Statistical Modeling of Neuroimaging Data: Targeting Activation, Task-Related Connectivity, and Prediction

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DuBois Bowman Department of Biostatistics and Bioinformatics Emory University,

1 Statistical Modeling of Neuroimaging Data: Targeting Activation, Task-Related Connectivity, and Prediction F. DuBois Bowman Department of Biostatistics and Bioinformatics Emory University, Atlanta, GA, CBIS Five-Year Anniversary Symposium February 8, 2013 F. D. Bowman (Emory University) Spatial Modeling CBIS Symposium 1 / 25

2 Acknowledgements Research Team Lijun Zhang, PhD, Emory, Biostatistics and Bioinformatics Jian Kang, PhD, Emory, Biostatistics and Bioinformatics Ying Guo, PhD, Emory, Biostatistics and Bioinformatics Gordana Derado, PhD, CDC Shuo Chen, PhD, Univ. of Maryland, Epidemiology and Biostatistics Wenqiong Xue, MS, Emory, Biostatistics and Bioinformatics Anthony Pileggi, Emory, Biostatistics and Bioinformatics Daniel Huddleston, MD, Kaiser Permanente Georgia Xiaoping Hu, PhD, Emory/GA Tech, Biomedical Engineering F. D. Bowman (Emory University) Spatial Modeling CBIS Symposium 2 / 25

3 Outline 1 Spatial Modeling for Activation and Connectivity 2 Determining Multimodal Imaging Biomarkers for Parkinson s Disease 3 Future Directions F. D. Bowman (Emory University) Spatial Modeling CBIS Symposium 3 / 25

4 Data Example Working Memory in Schizophrenia Patients N=28 subjects: 15 schizophrenia patients and 13 healthy controls fmri Tasks: Serial Item Recognition Paradigm (SIRP) Encoding set: Subjects asked to memorize 1, 3, or 5 target digits. Probing set: Subjects sequentially shown single digit probes and asked to press a button: with their index finger, if the probe matched with their middle finger, if not. 6 runs per subject: (177 scans per run for each subject) 3 runs of working memory tasks on each of 2 days Objective: Compare working memory-related brain activity between patients and controls Data from the Biomedical Informatics Research Network (BIRN) [1]: Potkin et al. (2002), Proc. 41st Annu. Meeting Am. College Neuropsychopharm. F. D. Bowman (Emory University) Spatial Modeling CBIS Symposium 4 / 25

5 fmri Data Characteristics Massive Data Sets Roughly 300,000 brain voxels for each scan at time of analysis S = 177 scans per run, 3 runs each day, 2 days (sessions) Over 300 million spatio-temporal data points per subject! Over 5 billion for all subjects!! Temporal correlations Scan to scan correlations Between session correlations Complex spatial correlations Correlations between neighboring voxels Long-range correlations between different brain regions Roughly 45 billion voxel pairs F. D. Bowman (Emory University) Spatial Modeling CBIS Symposium 5 / 25

Spatial Correlations Distances Functional Physical

complex neuroanatomy and neurophysiology make basic

neuroimaging Figure: Alternative measures of distance

6 Spatial Correlations Distances Functional Physical (Geometric) Anatomical (a) Functional (b) Geometric The complex neuroanatomy and neurophysiology make basic assumptions of many spatial methods questionable for neuroimaging Figure: Alternative measures of distance Bowman (2007), JASA. F. D. Bowman (Emory University) Spatial Modeling CBIS Symposium 6 / 25

7 Common Activation Analysis Framework Two-stage Model First, fit a linear model separately for each subject (at each voxel) Temporal correlations between scans: AR models (+ white noise) Second, fit linear model that combines subject-specific estimates For Inference: Compute t-statistics at each voxel and threshold Consider a multiple testing adjustment (Bonferonni-type, FDR, RFT) Properties Two-stage (random effects) model Simplifies computations Sacrifices efficiency Assumes independence between different brain locations Targets activation analyses, disregarding functional connectivity F. D. Bowman (Emory University) Spatial Modeling CBIS Symposium 7 / 25

Spatial Modeling Framework Bayesian Spatial Model for Activation and Connectivity (BSMac): Stage I: Individual level - addresses temporal correlations Stage II: Group level Define brain regions using

