Time series analysis in the time domain and resampling methods for studies of functional magnetic resonance brain imaging

Deep learning-based magnetic resonance imaging of the spine in the diagnosis and physiological evaluation of spinal metastases

Background and objective

Spinal metastasis accounts for 70% of the bone metastases of tumors, so how to diagnose and predict spinal metastasis in time through effective methods is very important for the physiological evaluation of the therapy of patients.

Methods

MRI scans of 941 patients with spinal metastases from the affiliated hospital of Guilin Medical University were collected, analyzed, and preprocessed, and the data were submitted to a deep learning model designed with our convolutional neural network. We also used the Softmax classifier to classify the results and compared them with the actual data to judge the accuracy of our model.

Results

Our research showed that the practical model method could effectively predict spinal metastases. The accuracy was up to 96.45%, which could be used to diagnose the physiological evaluation of spinal metastases.

Conclusion

The model obtained in the final experiment can capture the focal signs of patients with spinal metastases more accurately and can predict the disease in time, which has a good application prospect.

Time Series Analysis of Congestive Heart Failure Discharges in Florida (USA) Post Tropical Cyclones

OBJECTIVES

The aim of this study was to analyze congestive heart failure (CHF) discharges in Florida (USA) post tropical cyclones from 2007 through 2017.

METHODS

This was a retrospective longitudinal time series analysis of hospital CHF quarterly discharges across Florida using the Healthcare Cost and Utilization Project (HCUP) database. The autoregressive integrated moving average (ARIMA) model was used with correlated seasonal regressor variables such as cyclone frequency, maximum cyclone wind speed, average temperature, and reports of influenza-like illness (ILI).

RESULTS

A total of 3,372,993 patients were identified, with average age in each quarter ranging 72.2 to 73.9 years and overall mortality ranging 4.3% to 6.4%. The CHF discharges within each year peaked from October through December and nadired from April through June with an increasing overall time trend. Significant correlation was found between CHF discharge and the average temperature (P <.001), with approximately 331.8 less CHF discharges (SE = 91.7) per degree of increase in temperature. However, no significant correlation was found between CHF discharges and frequency of cyclones, the maximum wind speed, and reported ILI.

CONCLUSIONS

This study suggests that with the current methods and the HCUP dataset, there is no significant increase in overall CHF discharges in Florida as a result of recent previous cyclone occurrences.

The brain landscape of the two-hit model of posttraumatic stress disorder

The neurophysiological mechanisms underlying the development of posttraumatic stress disorder (PTSD) are poorly understood. Here we test a proposal that PTSD symptoms reflect fixed, highly correlated neural networks resulting from massive engagement of sensory inputs and the sequential involvement of those projections to limbic areas. Three-tesla functional magnetic resonance imaging (fMRI) data were acquired at rest in 15 veterans diagnosed with PTSD and 21 healthy control veterans from which zero-lag cross correlations between 50 brain areas (N = 1,225 pairs) were computed and analyzed. The brain areas were assigned to tiers based on the neurocircuitry of successively converging sensory pathways proposed by Jones and Powell (Jones EG, Powell TP. Brain 93: 793-820, 1970). The primary analyses assessed normalized proportional differences in cross correlation strength within and across tiers in veterans with PTSD and control veterans. Compared with control veterans, cross correlation strength was higher in veterans with PTSD, within and across tiers of areas involved in processing sensory inputs, and systematically increased from sensory processing areas to limbic areas. The functional relevance of this hypercorrelation was further documented by the finding that the severity of self-reported PTSD symptomatology was positively associated with higher neural correlations.NEW & NOTEWORTHY The neurophysiological mechanisms underlying the development of PTSD are poorly understood. Here we document that massive engagement of sensory modalities during trauma exposure leads to fixed, hypercorrelated frontal, parietal, temporal, and limbic networks, reflecting the successive integration of salient sensory inputs along the framework of Jones and Powell.

The potential of MR-Encephalography for BCI/Neurofeedback applications with high temporal resolution

Real-time functional magnetic resonance imaging (rt-fMRI) enables the update of various brain-activity measures during an ongoing experiment as soon as a new brain volume is acquired. However, the recorded Blood-oxygen-level dependent (BOLD) signal also contains physiological artifacts such as breathing and heartbeat, which potentially cause misleading false positive effects especially problematic in brain-computer interface (BCI) and neurofeedback (NF) setups. The low temporal resolution of echo planar imaging (EPI) sequences (which is in the range of seconds) prevents a proper separation of these artifacts from the BOLD signal. MR-Encephalography (MREG) has been shown to provide the high temporal resolution required to unalias and correct for physiological fluctuations and leads to increased specificity and sensitivity for mapping task-based activation and functional connectivity as well as for detecting dynamic changes in connectivity over time. By comparing a simultaneous multislice echo planar imaging (SMS-EPI) sequence and an MREG sequence using the same nominal spatial resolution in an offline analysis for three different experimental fMRI paradigms (perception of house and face stimuli, motor imagery, Stroop task), the potential of this novel technique for future BCI and NF applications was investigated. First, adapted general linear model pre-whitening which accounts for the high temporal resolution in MREG was implemented to calculate proper statistical results and be able to compare these with the SMS-EPI sequence. Furthermore, the respiration- and cardiac pulsation-related signals were successfully separated from the MREG signal using independent component analysis which were then included as regressors for a GLM analysis. Only the MREG sequence allowed to clearly separate cardiac pulsation and respiration components from the signal time course. It could be shown that these components highly correlate with the recorded respiration and cardiac pulsation signals using a respiratory belt and fingertip pulse plethysmograph. Temporal signal-to-noise ratios of SMS-EPI and MREG were comparable. Functional connectivity analysis using partial correlation showed a reduced standard error in MREG compared to SMS-EPI. Also, direct time course comparisons by down-sampling the MREG signal to the SMS-EPI temporal resolution showed lower variance in MREG. In general, we show that the higher temporal resolution is beneficial for fMRI time course modeling and this aspect can be exploited in offline application but also, is especially attractive, for real-time BCI and NF applications.

Effect of confounding variables on hemodynamic response function estimation using averaging and deconvolution analysis: An event-related NIRS study

Slow and rapid event-related designs are used in fMRI and functional near-infrared spectroscopy (fNIRS) experiments to temporally characterize the brain hemodynamic response to discrete events. Conventional averaging (CA) and the deconvolution method (DM) are the two techniques commonly used to estimate the Hemodynamic Response Function (HRF) profile in event-related designs. In this study, we conducted a series of simulations using synthetic and real NIRS data to examine the effect of the main confounding factors, including event sequence timing parameters, different types of noise, signal-to-noise ratio (SNR), temporal autocorrelation and temporal filtering on the performance of these techniques in slow and rapid event-related designs. We also compared systematic errors in the estimates of the fitted HRF amplitude, latency and duration for both techniques. We further compared the performance of deconvolution methods based on Finite Impulse Response (FIR) basis functions and gamma basis sets. Our results demonstrate that DM was much less sensitive to confounding factors than CA. Event timing was the main parameter largely affecting the accuracy of CA. In slow event-related designs, deconvolution methods provided similar results to those obtained by CA. In rapid event-related designs, our results showed that DM outperformed CA for all SNR, especially above -5 dB regardless of the event sequence timing and the dynamics of background NIRS activity. Our results also show that periodic low-frequency systemic hemodynamic fluctuations as well as phase-locked noise can markedly obscure hemodynamic evoked responses. Temporal autocorrelation also affected the performance of both techniques by inducing distortions in the time profile of the estimated hemodynamic response with inflated t-statistics, especially at low SNRs. We also found that high-pass temporal filtering could substantially affect the performance of both techniques by removing the low-frequency components of HRF profiles. Our results emphasize the importance of characterization of event timing, background noise and SNR when estimating HRF profiles using CA and DM in event-related designs.

