Improved autoregressive model for correction of noise serial correlation in fast fMRI

Unraveling Alzheimer's Disease: Investigating Dynamic Functional Connectivity in the Default Mode Network through DCC-GARCH Modeling

Alzheimer's disease (AD) has a prolonged latent phase. Sensitive biomarkers of amyloid beta ( A β ), in the absence of clinical symptoms, offer opportunities for early detection and identification of patients at risk. Current A β biomarkers, such as CSF and PET biomarkers, are effective but face practical limitations due to high cost and limited availability. Recent blood plasma biomarkers, though accessible, still incur high costs and lack physiological significance in the Alzheimer's process. This study explores the potential of brain functional connectivity (FC) alterations associated with AD pathology as a non-invasive avenue for A β detection. While current stationary FC measurements lack sensitivity at the single-subject level, our investigation focuses on dynamic FC using resting-state functional MRI (rs-fMRI) and introduces the Generalized Auto-Regressive Conditional Heteroscedastic Dynamic Conditional Correlation (DCC-GARCH) model. Our findings demonstrate the superior sensitivity of DCC-GARCH to CSF A β status, and offer key insights into dynamic functional connectivity analysis in AD.

Sources of residual autocorrelation in multiband task fMRI and strategies for effective mitigation

Introduction

Analysis of task fMRI studies is typically based on using ordinary least squares within a voxel- or vertex-wise linear regression framework known as the general linear model. This use produces estimates and standard errors of the regression coefficients representing amplitudes of task-induced activations. To produce valid statistical inferences, several key statistical assumptions must be met, including that of independent residuals. Since task fMRI residuals often exhibit temporal autocorrelation, it is common practice to perform "prewhitening" to mitigate that dependence. Prewhitening involves estimating the residual correlation structure and then applying a filter to induce residual temporal independence. While theoretically straightforward, a major challenge in prewhitening for fMRI data is accurately estimating the residual autocorrelation at each voxel or vertex of the brain. Assuming a global model for autocorrelation, which is the default in several standard fMRI software tools, may under- or over-whiten in certain areas and produce differential false positive control across the brain. The increasing popularity of multiband acquisitions with faster temporal resolution increases the challenge of effective prewhitening because more complex models are required to accurately capture the strength and structure of autocorrelation. These issues are becoming more critical now because of a trend toward subject-level analysis and inference. In group-average or group-difference analyses, the within-subject residual correlation structure is accounted for implicitly, so inadequate prewhitening is of little real consequence. For individual subject inference, however, accurate prewhitening is crucial to avoid inflated or spatially variable false positive rates.

Methods

In this paper, we first thoroughly examine the patterns, sources and strength of residual autocorrelation in multiband task fMRI data. Second, we evaluate the ability of different autoregressive (AR) model-based prewhitening strategies to effectively mitigate autocorrelation and control false positives. We consider two main factors: the choice of AR model order and the level of spatial regularization of AR model coefficients, ranging from local smoothing to global averaging. We also consider determining the AR model order optimally at every vertex, but we do not observe an additional benefit of this over the use of higher-order AR models (e.g. (AR(6)). To overcome the computational challenge associated with spatially variable prewhitening, we developed a computationally efficient R implementation using parallelization and fast C++ backend code. This implementation is included in the open source R package BayesfMRI.

Results

We find that residual autocorrelation exhibits marked spatial variance across the cortex and is influenced by many factors including the task being performed, the specific acquisition protocol, mis-modeling of the hemodynamic response function, unmodeled noise due to subject head motion, and systematic individual differences. We also find that local regularization is much more effective than global averaging at mitigating autocorrelation. While increasing the AR model order is also helpful, it has a lesser effect than allowing AR coefficients to vary spatially. We find that prewhitening with an AR(6) model with local regularization is effective at reducing or even eliminating autocorrelation and controlling false positives.

Conclusion

Our analysis revealed dramatic spatial differences in autocorrelation across the cortex. This spatial topology is unique to each session, being influenced by the task being performed, the acquisition technique, various modeling choices, and individual differences. If not accounted for, these differences will result in differential false positive control and power across the cortex and across subjects.

Imaging the temporal dynamics of brain states with highly sampled fMRI

The spontaneous dynamics of the brain modulate its function from moment to moment, shaping neural computation and cognition. Functional MRI (fMRI), while classically used as a tool for spatial localization, is increasingly being used to identify the temporal dynamics of brain activity. fMRI analyses focused on the temporal domain have revealed important new information about the dynamics underlying states such as arousal, attention, and sleep. Dense temporal sampling – either by using fast fMRI acquisition, or multiple repeated scan sessions within individuals – can further enrich the information present in these studies. This review focuses on recent developments in using fMRI to identify dynamics across brain states, particularly vigilance and sleep states, and the potential for highly temporally sampled fMRI to answer these questions.

Statistical power or more precise insights into neuro-temporal dynamics? Assessing the benefits of rapid temporal sampling in fMRI

Functional magnetic resonance imaging (fMRI), a non-invasive and widely used human neuroimaging method, is most known for its spatial precision. However, there is a growing interest in its temporal sensitivity. This is despite the temporal blurring of neuronal events by the blood oxygen level dependent (BOLD) signal, the peak of which lags neuronal firing by 4-6 seconds. Given this, the goal of this review is to answer a seemingly simple question - "What are the benefits of increased temporal sampling for fMRI?". To answer this, we have combined fMRI data collected at multiple temporal scales, from 323 to 1000 milliseconds, with a review of both historical and contemporary temporal literature. After a brief discussion of technological developments that have rekindled interest in temporal research, we next consider the potential statistical and methodological benefits. Most importantly, we explore how fast fMRI can uncover previously unobserved neuro-temporal dynamics - effects that are entirely missed when sampling at conventional 1 to 2 second rates. With the intrinsic link between space and time in fMRI, this temporal renaissance also delivers improvements in spatial precision. Far from producing only statistical gains, the array of benefits suggest that the continued temporal work is worth the effort.

