entropy of the continuous random variable X(Cover and Thomas, 1991).

Information analysis of BOLD responses: localization oftask-related activities

We use the measure of mutual information (Eq. (3)) toquantify the reduction in uncertainty about the reference taskcondition (REF), which is achieved by knowing the magnitude ofBOLD response at a fixed time delay (latency, dt) later. Latenciesare chosen as multiples of TRs. All time series of BOLD signalsare z-normalized to have zero mean and unit variance. If morethan one scanning epoch is performed, the time series from eachscanning epoch are z-normalized separately. Therefore, theanalysis focuses on changes of responses relative to baselineactivity.

To evaluate the unconditional entropy of responses, we start byestimating the probability distribution of all BOLD responses of avoxel that ever occurred anytime during the experiment (Figs. 2A, B,top histograms). In a sense, temporal information is collapsed. Toestimate the distributions, we break the responses into Nbins equallyspaced bins. The conditional entropy of responses is computedsimilarly by estimating the probability distributions of only thoseresponses that followed all the instances of the chosen (e.g.,LEARN) condition, after a fixed time delay (dt) (Figs. 2A, B, middlehistograms) and in the same way, the responses that follow any othertask condition (Figs. 2A, B, bottom histogram).

For most voxels, the histogram of responses following thechosen (LEARN) condition is very similar to the histogram of allresponses. In fact, most of the voxels did not exhibit a cleardifference between these two histograms.

However, some voxels, as the one depicted in Fig. 2A, do showa marked difference. In these voxels, the histogram of responsesthat follow the chosen condition is somewhat shifted to the right,meaning that larger BOLD responses at this voxel are more likelyto follow the chosen condition. This reveals that increasedresponses code for the fact that the chosen condition waspresented. Other voxels could code the specific condition asrelatively decreased responses instead, and this would be evidentfrom a conditional distribution, which is shifted to the left. In eithercase, as the two bottom distributions become more separable, it iseasier to guess the preceding condition (LEARN/not-LEARN)simply by knowing the amplitude of response.

According to the a priori distribution of all responses,regardless of the task condition preceding it, we compute theunconditional distribution of all responses. All responses includethe responses to the chosen condition (LEARN) and the responsesto all other conditions. Then, from all responses that specificallyfollow the chosen condition (LEARN), we can estimate theconditional distribution. The same is done for responses that followthe other conditions, and the unconditional entropy of responses iscomputed. The MI is computed as the difference between thesetwo entropies.

IðBOLD; REFÞ ¼ HðBOLDÞ � HðBOLDjREFÞ ð7Þ


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pyi.e., the reduction in uncertainty about the preceding task

condition, due to the knowledge of the magnitude of BOLDresponse.

The number of bins (Nbins) used to estimate the probabilitydistributions was chosen to be 1000, after testing convergence ofI(XΔ;YΔ) to I(X;Y) for different bin sizes (Δ, see Eqs. (5) and (6)).A bin size of 0.001 of the maximal amplitude of the response wassmall enough to reach convergence to I(X; Y).

Calculating MI for all voxels in the scanned volume of the brainresults in a higher value of MI for voxels that are informativeabout, or involved in coding the task condition, than for those thatare not. For localization of task-related activity, we search forvoxels that best code for the chosen task condition.

In addition, we note that the information content of a givenvoxel about the chosen condition depends on the consideredlatency (dt) between the task condition presentation and the BOLDresponse. For the voxel depicted in Fig. 2, we show on the right (B)that, for a non-optimal considered latency, the information contentof the voxel about the task condition is reduced. Fig. 2Csummarizes the dependence of the mutual information content ofthe same example voxel, for different considered time delays. It isapparent that the voxel has a preferred latency of response (at about3 s) for which information content is maximal.

MI of each voxel is therefore computed for different possiblelatencies (dt), and each voxel is attached with its maximal

information at whatever latency. To account for a wide range ofevent-related BOLD responses, the range of possible dt wasdetermined in increments of TR starting from 1 TR up to 17 TRs(9.231 s). Task-related (significantly informative) voxels arechosen as those with MI value (at the maximal point) that exceedsMI-significance threshold.

In order to estimate MI-significance threshold, we use the 15voxels with the highest information content about the chosencondition, at whatever latency they occur. For each of these voxels(i), we compute the average MI value for 100 randomizedpermutations of the BOLD time series relative to the experimentalreference function (MIirand100). The MI-significance threshold(ϑMI

mean) is then set as the average of those values over the 15voxels (<MIirand100>i=1:15). An alternative significance threshold(ϑMI

std), set as the mean plus one standard deviation of those values,is also computed and used to threshold the data. Unless statedotherwise, results are presented for information threshold ϑMI

mean.Contrast maps for two active task conditions (A, B), analogous

to GLM contrast maps, although not presented in this paper, maybe obtained by computing for each voxel:

ΔIA; B ¼ IðBOLD;AÞ � IðBOLD;BÞ: ð8ÞΔIA,B>0 indicates that a voxel is preferentially coding task B

than task A, equivalent to being preferentially activated by task Bin the GLM framework. In theory, each voxel may have a different

Fig. 2. (A, B) histograms of responses for the same voxel at 2 different considered time delays (latencies) between the task condition and the amplitude of theBOLD response. A, left: at the estimated preferred latency of this voxel (3.258 s). B, right: at a different estimated latency (7.059 s). For each of the latencies, thetop histogram is a histogram of all responses (LEARN+all others). Middle: histogram of responses that follow the chosen condition only (LEARN). Bottom:histogram of responses that follow any other condition. (C), bottom curve: MI plotted as a function of the considered latency between a task condition and theresponse for the same voxel.


