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1Department of Neurology and Neurological Surgery, 2Alzheimer's Disease Research Center, 3Department of Radiology, and 4Department of Anatomy and Neurobiology, Washington University, St. Louis, Missouri 63110
Submitted 18 November 2002; accepted in final form 3 December 2002
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ABSTRACT |
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INTRODUCTION |
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).
Furthermore, both the region and the task affect the duration and shape of
regional BOLD responses (Corbetta et al.
2000; Courtney at al.
1998). The observed variability is not due to intrinsic
unreliability of the BOLD signal. In fact, the shape of local BOLD responses
can be robustly replicated within a scanning session
(Aguirre et al. 1998). Indeed,
insight into the local organization of the underlying neural responses can be
gained from the comparison of the shape and magnitude of BOLD time-courses
within a given region (Boynton et al.
1996). It is less clear that comparisons of BOLD response shapes
across regions may be useful in establishing the organization of neuronal
responses across the cerebrum because of potential regional heterogeneity in
vascular responses. However, if vascular heterogeneity is negligible, one
could predict, based on the finding that neuronal activity of distinct
cerebral areas can become correlated during behavioral events
(von Stein at al. 2000), that
these areas may also exhibit similar temporal modulations of the BOLD
signal.
The idea that the shape of the BOLD response may help assign function to a
region is not novel. In a task in which subjects had to match either the
location or the identity of faces after a delay period, Courtney et al.
(1997) used the duration of
the evoked BOLD response to distinguish the areas involved in holding a
memorized trace of the task-relevant feature of the stimulus. Within the
auditory domain, Giraud et al.
(2000) speculated that
transient and sustained BOLD signals corresponded to transient and sustained
neuronal responses to high and low frequency components of amplitude modulated
broadband acoustic stimuli.
Previous studies have documented BOLD shape response changes across some of
the cerebral regions active during a given task. For example, Harms and
Melcher (2002) have
demonstrated highly heterogeneous BOLD shapes in response to repeated auditory
noise bursts. Some regions had sustained responses; others had transient
responses at the onset and offset of the stimulus with a late, slowly varying
component. Other investigators have shown that differences within and between
cerebral regions correlate with behavior on a trial by trial basis
(Menon and Kim 1999;
Menon at al. 1998; Palmisano
et al. 2002; Richter et al.
1997).
Despite the potential relevance of the shape of the BOLD response for inferring aspects of neural activity at the level of single regions and even cortical networks, there has been no description to date of the modulations of the overall shape of the BOLD response across the entire brain.
This issue is addressed on quantitative grounds by the this study. We study the distribution of BOLD response shapes across the whole brain during a visual match to sample task, in which the activity during the cue phase of the task is separated from the activity following the presentation of the target. Formal methods are used to first describe and then classify the shape of the BOLD signal. Thus whole brain maps of temporally modulated BOLD activity are obtained. These maps allow us to compare modes of BOLD response across the whole brain at a glance. While we cannot determine whether neural or vascular factors contribute mostly to inter-regional differences in BOLD response shape, large focal changes of the BOLD response shape were found depending on whether subjects were instructed to attend to the color or motion of the stimulus. We conclude that subtle changes in the task and presumably local neural activity can reliably modulate the shape of the local BOLD response. Furthermore, finding that regions implicated by previous empirical evidence in higher cognitive operations during attentional and match to sample tasks also show sustained BOLD responses suggests that neural factors may be paramount in determining heterogeneity of the BOLD response shape across regions.
In a separate paper, we describe attentional modulations in posterior
parietal cortex during the match to sample task, using established methods
that did not distinguish between changes in shape and magnitude of the BOLD
signal (Shulman et al.
2002).
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METHODS |
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Nineteen right-handed young adults with normal or corrected to normal vision completed the functional imaging experiment and a preliminary behavioral session that was conducted to determine the stimulus parameters necessary to produce an appropriate performance level (80% correct). Subjects were paid for their time and gave informed consent prior to the experimental sessions. The study protocol was approved by the Washington University Human Study Committee.
