Modeling both the magnitude and phase of complex-valued fMRI data

In MRI and fMRI, images or voxel measurement are complex valued or bivariate at each time point. Recently, (Rowe, D.B., Logan, B.R., 2004. A complex way to compute fMRI activation. NeuroImage 23 (3), 1078-1092) introduced an fMRI magnitude activation model that utilized both the real and imaginary data in each voxel. This model, following traditional beliefs, specified that the phase time course were fixed unknown quantities which may be estimated voxel-by-voxel. Subsequently, (Rowe, D.B., Logan, B.R., 2005. Complex fMRI analysis with unrestricted phase is equivalent to a magnitude-only model. NeuroImage 24 (2), 603-606) generalized the model to have no restrictions on the phase time course. They showed that this unrestricted phase model was mathematically equivalent to the usual magnitude-only data model including regression coefficients and voxel activation statistic but philosophically different due to it derivation from complex data. Recent findings by (Hoogenrad, F.G., Reichenbach, J.R., Haacke, E.M., Lai, S., Kuppusamy, K., Sprenger, M., 1998. In vivo measurement of changes in venous blood-oxygenation with high resolution functional MRI at .95 Tesla by measuring changes in susceptibility and velocity. Magn. Reson. Med. 39 (1), 97-107) and (Menon, R.S., 2002. Postacquisition suppression of large-vessel BOLD signals in high-resolution fMRI. Magn. Reson. Med. 47 (1), 1-9) indicate that the voxel phase time course may exhibit task related changes. In this paper, a general complex fMRI activation model is introduced that describes both the magnitude and phase in complex data which can be used to specifically characterize task related change in both. Hypotheses regarding task related magnitude and/or phase changes are evaluated using derived activation statistics. It was found that the Rowe-Logan complex constant phase model strongly biases against voxels with task related phase changes and that the current very general complex linear phase model can be cast to address several different hypotheses sensitive to different magnitude/phase changes.     

Nonadditive two-way ANOVA for event-related fMRI data analysis

A significant recent development in functional magnetic resonance imaging (fMRI) is the introduction of event-related fMRI, also known as time-resolved fMRI. Because the exact shape of the MR response in an event-related fMRI experiment is often not known, traditional methods developed for block design experiments, such as t test and correlation analysis, are not well-suited for extracting activated pixels from the event-related data. In this work, a statistical technique based on nonadditive two-way analysis of variance is developed for use in event-related studies. Theoretical and experimental work were carried out for establishing a statistical threshold to determine pixel activation. Experimental studies were performed to demonstrate the utility of this approach.     

Dissociating response conflict from numerical magnitude processing in the brain: an event-related fMRI study

Functional neuroimaging studies of numerical cognition have repeatedly associated activation of the intraparietal sulcus (IPS) with number processing. During number comparison, the IPS has been found to be modulated by the numerical distance. This has lead to the contention that the IPS houses the internal representation of numerical magnitude. However, this theory has been challenged by the argument that IPS activation may reflect domain-general response selection. In the present study, we used the numerical size congruity paradigm to further elucidate the role played by the IPS in number comparison. In an event-related, functional magnetic resonance imaging (fMRI) study, participants judged which of two number words was numerically larger. In addition to the numerical distance, physical stimulus size was varied such that physical size and numerical magnitude were either (a) congruent (e.g., numerically smaller number printed in smaller font) or (b) incongruent (e.g., numerically larger number printed in smaller font). This allowed for the study of both the main effects and the interaction of numerical distance and stimulus congruency. A main effect of numerical distance was found in bilateral regions of the IPS. However, these parietal areas were not significantly modulated by congruency or the interaction of distance and congruency. Instead, the main effect of congruency and an interaction of distance and congruency were observed in anterior cingulate and prefrontal cortices. These findings suggest some degree of independence between the processing of numerical distance and size congruity, lending support for the hypothesis that distance effects in IPS reflect the underlying representation of numerical magnitude.     