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preferred delay to either task condition, for example having shorterlatency for A (dtA) than for B (dtB). Therefore, in the same way, adifferential time lag ΔdtA, B=dtA−dtB can be computed, represent-ing the difference in the latency of the most informative response toeach of these conditions (>0 if the maximal information about B isobtained at a shorter latency than for A, and vice versa for <0).

We note, however, that ΔIA,B~=0, in the case where a voxelhas a similar information content about either task condition (A orB), does not necessarily mean that the voxel cannot distinguishbetween A and B. (This is analogous, in the GLM framework, tovoxels which are being activated to the same degree for both taskconditions).

It could be that a voxel carries the same amount of informationabout the precedence of either of these tasks (with respect to anyother tasks), but at the same time it has the capacity to distinguishbetween them. If this is the case, and one is searching for voxelsthat can best distinguish whether the preceding task condition wasA or B, given that it was one of them, the following approach canbe used. To estimate the unconditional distribution of responses (asthe top in Fig. 2), one should take only responses that follow eitherof the task conditions (A, B). The responses to the condition A areresponses that follow A by a certain dtA, and the responses to B arethe responses that follow B by dtB. The conditional distributions(as the middle and bottom in Fig. 2) should each hold the responsesto A (after dtA), and the responses to B (after dtB).

Therefore, in order to allow for each voxel to have a differentpreferred delay to each task condition, one should search forthe maximal information content in a two dimensional surface of(dtA, dtB).

Preferred latency of task-related voxelsWe define the preferred latency of a voxel as the latency that

maximizes the information contained in its BOLD response about achosen task condition (see example in Fig. 2C). For each task-related voxel, we determine its preferred latency as the timeinterval (dt) that maximizes information content of its responsesabout the chosen task condition. We construct whole brain latencymaps, in which the color at each voxel indicates its preferredlatency.

Assessing relative amplitudes of responses at the preferred latencySince mutual information is not sensitive to whether there was

an increase or decrease in the magnitude of response to the taskcondition, for each task-related voxel, we determine what was itsamplitude of response at its preferred latency. Specifically, we areinterested in the latency in which the event-related response ismaximally informative about the task condition, and whether themagnitude of response with which it was coding it is relativelyincreased or decreased.

Localization and preferred latency assessment by mean andvariance of BOLD responses

As a complementary issue, task-related localization wasperformed in two other methods. According to the first, task-related voxels are chosen as those in which a maximal change inamplitude (from baseline) is observed on average in response to thechosen condition; in other words, voxels with maximal averagepeak of event-related responses. The change can be obtained at anylatency, thus at different latencies for different voxels. In the sameway, according to the second method, task-related voxels arechosen as those with minimal variance in the responses to the

chosen condition. In both these methods, preferred latencies ofchosen voxels are also determined, i.e., latencies which maximizeaverage peak of event-related response, or minimize variance ofresponses. We will refer to these as the M-latency map and V-latency maps, respectively.

Studying sequence of activations of regions of interest (ROIs)Finally, temporal sequence of activation of specific regions of

interest (ROIs) is determined in the two following ways. Accordingto the first, latency of an ROI is determined for each individualsubject as the average latency in all voxels within the subject-specific ROI mask (in MNI space); then for each ROI, the averageROI latency, as well as standard error, over all subjects iscomputed. According to the second way, latency of each ROI iscomputed directly from the grand average latency maps (computedas the average of individual subjects latency maps, each in MNIspace), using grand average ROI masks (see below). Standard errorin this case is computed across all voxels within the ROI. This isdone for all three types of latency maps: information latency maps,M-latency maps, and V-latency maps.

Based on evidence in the literature and results from theunivariate analysis, we chose the ROIs within the primarysensorimotor cortex (S1/M1), premotor cortex (PM), supplemen-tary motor area (SMA), and posterior parietal cortex (PPC). Foreach of the ROIs, anatomical masks were defined in the subjects’native space. The S1/M1 mask included cortex adjacent to thecentral sulcus, extending anteriorly to the mid-line between thecentral and precentral sulcus, posteriorly to the mid-line betweenthe central and post-central sulcus, and dorsally and ventrally toinclude the primary motor hand area (Yousry et al., 1997). Thedorsal PM mask extended from the mid-line between the centraland precentral sulcus, anteriorly to the junction of the superiorfrontal sulcus and the precentral sulcus. To exclude ventralpremotor regions, the PM mask included only cortex dorsal tothe inferior frontal sulcus (Picard and Strick, 2001). The SMAmask was located on the medial wall, dorsal to the cingulate gyrus,and between the central sulcus and the vertical plane through theanterior commissure (VAC) (Picard and Strick, 2001). The PPCmask included cortex in the superior parietal lobe posterior to andinclusive of the post-central sulcus and adjacent to the intra-parietalsulcus at the junction of the two sulci (Simon et al., 2002). Allmasks were non-overlapping. For each ROI, grand average maskswere defined as the union of all individual subjects’ masks in MNIspace.