The stimuli were generated and presented using a Power MacIntosh 7500/100. The stimuli were kinematograms made of 50 colored dots moving coherently at a speed of 4.3°/s within a circular window of 3.25° diam centered on the fixation cross. Subjects decided whether the target kinematograms matched the direction of motion or color of a set of highly learned sample kinematograms presented at the beginning of each block of trials. The direction of motion of the sample stimuli was either 20° counter-clockwise with respect to the right hemi-meridian or 20° clockwise with respect to the left hemi-meridian. The sample dot colors were either red or green. Nonsample directions had a greater tilt, while nonsample colors had an increased luminance along the blue channel. On a trial to trial basis, the overall Commission Internationale de l'Eclairage (CIE) luminance of both matching and nonmatching stimuli was varied randomly within ±10% of the luminance of the sample stimuli.
Prior to the presentation of each target stimulus, a cue word, either
"LEFT,"RIGHT", RED" or "GREEN," was shown.
The cue word instructed the subject to match the direction or color of the
upcoming target stimulus. The cue word and the kinematograms were presented
for 480 ms, with a stimulus onset asynchrony interval of 4.64 s. The interval
between the offset of the visual target in a trial and the onset of the
following trial varied unpredictably between 3.82 and 9.36 s. During scans,
25% of the trials ended following the completion of the cue period. A brief
dimming of the fixation point signaled the end of the trial. These trials
enabled the activation following the cue presentation to be separated from the
activation following the target presentation
(Ollinger et al. 2001).
Subjects pressed one key using the index finger of the right hand to indicate a match and a second key using the index finger of the left hand to indicate a nonmatch. No feedback about performance was provided.
Imaging methods
Functional MRI scans were acquired with a Siemens 1.5 Tesla Vision system. An asymmetric spin-echo EPI sequence was used [repeat time (TR) = 2,350 ms, echo time (TE) = 50 ms, flip angle = 90°].
A total of 128 images of 16 contiguous 8-mm-axial slices (3.75 x 3.75 mm in plane) were acquired. Structural images were collected with a sagittal MP-RAGE T1 weighted sequence [TR = 9.7 ms, echo-time TE = 4 ms, flip angle = 12°, inversion time (TI) = 300 ms], and T2-weighted spin-echo sequence (TR = 3,800 ms, echo-time TE = 90 ms, flip angle = 90°).
Overview of analysis
Our goal was to generate cerebral maps of temporally modulated BOLD activity. Figure 1 presents a summary of the steps involved in the analysis. First images were preprocessed to remove artifacts. Statistical maps of BOLD changes evoked by the cue and the target presentation were used to identify respectively regions that responded significantly to the cue (cue regions) or the target (target regions). Time-courses of BOLD responses to the cue and target were estimated in cue and target regions, respectively, whereas time-courses of nonsignificant BOLD responses to the cue and target were estimated in target and cue regions, respectively. After computing the principal components of the significant time-courses, both significant and nonsignificant time-courses were transformed in the coordinate system of the principal components. The signal-to-noise ratio (SNR) was computed by dividing the variance of significant time-courses by the variance of nonsignificant time-courses. The dimensionality of the time-courses was reduced, and a further coordinate transformation was used to dissociate the shape of the time-courses from their magnitude. Next, the number of BOLD shape classes and their prototypical shape was estimated. Finally, we generated cerebral maps of the shape of BOLD responses to the cue and target. A detailed description of the image and time-course analysis follows.
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Analysis: image processing, statistical maps, and time-courses
Image preprocessing included 1) compensation for slice-independent
time shifts (148 ms/slice), 2) elimination of odd/even slice
intensity differences due to interpolated acquisition, 3) realignment
of all data acquired in each subject within and across runs to compensate for
rigid body motion (Ojemann et al.
1997), and 4) normalization to a whole brain mode value
of 1,000. The functional data were transformed into a stereotaxic atlas space
(Talairach and Tournoux 1988)
by computing a sequence of affine transformations (first frame echo planar
imaging (EPI) sequence to T2-weighted turbo spin echo to MP-RAGE to atlas
representative target), which were combined by matrix multiplication.
Reslicing the functional data in conformity with the atlas then involved only
one interpolation. For cross-modal (e.g., functional to structural) image
registration, a locally developed algorithm was used.
