Accounting for Non-Gaussian Sources of Spatial Correlation in Parametric Functional Magnetic Resonance Imaging Paradigms II: A Method to Obtain First-Level Analysis Residuals with Uniform and Gaussian Spatial Autocorrelation Function and Independent and Identically Distributed Time-Series

Kaundinya Gopinath, Venkatagiri Krishnamurthy, Simon Lacey, K. Sathian

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5 Citations (Scopus)

Abstract

In a recent study Eklund et al. have shown that cluster-wise family-wise error (FWE) rate-corrected inferences made in parametric statistical method-based functional magnetic resonance imaging (fMRI) studies over the past couple of decades may have been invalid, particularly for cluster defining thresholds less stringent than p < 0.001; principally because the spatial autocorrelation functions (sACFs) of fMRI data had been modeled incorrectly to follow a Gaussian form, whereas empirical data suggest otherwise. Hence, the residuals from general linear model (GLM)-based fMRI activation estimates in these studies may not have possessed a homogenously Gaussian sACF. Here we propose a method based on the assumption that heterogeneity and non-Gaussianity of the sACF of the first-level GLM analysis residuals, as well as temporal autocorrelations in the first-level voxel residual time-series, are caused by unmodeled MRI signal from neuronal and physiological processes as well as motion and other artifacts, which can be approximated by appropriate decompositions of the first-level residuals with principal component analysis (PCA), and removed. We show that application of this method yields GLM residuals with significantly reduced spatial correlation, nearly Gaussian sACF and uniform spatial smoothness across the brain, thereby allowing valid cluster-based FWE-corrected inferences based on assumption of Gaussian spatial noise. We further show that application of this method renders the voxel time-series of first-level GLM residuals independent, and identically distributed across time (which is a necessary condition for appropriate voxel-level GLM inference), without having to fit ad hoc stochastic colored noise models. Furthermore, the detection power of individual subject brain activation analysis is enhanced. This method will be especially useful for case studies, which rely on first-level GLM analysis inferences.

Original languageEnglish (US)
Pages (from-to)10-21
Number of pages12
JournalBrain Connectivity
Volume8
Issue number1
DOIs
StatePublished - Feb 2018

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Spatial Analysis
Linear Models
Magnetic Resonance Imaging
Noise
Physiological Phenomena
Activation Analysis
Brain
Principal Component Analysis
Artifacts

All Science Journal Classification (ASJC) codes

  • Neuroscience(all)

Cite this

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title = "Accounting for Non-Gaussian Sources of Spatial Correlation in Parametric Functional Magnetic Resonance Imaging Paradigms II: A Method to Obtain First-Level Analysis Residuals with Uniform and Gaussian Spatial Autocorrelation Function and Independent and Identically Distributed Time-Series",
abstract = "In a recent study Eklund et al. have shown that cluster-wise family-wise error (FWE) rate-corrected inferences made in parametric statistical method-based functional magnetic resonance imaging (fMRI) studies over the past couple of decades may have been invalid, particularly for cluster defining thresholds less stringent than p < 0.001; principally because the spatial autocorrelation functions (sACFs) of fMRI data had been modeled incorrectly to follow a Gaussian form, whereas empirical data suggest otherwise. Hence, the residuals from general linear model (GLM)-based fMRI activation estimates in these studies may not have possessed a homogenously Gaussian sACF. Here we propose a method based on the assumption that heterogeneity and non-Gaussianity of the sACF of the first-level GLM analysis residuals, as well as temporal autocorrelations in the first-level voxel residual time-series, are caused by unmodeled MRI signal from neuronal and physiological processes as well as motion and other artifacts, which can be approximated by appropriate decompositions of the first-level residuals with principal component analysis (PCA), and removed. We show that application of this method yields GLM residuals with significantly reduced spatial correlation, nearly Gaussian sACF and uniform spatial smoothness across the brain, thereby allowing valid cluster-based FWE-corrected inferences based on assumption of Gaussian spatial noise. We further show that application of this method renders the voxel time-series of first-level GLM residuals independent, and identically distributed across time (which is a necessary condition for appropriate voxel-level GLM inference), without having to fit ad hoc stochastic colored noise models. Furthermore, the detection power of individual subject brain activation analysis is enhanced. This method will be especially useful for case studies, which rely on first-level GLM analysis inferences.",
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AU - Gopinath, Kaundinya

AU - Krishnamurthy, Venkatagiri

AU - Lacey, Simon

AU - Sathian, K.

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N2 - In a recent study Eklund et al. have shown that cluster-wise family-wise error (FWE) rate-corrected inferences made in parametric statistical method-based functional magnetic resonance imaging (fMRI) studies over the past couple of decades may have been invalid, particularly for cluster defining thresholds less stringent than p < 0.001; principally because the spatial autocorrelation functions (sACFs) of fMRI data had been modeled incorrectly to follow a Gaussian form, whereas empirical data suggest otherwise. Hence, the residuals from general linear model (GLM)-based fMRI activation estimates in these studies may not have possessed a homogenously Gaussian sACF. Here we propose a method based on the assumption that heterogeneity and non-Gaussianity of the sACF of the first-level GLM analysis residuals, as well as temporal autocorrelations in the first-level voxel residual time-series, are caused by unmodeled MRI signal from neuronal and physiological processes as well as motion and other artifacts, which can be approximated by appropriate decompositions of the first-level residuals with principal component analysis (PCA), and removed. We show that application of this method yields GLM residuals with significantly reduced spatial correlation, nearly Gaussian sACF and uniform spatial smoothness across the brain, thereby allowing valid cluster-based FWE-corrected inferences based on assumption of Gaussian spatial noise. We further show that application of this method renders the voxel time-series of first-level GLM residuals independent, and identically distributed across time (which is a necessary condition for appropriate voxel-level GLM inference), without having to fit ad hoc stochastic colored noise models. Furthermore, the detection power of individual subject brain activation analysis is enhanced. This method will be especially useful for case studies, which rely on first-level GLM analysis inferences.

AB - In a recent study Eklund et al. have shown that cluster-wise family-wise error (FWE) rate-corrected inferences made in parametric statistical method-based functional magnetic resonance imaging (fMRI) studies over the past couple of decades may have been invalid, particularly for cluster defining thresholds less stringent than p < 0.001; principally because the spatial autocorrelation functions (sACFs) of fMRI data had been modeled incorrectly to follow a Gaussian form, whereas empirical data suggest otherwise. Hence, the residuals from general linear model (GLM)-based fMRI activation estimates in these studies may not have possessed a homogenously Gaussian sACF. Here we propose a method based on the assumption that heterogeneity and non-Gaussianity of the sACF of the first-level GLM analysis residuals, as well as temporal autocorrelations in the first-level voxel residual time-series, are caused by unmodeled MRI signal from neuronal and physiological processes as well as motion and other artifacts, which can be approximated by appropriate decompositions of the first-level residuals with principal component analysis (PCA), and removed. We show that application of this method yields GLM residuals with significantly reduced spatial correlation, nearly Gaussian sACF and uniform spatial smoothness across the brain, thereby allowing valid cluster-based FWE-corrected inferences based on assumption of Gaussian spatial noise. We further show that application of this method renders the voxel time-series of first-level GLM residuals independent, and identically distributed across time (which is a necessary condition for appropriate voxel-level GLM inference), without having to fit ad hoc stochastic colored noise models. Furthermore, the detection power of individual subject brain activation analysis is enhanced. This method will be especially useful for case studies, which rely on first-level GLM analysis inferences.

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