8 Spatial Modeling Framework Bayesian Spatial Model for Activation and Connectivity (BSMac): Stage I: Individual level - addresses temporal correlations Stage II: Group level Define brain regions using neuroanatomic parcellation (e.g. Brodmann or AAL) Spatial correlations Within regions Between regions Inferences Voxel-level Regional Bowman et al. (2008), NeuroImage Zhang et al. (2011), Journal of Neuroscience Methods F. D. Bowman (Emory University) Spatial Modeling CBIS Symposium 8 / 25

9 BSMac Stage II: Bayesian Spatial Model for Activation and Connectivity (BSMac): Y igj µ gj, α igj, σ 2 gj Normal(µ gj + 1α igj, σ 2 gji) µ gj λ 2 gj Normal(1µ 0gj, λ 2 gji) σ 2 gj Gamma(a 0, b 0 ) α ij Γ j Normal(0, Γ j ) λ 2 gj Gamma(c 0, d 0 ) Γ 1 j Wishart { (h 0 H 0j ) 1 }, h 0 Y igj = (Y igj1,..., Y igjvg ), µ gj = (µ gj1,..., µ gjvg ), and α ij = (α i1j,..., α igj ) Bowman et al. (2008), NeuroImage Zhang et al. (2011), Journal of Neuroscience Methods F. D. Bowman (Emory University) Spatial Modeling CBIS Symposium 9 / 25

BSMac MATLAB Toolbox GUI Interface: Available at www.sph.emory.

10 BSMac MATLAB Toolbox GUI Interface: Available at F. D. Bowman (Emory University) Spatial Modeling CBIS Symposium 10 / 25

11 BSMac MATLAB Toolbox Interactive Activation Maps F. D. Bowman (Emory University) Spatial Modeling CBIS Symposium 11 / 25

12 BSMac MATLAB Toolbox Task-Related Connectivity Maps: Schizophrenia Patients, WM Load 5 F. D. Bowman (Emory University) Spatial Modeling CBIS Symposium 12 / 25

13 BSMac MATLAB Toolbox Task-Related Connectivity Maps: Healthy Controls, WM Load 5 F. D. Bowman (Emory University) Spatial Modeling CBIS Symposium 13 / 25

14 BSMac Properties BSMac framework Considers activation objectives and task-related FC Models spatial correlations in brain activity Within and between defined neuroanatomic regions Yields easily interpretable posterior probabilities of activation Permits voxel-level and region-level inferences Can apply FDR-like concepts Limitations Does not account for temporal dependence between multiple sessions Fairly simple intra-regional correlation model F. D. Bowman (Emory University) Spatial Modeling CBIS Symposium 14 / 25

15 Extensions: Spatial Modeling Model Correlations Between scanning sessions [Derado et al. (2010), Biometrics] E.g. between days or treatment periods Does NOT model between-region spatial correlations Between sessions, between regions, and locally between voxels (within regions) [Derado et al. (2012), Statistical Methods in Medical Research] Use imaging data to predict future neural responses Forecast neural representations of disease progression Predict neural responses to various treatments *Between brain regions, between subregions (within regions), between voxels locally within subregions [Xue et al. (2013), in progress] Use imaging data to predict/classify patient characteristics Forecast clinical diagnosis Predict clinical response to various treatments Permits multimodal imaging data F. D. Bowman (Emory University) Spatial Modeling CBIS Symposium 15 / 25

Determining Multimodal Biomarkers for PD Data from Multimodal Imaging Studies The data will include 81 subjects across three studies 38 Parkinson s disease patients 32 Healthy control subjects 11

16 Determining Multimodal Biomarkers for PD Data from Multimodal Imaging Studies The data will include 81 subjects across three studies 38 Parkinson s disease patients 32 Healthy control subjects 11 Alzheimers disease patients Potential Biomarkers Imaging (MRI, fmri, DTI, NM-MRI, CSI) Genetic Neurocognitive Testing Questionnaire-Derived Scores Clinical CSF Neuroinflammation CSF Catecholamine Metabolites F. D. Bowman (Emory University) Spatial Modeling CBIS Symposium 16 / 25

17 Determining Multimodal Biomarkers for PD Project in the NINDS Parkinson s Disease Biomarker Program Aim 1: To develop new statistical techniques to reveal multimodal biomarkers for PD including imaging, clinical, and biologic variables. Develop statistical models for high-dimensional data, which pool predictive strength across multiple data modalities for classifying PD versus HC. Joint multimodal probability models Penalized likelihood approaches, with variable selection using modality-specific penalties l p (β, λ) = l(β) + k λ kp k (β k ) l(β) = i [y ilogπ i + (1 y i )log(1 π i ] Model development, training, testing, and validation F. D. Bowman (Emory University) Spatial Modeling CBIS Symposium 17 / 25