Separate estimates of the time-courses following the presentation of the
cue and the kinematograms were obtained using a linear regression model,
without making any assumption about the shape of the hemodynamic response
(Ollinger et al. 2001). An
intercept, a linear trend, and a temporal high-pass filter with a cut-off
frequency of 0.009 Hz were also included among the independent variables.
The time-courses were put into atlas space and spatially smoothed with a
4-mm full-width-at-half-maximum Gaussian kernel. Statistical significance for
the group data were established using a voxel-level ANOVA, in which subjects
were treated as a random effect. The significance levels of the statistical
images were adjusted for correlations across time-points and corrected for
multiple comparisons (Ollinger and McAvoy
2000). Regions that were activated by the motion and color task
following the cue and stimulus presentation were determined by the main effect
of MR frame (for the 8 frames following the presentation of the stimulus).
Regional ANOVAs were calculated to establish whether regions significantly
activated during the cue (target) period were also active during the target
(cue) period. These regional ANOVAs had less stringent significance levels
than voxel level ANOVAs since they were not corrected for multiple
comparisons. The average time-courses of the BOLD response over eight MR
frames (18.8 s) were estimated from these regions. Separate time-course
estimates were obtained for the following trial types, namely when subjects
matched left motion, right motion, red hues, or green hues.
Principal component analysis
Principal component analysis (PCA) is used to reduce the dimensionality of
complex data (Jolliffe 1986).
It has been applied widely to biological signals, including single unit
activity (e.g., Osborn and Poppele
1989; Richmond and Optican
1987). PCA yields a compact description of time varying signals by
using a limited set of orthogonal waveforms.
The principal components (PCs) of the estimated regional BOLD responses following the presentation of both the cue word and the target (for motion and color trials respectively) were obtained by computing the eigen-vectors of an 8 x 8 variance-covariance matrix. The ith-jth element of the matrix was the covariance between the percent BOLD signal change in the ith and jth frames.
The PCs were normalized so that the sum of the squared values of the
percent BOLD signal change across the eight frames equaled one. The regional
BOLD time-courses were back-projected into the subspace of the first three PCs
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Signal-to-noise estimation
If the noise is additive and independent from the magnitude of the
activation (Huk and Heeger
2000), the ratio of the variances for time-courses estimated from
regions that showed a significant modulation of the BOLD signal and regions
that did not can be taken as an estimate of the SNR.
For each PC, an estimate of the distribution of the noise was computed on
time-courses obtained from a subset of those regions identified in the present
experiment. The regions used to estimate the distribution of the noise had
significant responses during the target or cue period (in voxel-wise
analysis), but not both (in region-wise analysis). In choosing regions in
which significant activation was observed during one of the experimental
periods, we sought to minimize spatial inhomogeneities in the noise magnitude
(Purdon et al. 2001).
Time-courses that failed a liberal significance level (P > 0.1,
not corrected for multiple comparisons) were used to estimate the noise
variance. The variance of the projections of these time-courses along the PCs
was computed.
Cluster analysis
The regional BOLD responses were classified using a fuzzy clustering scheme
(Duda at al. 2000). This
algorithm automatically parses the data set into overlapping clusters and
computes the average coordinate of each cluster. The number of clusters must
be established a priori by the operator.
The shape of the time-courses was measured using the two directional
components of their spherical coordinates in the space of the first three PCs.
Given a set of time-course shapes {tci i = 1,...,
n} and number of classes, the clustering algorithm began with an
initial guess of the two-dimensional (2-D) coordinates of the centroids
µj of each cluster 
j. The probability of a
time-course belonging to a particular class was estimated according to
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The centroid of each cluster was computed according to
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The centroids were initialized with the coordinates of time-courses chosen at random and the algorithm proceeds iteratively until the change in the coordinates of the values was less than a criterion value. Differences among coordinates of the centroids were negligible across initializations. Centroids coordinates were obtained by averaging over 100 initializations.
Choosing the number of clusters
A major limitation of the clustering algorithm is that it does not determine automatically the number of classes that should be used. Unless some prior information is available regarding the number of classes, the investigator must determine the optimal number of classes by comparing the outcomes of classifications using different numbers of classes.