Spatiotemporal analysis of event-related fMRI data using partial least squares

Partial least squares (PLS) has proven to be a important multivariate analytic tool for positron emission tomographic and, more recently, event-related potential (ERP) data. The application to ERP incorporates the ability to analyze space and time together, a feature that has obvious appeal for event-related functional magnetic resonance imaging (fMRI) data. This paper presents the extension of spatiotemporal PLS (ST-PLS) to fMRI, explaining the theoretical foundation and application to an fMRI study of auditory and visual perceptual memory. Analysis of activation effects with ST-PLS was compared with conventional univariate random effects analysis, showing general consensus for both methods, but several unique observations by ST-PLS, including enhanced statistical power. The application of ST-PLS for assessment of task-dependent brain-behavior relationships is also presented. Singular features of ST-PLS include (1) no assumptions about the shape of the hemodynamic response functions (HRFs); (2) robust statistical assessment at the image level through permutation tests; (3) protection against outlier influences at the voxel level through bootstrap resampling; (4) flexible analytic configurations that allow assessment of activation difference, brain-behavior relations, and functional connectivity. These features enable ST-PLS to act as an important complement to other multivariate and univariate approaches used in neuroimaging research.     

Stochastic designs in event-related fMRI.

This article considers the efficiency of event-related fMRI designs in terms of the optimum temporal pattern of stimulus or trial presentations. The distinction between "stochastic" and "deterministic" is used to distinguish between designs that are specified in terms of the probability that an event will occur at a series of time points (stochastic) and those in which events always occur at prespecified time (deterministic). Stochastic designs may be "stationary," in which the probability is constant, or nonstationary, in which the probabilities change with time. All these designs can be parameterized in terms of a vector of occurrence probabilities and a prototypic design matrix that embodies constraints (such as the minimum stimulus onset asynchrony) and the model of hemodynamic responses. A simple function of these parameters is presented and used to compare the relative efficiency of different designs. Designs with slow modulation of occurrence probabilities are generally more efficient than stationary designs. Interestingly the most efficient design is a conventional block design. A critical point, made in this article, is that the most efficient design for one effect may not be the most efficient for another. This is particularly important when considering evoked responses and the differences among responses. The most efficient designs for evoked responses, as opposed to differential responses, require trial-free periods during which baseline levels can be attained. In the context of stochastic, rapid-presentation designs this is equivalent to the inclusion of "null events." Copyright 1999 Academic Press.     

Head-repositioning does not reduce the reproducibility of fMRI activation in a block-design motor task

It is hypothesized that, based upon partial volume effects and spatial non-uniformities of the scanning environment, repositioning a subject's head inside the head coil between separate functional MRI scans will reduce the reproducibility of fMRI activation compared to a series of functional runs where the subject's head remains in the same position. Nine subjects underwent fMRI scanning where they performed a sequential, oppositional finger-tapping task. The first five runs were conducted with the subject's head remaining stable inside the head coil. Following this, four more runs were collected after the subject removed and replaced his/her head inside the head coil before each run. The coefficient of variation was calculated for four metrics: the distance from the anterior commisure to the center of mass of sensorimotor activation, maximum t-statistic, activation volume, and average percent signal change. These values were compared for five head-stabilization runs and five head-repositioning runs. Voxelwise intraclass correlation coefficients were also calculated to assess the spatial distribution of sources of variance. Interestingly, head repositioning was not seen to significantly affect the reproducibility of fMRI activation (p<0.05). In addition, the threshold level affected the reproducibility of activation volume and percent signal change.     

Cognitive control explored by linear modelling behaviour and fMRI data during Stroop tasks

Most previous neuroimaging studies of Stroop paradigms have not provided sufficient information about the relationship between response times (RTs) and imaging signals. The objective of the present study is to build a linear model to explore the relationship between RTs and imaging signals. Neural information in Stroop tasks under the preconditions of high conflict and adjustment was extracted by using a method of modifying the ratio of congruent trials to incongruent trials in blocks. It was shown that the signals of the dorsal lateral prefrontal cortex (DLPFC) were negatively associated with the RTs for high-ratio trials in both blocks, and the signals of the anterior cingulate cortex (ACC) were negatively associated with the RTs for incongruence in high-conflict blocks. These results suggest that the DLPFC and ACC have more effects on executive modification and conflict monitoring, respectively.     