Wavelets and statistical analysis of functional magnetic resonance images of the human brain

Wavelets provide an orthonormal basis for multiresolution analysis and decorrelation or ‘whitening’ of nonstationary time series and spatial processes. Wavelets are particularly well suited to analysis of biological signals and images, such as human brain imaging data, which often have fractal or scale-invariant properties. We briefly define some key properties of the discrete wavelet transform (DWT) and review its applications to statistical analysis of functional magnetic resonance imaging (fMRI) data. We focus on time series resampling by ‘wavestrapping’ of wavelet coefficients, methods for efficient linear model estimation in the wavelet domain, and wavelet-based methods for multiple hypothesis testing, all of which are somewhat simplified by the decorrelating property of the DWT.

Mixed Spectrum Analysis on fMRI Time-Series

Temporal autocorrelation present in functional magnetic resonance image (fMRI) data poses challenges to its analysis. The existing approaches handling autocorrelation in fMRI time-series often presume a specific model of autocorrelation such as an auto-regressive model. The main limitation here is that the correlation structure of voxels is generally unknown and varies in different brain regions because of different levels of neurogenic noises and pulsatile effects. Enforcing a universal model on all brain regions leads to bias and loss of efficiency in the analysis. In this paper, we propose the mixed spectrum analysis of the voxel time-series to separate the discrete component corresponding to input stimuli and the continuous component carrying temporal autocorrelation. A mixed spectral analysis technique based on M-spectral estimator is proposed, which effectively removes autocorrelation effects from voxel time-series and identify significant peaks of the spectrum. As the proposed method does not assume any prior model for the autocorrelation effect in voxel time-series, varying correlation structure among the brain regions does not affect its performance. We have modified the standard M-spectral method for an application on a spatial set of time-series by incorporating the contextual information related to the continuous spectrum of neighborhood voxels, thus reducing considerably the computation cost. Likelihood of the activation is predicted by comparing the amplitude of discrete component at stimulus frequency of voxels across the brain by using normal distribution and modeling spatial correlations among the likelihood with a conditional random field. We also demonstrate the application of the proposed method in detecting other desired frequencies.

Permutation inference for the general linear model

Permutation methods can provide exact control of false positives and allow the use of non-standard statistics, making only weak assumptions about the data. With the availability of fast and inexpensive computing, their main limitation would be some lack of flexibility to work with arbitrary experimental designs. In this paper we report on results on approximate permutation methods that are more flexible with respect to the experimental design and nuisance variables, and conduct detailed simulations to identify the best method for settings that are typical for imaging research scenarios. We present a generic framework for permutation inference for complex general linear models (GLMS) when the errors are exchangeable and/or have a symmetric distribution, and show that, even in the presence of nuisance effects, these permutation inferences are powerful while providing excellent control of false positives in a wide range of common and relevant imaging research scenarios. We also demonstrate how the inference on GLM parameters, originally intended for independent data, can be used in certain special but useful cases in which independence is violated. Detailed examples of common neuroimaging applications are provided, as well as a complete algorithm - the "randomise" algorithm - for permutation inference with the GLM.

Regional fluorodeoxyglucose metabolism and instrumental activities of daily living across the Alzheimer's disease spectrum

BACKGROUND

Impairment in instrumental activities of daily living (IADL) begins as individuals with amnestic mild cognitive impairment (MCI) transition to Alzheimer's disease (AD) dementia. IADL impairment in AD dementia has been associated with inferior parietal, inferior temporal, and superior occipital hypometabolism using 18F-fluorodeoxyglucose (FDG) positron emission tomography (PET).

OBJECTIVE

To investigate the relationship between regional FDG metabolism and IADL in clinically normal (CN) elderly, MCI, and mild AD dementia subjects cross-sectionally and longitudinally.

METHODS

One hundred and four CN, 203 MCI, and 95 AD dementia subjects from the Alzheimer's Disease Neuroimaging Initiative underwent clinical assessments every 6 to 12 months for up to three years and baseline FDG PET. The subjective, informant-based Functional Activities Questionnaire was used to assess IADL. General linear models and mixed effects models were used, covarying for demographics, cognition, and behavior.

RESULTS

The cross-sectional analysis revealed middle frontal and orbitofrontal hypometabolism were significantly associated with greater IADL impairment. Additionally, the interaction of diagnosis with posterior cingulate and with parahippocampal hypometabolism showed a greater decline in IADL performance as metabolism decreased for the AD dementia relative to the MCI group, and the MCI group relative to the CN group. The longitudinal analysis showed that baseline middle frontal and posterior cingulate hypometabolism were significantly associated with greater rate of increase in IADL impairment over time.

CONCLUSION

These results suggest that regional synaptic dysfunction, including the Alzheimer-typical medial parietal and less typical frontal regions, relates to daily functioning decline at baseline and over time across the early AD spectrum.

Alternative thresholding methods for fMRI data optimized for surgical planning

Current methods for thresholding functional magnetic resonance imaging (fMRI) maps are based on the well-known hypothesis-test framework, optimal for addressing novel theoretical claims. However, these methods as typically practiced have a strong bias toward protecting the null hypothesis, and thus may not provide an optimal balance between specificity and sensitivity in forming activation maps for surgical planning. Maps based on hypothesis-test thresholds are also highly sensitive to sample size and signal-to-noise ratio, whereas many clinical applications require methods that are robust to these effects. We propose a new thresholding method, optimized for surgical planning, based on normalized amplitude thresholding. We show that this method produces activation maps that are more reproducible and more predictive of postoperative cognitive outcome than maps produced with current standard thresholding methods.

A compact and realistic cerebral cortical layout derived from prewhitened resting-state fMRI time series: Cherniak's adjacency rule, size law, and metamodule grouping upheld

We used hierarchical tree clustering to derive a functional organizational chart of 52 human cortical areas (26 per hemisphere) from zero-lag correlations calculated between single-voxel, prewhitened, resting-state BOLD fMRI time series in 18 subjects. No special “resting-state networks” were identified. There were four major features in the resulting tree (dendrogram). First, there was a strong clustering of homotopic, left-right hemispheric areas. Second, cortical areas were concatenated in multiple, partially overlapping clusters. Third, the arrangement of the areas revealed a layout that closely resembled the actual layout of the cerebral cortex, namely an orderly progression from anterior to posterior. And fourth, the layout of the cortical areas in the tree conformed to principles of efficient, compact layout of components proposed by Cherniak. Since the tree was derived on the basis of the strength of neural correlations, these results document an orderly relation between functional interactions and layout, i.e., between structure and function.