To pool or not to pool: Can we ignore cross-trial variability in FMRI?

In this work, we investigate the importance of explicitly accounting for cross-trial variability in neuroimaging data analysis. To attempt to obtain reliable estimates in a task-based experiment, each condition is usually repeated across many trials. The investigator may be interested in (a) condition-level effects, (b) trial-level effects, or (c) the association of trial-level effects with the corresponding behavior data. The typical strategy for condition-level modeling is to create one regressor per condition at the subject level with the underlying assumption that responses do not change across trials. In this methodology of complete pooling, all cross-trial variability is ignored and dismissed as random noise that is swept under the rug of model residuals. Unfortunately, this framework invalidates the generalizability from the confine of specific trials (e.g., particular faces) to the associated stimulus category ("face"), and may inflate the statistical evidence when the trial sample size is not large enough. Here we propose an adaptive and computationally tractable framework that meshes well with the current two-level pipeline and explicitly accounts for trial-by-trial variability. The trial-level effects are first estimated per subject through no pooling. To allow generalizing beyond the particular stimulus set employed, the cross-trial variability is modeled at the population level through partial pooling in a multilevel model, which permits accurate effect estimation and characterization. Alternatively, trial-level estimates can be used to investigate, for example, brain-behavior associations or correlations between brain regions. Furthermore, our approach allows appropriate accounting for serial correlation, handling outliers, adapting to data skew, and capturing nonlinear brain-behavior relationships. By applying a Bayesian multilevel model framework at the level of regions of interest to an experimental dataset, we show how multiple testing can be addressed and full results reported without arbitrary dichotomization. Our approach revealed important differences compared to the conventional method at the condition level, including how the latter can distort effect magnitude and precision. Notably, in some cases our approach led to increased statistical sensitivity. In summary, our proposed framework provides an effective strategy to capture trial-by-trial responses that should be of interest to a wide community of experimentalists.

Use of random matrix theory in the discovery of resting state brain networks

Connectomics identifies brain networks in vivo in resting state functional MRI. However, the presence of noise produces spurious identification of brain networks, which have low test-retest reliability. A Network Based Statistics approach to network identification has been previously proposed that affords much better statistical power relative to Bonferroni method but nevertheless provides a sufficiently conservative, family-wise control for false positives. We propose the use of Random Matrix Theory (RMT) to discover brain networks and to associate those networks with demographic and clinical variables. We parcellated the brain into cortical and subcortical regions using either an anatomical or a functional brain atlas. We applied RMT to study functional connectivity across brain regions by first computing the correlation matrix for time courses in those brain regions and then identifying eigenvalues that deviate from the theoretical random distribution that RMT predicts, on the assumption that real brain networks would produce eigenvalues that differ significantly from the random distribution. We assessed the specificity and test-retest reliability of identified networks through application of this RMT-based approach to (1) synthetic data generated under the null-hypothesis, (2) resting state functional MRI data from 4 real-world cohorts of patients and healthy controls, and (3) synthetic data generated by the addition of increasing amounts of noise to real-world datasets. Our findings showed that RMT method was robust to the atlas used for parcellating the brain and did not discover a brain network in synthetic data when in fact a network was not present (i.e., specificity was high); RMT-identified networks in the real-world dataset had high test-retest reliability; and RMT-based method consistently discovered the same network in the presence of increasing noise in the real-world dataset.

Improved autoregressive model for correction of noise serial correlation in fast fMRI

PURPOSE

In rapidly acquired functional MRI (fast fMRI) data, the noise serial correlations (SC) can produce problematically overestimated T-statistics which lead to invalid statistical inferences. This study aims to evaluate and improve the accuracy of high-order autoregressive model (AR(p), where p is the model order) based prewhitening method in the SC correction.

METHODS

Fast fMRI images were acquired at rest (null data) using a multiband simultaneous multi-slice echo planar imaging pulse sequence with repetition time (TR) = 300 and 500 ms. The SC effect in the fast fMRI data was corrected using the prewhitening method based on two AR(p) models: (1) the conventional model (fixed AR(p)) which preselects a constant p for all the image voxels; (2) an improved model (AR_AICc ) that employs the corrected Akaike information criterion voxel-wise to automatically select the model orders for each voxel. To evaluate accuracy of SC correction, false positive characteristics were measured by assuming the presence of block and event-related tasks in the null data without image smoothing. The performance of prewhitening was also examined in smoothed images by adding pseudo task fMRI signals into the null data and comparing the detected to simulated activations (ground truth).

RESULTS

The measured false positive characteristics agreed well with the theoretical curve when using the AR_AICc , and the activation maps in the smoothed data matched the ground truth. The AR_AICc showed improved performance than the fixed AR(p) method.

CONCLUSION

The AR_AICc can effectively remove noise SC, and accurate statistical analysis results can be obtained with the AR_AICc correction in fast fMRI.