Comparing event-related and epoch analysis in blocked design fMRI

In this study we demonstrate that, even in blocked design fMRI, an event-related analysis may provide a more accurate model of the hemodynamic responses than an epoch-related analysis. This is because the temporal shape of the predicted response differs between the event-related and the epoch model, with the former reaching its peak sooner and returning to baseline later than the latter. We present data from a blocked design fMRI study of single word reading alternated with rest. Conventionally, such a design would be analyzed using an epoch analysis with boxcar regressors. However, here we used a combined model in which trials were modeled as both single events and epochs. This allowed us to estimate the variance in the BOLD signal that was explained by either the event-related or the epoch regressors having discounted the effect of the other. We found that, in a number of language regions, the event-related model explained changes in activity that were not accounted for by the epoch model. In addition, we show that the advantage of the event-related over epoch model was engendered by its early onset rather than its late offset, relative to the epoch model.     

Deconvolution of impulse response in event-related BOLD fMRI

The temporal characteristics of the BOLD response in sensorimotor and auditory cortices were measured in subjects performing finger tapping while listening to metronome pacing tones. A repeated trial paradigm was used with stimulus durations of 167 ms to 16 s and intertrial times of 30 s. Both cortical systems were found to be nonlinear in that the response to a long stimulus could not be predicted by convolving the 1-s response with a rectangular function. In the short-time regime, the amplitude of the response varied only slowly with stimulus duration. It was found that this character was predicted with a modification to Buxton's balloon model. Wiener deconvolution was used to deblur the response to concatenated short episodes of finger tapping at different temporal separations and at rates from 1 to 4 Hz. While the measured response curves were distorted by overlap between the individual episodes, the deconvolved response at each rate was found to agree well with separate scans at each of the individual rates. Thus, although the impulse response cannot predict the response to fully overlapping stimuli, linear deconvolution is effective when the stimuli are separated by at least 4 s. The deconvolution filter must be measured for each subject using a short-stimulus paradigm. It is concluded that deconvolution may be effective in diminishing the hemodynamically imposed temporal blurring and may have potential applications in quantitating responses in eventrelated fMRI.     

Detection of time-varying signals in event-related fMRI designs

In neuroimaging research on attention, cognitive control, decision-making, and other areas where response time (RT) is a critical variable, the temporal variability associated with the decision is often assumed to be inconsequential to the hemodynamic response (HDR) in rapid event-related designs. On this basis, the majority of published studies model brain activity lasting less than 4 s with brief impulses representing the onset of neural or cognitive events, which are then convolved with the hemodynamic impulse response function (HRF). However, electrophysiological studies have shown that decision-related neuronal activity is not instantaneous, but in fact, often lasts until the motor response. It is therefore possible that small differences in neural processing durations, similar to human RTs, will produce noticeable changes in the HDR, and therefore in the results of regression analyses. In this study we compare the effectiveness of traditional models that assume no temporal variance with a model that explicitly accounts for the duration of very brief epochs of neural activity. Using both simulations and fMRI data, we show that brief differences in duration are detectable, making it possible to dissociate the effects of stimulus intensity from stimulus duration, and that optimizing the model for the type of activity being detected improves the statistical power, consistency, and interpretability of results.     

Spatiotemporal independent component analysis of event-related fMRI data using skewed probability density functions.

We introduce two independent component analysis (ICA) methods, spatiotemporal ICA (stICA) and skew-ICA, and demonstrate the utility of these methods in analyzing synthetic and event-related fMRI data. First, stICA simultaneously maximizes statistical independence over both time and space. This contrasts with conventional ICA methods, which maximize independence either over time only or over space only; these methods often yield physically improbable solutions. Second, skew-ICA is based on the assumption that images have skewed probability density functions (pdfs), an assumption consistent with spatially localized regions of activity. In contrast, conventional ICA is based on the physiologically unrealistic assumption that images have symmetric pdfs. We combine stICA and skew-ICA, to form skew-stICA, and use it to analyze synthetic data and data from an event-related, left-right visual hemifield fMRI experiment. Results obtained with skew-stICA are superior to those of principal component analysis, spatial ICA (sICA), temporal ICA, stICA, and skew-sICA. We argue that skew-stICA works because it is based on physically realistic assumptions and that the potential of ICA can only be realized if such prior knowledge is incorporated into ICA methods.     