To determine the number of classes, we developed a method based on the
minimal description length (MML) criterion
(Cover and Thomas 1991). Since
each time-course is an estimate based on repeated measurements obtained from
presentations of similar cue words or target stimuli, a cross-validation
technique can be used to compare the results of classifying with 2,3,...,
n classes.
Four time-courses were estimated from each region corresponding to the "GREEN," "RED," "LEFT," and "RIGHT" trials. Thus two independent estimates of the regional BOLD response time-course were obtained for motion and color trials. Each time-course was then assigned to one of the classes by determining which prototypical waveform was closest to the time-course. The probabilities that time-courses estimated from the RED and GREEN trials (or the LEFT and RIGHT trials) were assigned to the ith and jth class were computed.
The consistency of class assignments was quantified by using an information
theoretical measure, the mutual information (MI). This measure, expressed in
bits, was calculated according to
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Since MI increases monotonically as the number of classes is increased, the MI by itself cannot determine the number of classes. The MML criterion guides model selection by maximizing the explanatory power of the model while minimizing the joint complexity of the model and the data description given the model. The difficulty with the MML lies in measuring the complexity of the model.
In the present context, the complexity of the model, i.e., the clustering
algorithm, is a constant whose value does not depend on the number of classes.
The complexity of the data given the model is the number of bits necessary to
specify the class membership of each time-course. The joint complexity,
expressed in bits, is then
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For example, if four classes are used to classify the time-courses, then
twice as many bits are used to represent the data compared with when two
classes are used. By setting the value of the complexity of the model to zero,
an approximation to the true efficiency measure is
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This ratio approaches asymptotically the true efficiency from above and offers a biased but conservative estimate of the optimal number of classes.
The maximal number of classes used to categorize the shape of the time-courses was 10. Since a small number of regions was activated during the cue period of the task, some classes did not have paired entries (left and right or red and green time-courses belonging to the same region) when 9 or 10 classes were used to classify BOLD shape of cue time-courses. Thus BOLD response shapes from the cue period were classified using up to eight classes.
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RESULTS |
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Fifty-one nonoverlapping regions were significantly active following the presentation of the cue word, while 106 regions were active following the presentation of the target stimulus. They encompass both cortical and sub-cortical regions.
For each region, BOLD time-courses were estimated over the eight frames that followed the cue and target presentation. To reduce the dimensionality of the BOLD time-courses PCs were computed from the time-courses of the BOLD response evoked by cue and target presentation for the two trial types (motion and color).
Figure 2 shows the normalized PCs ordered according to the amount of data variance accounted. The first three components accounted for more than 94% of the variations in the BOLD signal across regions. The shape of the PCs suggests that while the first PCs capture systematic variations, higher order PCs reflect mostly noisy variations in the BOLD signal. Whereas in the initial frame the normalized BOLD signal is close to baseline for the first three PCs, it is not so for the higher order PCs (see Fig. 2). In other words, higher order PCs reflect changes in the BOLD signal that were not time-locked to the presentation of either the cue word or the target stimulus.
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As the order of the PCs increases, so does the frequency of their temporal modulation. Hence, the higher the order of the PCs, the closer the temporal modulation to the Nyquist limit imposed by the sampling rate of the functional images.
To determine how systematic and stochastic changes in the BOLD signal are represented among the PCs, an estimate of the SNR was obtained (see METHODS). Figure 3 shows the SNR for the eight PCs. A SNR of one implies that no signal was present. The SNR is close to one for all except the first three PCs, indicating that little if any systematic modulation of the BOLD signal is carried by high order PCs.
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We conclude that a simplified representation based on three orthogonal waveforms, that is the first three PCs, accounts for most of the systematic variations in the BOLD response.
A representation based on PCs also provides a natural separation between the shape and magnitude of the BOLD response. In Fig. 4, a pictorial view of BOLD time-courses based on PCs is shown. Each BOLD response is a vector in a 3-D space spanned by the set of PCs. The origin of the coordinate system corresponds to the null BOLD response. The direction of the vector defines the shape of the BOLD response, whereas the length of the vector defines the magnitude of the BOLD response. Therefore all the BOLD responses of a given magnitude will lie on the surface of a sphere of constant radius centered at the origin. Figure 4 shows the directional coordinates used to define the shape of the BOLD responses in the space of PCs. These angular quantities are geometrically identical to the longitudinal and latitudinal coordinates used to map the terrestrial surface.