In addition, an anatomical mask was also constructed for theprefrontal cortex. The mask included the dorsal half of theprefrontal cortex as defined in Duvernoy (1999). On theanterolateral surface of the frontal cortex, the ROI mask extendedposteriorly to the inferior frontal sulcus (IFrS), and dorsally to aline drawn between the anterior tip of the superior frontal sulcusand the intersection of the IFrS and the inferior precentral sulcus.Medially, the mask included portions of the superior and middlefrontal gyri, extending posteriorly to the sulcus just anterior to thecingulate sulcus (this sulcus roughly marks the anterior border ofBA 32). On the dorsal surface, the mask terminated posteriorly atthe limit of BA 9.

Relative timing of information coding between pairs of ROIs,regardless of the experimental design

To address functional connectivity, regardless of any priorknowledge of the stimulus (reference function), instead of studying


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the relation between BOLD responses and the reference conditions,we now study the relation between the average BOLD responses ofone specific ROI and the average BOLD response of anotherspecific ROI.

To do so, one ROI is considered as the “stimulus” ROI (ROI2)and we compute the reduction in uncertainty about the responses(magnitude of signals) in the other region (ROI1), which isobtained by knowing how large the signal in ROI2 was. In otherwords, we are testing whether having a relatively large ROI2 signalwould, for instance, suggest that a relatively small ROI1 responsewould follow and that a small ROI2 response would predict alarge ROI1 response. This would indicate that signals in oneregion are informative about the magnitude of the signal in the otherregion.

Instead of having just two conditions (LEARN; NON-LEARN), as in the voxel-based information analysis, here wehave a whole range of ROI2 response magnitudes used to conditionthe ROI1 responses upon. Therefore, the responses of ROI2 aresplit into a small number of bins (typically 6, unless statedotherwise), according to their magnitudes (very small to verylarge). We then estimate the unconditional distribution of all ROI1responses, as well as the distributions conditioned on each of these6 bins of ROI2 responses.

The responses of ROI1 are responses that follow or precededthose of ROI2 by a certain latency dt. MI between the two ROIs iscomputed for both positive and negative values of dt.

The number of bins used to break up the ROI2 data is setaccording to data size limitations, to allow the estimation of the

distribution of the responses of ROI1 conditioned on each of theROI2 bins. The bin size used to estimate the distributions of ROI1responses (conditioned and unconditioned) is 1000, as used for thevoxel-based information analysis.

Note that the analysis is based on a stationarity assumption,according to which the same sequence of brain activations isobserved throughout the analyzed time period (i.e., that one ROI isalways responsive before the other).

A modified version of this analysis could also be used to studycondition-based relative timing, i.e., the sequence of brainactivations following a specific task condition (e.g., LEARN). Inthis case, the continuous time series for each of the 2 ROIs wouldbe segmented into trials of certain epoch duration (typically ∼10–15 s, depending on the relevant duration of the event-relatedresponse). The responses from all trials are collapsed together toestimate both the conditional and unconditional distributions. Thisapproach also reduces the stationarity assumption to only theepoch, such that the sequence of ROI activations is only assumedto persist during the relatively short epoch. This analysis, however,naturally requires knowledge of the experimental design. More-over, it requires the design of an experiment with a very largenumber of trials to allow the estimation of both unconditional ROI1responses, as well as ROI2-conditioned ROI1 responses, from thoserelatively short epochs.

For comparison, we also compute the simple linear correlationbetween the time-lagged time series from the two ROIs. This isdone by computing the correlation coefficient between the time-shifted time series, with varying latencies.

Fig. 3. Spatial localization of task-related activity (subject 212). (A) using information analysis. Task-related voxels are highlighted in red-orange. Top left:ϑMI

mean is used as threshold for significantly informative voxels. Top right: ϑMIstd threshold is used. Activations outside the brain are unmasked, and ghosting

artifacts are observed. (B) using standard GLM analysis (contrast FIXATION, t-threshold 4.46). Activations outside the brain are masked. (C) using informationanalysis. For the comparison with GLM results, activations outside the brain are masked (same mask as in panel B) and threshold is determined to pick the samenumber of mostly informative voxels as determined by GLM (B).


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Localization using GLMFor comparison of spatial localization results to standard GLM

analysis, we use SPM2. To model task-related activity, we usedSPM’s canonical hemodynamic response function (HRF; Josephset al., 1997) convolved with independent variables for the onsetand duration of each sequence. Here, the duration of each sequencewas modeled as an epoch of 5800 ms. These covariates wereentered into the modified GLM for analysis.

Following the preprocessing stage (see above), parameterestimates, reflecting the percent signal change relative to baselinewere estimated for each covariate. Statistical parametric maps (t-statistics) of contrasts were generated for individual subjects withsignificance values of p<0.05, corrected (FWE). Brain activationswere masked using SPM2.

Results

The proposed method of analysis was applied to data acquiredfrom subjects performing a motor learning task.