Objectives Multimodal biomarker detection Numerous findings suggest links between PD and single genetic, imaging, and biologic factors Many of

systems-level, multi-dimensional disorder with discrete, but functionally integrated manifestations We will develop methods to define multimodal

18 Objectives Multimodal biomarker detection Numerous findings suggest links between PD and single genetic, imaging, and biologic factors Many of these are non-specific or insensitive Single modality biomarkers may not fully address the complexity of PD We regard PD as a complex, systems-level, multi-dimensional disorder with discrete, but functionally integrated manifestations We will develop methods to define multimodal PD biomarkers from a massive number of hypothesis driven and exploratory candidate markers F. D. Bowman (Emory University) Spatial Modeling CBIS Symposium 18 / 25

19 Exploratory Analysis Selected features from multiple imaging modalities [Blue represents PD patients and red represents HC subjects. Networks: FC; Local activity: ALFF; Volumetric: VBM; Chemical shift imaging: RLC and LLC] [NM-MRI Estimated Locus Coeruleus Volume. Controls: N=6; PD: N=9] F. D. Bowman (Emory University) Spatial Modeling CBIS Symposium 19 / 25

regions: Unstructured covariance matrix Borrow strength between subregions within each AAL region: CAR model Between

20 Bayesian Spatial Prediction Model We predict (or classify according to) patient characteristics from multimodal imaging data (and other patient information) Two-level parcellation: AAL Regions Subregions Spatial correlations: Between AAL regions: Unstructured covariance matrix Borrow strength between subregions within each AAL region: CAR model Between voxels within each subregion: Exchangeable structure F. D. Bowman (Emory University) Spatial Modeling CBIS Symposium 20 / 25

21 Bayesian Spatial Prediction Model Example of modelling framework using ALFF and VBM data Let D i {0, 1} represent disease status (e.g. 1=PD, 0=HC) Let X ilg (v) and Z ilg (v) respectively denote the ALFF and VBM for subject i at voxel v in subregion l (in region g), and B i = [X ilg (v), Z ilg (v)] Construct a Bayesian joint (multimodal) probability model f (X ilg (v), Z ilg (v) D i ) f 1 (X ilg (v) Zilg(v), D i ) f 2 (Z ilg (v) D i ) Generate predictions for a new subject n + 1 based on Pr(D n+1 = k B n+1, {B i, D i } n i=1 ) F. D. Bowman (Emory University) Spatial Modeling CBIS Symposium 21 / 25

22 Bayesian Spatial Prediction Model Generates whole brain, region-level, and voxel-level predictions Region- and voxel-level predictions reveal brain regions with strong discriminatory power Use leave-one-out cross validation to assess accuracy Whole-brain prediction achieves 100% accuracy for distinguishing PD patients from healthy controls based on ALFF and VBM data F. D. Bowman (Emory University) Spatial Modeling CBIS Symposium 22 / 25

23 Bayesian Spatial Prediction Model Regional accuracies: F. D. Bowman (Emory University) Spatial Modeling CBIS Symposium 23 / 25

24 Future Directions Expand the imaging modalities used to determine PD biomarkers MRI, fmri, DTI, NM-MRI, CSI Some provide whole-brain assessments Some focus on specific regions of interest: locus coeruleus (LC) and substantia nigra (SN) Expand our joint Bayesian multimodal probability model Consider penalized likelihood approaches: l p (β, λ) = l(β) + k λ kp k (β k ) l(β) = i [y ilogπ i + (1 y i )log(1 π i ] Validation of identified biomarkers F. D. Bowman (Emory University) Spatial Modeling CBIS Symposium 24 / 25

25 Acknowledgements Thank you! F. D. Bowman (Emory University) Spatial Modeling CBIS Symposium 25 / 25

Bayesian Spatiotemporal Modeling with Hierarchical Spatial Priors for fmri

Bayesian Spatiotemporal Modeling with Hierarchical Spatial Priors for fmri Galin L. Jones 1 School of Statistics University of Minnesota March 2015 1 Joint with Martin Bezener and John Hughes Experiment