How ignoring physiological noise can bias the conclusions from fMRI simulation results

Neuroimaging researchers use simulation studies to validate their statistical methods because it is acknowledged that this is the most feasible way to know the ground truth of the data. The noise model used in these studies typically varies from a simple Gaussian distribution to an estimate of the noise distribution from real data. However, although several studies point out the presence of physiological noise in fMRI data, this noise source is currently lacking in simulation studies. Therefore, we explored the impact of adding physiological noise to the simulated data. For several experimental designs, fMRI data were generated under different noise models while the signal-to-noise ratio was kept constant. The sensitivity and specificity of a standard statistical parametric mapping (SPM) analysis were determined by comparing the known activation with the detected activation. We show that by including physiological noise in the data generation process, the simulation results in terms of sensitivity and specificity drop dramatically. Additionally, we used the new proposed simulation model to compare a standard SPM analysis against the method proposed by Cabella et al. (2009). The results indicate that the analysis of data containing no physiological noise yields a better performance of the SPM analysis. However, if physiological noise is included in the data, the sensitivity and specificity of the Cabella method are higher compared to the SPM analysis. Based on these results, we argue that the results of current simulation studies are likely to be biased, especially when analysis methods are compared using ROC curves.

Spatio-Spectral Mixed Effects Model for Functional Magnetic Resonance Imaging Data

The goal of this paper is to model cognitive control related activation among predefined regions of interest (ROIs) of the human brain while properly adjusting for the underlying spatio-temporal correlations. Standard approaches to fMRI analysis do not simultaneously take into account both the spatial and temporal correlations that are prevalent in fMRI data. This is primarily due to the computational complexity of estimating the spatio-temporal covariance matrix. More specifically, they do not take into account multi-scale spatial correlation (between-ROIs and within-ROI). To address these limitations, we propose a spatio-spectral mixed effects model. Working in the spectral domain simplifies the temporal covariance structure because the Fourier coefficients are approximately uncorrelated across frequencies. Additionally, by incorporating voxel-specific and ROI-specific random effects, the model is able to capture the multi-scale spatial covariance structure: distance-dependent local correlation (within an ROI), and distance-independent global correlation (between-ROIs). Building on existing theory on linear mixed effects models to conduct estimation and inference, we applied our model to fMRI data to study activation in pre-specified ROIs in the prefontal cortex and estimate the correlation structure in the network. Simulation studies demonstrate that ignoring the multi-scale correlation leads to higher false positives.

Multiple testing corrections, nonparametric methods, and random field theory

I provide a selective review of the literature on the multiple testing problem in fMRI. By drawing connections with the older modalities, PET in particular, and how software implementations have tracked (or lagged behind) theoretical developments, my narrative aims to give the methodological researcher a historical perspective on this important aspect of fMRI data analysis.

Carryover Effects Alter fMRI Statistical Analysis in an Acupuncture Study

Carryover effects can contaminate ON/OFF BOLD contrasts designated in an fMRI experiment. Yet, the ON/OFF contrasts are essential to facilitate statistical analysis based on the significance of contrast levels. Here, we conducted an fMRI experiment with acupuncture stimulation applied on ST42 acupoint as well as with tactile stimulation on its skin surface. Experiment consisted of three two-block acupuncture and one two-block tactile fMRI runs. Each block started with 26-sec OFF period followed by either 26-sec needle manipulation in the acupuncture runs or by scratching skin surface with sand paper in the tactile. To test if carryover effects could alter the BOLD contrasts, we analyzed different portions of fMRI data using GLM method. Our results showed analyses on different portions of acupuncture fMRI data gave significantly different results. Statistical parametric maps of group random effects resulted from the analysis on the very first fMRI trial formed the broadest coverage of the active brain areas. BOLD model time course also best explained the adjusted raw time course at peak active voxel ( coefficient of determination = 0.88). Analyses on other portions of fMRI data only selected subset of the active brain areas delineated by the analysis on the very first data trial and the BOLD model only mildly accounted for the adjusted raw time courses. In tactile runs, results were more consistent across analyses. Therefore, in fMRI experiments with strong carryover effects, a single-block experimental design with multiple repetitions, separated by long enough periods of time, should be more suitable to extract task BOLD effects.

Extending local canonical correlation analysis to handle general linear contrasts for FMRI data

Local canonical correlation analysis (CCA) is a multivariate method that has been proposed to more accurately determine activation patterns in fMRI data. In its conventional formulation, CCA has several drawbacks that limit its usefulness in fMRI. A major drawback is that, unlike the general linear model (GLM), a test of general linear contrasts of the temporal regressors has not been incorporated into the CCA formalism. To overcome this drawback, a novel directional test statistic was derived using the equivalence of multivariate multiple regression (MVMR) and CCA. This extension will allow CCA to be used for inference of general linear contrasts in more complicated fMRI designs without reparameterization of the design matrix and without reestimating the CCA solutions for each particular contrast of interest. With the proper constraints on the spatial coefficients of CCA, this test statistic can yield a more powerful test on the inference of evoked brain regional activations from noisy fMRI data than the conventional t-test in the GLM. The quantitative results from simulated and pseudoreal data and activation maps from fMRI data were used to demonstrate the advantage of this novel test statistic.

fMRI analysis on the GPU-possibilities and challenges

Functional magnetic resonance imaging (fMRI) makes it possible to non-invasively measure brain activity with high spatial resolution. There are however a number of issues that have to be addressed. One is the large amount of spatio-temporal data that needs to be processed. In addition to the statistical analysis itself, several preprocessing steps, such as slice timing correction and motion compensation, are normally applied. The high computational power of modern graphic cards has already successfully been used for MRI and fMRI. Going beyond the first published demonstration of GPU-based analysis of fMRI data, all the preprocessing steps and two statistical approaches, the general linear model (GLM) and canonical correlation analysis (CCA), have been implemented on a GPU. For an fMRI dataset of typical size (80 volumes with 64×64×22voxels), all the preprocessing takes about 0.5s on the GPU, compared to 5s with an optimized CPU implementation and 120s with the commonly used statistical parametric mapping (SPM) software. A random permutation test with 10,000 permutations, with smoothing in each permutation, takes about 50s if three GPUs are used, compared to 0.5-2.5h with an optimized CPU implementation. The presented work will save time for researchers and clinicians in their daily work and enables the use of more advanced analysis, such as non-parametric statistics, both for conventional fMRI and for real-time fMRI.