Spatial analysis: localization of task-related activity

We perform whole brain information analysis for the localiza-tion of brain activations that are related to learning of the motortask. Fig. 3A (top left) depicts an example of one brain slice ofsuch a functional map, constructed for a single subject. Onlyvoxels found to be significantly informative (MI>ϑMI

mean) aboutthe LEARN condition are shown. Task-related activations werefound mainly in the motor network, including the primary andpremotor motor areas (M1, PM), supplementary motor areas (SMAand preSMA), as well as in the posterior-parietal cortex (PPC).These activations are in agreement with task-related activationsreported in previous studies (see Swinnen, 2002 and Willingham,1998 for reviews) as well as with a functional map constructedusing standard GLM analysis (Sun et al., 2005) for the same dataset (Fig. 3B; p<0.05, FWE corrected).

An alternative significance threshold (ϑMIstd; see Materials and

methods) was also tested (Fig. 3A, top right). From comparison ofthe resulting functional maps to those created using GLM analysis(Fig. 3C), this threshold is conservative. Therefore, results in thispaper are presented for ϑMI

mean.To provide an accurate comparison between the MI and GLM

localization, in terms of the spatial distribution of task-relatedactivity, we masked the subject’s MI-maps using the brain maskcreated by SPM (see Materials and methods for GLM localization)and picked the same number of the most informative voxels aschosen by GLM (Fig. 3D).

Note that, as apparent in the presented slice (as well as highlyevident in slices not shown), even with the most conservativethreshold (ϑMI

std), information analysis localized task-relatedactivity in more extensive prefrontal regions, including areas thatare not chosen to be task-related using the standard GLM analysis.Task-related activity in prefrontal regions was observed in mostsubjects (Fig. 4, top; as well as subjects not shown). This effect issummarized in Table 1.

To understand these effects, we studied the event-relatedresponses of voxels in the regions of interest (Fig. 5). Fig. 5Adepicts the canonical HRF, which is used in this study in order tomodel the hemodynamic response to the task reference function forthe GLM analysis. The HRF represents the model response to abrief stimulus. The typical event-related responses in the motor

regions (Fig. 5B) resemble the canonical HRF, with a clearamplitude peak of the event-related response around the samelatency as the peak of the canonical HRF. These responses cantherefore be modeled by the GLM, and voxels within thoseregions will be selected later on as being significantly activated.In contrast, the responses in the prefrontal cortex (Fig. 5C) seemto be less typical, commonly having double opposite-sign peaks(left), a shifted peak (~8–10 s or later; right), or even a stateswitch with no peak at all (middle). These responses could notbe modeled correctly by the canonical HRF, and therefore thesevoxels are missed by the GLM analysis.

To test contrast maps between two active conditions, activationmaps were also created for the contrast between the LEARN versusthe PLAY condition (results not shown). In the group average data,there was no statistical significant difference for the GLM map(p<0.05, FWE corrected, and a few supra-threshold voxels onlyfor p<0.001 uncorrected). However, to test the underlying spatialdistribution of differential activation, we also looked at the GLMcontrast map for a liberal threshold (p<0.05, no correction) andcompared it with the map created using the analogous informationtheory approach (see Materials and methods, Eq. (8)), using asignificance threshold matched to yield the same number ofsignificantly activated voxels. We found that the spatial distribu-tion is similar using the two approaches, such that voxels whichare preferentially activated, or coding, one of the two activeconditions are found mainly in the motor network (PM, M1, SMA,and PPC), with some distinctions between the two analysisapproaches (e.g., more bilateral activation using the informationtheory approach, in return of several white matter blobs ofactivation using the GLM). We note that a third contrast map,created directly by computing the mutual information between theBOLD response and the preceding task condition where the onlytwo considered conditions are the PLAY vs. LEARN (seeMaterials and methods; using dtA and dtB), reveals the involve-ment of more association areas.

Temporal analysis: preferred latency maps

To study the dynamics of event-related brain activations,latency maps are constructed. The information contained in theamplitude of the event-related response about the task conditionwhich preceded it by a certain dt is computed for all dt valuesranging from one TR to 10 s (in steps of TR). Each voxel is thenassigned with its preferred latency, the latency for which the event-related response of the voxel is most informative about thepreceding task condition (see also Materials and methods).

In Fig. 6 and Fig. 7B (same, with colorbar), latency map ispresented for the significantly informative voxels for the samesubject as in Fig. 3. From this slice, it can be seen that task-relatedinformative activity begins in the SMA, premotor, and primarymotor areas at about 3–4 s after the chosen task condition,propagates to the PPC at about 5 s, and finally reaches lateralportions of the left PPC even as late as 7 s after event initiation.Task-related activity of different voxels at prefrontal areas isinformative about the task at a variety of latencies, some of whichare as late as 8–9 s after the beginning of the event.

In Fig. 8A, latency maps of 9 of the subjects are presented forthe significantly informative voxels, and inter-subject similaritiesin the spatio-temporal distribution of informative responses can beobserved. In all subjects, the preferred latencies of voxels withinthe SMA, premotor, and primary motor regions (at about 3–4 s


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delay) are shorter than those of the higher association areas, mainlythe PPC (at about 5–7 s). In most subjects, the majority of voxelswithin the task-related voxels in prefrontal cortex respondsignificantly later (>8 s).

Amplitude of response at best coding latency

For each voxel, we computed the mean amplitude of all event-related responses at the preferred latency of the voxel. Amplitudes

Fig. 4. Comparison of spatial localization of task-related activity according to the 3 approaches (MI, M, V) for 9 representative subjects (axes: anterior–posterior:top–bottom). (Top) MI value (at the preferred latency) for significantly informative voxels. Same brain slice is shown as in Fig. 3. (Middle) M-value for the samenumber of voxels with highest M-values. (Bottom) V-value for the same number of voxels with minimal V-values.