Analysis and design of perfusion-based event-related fMRI experiments

Perfusion-based functional magnetic resonance imaging (fMRI) using arterial spin labeling (ASL) methods has the potential to provide better localization of the functional signal to the sites of neural activity compared to blood oxygenation level-dependent (BOLD) contrast fMRI. At present, experiments using ASL have been limited to simple block and periodic single-trial designs. We present here an adaptation of the general linear model to perfusion-based fMRI that enables the design and analysis of more complicated designs, such as random and semirandom event-related designs. Formulas for the least-squares estimate of the perfusion response and the F statistic for the detection of a response are derived. Exact expressions and useful approximations for detection power and estimation efficiency are presented, and it is shown that the trade-off between power and efficiency for perfusion experiments is similar to that previously observed for BOLD experiments. The least-squares estimate is compared with an estimate formed from the running subtraction of tag and control images. The running subtraction estimate is shown to be approximately equal to a temporally low-pass-filtered version of the least-squares estimate. Numerical simulations and results from ASL experiments are used to support the theoretical findings.     

Feeling-of-knowing in episodic memory: an event-related fMRI study

An individual may fail to recall an item from memory but still feel that it would be recognized on a later test, a retrieval state termed the "feeling-of-knowing" (FOK). In this study we used event-related fMRI and the FOK to examine both encoding- and retrieval-related factors that are associated with different levels of recall performance: successful retrieval of a previously studied item, retrieval failure accompanied by the FOK, and retrieval failure without any FOK. The results revealed one predominant pattern of retrieval-related activation: an intermediate level of activation for FOK-less than that associated with successful recall and greater than that associated with unsuccessful recall (frontal and left parietal cortices). Two further patterns were also observed: greater activation for both successful recall and FOK than for unsuccessful recall (left midlateral prefrontal cortex) and greater activation for successful recall than for both FOK and unsuccessful recall (left MTL). Analysis of encoding trials conditional upon subsequent retrieval success revealed a pattern of activation that appeared to predict subsequent recall, but which further analysis indicated to be a better predictor of subsequent recognition. These results provide evidence that the phenomenology of graded recall is represented neurally in frontal and parietal cortices, but that activation at encoding may not precipitate the different levels of recall experience.     

Characterization of event-related designs using BOLD and IRON fMRI

Despite many desirable characteristics, event-related (ER) stimulus designs for BOLD and IRON suffer from low detection power relative to block designs because the hemodynamic impulse response function (IRF) acts as a low-pass filter on neural activation to attenuate the size of differential responses to alternate stimuli. While the use of exogenous contrast agent (IRON technique) provides an alternative fMRI method in animal models to improve sensitivity and spatial localization, the inherently slower hemodynamic IRF causes IRON detection efficiency to decrease faster than BOLD efficiency as the interstimulus interval (ISI) is shortened. Using simulations based upon assumptions of stimulus-response linearity and experimental data obtained in awake, non-human primates, this study compared detection efficiencies for fixed, random and semi-random ISI distributions for BOLD and IRON techniques. A larger relative gain in detection efficiency at short ISI was obtained by randomized designs using IRON contrast relative to BOLD contrast due to the slower IRF of the IRON method. To quantify tradeoffs between detection efficiency and the predictability of stimulus presentation, the Shannon entropy was introduced as an objective measure of predictability. Small amounts of entropy can be traded for large gains in efficiency, particularly for the IRON method.     

Nonlinearities in rapid event-related fMRI explained by stimulus scaling

Because of well-known nonlinearities in fMRI, responses measured with rapid event-related designs are smaller than responses measured with spaced designs. Surprisingly, no study to date has tested whether rapid designs also change the pattern of responses across different stimulus conditions. Here we report the results of such a test. We measured cortical responses to a flickering checkerboard at different contrasts using rapid and spaced event-related fMRI. The relative magnitude of responses across contrast conditions differed between rapid and spaced designs. Modeling the effect of the rapid design as a scaling of stimulus strength provided a good account of the data. The data were less well fit by a model that scaled the strength of responses. A similar stimulus scaling model has explained effects of neural adaptation, which suggests that adaptation may account for the observed difference between rapid and spaced designs. In a second experiment, we changed the stimulus in ways known to reduce neural adaptation and found much smaller differences between the two designs. Stimulus scaling provides a simple way to account for nonlinearities in event-related fMRI and relate data from rapid designs to data gathered using slower presentation rates.     