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Classification of regional BOLD responses
The shape of the BOLD response was categorized using a finite number of classes.
The time-courses of BOLD responses to the presentation of the cue and target were classified separately. Since no prior information was available to establish the number of classes, this number was determined by computing a measure of classification efficiency (see METHODS).
Figure 5A shows the
efficiency when time-courses for the cue word were classified using between
two and eight classes. The efficiency peaked when three classes were used. A
problem with these calculations is that the MI, the numerator in the
efficiency measure, is overestimated when using finite data sets
(Optican et al. 1991). An
estimate of this bias was obtained by computing the expected value of the MI
when time-courses were paired at random rather than by region. For an infinite
data set the expected value of the MI is zero in this case.
Figure 5B shows that
1) the efficiency bias changes little with class number and
2) the bias is smaller than the efficiency. We conclude that the bias
does not affect greatly the choice of class number and that the magnitude of
the efficiency must be affected by systematic regional differences in the
shape of the BOLD response.
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The difference in the efficiency measure is trivial when two rather than three classes are used (see Fig. 5A). Two reasons suggested to us that three classes should be used. First, the efficiency measure provides an approximate and conservative estimate of the true efficiency. That is, compared with the true efficiency, it has a relatively greater magnitude when fewer classes are used (see METHODS). Therefore classifying with more classes should be preferred. Second, even when three classes were used, systematic differences between prototypical responses and regional responses persisted, indicating that shape differences were not fully captured. To demonstrate this, the difference between prototypical and regional time-courses directional coordinates was computed. These differences were significantly correlated for RED/GREEN and LEFT/RIGHT pairs (for the longitudinal coordinate: Pearson's r = 0.51, CI = 0.35–0.64; latitudinal coordinate: r = 0.82, CI = 0.74–0.87).
Figure 5C shows the efficiency when 2–10 classes were used to classify BOLD responses from the target period. The function peaked when four classes were used. Figure 5D shows that the bias increases slowly with the number of classes for the target evoked responses and that it is smaller than the efficiency. Again correlated deviations from the prototypical waveforms were found for the longitudinal (r = 0.53, CI = 0.42–0.63) and latitudinal coordinate (r = 0.80, CI = 0.74–0.84), indicating that the four classes did not fully describe systematic variations in shape of the BOLD response during the target period. We conclude that our procedure yields a coarse representation of shape variations. A finer representation of BOLD response shape could be obtained by carrying out the same classification procedure within classes.
Figure 6 shows the prototypical waveforms. The three waveforms from cue evoked responses were easily distinguished by visual inspection (see Fig. 6A). Sustained responses (marked S in Figs. 6A and 7A) showed modulations of the BOLD signal of comparable amplitude on the third and fourth frame. Transient responses peaked on the third frame and had a late undershoot starting on the fifth frame (marked T in Figs. 6A and 7A). Negative responses had a trough on the fifth frame (marked N in Figs. 6A and 7A) and were delayed in comparison to the positive responses.
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The responses evoked by the target (see Fig. 6B) varied from sustained to transient responses with prominent negative lobes. Interestingly, sustained responses evoked by the cue crossed the baseline about 2 s later than the sustained responses evoked by the target (compare the S waveforms in Fig. 6, A and B). This suggests that cue-evoked sustained responses correspond to tonic neural activity throughout the cue interval.
Figure 7 shows the distribution of the directional coordinates for the time-courses in a standard planar projection for spherical data (Mercator mapping). The origin of coordinate system (the point with coordinate 0,0) corresponds to the BOLD responses with the same shape as the first PC. A rightward (leftward) shift between –1.57 and 1.57 longitude corresponds to adding (subtracting) a contribution from the second PC. An upward (downward) shift corresponds to adding a positive (negative) contribution from the third PC.