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of event-related responses are determined after z-normalization ofthe voxel’s signal (see also Materials and methods). Amplitudemaps show the mean amplitude of event-related response at thepreferred latency, averaged over all events.

Combining the information of the amplitude maps (Fig. 7C)with latency maps (Fig. 7B) enables one to acquire at glance agreat deal of information regarding functional organization in thewhole brain. It is clear for example that, for this subject, brain areasin the motor network (M1, SMA, PM), as well as the PPC, are allincreasing their activation when processing the task condition, withthe left PPC showing increased activity significantly later thanunimodal motor areas, and that the prefrontal activation is of adecreasing nature, with variable latencies, some of which are atsignificantly later times.

M,V-localization and M,V-latency maps

Mutual information, computed for each voxel according tochanges in the conditional distributions of responses relative to theunconditional distribution of all responses, is dependent on theestimated distribution of responses, which in turn depend on boththe mean and variance of responses. Therefore, as a complemen-tary issue, task-related activation was addressed by computing themaximal average changes in the event-related BOLD responseseparately (M-maps), as well as the minimal variance of responsesfollowing the chosen condition (V-maps). For comparison ofspatial localization of task-related activity, we show in Fig. 4, foreach subject, the same number of most task-related voxels, asdetermined by each of the three approaches.

In addition, preferred M-latencies were determined as thelatencies that maximize mean of maximal (peak) event-relatedresponse, averaged over all events. Similarly, preferred V-latencieswere defined as the latencies in which the variance in the event-related response is minimal. Both M-latency and V-latency mapswere constructed (Fig. 8).

We found that localization using M-values was far noisier, withmuch more false activation outside the brain, as compared to

localization according to maximal mutual information, as well asaccording to minimal event-related variance (see Fig. 4). Both MIand V-localizations were better confined to brain regions.However, in terms of temporal analysis, M-latency maps seemmore spatially structured, and possibly more consistent acrosssubjects, as compared with the preferred latency maps constructedaccording to MI and variance analysis (Fig. 8).

Latency of specific ROIs using the different methods

Due to observed similarities in latency maps across subjects(Fig. 8), we attempted to determine a sequence of ROIactivations, according to a grand average of spatial latency mapsof all subjects. To address propagation of task-related signalsbetween specific regions of interest (ROIs), we compute theaverage latency of an ROI in two different ways (see Materialsand methods). In the first, latency of an ROI is first extractedfrom the latency maps of individual subjects, each according to itsownROI anatomically definedmasks; single subjects’ROI latenciesare then averaged. In the second way, latency of ROI is computeddirectly from the grand average maps, using grand average ROImasks defined as the union of all bilateral individual subjects’masksin MNI space.

According to grand average ROI masks, we find the followingsequence of task-related information coding: preSMA (5.64±0.021 s), SMA (5.8±0.022 s), PM (6.24±0.006 s), M1 (6.44±0.006 s), and finally PPC (6.46±0.004 s). According to infor-mation analysis and individual subjects ROI masks, we find thefollowing sequence of task-related information coding: SMA(5.1905±0.232 s), right PM (5.3534±0.292 s), left PM (5.5173±0.292 s), preSMA (5.6472±0.237 s), left PPC (5.6754±0.143 s),left M1 (5.919±0.25 s), right PPC (6.0108±0.322 s), and finallyright M1 (6.5508±0.339 s). In both cases, the informative responsein SMA is significantly earlier than the informative responses inthe both primary motor cortices, as well as the PPC.

Examining the individual subjects’ latency maps (as in Fig. 8),we observe within the PPC (mainly on the left hemisphere), insome slices, a traveling wave of task-related activity, which startsat medial portions of the PPC and expands gradually into lateralportions of the PPC. This pattern of activation is seen in many ofthe subjects, both in MI-latency maps as well as in M-latencymaps. We note that ROI analysis of latency maps is in some cases asimplification of the detailed spatial distribution of latencies,representing the temporal spread of brain activity.

According to the analysis on grand average M-latency maps,using grand average ROI masks, we estimate the followingsequence of activation: SMA (4.13±0.01 s), PM (4.61±0.005 s),preSMA (4.53±0.014 s), M1 (4.66±0.006 s), and PPC (5.04±0.005 s).

Comparison of the latencies determined according to thedifferent methods reveals that ROI latencies determined accordingto mutual information were typically longer than those determinedaccording to M-latency maps, suggesting that the time in whichthe event-related BOLD response is most informative about thetask condition is not at the peak of the response, but rather 1–2 slater.

Finally, the same analysis was performed on V-latency maps.Using grand average ROI masks, we find the following estimationof activation sequence: M1 (4.45±0.007 s), PM (4.56±0.006 s),SMA (4.64±0.017 s), preSMA (4.67±0.018 s), and PPC (4.86±0.005 s).