Detection power, estimation efficiency, and predictability in event-related fMRI

Experimental designs for event-related functional magnetic resonance imaging can be characterized by both their detection power, a measure of the ability to detect an activation, and their estimation efficiency, a measure of the ability to estimate the shape of the hemodynamic response. Randomized designs offer maximum estimation efficiency but poor detection power, while block designs offer good detection power at the cost of minimum estimation efficiency. Periodic single-trial designs are poor by both criteria. We present here a theoretical model of the relation between estimation efficiency and detection power and show that the observed trade-off between efficiency and power is fundamental. Using the model, we explore the properties of semirandom designs that offer intermediate trade-offs between efficiency and power. These designs can simultaneously achieve the estimation efficiency of randomized designs and the detection power of block designs at the cost of increasing the length of an experiment by less than a factor of 2. Experimental designs can also be characterized by their predictability, a measure of the ability to circumvent confounds such as habituation and anticipation. We examine the relation between detection power, estimation efficiency, and predictability and show that small increases in predictability can offer significant gains in detection power with only a minor decrease in estimation efficiency.     

A method for using blocked and event-related fMRI data to study "resting state" functional connectivity

Resting state functional connectivity MRI (fcMRI) has become a particularly useful tool for studying regional relationships in typical and atypical populations. Because many investigators have already obtained large data sets of task-related fMRI, the ability to use this existing task data for resting state fcMRI is of considerable interest. Two classes of data sets could potentially be modified to emulate resting state data. These data sets include: (1) "interleaved" resting blocks from blocked or mixed blocked/event-related sets, and (2) residual timecourses from event-related sets that lack rest blocks. Using correlation analysis, we compared the functional connectivity of resting epochs taken from a mixed blocked/event-related design fMRI data set and the residuals derived from event-related data with standard continuous resting state data to determine which class of data can best emulate resting state data. We show that, despite some differences, the functional connectivity for the interleaved resting periods taken from blocked designs is both qualitatively and quantitatively very similar to that of "continuous" resting state data. In contrast, despite being qualitatively similar to "continuous" resting state data, residuals derived from event-related design data had several distinct quantitative differences. These results suggest that the interleaved resting state data such as those taken from blocked or mixed blocked/event-related fMRI designs are well-suited for resting state functional connectivity analyses. Although using event-related data residuals for resting state functional connectivity may still be useful, results should be interpreted with care.     

Word frequency and subsequent memory effects studied using event-related fMRI

Event-related fMRI was used to evaluate the effect of printed word frequency on the subsequent recognition of words incidentally encoded while 16 healthy right-handed volunteers performed living/nonliving judgments. Semantic judgment took longer for low-frequency words. These words were more accurately recognized than high-frequency words at later testing. Low-frequency words were also associated with relatively greater left prefrontal, left fusiform gyrus, and anterior cingulate activation. Words that were subsequently recognized were associated with greater activation in the left prefrontal region compared to those that were forgotten. These findings suggest the specific brain regions where less commonly encountered words are processed in a manner that facilitates their subsequent recognition.     

Mixed blocked/event-related designs separate transient and sustained activity in fMRI

Recent functional magnetic resonance imaging (fMRI) studies using mixed blocked/event-related designs have shown activity consistent with separable sustained task-related processes and transient trial-related processes. In the mixed design, control blocks are intermixed with task blocks, during which trials are presented at varying intervals. Two studies were conducted to assess the ability of this design to detect and dissociate sustained task-related from transient trial-related activity. Analyses on both simulated and empirical data were performed by using the general linear model with a shape assumed for sustained effects, but not transient effects. In the first study, simulated data were produced with sustained time courses, transient time courses, and the sum of both together. Analyses of these data showed appropriate parsing of sustained and transient activity in all three cases. For the empirical fMRI experiment, counterphase-flickering checkerboard stimuli were constructed to produce sustained, transient, and combined sustained and transient responses in visual cortex. As with the simulation, appropriate parsing of sustained and transient activity was seen in all three cases; i.e., sustained stimuli produced sustained time courses and transient stimuli produced transient time courses. Combined stimuli produced both transient and sustained time courses. Critically, transient stimuli alone did not produce spurious positive sustained responses; sustained stimuli alone produced negligible spurious transient time courses. The results of these two studies along with supplemental simulations provide strong evidence that mixed designs are an effective tool for separating transient, trial-related activity from sustained activity in fMRI experiments. Mixed designs can allow researchers a means to examine brain activity associated with sustained processes, potentially related to task-level control signals.