An empirical comparison of information-theoretic criteria in estimating the number of independent components of fMRI data

BACKGROUND

Independent Component Analysis (ICA) has been widely applied to the analysis of fMRI data. Accurate estimation of the number of independent components of fMRI data is critical to reduce over/under fitting. Although various methods based on Information Theoretic Criteria (ITC) have been used to estimate the intrinsic dimension of fMRI data, the relative performance of different ITC in the context of the ICA model hasn't been fully investigated, especially considering the properties of fMRI data. The present study explores and evaluates the performance of various ITC for the fMRI data with varied white noise levels, colored noise levels, temporal data sizes and spatial smoothness degrees.

METHODOLOGY

Both simulated data and real fMRI data with varied Gaussian white noise levels, first-order auto-regressive (AR(1)) noise levels, temporal data sizes and spatial smoothness degrees were carried out to deeply explore and evaluate the performance of different traditional ITC.

PRINCIPAL FINDINGS

Results indicate that the performance of ITCs depends on the noise level, temporal data size and spatial smoothness of fMRI data. 1) High white noise levels may lead to underestimation of all criteria and MDL/BIC has the severest underestimation at the higher Gaussian white noise level. 2) Colored noise may result in overestimation that can be intensified by the increase of AR(1) coefficient rather than the SD of AR(1) noise and MDL/BIC shows the least overestimation. 3) Larger temporal data size will be better for estimation for the model of white noise but tends to cause severer overestimation for the model of AR(1) noise. 4) Spatial smoothing will result in overestimation in both noise models.

CONCLUSIONS

1) None of ITC is perfect for all fMRI data due to its complicated noise structure. 2) If there is only white noise in data, AIC is preferred when the noise level is high and otherwise, Laplace approximation is a better choice. 3) When colored noise exists in data, MDL/BIC outperforms the other criteria.

An overview of longitudinal data analysis methods for neurological research

The purpose of this article is to provide a concise, broad and readily accessible overview of longitudinal data analysis methods, aimed to be a practical guide for clinical investigators in neurology. In general, we advise that older, traditional methods, including (1) simple regression of the dependent variable on a time measure, (2) analyzing a single summary subject level number that indexes changes for each subject and (3) a general linear model approach with a fixed-subject effect, should be reserved for quick, simple or preliminary analyses. We advocate the general use of mixed-random and fixed-effect regression models for analyses of most longitudinal clinical studies. Under restrictive situations or to provide validation, we recommend: (1) repeated-measure analysis of covariance (ANCOVA), (2) ANCOVA for two time points, (3) generalized estimating equations and (4) latent growth curve/structural equation models.

Fast random permutation tests enable objective evaluation of methods for single-subject FMRI analysis

Parametric statistical methods, such as Z-, t-, and F-values, are traditionally employed in functional magnetic resonance imaging (fMRI) for identifying areas in the brain that are active with a certain degree of statistical significance. These parametric methods, however, have two major drawbacks. First, it is assumed that the observed data are Gaussian distributed and independent; assumptions that generally are not valid for fMRI data. Second, the statistical test distribution can be derived theoretically only for very simple linear detection statistics. With nonparametric statistical methods, the two limitations described above can be overcome. The major drawback of non-parametric methods is the computational burden with processing times ranging from hours to days, which so far have made them impractical for routine use in single-subject fMRI analysis. In this work, it is shown how the computational power of cost-efficient graphics processing units (GPUs) can be used to speed up random permutation tests. A test with 10000 permutations takes less than a minute, making statistical analysis of advanced detection methods in fMRI practically feasible. To exemplify the permutation-based approach, brain activity maps generated by the general linear model (GLM) and canonical correlation analysis (CCA) are compared at the same significance level.

True associations between resting fMRI time series based on innovations

We calculated voxel-by-voxel pairwise crosscorrelations between prewhitened resting-state BOLD fMRI time series recorded from 60 cortical areas (30 per hemisphere) in 18 human subjects (nine women and nine men). Altogether, more than a billion-and-a-quarter pairs of BOLD time series were analyzed. For each pair, a crosscorrelogram was computed by calculating 21 crosscorrelations, namely at zero lag ± 10 lags of 2 s duration each. For each crosscorrelogram, in turn, the crosscorrelation with the highest absolute value was found and its sign, value, and lag were retained for further analysis. In addition, the crosscorrelations at zero lag (irrespective of the location of the peak) were also analyzed as a special case. Based on known varying density of anatomical connectivity, we distinguished four general brain groups for which we derived summary statistics of crosscorrelations between voxels within an area (group I), between voxels of paired homotopic areas across the two hemispheres (group II), between voxels of an area and all other voxels in the same (ipsilateral) hemisphere (group III), and voxels of an area and all voxels in the opposite (contralateral) hemisphere (except those in the homotopic area) (group IV). We found the following. (a) Most of the crosscorrelogram peaks occurred at zero lag, followed by ± 1 lag; (b) over all groups, positive crosscorrelations were much more frequent than negative ones; (c) average crosscorrelation was highest for group I, and decreased progressively for groups II-IV; (d) the ratio of positive over negative crosscorrelations was highest for group I and progressively smaller for groups II-IV; (e) the highest proportion of positive crosscorrelations (with respect to all positive ones) was observed at zero lag; and (f) the highest proportion of negative crosscorrelations (with respect to all negative ones) was observed at lag = 2. These findings reveal a systematic pattern of crosscorrelations with respect to their sign, magnitude, lag and brain group, as defined above. Given that these groups were defined along a qualitative gradient of known overall anatomical connectivity, our results suggest that functional interactions between two voxels may simply reflect the density of such anatomical connectivity between the areas to which the voxels belong.

A multiscale analysis of the temporal characteristics of resting-state fMRI data

In this paper, we conduct an investigation of the null hypothesis distribution for functional magnetic resonance imaging (fMRI) time series using multiscale analysis tools, SiZer (significance of zero crossings of the derivative) and wavelets. Most current approaches to the analysis of fMRI data assume simple models for temporal (short term or long term) dependence structure. Such simplifications are to some extent necessary due to the complex, high-dimensional nature of the data, but to date there have been few systematic studies of the dependence structures under a range of possible null hypotheses, using data sets gathered specifically for that purpose. We aim to address some of these issues by analyzing the detrended data with a long enough time horizon to study possible long-range temporal dependence. Our multiscale approach shows that even for resting-state data, data, i.e. "null" or ambient thought, some voxel time series cannot be modeled by white noise and need long-range dependent type error structure. This finding suggests the use of different time series models in different parts of the brain in fMRI studies.

Feature-space-based FMRI analysis using the optimal linear transformation

The optimal linear transformation (OLT), an image analysis technique of feature space, was first presented in the field of MRI. This paper proposes a method of extending OLT from MRI to functional MRI (fMRI) to improve the activation-detection performance over conventional approaches of fMRI analysis. In this method, first, ideal hemodynamic response time series for different stimuli were generated by convolving the theoretical hemodynamic response model with the stimulus timing. Second, constructing hypothetical signature vectors for different activity patterns of interest by virtue of the ideal hemodynamic responses, OLT was used to extract features of fMRI data. The resultant feature space had particular geometric clustering properties. It was then classified into different groups, each pertaining to an activity pattern of interest; the applied signature vector for each group was obtained by averaging. Third, using the applied signature vectors, OLT was applied again to generate fMRI composite images with high SNRs for the desired activity patterns. Simulations and a blocked fMRI experiment were employed for the method to be verified and compared with the general linear model (GLM)-based analysis. The simulation studies and the experimental results indicated the superiority of the proposed method over the GLM-based analysis in detecting brain activities.