The comparison of Fig. 7, A and B, indicates that cue response shapes have greater regional heterogeneity than target responses. The prototypical waveforms calculated from cue-evoked responses had a twofold greater variation along the first coordinate than those computed from target evoked responses. In four regions, the shape class of cue responses changed with trial type (Fig. 8). The shape changes within those regions greatly exceeded those within the remaining regions. Figure 7A shows the magnitude of the shape difference between motion and color trials for these four regions. A region in the left FEF and a region in the left IPs showed the largest shift, from sustained responses in motion trials to transient responses in color trials. A region in the left lateral occipital cortex (LO) and right thalamus showed the largest change from transient responses in motion trials to sustained responses in color trials. Figure 7, A and B, shows the vector and the uncertainty ellipse corresponding to the first and second moment of the distribution of shape differences between motion and color responses across regions. The average shape change from motion to color trial was greater for responses to the target than to the cue (compare the vectors in Fig. 7, A and B). Nevertheless, the variability of the shape differences was no greater for responses to the target than responses to the cue (compare the uncertainty ellipses in Fig. 7, A and B).
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We conclude that 1) changes in BOLD response shape class within regions were due to large differences in the BOLD response shape and that 2) systematic changes in BOLD response shape took place across the brain following the target presentation.
The two main questions of interest can now be addressed: 1) do response shape classes show any systematic topographical organization and 2) what is the effect of the task variable on the shape of regional BOLD responses?
Maps of BOLD response shapes— cue period
Figure 8 shows two maps of
response shapes obtained by color coding each region of interest, according to
the prototypical waveform closest (using an Euclidian metric in the space of
directional coordinates) to the time-course of the local BOLD response.
Responses to motion and color cues are presented separately. Most of the
sustained responses were found in the dorsal regions of the brain along the
IPs, its ventral and dorsal extension, SMA, and FEF. Transient responses were
found in sensory regions: the posterior thalamus and lateral occipital cortex.
Other regions, such as the most anterior extension of the IPs, showed
transient activations. The remaining regions showed negative activations. Some
of these regions are similar to those found previously in a meta-analysis of
deactivations during cognitive tasks
(Shulman et al. 1997).
Few regions showed differences in the shape of the BOLD response depending on whether subjects were cued to attend to the direction of motion or the color of the target. The left FEF and a region along the posterior extension of the left IPs switched from sustained responses, when the direction of motion was cued, to transient responses when color was cued. A right thalamic region and the left LO showed sustained activity when the color of the stimulus was cued and transient responses when the direction of motion was cued. The changes in shape class changes depend on large changes in the shape indexes (see Fig. 7A).
This finding suggests that not all of the shape properties of regional BOLD responses can be ascribed to purely hemodynamic factors. Rather, since the response shape is also dependent on task variables (i.e., being cued to attend to the direction of motion vs. the color of an upcoming visual stimulus), the modulation of the underlying neuronal signal can affect the shape of the BOLD response. We will show that in the target period BOLD response shape changes systematically across the brain.
Maps of BOLD response shapes—target period
Figure 9 shows the topographic distribution of response shapes following the presentation of the target. During motion and color trials, the most sustained responses were found in a set of regions, which included the right dorso-lateral prefrontal cortex (DLPFC), left posterior lingual/fusiform cortex, anterior fusiform cortex bilaterally, and cerebellum.
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Also, differences in the response shapes of several regions were found when subjects attended to the direction of motion or color of the target. These regions included, among others, the FEFs bilaterally, cingulate cortices bilaterally, left caudate nucleus, right insular regions, right lingual/fusiform, right MT, and cerebellum. Only a left ventral intraparietal (VIP) region showed more sustained responses during color than motion trials.
To gain better insight into the shape transformations of the BOLD responses
evoked by presentation of the target stimulus, a confusion matrix of response
shapes was constructed and is shown in
Fig. 10. All the regions which
showed a shape mismatch, except one, had more transient activations for color
than motion trials (which correspond to those cells in the matrix below the
main diagonal). This effect was highly significant. The likelihood that the
frequencies of cells located above and below the main diagonal were equal was
<0.0001. Moreover, the probability that the shape of the BOLD response
would undergo a class transition decreased as the BOLD response became less
sustained (
2 = 7.37, df = 2, P < 0.05). Fifty
percent of those regions that showed a sustained response in the motion
condition showed the same response in the color condition. Sixty-two percent
of those regions that showed a transient response in the motion condition
showed the same response in the color condition, and 82% of those regions that
showed a transient-biphasic response in the motion condition showed the same
response in the color condition.