Table 1% Significant task-related activation in the PFC

Subject GLM MI M V

209 2.69 18.65 1.67 11.55211 3.33 10.58 5.17 11.00212 16.46 42.02 9.31 7.84213 4.34 41.62 6.47 4.85214 2.08 4.49 5.74 11.39215 3.26 14.68 5.91 15.36219 0.18 2.68 0.00 10.01218 0.26 19.38 5.33 2.12220 2.58 10.42 4.54 4.90221 0.19 9.79 0.67 2.98222 1.29 10.00 3.79 3.53223 0.00 2.75 0.00 0.47224 0.00 27.44 1.81 6.33225 3.22 27.03 2.62 1.74

Comparison of % task-related activation within the prefrontal cortex (PFC),according to GLM, MI, M, and V approaches for each of the subjects.Numbers represent the percent of significantly activated voxels within thePFC. This is computed after thresholding all activation maps (MI, M, V)such that the number of significantly activated voxels within the brain ismatched to the number determined by the thresholded GLM t-map withp<0.05, FWE corrected (see also Fig. 3D).


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Preferred latency differences between pairs of regions of interest(ROIs), regardless of the stimulus pattern

The information analysis presented thus far computes theinformation between the hemodynamic response and the precedingtask condition. Therefore, it requires knowledge of the experi-mental design. Namely, the information content of a response istested with respect to a specific design that we assume to affect theresponses. However, it is clear that activity of cortical neurons isnot associated uniquely with the experimentally studied paradigm,but is also affected by background information processing. It is ofinterest, therefore, to study mutual information between differentregions of interest (ROIs), irrespective of the stimulus pattern. Thisenables one to study possible interactions during information pro-

cessing, which are not necessarily related to an imposed experi-mental paradigm. Moreover, the approach could be used to studyinformation interactions between ROIs during the processing ofany arbitrary stimulus pattern, in particular that of natural stimuli.

Therefore, in this case, rather than computing the mutualinformation between the event-related responses of an ROI and theexperimentally designed task condition, here we compute themutual information between the mean event-related signals of twodifferent ROIs, each averaged over all voxels within the ROI. Thecontinuous signal from each ROI is taken as a whole, rather thanonly task-related portions of it, as in the previous analysis. In orderto estimate the probability distributions of the responses, the signalin one of the ROIs is considered as the “stimulus” and thedistributions of the responses of the second ROI, both uncondi-

Fig. 5. Study of event-related responses. (A) the canonical HRF used in order to model the hemodynamic response to the task reference function for the GLManalysis. The HRF represents the modeled response to a brief stimulus. (B) typical event-related BOLD responses (ERBs) to the LEARN condition resemble thecanonical HRF. Examples from voxels in motor related regions. (C) event-related responses of voxels within the prefrontal cortex to the LEARN condition. ERBsare less typical and do not resemble the canonical HRFs. Left: the most abundant event-related response at prefrontal regions has a double peak (a negativefollowed by a positive peak), crossing zero signal change at a latency of around 6 s. Middle: non-peaked state-switch responses. Right: long latency peakedresponses. All examples are taken from subject 212.


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tioned and conditioned on the signal amplitude in the first ROI,are estimated. The responses of the second ROI are those thatfollow the signal in the first by a chosen latency dt. We computethis for both positive and negative values of dt to construct plotsas the one presented in Fig. 9 (solid dark line). We then estimate

at which latency signals in the two ROIs are most informativeabout one another; namely, the latency in which the signal in oneROI is most informative about the signal that preceded, orfollowed it, in the other ROI. It can be seen that, for instance inthe case of this subject, in terms of information content withinthe signals, SMA preferably precedes left PM by approximately1 s, preSMA precedes left PPC by 1.5 s, left PPC follows rightPPC by about 0.5–1 s, while SMA and preSMA are mostinformative about each other’s activity with zero delay betweentheir signals.

For comparison, we also compute the simple linear correlationbetween the signals of the two regions at varying time lags (Fig.9, dashed lines). In the case of study, where the signals in thedifferent ROIs seem to be noisy time-shifted versions of oneanother, the results from the correlation analysis are similar tothose from the information analysis. In the general case,information analysis would be superior if there is a non-linearrelation between the amplitudes of response in the time-laggedtime series from the two ROIs.

Discussion

A new approach for the analysis of event-related BOLD signalsis proposed. The analysis is based on computing the mutualinformation (MI) between a stimulus function and the correspondingevent-related BOLD response. The approach is useful both forspatial localization of task-related activity, as well as for extractingtemporal information about the dynamic propagation of task-relatedactivity in the brain.

Fig. 6. Slice of a preferred latency map as computed for a single subject(same subject as in Fig. 3). Preferred latencies of the task-related voxels arecolor coded and overlaid on the subject's brain. Scale of colors from blue tored indicates short to longer latencies (for quantitative scale, see Fig. 7B).

Fig. 7. (A) mutual information values for significantly informative (LEARN-related) voxels. MI values are shown for the latencies in which each voxel is mostinformative about the task (axes: anterior–posterior: top–bottom). (B) Preferred latency map (s) for the corresponding voxels as in panel A (see also Fig. 3). (C)mean amplitude change (after z-norm) of event-related responses at preferred latencies of individual voxels. (D) variance of responses to single events at thepreferred latencies relative to the chosen task condition.


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In the basic analysis, we regard the experimental design as thestimulus function and compute the MI between a specific taskcondition (in the example presented in this study—a motorlearning condition) and the amplitude of event-related BOLDresponse that follows it by certain latency (dt). For each voxel, wedefine a preferred latency as the latency which maximizes itsinformation content about the stimulus (task condition). Weperform a whole brain analysis and choose task-related voxels asthose whose signal holds the highest information content about thestimulus condition, each voxel at its own preferred latency.