Robust and unbiased variance of GLM coefficients for misspecified autocorrelation and hemodynamic response models in fMRI

As a consequence of misspecification of the hemodynamic response and noise variance models, tests on general linear model coe cients are not valid. Robust estimation of the variance of the general linear model (GLM) coecients in fMRI time series is therefore essential. In this paper an alternative method to estimate the variance of the GLM coe cients accurately is suggested and compared to other methods. The alternative, referred to as the sandwich, is based primarily on the fact that the time series are obtained from multiple exchangeable stimulus presentations. The analytic results show that the sandwich is unbiased. Using this result, it is possible to obtain an exact statistic which keeps the 5% false positive rate. Extensive Monte Carlo simulations show that the sandwich is robust against misspeci cation of the autocorrelations and of the hemodynamic response model. The sandwich is seen to be in many circumstances robust, computationally efficient, and flexible with respect to correlation structures across the brain. In contrast, the smoothing approach can be robust to a certain extent but only with specific knowledge of the circumstances for the smoothing parameter.

Unified framework for robust estimation of brain networks from FMRI using temporal and spatial correlation analyses

There is a rapidly growing interest in the neuroimaging field to use functional magnetic resonance imaging (fMRI) to explore brain networks, i.e., how regions of the brain communicate with one another. This paper presents a general and novel statistical framework for robust and more complete estimation of brain functional connectivity from fMRI based on correlation analyses and hypothesis testing. In addition to the ability of examining the correlations with each individual seed as in the standard and existing methods, the proposed framework can detect functional interactions by simultaneously examining multiseed correlations via multiple correlation coefficients. Spatially structured noise in fMRI is also taken into account during the identification of functional interconnection networks through noncentral F hypothesis tests. The associated issues for the multiple testing and the effective degrees-of-freedom are considered as well. Furthermore, partial multiple correlations are introduced and formulated to measure any additional task-induced but not stimulus-locked relation over brain regions so that we can take the analysis of functional connectivity closer to the characterization of direct functional interactions of the brain. Evaluation for accuracy and advantages, and comparisons of the new approaches in the presented general framework are performed using both realistic synthetic data and in vivo fMRI data.

Modeling low-frequency fluctuation and hemodynamic response timecourse in event-related fMRI

Functional magnetic resonance imaging (fMRI) suffers from many problems that make signal estimation difficult. These include variation in the hemodynamic response across voxels and low signal-to-noise ratio (SNR). We evaluate several analysis techniques that address these problems for event-related fMRI. (1) Many fMRI analyses assume a canonical hemodynamic response function, but this assumption may lead to inaccurate data models. By adopting the finite impulse response model, we show that voxel-specific hemodynamic response functions can be estimated directly from the data. (2) There is a large amount of low-frequency noise fluctuation (LFF) in blood oxygenation level dependent (BOLD) time-series data. To compensate for this problem, we use polynomials as regressors for LFF. We show that this technique substantially improves SNR and is more accurate than high-pass filtering of the data. (3) Model overfitting is a problem for the finite impulse response model because of the low SNR of the BOLD response. To reduce overfitting, we estimate a hemodynamic response timecourse for each voxel and incorporate the constraint of time-event separability, the constraint that hemodynamic responses across event types are identical up to a scale factor. We show that this technique substantially improves the accuracy of hemodynamic response estimates and can be computed efficiently. For the analysis techniques we present, we evaluate improvement in modeling accuracy via 10-fold cross-validation.

Whole brain voxel-wise analysis of single-subject serial DTI by permutation testing

Diffusion tensor MRI (DTI) has been widely used to investigate brain microstructural changes in pathological conditions as well as for normal development and aging. In particular, longitudinal changes are vital to the understanding of progression but these studies are typically designed for specific regions of interest. To analyze changes in these regions traditional statistical methods are often employed to elucidate group differences which are measured against the variability found in a control cohort. However, in some cases, rather than collecting multiple subjects into two groups, it is necessary and more informative to analyze the data for individual subjects. There is also a need for understanding changes in a single subject without prior information regarding the spatial distribution of the pathology, but no formal statistical framework exists for these voxel-wise analyses of DTI. In this study, we present PERVADE (permutation voxel-wise analysis of diffusion estimates), a whole brain analysis method for detecting localized FA changes between two separate points in time of any given subject, without any prior hypothesis about where changes might occur. Exploiting the nature of DTI that it is calculated from multiple diffusion-weighted images of each region, permutation testing, a non-parametric hypothesis testing technique, was modified for the analysis of serial DTI data and implemented for voxel-wise hypothesis tests of diffusion metric changes, as well as for suprathreshold cluster analysis to correct for multiple comparisons. We describe PERVADE in detail and present results from Monte Carlo simulation supporting the validity of the technique as well as illustrative examples from a healthy subject and patients in the early stages of multiple sclerosis.

Model-free analysis of brain fMRI data by recurrence quantification

We propose a novel model-free univariate strategy for functional magnetic resonance imaging (fMRI) studies based upon recurrence quantification analysis (RQA). RQA is an auto-regressive method, which identifies recurrences in signals without any a priori assumptions. The performance of RQA is compared to that of univariate statistics based on a general linear model (GLM) and probabilistic independent component analysis (P-ICA) for a set of simulated and real fMRI data. RQA provides an appealing alternative to conventional GLM techniques, due to its exclusive feature of being model-free and of detecting potentially both linear and nonlinear dynamic processes, without requiring signal stationarity. The overall performance of the method compares positively also with P-ICA, another well-known model-free algorithm, which requires prior information to discriminate between different spatio-temporal processes. For simulated data, RQA is endowed with excellent accuracy for contrast-to-noise ratios greater than 0.2, and has a performance comparable to that of GLM for t(CNR)>or=0.8. For cerebral fMRI data acquired from a group of healthy subjects performing a finger-tapping task, (i) RQA reveals activations in the primary motor area contra-lateral to the employed hand and in the supplementary motor area, in agreement with the outcome of GLM analysis and (ii) identifies an additional brain region with transient signal changes. Moreover, RQA identifies signal recurrences induced by physiological processes other than BOLD (movement-related or of vascular origin). Finally, RQA is more robust than the GLM with respect to variations in the shape and timing of the underlying neuronal and hemodynamic responses which may vary between brain regions, subjects and tasks.