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DISCUSSION |
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Following the presentation of the cue changes in response shape were focal, involving a fronto-parietal system in the left hemisphere and a region in left LO cortex and right thalamus. BOLD response shape was more sustained in motion than color trials in the fronto-parietal system, while the opposite pattern was observed in LO and the thalamus. Following the target presentation, the responses during motion trials were more sustained than responses during color trials in several regions of the brain. Only a region in the left VIP showed more sustained activity during color than motion trials. On average the task affected the BOLD response shape more following the presentation of the target than the cue (compare the magnitude of the average change in Fig. 7, A and B). This systematic change in BOLD response shape across several regions in the target period could not be explained by performance differences between motion and color trials. In fact, the mean reaction time in motion trials was 1.113 s and in color trials it was 1.192 s.
BOLD response shape: vascular versus neural factors
We hypothesize that the BOLD response shape reflects primarily task-dependent, functional aspects of the neuronal activity rather than task invariant hemo-dynamic properties. This point of view is supported by the observation that during both cue and target periods in a number of regions the shape of the BOLD response to the same stimuli changed depending on whether the color or motion of the visual stimulus was attended to.
Furthermore, changes in BOLD response shape within a region can be substantial and comparable to shape changes across regions (see Fig. 7A).
While differences in the temporal dynamics provided by small and large
draining vessels may be expected to affect the timing of the BOLD responses,
prior work provides some limited evidence for the hypothesis that hemodynamic
effects on the BOLD response may be fairly homogenous across the brain.
Formisano et al. (2002) found
that when subjects had to perform speeded button presses to auditory stimuli,
the onset of BOLD responses was delayed in motor compared with auditory
cortex, with association areas showing delays that were intermediate to those
in auditory and motor cortex. Similarly, Menon et al.
(1998) found that in a speeded
reaching task to visually presented targets the onset of the BOLD responses in
primary motor cortex relative to primary visual cortex was predicted by the
reaction time up to a small additive constant. The authors suggested that
their data could be accounted for if the vascular response in visual cortex
led the vascular response in motor cortex by about one-tenth of a second.
Miezin et al. (2000) found
that when subjects pressed a button at the time of presentation of a visual
stimulus, the onset of the BOLD response in motor cortex could occasionally
precede the onset of the BOLD response in visual cortex. They suggested that
the vascular response in visual cortex lags the response in motor cortex.
These results indicate that local differences in time of onset, one aspect of
the shape of the local BOLD response, either reflect systematic differences in
the onset of neural activity across regions or small, inconsistent differences
in the onset of the vascular response to the neural input.
BOLD response and functional networks
During the cue period, the shape of the BOLD responses fell into three classes: sustained, transient, and negative responses. Sustained responses were predominant in dorsal regions of the brain, such as SMA, right FEFs, and left anterior IPs, and likely encompassed the cerebral network involved in the preparatory phase of the task.
When the cue word instructed the subjects to attend to the motion of the
upcoming target, the BOLD response in the medial bank of the posterior left
IPs and the left FEF was sustained. However, when the color of the stimulus
was cued, both regions showed transient BOLD responses. Posterior IPs and FEFs
are reciprocally connected and belong to a functional network that is active
whenever attention is directed to a particular object or location in space
(Corbetta and Shulman
2002).
Sustained activity was also found following the presentation of the target in right DLPFC, left posterior lingual/fusiform cortex, anterior fusiform cortex bilaterally, and cerebellum. These regions may be part of a functional network involved in matching the memorized representation of the relevant feature (i.e., direction of motion and color) to the internal representation of the visual target.
While the effect of lesions to DLPFC on visual recognition of memorized
templates is subtle (Bachevalier and
Mishkin 1986), imaging data suggest that DLPFC is involved in
visual working memory tasks (Courtney et al.
1997,
1998). Single units in
prefrontal cortex of behaving monkeys performing a match to sample task are
tuned to specific samples and have target evoked activities that are highly
modulated by the sample (Miller at al.
