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84
Temporal autocorrelation in univariate linear modelling of fMRI data
 pP Y C W P k nk N p Var(Yk ) (Yk ) 0 1 C CR 1 Var(Y ) P k nk N Var(Y k ) 0 1 C MI H(X;Y ) H(X) H(Y ) 1 0 C NMI H(X;Y ) H(X)+H(Y
, 2000
"... In functional magnetic resonance imaging statistical analysis there are problems with accounting for temporal autocorrelations when assessing change within voxels. Techniques to date have utilized temporal filtering strategies to either shape these autocorrelations or remove them. Shaping, or “color ..."
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Cited by 69 (9 self)
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In functional magnetic resonance imaging statistical analysis there are problems with accounting for temporal autocorrelations when assessing change within voxels. Techniques to date have utilized temporal filtering strategies to either shape these autocorrelations or remove them. Shaping, or “coloring, ” attempts to negate the effects of not accurately knowing the intrinsic autocorrelations by imposing known autocorrelation via temporal filtering. Removing the autocorrelation, or “prewhitening, ” gives the best linear unbiased estimator, assuming that the autocorrelation is accurately known. For singleevent designs, the efficiency of the estimator is considerably higher for prewhitening compared with coloring. However, it has been suggested that sufficiently accurate estimates of the autocorrelation are currently not available to give prewhitening acceptable bias. To overcome this, we consider different ways to estimate the autocorrelation for use in prewhitening. After highpass filtering is performed, a Tukey taper (set to smooth the spectral density more than would normally be used in spectral density estimation) performs best. Importantly, estimation is further improved by using nonlinear spatial filtering to smooth the estimated autocorrelation, but only within tissue type. Using this approach when prewhitening reduced bias to close to zero at probability levels as low as 1 � 10 �5. © 2001 Academic Press Key Words: FMRI analysis; GLM; temporal filtering; temporal autocorrelation; spatial filtering; singleevent; autoregressive model; spectral density estimation; multitapering.
Multisubject fMRI studies and conjunction analyses
 NeuroImage
, 1999
"... In this paper we present an approach to making inferences about generic activations in groups of subjects using fMRI. In particular we suggest that activations common to all subjects reflect aspects of functional anatomy that may be ‘‘typical’ ’ of the population from which that group was sampled. T ..."
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Cited by 61 (6 self)
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In this paper we present an approach to making inferences about generic activations in groups of subjects using fMRI. In particular we suggest that activations common to all subjects reflect aspects of functional anatomy that may be ‘‘typical’ ’ of the population from which that group was sampled. These commonalities can be identified by a conjunction analysis of the activation effects in which the contrasts, testing for an activation, are specified separately for each subject. A conjunction is the joint refutation of multiple null hypotheses, in this instance, of no activation in any subject. The motivation behind this use of conjunctions is that fixedeffect analyses are generally more ‘‘sensitive’ ’ than equivalent randomeffect analyses. This is because fixedeffect analyses can harness the large degrees of freedom and small scantoscan variability (relative to the variability in responses from subject to subject) when assessing the significance of an estimated response. The price one pays for the apparent sensitivity of fixedeffect analyses is that the ensuing inferences pertain to, and only to, the subjects studied. However, a conjunction analysis, using a fixedeffect model, allows one to infer: (i) that every subject studied activated and (ii) that at least a certain proportion of the population would have shown this effect. The second inference depends upon a metaanalytic formulation in terms of a confidence region for this proportion. This approach retains the sensitivity of fixedeffect analyses when the inference that only a substantial proportion of the population activates is sufficient.
Classical and Bayesian inference in neuroimaging: applications
 NeuroImage
"... introduced empirical Bayes as a potentially useful way to estimate and make inferences about effects in hierarchical models. In this paper we present a series of models that exemplify the diversity of problems that can be addressed within this framework. In hierarchical linear observation models, bo ..."
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Cited by 54 (11 self)
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introduced empirical Bayes as a potentially useful way to estimate and make inferences about effects in hierarchical models. In this paper we present a series of models that exemplify the diversity of problems that can be addressed within this framework. In hierarchical linear observation models, both classical and empirical Bayesian approaches can be framed in terms of covariance component estimation (e.g., variance partitioning). To illustrate the use of the expectation– maximization (EM) algorithm in covariance component estimation we focus first on two important problems in fMRI: nonsphericity induced by (i) serial or temporal correlations among errors and (ii) variance components caused by the hierarchical nature of multisubject studies. In hierarchical observation models,
On clustering of fMRI time series
, 1997
"... Introduction. The spatiotemporal fMRI signal is a combination of several interacting components: The locally correlated hemodynamic response, the network of neuronal activations, and global components such as the cardiac cycle, breathing etc. A priori this implies that the signal is correlated in t ..."