Independent component analysis in the presence of noise in fMRI

A noisy version of independent component analysis (noisy ICA) is applied to simulated and real functional magnetic resonance imaging (fMRI) data. The noise covariance is explicitly modeled by an autoregressive (AR) model of order 1. The unmixing matrix of the data is determined using a variant of the FastICA algorithm based on Gaussian moments. The sources are estimated using the principle of maximum likelihood by modeling the source densities as asymmetric exponential functions. Effect of dimensionality reduction on the effective noise covariance used, accuracy of the obtained mixing matrix and degree of improvement in estimating fMRI sources are investigated. The primary conclusions after using this method of evaluation are as follows: (a) weighting matrix estimates are similar for noisy and conventional ICA in the realm of typical fMRI data, and (b) source estimates are improved by 5% (as measured by the correlation coefficient) in realistic simulated data by explicitly modeling the source densities and the noise, even when just a simple white noise model is used.

A semi-parametric approach to estimate the family-wise error rate in fMRI using resting-state data

One of the most important considerations in any hypothesis based fMRI data analysis is to choose the appropriate threshold to construct the activation maps, which is usually based on p-values. However, in fMRI data, there are three factors which necessitate severe corrections in the process of estimating the p-values. First, the fMRI time series at an individual voxel has strong temporal autocorrelation which needs to be estimated to obtain the corrected parametric p-value. The second factor is the multiple comparisons problem arising from simultaneously testing tens of thousands of voxels for activation. A common way in the statistical literature to account for multiple testing is to consider the family-wise error rate (FWE) which is related to the distribution of the maximum observed value over all voxels. The third problem, which is not mentioned frequently in the context of adjusting the p-value, is the effect of inherent low frequency processes present even in resting-state data that may introduce a large number of false positives without proper adjustment. In this article, a novel and efficient semi-parametric method, using resampling of normalized spacings of order statistics, is introduced to address all the three problems mentioned above. The new method makes very few assumptions and demands minimal computational effort, unlike other existing resampling methods in fMRI. Furthermore, it will be demonstrated that the correction for temporal autocorrelation is not critical in implementing the proposed method. Results using the proposed method are compared with SPM2.

Rank-order versus mean based statistics for neuroimaging

Traditional analysis of neuroimaging data uses parametric statistics, such as the t-test. These tests are designed to detect mean differences. In fact, even nonparametric techniques such as Statistical non-Parametric Mapping (SnPM) use the mean-based t statistic to measure effect size. We note that these measures may not be particularly sensitive for detecting differences when the mean is not an accurate measure of central tendency--for example if one of the groups is experiencing a ceiling or floor effect (causing a skewed data distribution). Here we introduce a nonparametric approach for neuroimaging data analysis that is based on the rank-order of data (and is therefore less influenced by outliers than the t-test). We suggest that this approach may offer a small benefit for datasets where the assumptions of the t-test have been violated, for example datasets where data from one of the groups exhibits a skewed distribution due to floor or ceiling effects.

A cluster mass permutation test with contextual enhancement for fMRI activation detection

Gaussian random field (GRF)-based methods are commonly used for statistical inference and to control the family-wise error rate (FWE) in neuroimaging. They require that the error fields are reasonable lattice approximations to an underlying continuous multivariate Gaussian random field and have differentiable and invertible spatial autocorrelation function. Permutation test estimates the distribution of the test statistic from the data and adjusts automatically for the FWE. Here we present a new analysis procedure, the cluster mass permutation test with contextual enhancement (CMPCE), and compare it to GRF. In CMPCE, the data are first pre-whitened to remove temporal autocorrelations. The FWE rates, the cluster detection probability and delineation accuracy of CMPCE and GRF were compared using measured null data and null data containing simulated activations. We also applied both methods to an fMRI experiment where tactile somatosensory stimulation into the right hand was used. When analyzing the FWE using null data, both CMPCE and GRF gave significantly higher FWEs (CMPCE up to 0.12, GRF up to 0.18) than the nominal significance level 0.05, indicating that the pre-whitening, motion correction or high-pass filtering partially failed. In the simulated activation data, CMPCE gave less falsely classified voxels for the same cluster detection probability level than GRF. The maximal cluster detection probability was on the other hand higher in the GRF-based method. Both methods gave qualitatively similar results in the tactile fMRI data. CMPCE seems to be a promising fMRI analysis method, especially if high delineation accuracy is required.

fMRI MODELS OF DENDRITIC AND ASTROCYTIC NETWORKS

In order to elucidate the relationships between hierarchical structures within the neocortical neuropil and the information carried by an ensemble of neurons encompassing a single voxel, it is essential to predict through volume conductor modeling LFPs representing average extracellular potentials, which are expressed in terms of interstitial potentials of individual cells in networks of gap-junctionally connected astrocytes and synaptically connected neurons. These relationships have been provided and can then be used to investigate how the underlying neuronal population activity can be inferred from the measurement of the BOLD signal through electrovascular coupling mechanisms across the blood-brain barrier. The importance of both synaptic and extrasynaptic transmission as the basis of electrophysiological indices triggering vascular responses between dendritic and astrocytic networks, and sequential configurations of firing patterns in composite neural networks is emphasized. The purpose of this review is to show how fMRI data may be used to draw conclusions about the information transmitted by individual neurons in populations generating the BOLD signal.

Emotional task-dependent low-frequency fluctuations and methylphenidate: Wavelet scaling analysis of 1/f-type fluctuations in fMRI of the cerebellar vermis

Ion channel currents, neural firing patterns, and brain BOLD signals display 1/f-type fluctuations or fractal properties in time. By design, fMRI methods attempt to minimize the contribution of variance from low-frequency physiological 1/f-noise. New fMRI methods are described to visualize and measure 1/f-type BOLD fluctuations in volunteers recalling affectively neutral or emotional memories or meditating (i.e., attending to breathing) then retrospectively rating emotional content. A wavelet scaling exponent (alpha) was used to characterize signals from 0.015625 to 0.5Hz in cerebellar lobules VIII to X of the vermis (posterior inferior vermis; PIV), a region coordinating balance, eye tracking, locomotion, and vascular tone, and a possible site of pathology in attention deficit hyperactivity disorder (ADHD).

RESULTS

Changes in alpha and emotional measures were correlated in PIV voxels (r = 0.622, d.f .= 14, P < 0.0005), but not other regions examined. In contrast, conventional means and standard deviations of PIV voxels were unchanged. Methylphenidate, shown to decrease slow oscillations in rodent basal ganglia [Ruskin DN, Bergstrom DA, Shenker A, Freeman LE, Baek D, Walters JR. Drugs used in the treatment of attention-deficit/hyperactivity disorder affect postsynaptic firing rate and oscillation without preferential dopamine autoreceptor action. Biol Psychiatry 2001;49:340-50.], abolished task-dependent alpha changes in the PIV of an adult with ADHD. Wavelet analysis of long BOLD time series appears well suited to fractal physiology and studies of pharmacologically modulated cerebellar-thalamic-cortical function in ADHD or other psychiatric disorders.

Estimation of the intrinsic dimensionality of fMRI data

A new method based on an autoregressive noise model of order 1 is introduced to the problem of detecting the number of components in fMRI data. Unlike current information-theoretic criteria like AIC, MDL, and related PPCA, which do not incorporate autocorrelations in the noise, the new method leads to more consistent estimates of the model order, as illustrated in simulated and real fMRI resting-state data.