This approach is an alternative approach to spatial localizationof task-related activity that is most commonly performed using thestandard GLM analysis. Standard GLM analysis is based on twoquestionable assumptions. The first is that the hemodynamicresponse function (HRF) of all voxels in the brain is fixed, anassumption which is known to be inaccurate (Aguirre et al., 1998;Silva and Koretsky, 2002). In fact, localization is sensitive to themodel function in use, and differences in the areas which arehighlighted could be observed when different HRFs are used asmodel functions (Handwerker et al., 2004).

The second assumption is that there exists a linear relationbetween the stimulus and BOLD response, an assumption which atleast in some cases has been shown to be erroneous (Boynton et al.,1996; Friston et al., 1998; Glover, 1999; Huettel and McCarthy,2000; Liu and Gao, 2000; Kershaw et al., 2001). One of theadvantages of the information-theoretic approach is that it ismodel-free. There are no assumptions about the shape and delay ofHRF, and it can actually account for each voxel having its uniqueresponse dynamics. Additionally, no linearity assumptions arerequired regarding the nature of stimulus–response transformationeither.

In this approach, task-related activity is associated with areasthat show both increased as well as decreased activation, relative tobaseline activity, during task performance. Since the computed MIfor a voxel is insensitive to whether there is an increase or decreaseof the signal in response to a task condition, localization of task-related activity is not restricted to areas which show an increase inthe BOLD signal. In fact, by looking at the average event-relatedmagnitude of response of voxels at their preferred latencies, wefind that in the case of a motor learning task, some regions whichare highly informative about the task condition actually decreasetheir responses following its presentation. These areas are mostlyfound in prefrontal regions and posterior lateral cortex. The regionsfound in this study to be involved in the task by decreasedresponses are areas that were previously reported as the defaultnetwork in the brain. Those regions of the brain are associated withspontaneous activity of cortical networks and are regularlyobserved to decrease their activity during attention demandingcognitive tasks (Gusnard and Raichle, 2001; Raichle et al., 2001),as is the case in learning of a motor task presented in this study.

By comparing spatial localization of task-related activation usingthe suggested information-theoretic approach, with the resultsobtained using standard GLM analysis, we find the main differenceto be in prefrontal regions. According to standard GLM analysis,little task-related activity in prefrontal regions was observed, relativeto more extended areas of activation observed using informationanalysis. However, it is well known that prefrontal regions areinvolved in motor planning, execution and monitoring (Gehring andKnight, 2000). Study of event-related responses of voxels in theseregions suggests that this difference is mainly due to atypical HRFsof the voxels, as compared to the typical HRFs observed in primary

Fig. 8. MI, M- and V-latency maps for 9 of the subjects (for all subjects,approximately the same brain slice is shown). Maps are shown in nativespace. In all maps, latencies are shown for the significantly informativevoxels. Top: MI preferred latency. Middle: M-preferred latencies at whichthe mean event-related response, averaged over all events, is maximal.Bottom: V-preferred latencies at which minimal variability of event-relatedresponses is observed.


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sensori-motor areas for example. Many voxels in these areas exhibitan HRF response, which is relatively shifted in time. The HRF ofsome other voxels in these regions has a somewhat step-like, non-peaky, shape. By using broader or shifted HRFs, more elaboratedtask-related activations could be revealed in these regions even in theframework of GLM analysis (Solbakk et al., 2005). This againstresses even further the importance of using non-uniform HRFs forwhole brain analysis.

The numerous studies that have been performed using GLManalysis with fixed HRF responses have proven the approach to bea very useful method that is successful in identifying activationsrelated to a wide variety of tasks. However, many of these studiesfocus on activations in primary sensory and motor areas, mainly ofnormal control groups, typically young students. Fixed shapeHRFs may be indeed a good approximation for the typical responseof many brain regions of such normal controls. However,application of this approach to other populations, such as agingand patient populations, has been a constant challenge (D’Espositoet al., 2003). We expect that localization of task-related activationwould be particularly sensitive to the fixed HRF assumption, at

higher association brain regions, and at subject populations, inwhich untypical HRFs are commonly observed (Pineiro et al.,2002; Rother et al., 2002; Hamzei et al., 2003). Under thesescircumstances, we predict that the information-theoretic methodmay be superior over the model based GLM analysis. Theinformation-theoretic method may be more sensitive and revealmore task-related activations in higher order association regions andin populations with less typical HRFs, including older controls, andpatients with neurological disorders, particularly if they involvevascular pathology.

We demonstrated that the information-theoretic approach for theanalysis of fMRI data allows us to localize task-related activity anddetermine the average amplitudes of responses simultaneously. Thismethod can be used to combine amplitude and spatial localizationaspects of information about brain activity together with temporalinformation, which is also extracted from the data. Therefore, inaddition to localizing task-related activity and determining whetherit is associated with increased or decreased responses, we alsoconstruct spatio-temporal maps of preferred latencies for each voxel.These maps enable whole brain visualizations of the spread of task-

Fig. 9. Mutual information between the signals in pairs of ROIs, plotted as a function of the time delay between their activities (solid dark line). Positive latenciesmean that the “stimulus” ROI precedes the other ROI, whereas negative means the opposite relation. Results are presented for the same subject as in Fig. 3 andFig. 5. For comparison, results for time delayed correlation analysis between the times series of the two ROIs are presented (light dashed line).