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Cited by 44 (3 self)
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Introduction. The spatiotemporal fMRI signal is a combination of several interacting components: The locally correlated hemodynamic response, the network of neuronal activations, and global components such as the cardiac cycle, breathing etc. A priori this implies that the signal is correlated in time and space, and that these correlations have both short and long range components. Clustering is a classical nonparametric approach to explorative analysis data. By clustering we can group signals according to a given objective function. Clustering of waveforms has already been used in fMRI signal analysis, see e.g. (1). Clustering of stochastic data, however, is hard optimization problem with many potential pitfalls. The "optimal" cluster configuration depends on the particular choice of clustering scheme (e.g. kmeans, kmedians, hierachical clustering) examples are legio (2), but just as importantly on the choice of distance metr
Separating processes within a trial in eventrelated functional MRI. I. The method. NeuroImage 13
, 2001
"... Many cognitive processes occur on time scales that can significantly affect the shape of the blood oxygenation leveldependent (BOLD) response in eventrelated functional MRI. This shape can be estimated from event related designs, even if these processes occur in a fixed temporal sequence (J. M. Oll ..."
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Cited by 42 (1 self)
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Many cognitive processes occur on time scales that can significantly affect the shape of the blood oxygenation leveldependent (BOLD) response in eventrelated functional MRI. This shape can be estimated from event related designs, even if these processes occur in a fixed temporal sequence (J. M. Ollinger, G. L. Shulman, and M. Corbetta. 2001. NeuroImage 13: 210–217). Several important considerations come into play when interpreting these time courses. First, in single subjects, correlations among neighboring time points give the noise a smooth appearance that can be confused with changes in the BOLD response. Second, the variance and degree of correlation among estimated time courses are strongly influenced by the timing of the experimental design. Simulations show that optimal results are obtained if the intertrial intervals are as short as possible, if they follow an exponential distribution with at least three distinct values, and if 40 % of the trials are partial trials. These results are not particularly sensitive to the fraction of partial trials, so accurate estimation of time courses can be obtained with lower percentages of partial trials (20–25%). Third, statistical maps can be formed from F statistics computed with the extra sum of square principle or by t statistics computed from the crosscorrelation of the time courses with a model for the hemodynamic response. The latter method relies on an accurate model for the hemodynamic response. The most robust model among those tested was a single gamma function. Finally, the power spectrum of the measured BOLD signal in rapid eventrelated paradigms is similar to that of the noise. Nevertheless, highpass filtering is desirable if the appropriate model
Robust smoothness estimation in statistical parametric maps using standardized residuals from the general linear model
 NeuroImage
, 1999
"... The assessment of significant activations in functional imaging using voxelbased methods often relies on results derived from the theory of Gaussian random fields. These results solve the multiple comparison problem and assume that the spatial correlation or smoothness of the data is known or can b ..."
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Cited by 40 (4 self)
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The assessment of significant activations in functional imaging using voxelbased methods often relies on results derived from the theory of Gaussian random fields. These results solve the multiple comparison problem and assume that the spatial correlation or smoothness of the data is known or can be estimated. End results (i.e., P values associated with local maxima, clusters, or sets of clusters) critically depend on this assessment, which should be as exact and as reliable as possible. In some earlier implementations of statistical parametric mapping (SPM) (SPM94, SPM95) the smoothness was assessed on Gaussianized tfields (Gtf) that are not generally free of physiological signal. This technique has two limitations. First, the estimation is not stable (the variance of the estimator being far from negligible) and, second, physiological signal in the Gtf will bias the estimation. In this paper, we describe an estimation method that overcomes these drawbacks. The new approach involves estimating the smoothness of standardized residual fields which approximates the smoothness of the component fields of the associated tfield. Knowing the smoothness of these component fields is important because it allows one to compute corrected P values for statistical fields other than the tfield or the Gtf (e.g., the Fmap) and eschews bias due to deviation from the null hypothesis. We validate the method on simulated data and demonstrate it using data from a functional MRI study. � 1999 Academic Press
To smooth or not to smooth? Bias and efficiency in fMRI timeseries analysis
 NeuroImage
, 2000
"... This paper concerns temporal filtering in fMRI timeseries analysis. Whitening serially correlated data is the most efficient approach to parameter estimation. However, if there is a discrepancy between the assumed and the actual correlations, whitening can render the analysis exquisitely sensitive t ..."
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Cited by 34 (4 self)
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This paper concerns temporal filtering in fMRI timeseries analysis. Whitening serially correlated data is the most efficient approach to parameter estimation. However, if there is a discrepancy between the assumed and the actual correlations, whitening can render the analysis exquisitely sensitive to bias when estimating the standard error of the ensuing parameter estimates. This bias, although not expressed in terms of the estimated responses, has profound effects on any statistic used for inference. The special constraints of fMRI analysis ensure that there will always be a misspecification of the assumed serial correlations. One resolution of this problem is to filter the data to minimize bias, while maintaining a reasonable degree of efficiency. In this paper we present expressions for efficiency (of parameter estimation) and bias (in estimating standard error) in terms of assumed and actual correlation structures in the context of the general linear model. We show that: (i) Whitening strategies can result in profound bias and are therefore probably precluded in parametric fMRI data analyses. (ii) Bandpass filtering, and implicitly smoothing, has an important role in protecting against inferential
The effect of normal aging on the coupling of neural activity to the bold hemodynamic response. Neuroimage
, 1999
"... The use of functional neuroimaging to test hypotheses regarding agerelated changes in the neural substrates of cognitive processes relies on assumptions regarding the coupling of neural activity to neuroimaging signal. Differences in neuroimaging signal response between young and elderly subjects c ..."