Resampling fMRI time series

The problem of selecting a threshold for the statistical parameter maps in functional MRI (fMRI) is a delicate issue. The use of advanced test statistics and/or the complex dependence structure of fMRI noise may preclude parametric statistical methods for finding appropriate thresholds. Non-parametric statistical methodology has been presented as a feasible alternative. In this paper, we discuss resampling methods for finding thresholds in single subject fMRI analysis. It is shown that the presence of a BOLD response in the time series biases the estimation of the temporal autocorrelation, which in turn leads to biased thresholds. Therefore, proposed resampling methods based on Fourier and wavelet transforms, which employ implicit and weak models of the temporal noise characteristic, may produce erroneous thresholds. In contrast, resampling based on a pre-whitening transform, which is driven by an explicit noise model, is robust to the presence of a BOLD response. The size of the bias is, however, largely dependent on the complexity of the experimental design. While blocked designs can induce large biases, event-related designs generate significantly smaller biases. Results supporting these claims are provided.

Estimating the global order of the fMRI noise model

One of the major issues in GLM-based fMRI analysis techniques is the presence of temporal autocorrelations in the residual signal after regression. A possible correction method is that of prewhitening, which fits an autoregressive (or other) model to the residual and uses the expected temporal autocorrelations of the model to transform the data and design matrix such that the residual becomes white noise. In this article, a method is introduced to estimate the global autoregressive model order of a data set, based on the residuals after regression. The proposed global standardized partial autocorrelation (SPAC) method tests whether the spatial profile of partial autocorrelations at a certain lag is random, and uses random field theory to account for the spatial correlations typical for fMRI data. It is tested both on synthetic and fMRI data, and is compared to two traditional techniques for model order estimation.

Fractional Gaussian noise, functional MRI and Alzheimer's disease

Fractional Gaussian noise (fGn) provides a parsimonious model for stationary increments of a self-similar process parameterised by the Hurst exponent, H, and variance, sigma2. Fractional Gaussian noise with H < 0.5 demonstrates negatively autocorrelated or antipersistent behaviour; fGn with H > 0.5 demonstrates 1/f, long memory or persistent behaviour; and the special case of fGn with H = 0.5 corresponds to classical Gaussian white noise. We comparatively evaluate four possible estimators of fGn parameters, one method implemented in the time domain and three in the wavelet domain. We show that a wavelet-based maximum likelihood (ML) estimator yields the most efficient estimates of H and sigma2 in simulated fGn with 0 < H < 1. Applying this estimator to fMRI data acquired in the "resting" state from healthy young and older volunteers, we show empirically that fGn provides an accommodating model for diverse species of fMRI noise, assuming adequate preprocessing to correct effects of head movement, and that voxels with H > 0.5 tend to be concentrated in cortex whereas voxels with H < 0.5 are more frequently located in ventricles and sulcal CSF. The wavelet-ML estimator can be generalised to estimate the parameter vector beta for general linear modelling (GLM) of a physiological response to experimental stimulation and we demonstrate nominal type I error control in multiple testing of beta, divided by its standard error, in simulated and biological data under the null hypothesis beta = 0. We illustrate these methods principally by showing that there are significant differences between patients with early Alzheimer's disease (AD) and age-matched comparison subjects in the persistence of fGn in the medial and lateral temporal lobes, insula, dorsal cingulate/medial premotor cortex, and left pre- and postcentral gyrus: patients with AD had greater persistence of resting fMRI noise (larger H) in these regions. Comparable abnormalities in the AD patients were also identified by a permutation test of local differences in the first-order autoregression AR(1) coefficient, which was significantly more positive in patients. However, we found that the Hurst exponent provided a more sensitive metric than the AR(1) coefficient to detect these differences, perhaps because neurophysiological changes in early AD are naturally better described in terms of abnormal salience of long memory dynamics than a change in the strength of association between immediately consecutive time points. We conclude that parsimonious mapping of fMRI noise properties in terms of fGn parameters efficiently estimated in the wavelet domain is feasible and can enhance insight into the pathophysiology of Alzheimer's disease.

Improving permutation test power for group analysis of spatially filtered MEG data

Non-parametric statistical methods, such as permutation, are flexible tools to analyze data when the population distribution is not known. With minimal assumptions and better statistical power compared to the parametric tests, permutation tests have recently been applied to the spatially filtered magnetoencephalography (MEG) data for group analysis. To perform permutation tests on neuroimaging data, an empirical maximal null distribution has to be found, which is free from any activated voxels, to determine the threshold to classify the voxels as active at a given probability level. An iterative procedure is used to determine the distribution by computing the null distribution, which is recomputed when a possible activated voxel is found within the current distributions. Besides the high computational costs associated with this approach, there is no guarantee that all activated voxels are excluded when constructing the maximal null distribution, which may reduce the statistical power. In this study, we propose a novel way to construct the maximal null distribution from the data of the resting period. The approach is tested on the MEG data from a somatosensory experiment, and demonstrated that the approach could improve the power of the permutation test while reducing the computational cost at the same time.

Wavelets and functional magnetic resonance imaging of the human brain

The discrete wavelet transform (DWT) is widely used for multiresolution analysis and decorrelation or "whitening" of nonstationary time series and spatial processes. Wavelets are naturally appropriate for analysis of biological data, such as functional magnetic resonance images of the human brain, which often demonstrate scale invariant or fractal properties. We provide a brief formal introduction to key properties of the DWT and review the growing literature on its application to fMRI. We focus on three applications in particular: (i) wavelet coefficient resampling or "wavestrapping" of 1-D time series, 2- to 3-D spatial maps and 4-D spatiotemporal processes; (ii) wavelet-based estimators for signal and noise parameters of time series regression models assuming the errors are fractional Gaussian noise (fGn); and (iii) wavelet shrinkage in frequentist and Bayesian frameworks to support multiresolution hypothesis testing on spatially extended statistic maps. We conclude that the wavelet domain is a rich source of new concepts and techniques to enhance the power of statistical analysis of human fMRI data.

Spatiotemporal wavelet analysis for functional MRI

Characterizing the spatiotemporal behavior of the BOLD signal in functional Magnetic Resonance Imaging (fMRI) is a central issue in understanding brain function. While the nature of functional activation clusters is fundamentally heterogeneous, many current analysis approaches use spatially invariant models that can degrade anatomic boundaries and distort the underlying spatiotemporal signal. Furthermore, few analysis approaches use true spatiotemporal continuity in their statistical formulations. To address these issues, we present a novel spatiotemporal wavelet procedure that uses a stimulus-convolved hemodynamic signal plus correlated noise model. The wavelet fits, computed by spatially constrained maximum-likelihood estimation, provide efficient multiscale representations of heterogeneous brain structures and give well-identified, parsimonious spatial activation estimates that are modulated by the temporal fMRI dynamics. In a study of both simulated data and actual fMRI memory task experiments, our new method gave lower mean-squared error and seemed to result in more localized fMRI activation maps compared to models using standard wavelet or smoothing techniques. Our spatiotemporal wavelet framework suggests a useful tool for the analysis of fMRI studies.