1996; Rainer et al.
1999). We suggest that the DLPFC may have been involved in
retrieving the memorized template of the relevant visual feature.
The only extra-striate regions that showed sustained activations during
both color and motion trials were in ventral occipito-temporal cortex. A
similar anatomical specificity of matching signals was demonstrated in the
extra-striate visual system of nonhuman primates. In an experiment in which
monkeys matched a stimulus' direction of motion or shape, single unit activity
was modulated by the congruence between target and sample in area V4, but not
in area MT (Ferrera et al.
1994). The region of activation found in posterior
lingual/fusiform cortex may overlap with the human equivalent of area V4. A
similar region displayed greater activations when subjects matched the
direction of motion of a stimulus to that of a memorized template than when
they had to identify the direction of motion
(Cornette et al. 1998;
Dupont et al. 1998). In the
primate brain, anterior inferior-temporal areas are known to have exquisitely
specific tunings to visual shape. Some of the areas receive projections from
V4 (Martin-Elkins and Horel
1992) and connect to specific domains within prefrontal cortex
(Webster et al. 1994),
suggesting an occipital-temporal-prefrontal circuit.
Degrees of freedom of the BOLD response
An issue in modeling the time-course of BOLD responses is the
dimensionality of the BOLD response
(Josephs et al. 1997). We find
that the time-course of BOLD responses estimated from an event related fMRI
experiment in which subjects performed a match to sample task could be
described using three orthogonal waveforms. Therefore no less than three
linearly independent waveforms can account for all systematic variations of
the BOLD response. Friston et al.
(1998b) also reported that
three PCs sufficed to account for local variations in the shape of local BOLD
responses to single words. This number presumably may change with the
experimental paradigm. In fact, if local BOLD changes are a low-pass or
band-pass version of the local aggregated neural responses, the effective
degrees of freedom in the BOLD response should depend on the overlap between
the spectral properties of the vascular response and the spectral content of
the local neural activity.
An anonymous reviewer pointed out that the derivatives with respect to time
and dispersion of the gamma function used to model the canonical hemo-dynamic
response function (HRF) strongly resemble the second and third PCs. The former
time-courses were used by Friston et al.
(1998a) to accommodate
differences in the onset and duration of local BOLD responses. Accordingly,
the second and third PCs may be interpreted as the terms of a multivariate
linear approximation to deviations of the estimated local BOLD response from a
canonical response.
The low-dimensional nature of the BOLD signal in the match to sample task
allows a straightforward representation: each BOLD response can be viewed as a
vector in 3-D linear space. Other low-dimensional representations, such as
those obtained through independent component analysis (ICA), have been
proposed for the purpose of analyzing functional MRI (fMRI) time series
(Brown at al. 2001) and hold
the promise of revealing biologically meaningful aspects of these signals.
However, ICA does not yield an orthogonal set of waveforms, which makes the
comparison of response shapes convoluted (since it involves using an oblique
rather than an orthogonal coordinate system). The orthogonality of the PCs
allowed a straightforward coordinate transformation and a simple 2-D
representation of the shape of local BOLD responses.
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ACKNOWLEDGMENTS |
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This work was supported by National Eye Institute Grants EY-12148 and EY-00379 and the Washington University Alzheimer's Disease Research Center.
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FOOTNOTES |
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Address for reprint requests: G. d'Avossa, Alzheimer's Disease Research Center, Washington University School of Medicine, 4488 Forest Park Ave., Suite 130, St. Louis, MO 63108 (E-mail: davossag{at}neuro.wustl.edu).
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ABSTRACT
INTRODUCTION
and 
) are in a 1 to 1 relation to the shape of the BOLD response, whereas
the length of the vector is proportional to its magnitude.
) and
the related SE as a function of the number of classes. The function peaks for
3 classes. B: bootstrapped estimate of the bias (
) and its SE
for the efficiency measure are shown as a function of class number.
C: target evoked time-courses were classified using between 2 and 10
classes. Boot-strapped estimate of the efficiency measure and SE are shown as
function of class size. Efficiency peaked for 4 classes. D: bias
(