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Cited by 31 (0 self)
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The use of functional neuroimaging to test hypotheses regarding agerelated changes in the neural substrates of cognitive processes relies on assumptions regarding the coupling of neural activity to neuroimaging signal. Differences in neuroimaging signal response between young and elderly subjects can be mapped directly to differences in neural response only if such coupling does not change with age. Here we examined spatial and temporal characteristics of the BOLD fMRI hemodynamic response in primary sensorimotor cortex in young and elderly subjects during the performance of a simple reaction time task. We found that 75 % of elderly subjects (n � 20) exhibited a detectable voxelwise relationship with the behavioral paradigm in this region as compared to 100 % young subjects (n � 32). The median number of suprathreshold voxels in the young subjects was greater than four times that of the elderly subjects. Young subjects had a slightly greater signal:noise per voxel than the elderly subjects that was attributed to a greater level of noise per voxel in the elderly subjects. The evidence did not support the idea that the greater head motion observed in the elderly was the cause of this greater voxelwise noise. There were no significant differences between groups in either the shape of the hemodynamic response or in its the withingroup variability, although the former evidenced a near significant trend. The overall finding that some aspects of the hemodynamic coupling between neural activity and BOLD fMRI signal change with age cautions against simple interpretations of the results of imaging studies that compare young and elderly subjects.
A new statistical approach to detecting significant actication in functional MRI
 NeuroImage
, 2000
"... There are many ways to detect activation patterns in a time series of observations at a single voxel in a functional magnetic resonance imaging study. The critical problem is to estimate the statistical significance, which depends on the estimation of both the magnitude of the response to the stimul ..."
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Cited by 28 (1 self)
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There are many ways to detect activation patterns in a time series of observations at a single voxel in a functional magnetic resonance imaging study. The critical problem is to estimate the statistical significance, which depends on the estimation of both the magnitude of the response to the stimulus and the serial dependence of the time series and especially on the assumptions made in that estimation. We show that for experimental designs with periodic stimuli, only a few aspects of the serial dependence are important and these can be estimated reliably via nonparametric estimation of the spectral density of the time series, whereas existing techniques are biased by their assumptions. The linear model with (stationary) serially dependent errors can be analyzed entirely in frequency domain, and doing so provides many insights. In particular, we introduce a technique to detect periodic activations and show that it has a distribution theory that enables us to assign significance levels down to 1 in 100,000, levels which are needed when a whole brain image is under consideration. Nonparametric spectral density estimation is shown to be selfcalibrating and accurate when compared to several other timedomain approaches. The technique is especially resistant to high frequency artefacts that we have found in some datasets and we demonstrate that timedomain approaches may be sufficiently susceptible to these effects to give misleading results. The method is easily generalized to handle eventrelated designs. We found it necessary to consider the trends in the time series carefully and use nonlinear filters to remove the trends and robust techniques to remove “spikes. ” Using this in connection with our techniques allows us to detect activations in clumps of a few (even one) voxel in periodic designs, yet produce essentially no false positive detections at any voxels in null datasets. © 2000 Academic Press
Bach Speaks: A Cortical "LanguageNetwork" Serves the Processing of Music
, 2002
"... INTRODUCTION In recent ERPstudies, brain responses reflecting the processing of musical chordsequences were similar, although not identical, to brain activity elicited during the perception of language, in both musicians (Patel et al., 1998; Koelsch et al., in press) and nonmusicians (Koelsch et ..."
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Cited by 28 (9 self)
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INTRODUCTION In recent ERPstudies, brain responses reflecting the processing of musical chordsequences were similar, although not identical, to brain activity elicited during the perception of language, in both musicians (Patel et al., 1998; Koelsch et al., in press) and nonmusicians (Koelsch et al., 2000a, 2001, 2002). While relatively early (around 180350 ms) electrical brain responses to unexpected items in a structured sequence were often lateralized to the left when processing language (Friederici et al., 1993; Hahne and Friederici, 1999), they were often lateralized to the right when processing music (Patel et al., 1998; Koelsch et al., 2000a). The early brain responses (maximal around 200350 ms) elicited by violations of musical regualrities were taken to reflect the processing of musicsyntactic information (Patel et al., 1998; Koelsch et al., 2000a). Later brain responses (maximal around 500550 ms) were hypothesized to reflect the processing of meaning information in