Methods for Addressing Spatial Correlations in Functional Neuroimaging Data Open Access

Abstract

Neuroimaging studies yield massive data sets that pose challenges for statistical analyses due, in part, to the intricate anatomical and functional properties of neurons. Our main objective is to uncover aspects of the complex spatial relationships present in functional neuroimaging data and to develop statistical methods that either evaluate or leverage those correlations. We propose the following methods to achieve our research goal: (i) a novel statistical approach to model the complex spatio-temporal structure of neuroimaging data, (ii) a method to evaluate the level of connectivity within functionally defined neural processing networks and (iii) a novel prediction framework for neuroimaging data based on a hierarchical Bayesian spatial model.

To date, there has been limited research on simultaneously modeling spatial correlations between the neural activity in distinct brain locations and temporal correlations between repeated neural activity measurements. We propose a spatio-temporal, autoregressive model which simultaneously accounts for spatial dependencies between voxels within the same anatomical region and for temporal dependencies between a subject's estimates from multiple sessions. We illustrate the application of our method using fMRI data from a cocaine addiction study.

Data-driven statistical approaches, such as ICA and cluster analysis, help to identify neural processing networks exhibiting similar patterns of activity. These approaches, however, do not quantify or statistically test the strength of the within-network relatedness between voxels. We adapt Moran's I statistic for applicability to our neuroimaging analyses to measure the degree of functional autocorrelation within identified neural processing networks and to evaluate the statistical significance of the observed associations. We illustrate the use of our methodology with data from an fMRI resting-state study of unipolar depression and a PET study of working memory among individuals with schizophrenia.

Recently there has been growing interest in the use of neuroimaging data as a tool for classification and prediction. We propose a novel Bayesian hierarchical framework for predicting follow-up neural activity based on the baseline functional neuroimaging data. The proposed model is multivariate and captures the correlations between brain activity at different scanning sessions. We illustrate the use of our proposed methodology with PET data from a study of Alzheimer's disease.

Table of Contents

1 Introduction 1
1.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 An Introduction to Organization of the Human Brain . . . . . . . . . . . . 2
1.3 Functional Neuroimaging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.3.1 Functional Magnetic Resonance Imaging (fMRI) . . . . . . . . . . . . . 5
1.3.2 Positron Emission Tomography (PET) Imaging . . . . . . . . . . . . . . . 9
1.4 Analysis of Functional Neuroimaging Data . . . . . . . . . . . . . . . . . . 11
1.4.1 Preprocessing Pipeline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
1.4.2 Statistical Modeling for Activation Studies . . . . . . . . . . . . . . . . 13
1.4.3 Data-driven Descriptive Analysis Methods . . . . . . . . . . . . . . . . 16
1.4.4 Prediction and Classification . . . . . . . . . . . . . . . . . . . . . . . . . 20
1.5 Motivating Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
1.5.1 An fMRI Study on Inhibitory Control in Cocaine Addicts . . . . . . . . 22
1.5.2 A PET Study on Working Memory in Schizophrenia Patients . . . . . 23
1.5.3 An fMRI Resting-state Study of Depression . . . . . . . . . . . . . . . . 23
1.5.4 A PET Study of Alzheimer's Disease . . . . . . . . . . . . . . . . . . . . . 24
1.6 Proposed Research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
1.6.1 Simultaneous Spatio-temporal Modeling of fMRI data . . . . . . . . . 24
1.6.2 Functional Autocorrelation within Neural Processing Networks . . . . 25
1.6.3 A Novel Spatial Prediction Model . . . . . . . . . . . . . . . . . . . . . . . 26

2 Modeling the spatial and temporal dependence in fMRI data . . . . . . . 27
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
2.2 Experimental Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
2.3 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
2.3.1 Statistical Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
2.3.2 Parametric Covariance Model . . . . . . . . . . . . . . . . . . . . . . . . . 32
2.3.3 Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
2.3.4 Inferences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
2.4 Application to Inhibitory Control in Cocaine Addicts Study . . . . . . . 37
2.4.1 Voxel-level inferences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
2.4.2 Region-level inferences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
2.4.3 Spatial and temporal correlations . . . . . . . . . . . . . . . . . . . . . . . 39
2.4.4 Implications of Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
2.5 Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
2.6 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

3 Evaluating Functional Autocorrelation within Spatially Distributed

Neural Processing Networks. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
3.2 Experimental Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
3.3 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
3.3.1 Clustering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
3.3.2 Functional Autocorrelation Statistic . . . . . . . . . . . . . . . . . . . . . 58
3.3.3 Hypothesis Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
3.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
3.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

4 Bayesian Hierarchical Spatial Model for Predicting Brain Activity . . . . . . 76
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
4.1.1 Conditional Autoregressive (CAR) Models . . . . . . . . . . . . . . . . . . 79
4.2 Experimental Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
4.3 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
4.3.1 Model and Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
4.3.2 Full Conditional Distributions . . . . . . . . . . . . . . . . . . . . . . . . . . 87
4.3.3 Prediction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
4.3.4 Model Validation: Estimation of the prediction error. . . . . . . . . . . . 90
4.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
4.4.1 Prediction of brain activity for PET data from a study of Alzheimer's
disease (ADNI) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
4.4.2 Comparisons with competing prediction models . . . . . . . . . . . . . . 95
4.5 Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
4.6 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
5 Summary and Future Work. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104

Appendices. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
5.1 Chapter 2 Appendices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
5.1.1 Appendix A: Spatio-temporal Model in Matrix Form . . . . . . . . . . . 108
5.1.2 Appendix B: Exploratory Data Analysis . . . . . . . . . . . . . . . . . . . 108
5.1.3 Appendix C. Computing Variance-Covariance Matrix: Coeffcients

of Psig. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
5.1.4 Appendix D. Score Functions. . . . . . . . . . . . . . . . . . . . . . . . . .112
5.2 Chapter 4 Appendices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
5.2.1 Appendix E: Bayesian Spatial Hierarchical Model - region level . . . 115

5.2.2 Appendix F: Full Conditional Distributions for the
Bayesian Spatial Hierarchical Model . . . . . . . . . . . . . . . . . . . . . . . . 116
5.2.3 Appendix G: Additional results from the analysis of ADNI data . . . 128
5.2.4 Appendix H: Simulation Results. . . . . . . . . . . . . . . . . . . . . . . . 132

Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136

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School	Laney Graduate School
Department	Biostatistics
Degree	PhD
Submission	Dissertation
Language	English
Research Field	Biology, Biostatistics
Keyword	simultaneous autoregressive model neuroimaging spatial-temporal model fMRI functional autocorrelation Bayesian spatial prediction model
Committee Chair / Thesis Advisor	Bowman, F Dubois, Emory University
Committee Members	Waller, Lance, Emory University Guo, Ying, Emory University Manatunga, Amita, Emory University Kilts, Clinton D, Emory University

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