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related informative signals within the brain. We found informativeactivity in the SMA about the task condition, which precedes theinformative activity in PM, M1, and PPC, with a delay ofapproximately 650 ms between SMA and M1. These results are inaccordance with results obtained by a different approach, based oncoherence measures for latency analysis applied to the same data set(Sun et al., 2005).

For comparison, latency maps were also determined in two otherways. M-latency maps are maps of the latency of the average event-related maximal response. V-latency maps are maps showing thelatency of minimal variance in the responses to single events. In allcases, latency of task-related informative activation was shortest forSMA, primary, and motor cortices, and longest for the PPC.M-latencies were typically shorter than those computed to maximizeinformation coding, suggesting that the time in which the event-related BOLD response is most informative about the task conditionis not at the peak of the response, but rather 1–2 s later.

We also observed subdivisions within our regions of interest, interms of information flow. In particular, the activity within the leftPPC seems to propagate from medial to lateral subregions in thePPC, as is observed in individual subjects’ latency maps, computedaccording to all three methods.

Due to the gap in our understanding of the relation between thelatencies of BOLD responses and the underlying latencies ofneuronal activity, it is hard to concludewhich latencymap representsmore reliably the underlying sequence of neuronal activation(Logothetis et al., 2001; Henson et al., 2002; Nevado et al., 2004).In terms of the underlying neural responses, a delayed event-relatedresponse could be the result of a delayed neural response, as well asof an extended neuronal processing time (Henson et al., 2002). TheBOLD response is affected by both, and therefore a sequence ofactivation determined according to BOLD responses does not mapeasily to the sequence of activation of neuronal populations.Nevertheless, the fact that there are consistencies in event-relatedlatency maps across subjects suggests that these latencies have ameaningful relation to the task-related neuronal activity. Futurestudies, possibly combining fMRI, EEG, as well intra- or extra-cellular recordings, may help clarify these issues.

In terms of temporal analysis of the BOLD responses, weperform an additional analysis on the data. In this case, weperform the analysis on the mean signals extracted from pairs ofspecific regions of interest (ROIs) and regard the signal from oneROI as the stimulus to the other ROI. We compute the MI betweenthe amplitudes of the signals in the two ROIs for various possibletime delays between the two signals. We find that in most casesthere is a peak of MI value around a particular latency between thetwo signals, suggesting that in terms of information content, thesignal in one ROI precedes, or lags after, that of the other ROIwith that latency. Here we show, for example, that SMApreferably precedes left PM by approximately 1 s, preSMAprecedes left PPC by 1.5 s, left PPC follows right PPC by about0.5–1 s, and that the signals of SMA and preSMA are mostinformative about each other’s activity with zero delay (Ikeda et al.,1992; Kansaku et al., 1998; Menon et al., 1998; Weilke et al.,2001; Sun et al., 2005).

Information analysis between the two signals, in this case, doesnot rely on knowledge of the experimentally designed stimuluspattern. Therefore, it is not confined to the study of artificiallydesigned experimental paradigm and can thus allow the study offunctional connectivity during information processing of naturalstimuli.

Moreover, this approach to studying the preferred latency ofmutual information between two signals is easily elaborated to thestudy of EEG data and intracranial recordings, both of whichprovide brain signals that are of higher temporal resolution andbetter understood in terms of their relation to the underlying neuralprocesses. In these cases, information is computed between theevent-related signals recorded from two electrodes, and thepreferred latency is determined.

While the information-theoretic approach suggested here forthe spatio-temporal analysis of fMRI and EEG data is powerful,there are limitations to the approach. Mutual information analysisrequires a large data set, namely, many repetitions of the event(>200, depending on the SNR, as well as specificity of responsesto the chosen condition). Moreover, in terms of temporal analysis,we assume that there exists stationarity in the sequence of brainactivations within the analyzed time period (i.e., that one ROI isalways responsive before the other) and that there is some timepoint in the event-related response at which information reaches apeak. If the event-related response of a voxel is not characterizedby a peaked response, spatial localization of task-relatedactivation is possible, however, the determined preferred latencyof the voxel will be mainly affected by noise. Finally, we wish tonote that our analysis provides information regarding the sequenceof activations of different brain areas; however, these sequencesdo not imply causal relations between different areas, only therelative times at which their signals are most informative aboutone another, since they may as well be driven by a commonsource with variable delays. Assessing causal relations betweendifferent brain regions is of extreme importance to our under-standing of functional connectivity, and while some attempts havebeen made to address this issue, mainly using the concept of grangercausality (Goebel et al., 2003), more studies in this direction arerequired.

Acknowledgments

We would like to thank Dr. Ifat Levy and Dr. Tatsuhide Oga formany helpful discussions and comments on the manuscript, TimMullen for his interest and great help defining regions of interest,Natasha Pickard and Jesse Rissman for helpful tips, and ClayClayworth for his help with preparing the figures. Finally, we wouldlike to thank the anonymous referees for their very constructivecriticism. Supported by NINDS grants PONS40813, NS 21135, andMH63901.

Appendix A. Supplementary data

Supplementary data associated with this article can be found, inthe online version, at doi:10.1016/j.neuroimage.2006.10.020.

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