Optimal spatial regularisation of autocorrelation estimates in fMRI analysis

In the General Linear Model (GLM) framework for the statistical analysis of fMRI data, the problem of temporal autocorrelations in the residual signal (after regression) has been frequently addressed in the open literature. There exist various methods for correcting the ensuing bias in the statistical testing, among which the prewhitening strategy, which uses a prewhitening matrix for rendering the residual signal white (i.e., without temporal autocorrelations). This correction is only exact when the autocorrelation structure of the noise-generating process is accurately known, and the estimates derived from the fMRI data are too noisy to be used for correction. Recently, Worsley and co-workers proposed to spatially smooth the noisy autocorrelation estimates, effectively reducing their variance and allowing for a better correction. In this article, a systematic study into the effect of the smoothing kernel width is performed and a method is introduced for choosing this bandwidth in an "optimal" manner. Several aspects of the prewhitening strategy are investigated, namely the choice of the autocorrelation estimate (biased or unbiased), the accuracy of the estimates, the degree of spatial regularisation and the order of the autoregressive model used for characterising the noise. The proposed method is extensively evaluated on both synthetic and real fMRI data.

fMRI activation maps based on the NN-ARx model

The most significant progresses in the understanding of human brain functions have been possible due to the use of functional magnetic resonance imaging (fMRI), which when used in combination with other standard neuroimaging techniques (i.e., EEG) provides researchers with a potential tool to elucidate many biophysical principles, established previously by animal comparative studies. However, to date, most of the methods proposed in the literature seeking fMRI signs have been limited to the use of a top-down data analysis approach, thus ignoring a pool of physiological facts. In spite of the important contributions achieved by applying these methods to actual data, there is a disproportionate gap between theoretical models and data-analysis strategies while trying to focus on several new prospects, like for example fMRI/EEG data fusion, causality/connectivity patterns, and nonlinear BOLD signal dynamics. In this paper, we propose a new approach which will allow many of the abovementioned hot topics to be addressed in the near future with an underlying interpretability based on bottom-up modeling. In particular, the theta-MAP presented in the paper to test brain activation corresponds very well with the standardized t test of the SPM99 toolbox. Additionally, a new Impulse Response Function (IRF) has been formulated, directly related to the well-established concept of the hemodynamics response function (HRF). The model uses not only the information contained in the signal but also that in the structure of the background noise to simultaneously estimate the IRF and the autocorrelation function (ACF) by using an autoregressive (AR) model with a filtered Poisson process driving the dynamics. The short-range contributions of voxels within the near-neighborhood are also included, and the potential drift was characterized by a polynomial series. Since our model originated from an immediate extension of the hemodynamics approach [Friston, K.J., Mechelli, A., Turner, R., Price C.J. (2000a). Nonlinear responses in fMRI: the balloon model, volterra kernels, and other hemodynamics. NeuroImage 12, 466-477.], a natural interpretability of the results is feasible.

Comparing methods of analyzing fMRI statistical parametric maps

Approaches for the analysis of statistical parametric maps (SPMs) can be crudely grouped into three main categories in which different philosophies are applied to delineate activated regions. These being type I error control thresholding, false discovery rate (FDR) control thresholding and posterior probability thresholding. To better understand the properties of these main approaches, we carried out a simulation study to compare the approaches as they would be used on real data sets. Using default settings, we find that posterior probability thresholding is the most powerful approach, and type I error control thresholding provides the lowest levels of type I error. False discovery rate control thresholding performs in between the other approaches for both these criteria, although for some parameter settings this approach can approximate the performance of posterior probability thresholding. Based on these results, we discuss the relative merits of the three approaches in an attempt to decide upon an optimal approach. We conclude that viewing the problem of delineating areas of activation as a classification problem provides a highly interpretable framework for comparing the methods. Within this framework, we highlight the role of the loss function, which explicitly penalizes the types of errors that may occur in a given analysis.

Permutation tests for factorially designed neuroimaging experiments

Permutation methods for analysis of functional neuroimaging data acquired as factorially designed experiments are described and validated. The F ratio was estimated for main effects and interactions at each voxel in standard space. Critical values corresponding to probability thresholds were derived from a null distribution sampled by appropriate permutation of observations. Spatially informed, cluster-level test statistics were generated by applying a preliminary probability threshold to the voxel F maps and then computing the sum of voxel statistics in each of the resulting three-dimensional clusters, i.e., cluster "mass." Using simulations comprising two between- or within-subject factors each with two or three levels, contaminated by Gaussian and non-normal noise, the voxel-wise permutation test was compared to the standard parametric F test and to the performance of the spatially informed statistic using receiver operating characteristic (ROC) curves. Validity of the permutation-testing algorithm and software is endorsed by almost identical performance of parametric and permutation tests of the voxel-level F statistic. Permutation testing of suprathreshold voxel cluster mass, however, was found to provide consistently superior sensitivity to detect simulated signals than either of the voxel-level tests. The methods are also illustrated by application to an experimental dataset designed to investigate effects of antidepressant drug treatment on brain activation by implicit sad facial affect perception in patients with major depression. Antidepressant drug effects in left amygdala and ventral striatum were detected by this software for an interaction between time (within-subject factor) and group (between-subject factor) in a representative two-way factorial design.

Evaluation of mixed effects in event-related fMRI studies: impact of first-level design and filtering

With the introduction of event-related designs in fMRI, it has become crucial to optimize design efficiency and temporal filtering to detect activations at the 1st level with high sensitivity. We investigate the relevance of these issues for fMRI population studies, that is, 2nd-level analysis, for a set of event-related fMRI (er-fMRI) designs with different 1st-level efficiencies, adopting three distinct 1st-level filtering strategies as implemented in SPM99, SPM2, and FSL3.0. By theory, experiments, and simulations using physiological fMRI noise, we show that both design and filtering impact the outcome of the statistical analysis, not only at the 1st but also at the 2nd level. There are several reasons behind this finding. First, sensitivity is affected by both design and filtering, since the scan-to-scan variance, that is the fixed effect, is not negligible with respect to the between-subject variance, that is the random effect, in er-fMRI population studies. The impact of the fixed effects error on the sensitivity of the mixed effects analysis can be mitigated by an optimal choice of er-fMRI design and filtering. Moreover, the accuracy of the 1st- and 2nd-level parameter estimates also depend on design and filtering; especially, we show that inaccuracies caused by the presence of residual noise autocorrelations can be constrained by designs that have hemodynamic responses with a Gaussian distribution. In conclusion, designs with both good efficiency and decorrelating properties, for example, such as the geometric or Latin square probability distributions, combined with the "whitening" filters of SPM2 and FSL3.0, give the best result, both for 1st- and 2nd-level analysis of er-fMRI studies.