Spatial Statistical Inference in Functional Modeling fMRI data - PowerPoint PPT Presentation

Overview Introduction Spatial Statistical Inference in Functional Modeling fMRI data Magnetic Resonance Imaging (fMRI) data Predicted response GLM Model Examining the performace of a trend surface model Overview Inference on fMRI data The TSM ICP Divya Brundavanam Bayesian Model Data Analysis & Results Conclusion StaTalk2019 @ UniTS 22 November 2019 bdivya@umich.edu 1 / 28

Overview Overview Introduction Modeling fMRI data Predicted response GLM Model 1 Functional Magnetic Resonance Imaging (fMRI) data Overview Inference on fMRI data Nature The TSM ICP Modeling and Assumptions Bayesian Model Data Analysis & Results Conclusion 2 Performance of an alternative approach 2 / 28

Neuroimaging to study the brain Overview Introduction Modeling fMRI data Predicted response GLM Model Overview Non-invasive real-time study of the brain - Structural and Inference on fMRI data Functional The TSM ICP Several existing techniques: PET, fMRI, CT, EEG, MEG Bayesian Model Data Analysis & Results Methods to analyze the outputs of these techniques Conclusion 3 / 28

Modeling fMRI data Overview Introduction Modeling fMRI data Predicted response GLM Model Overview Inference on fMRI data The TSM ICP Bayesian Model Data Analysis & Results Conclusion Dimensionality 200,000 voxels for a 3T scanner 100-2000 images/subject 10-40 subjects/population inference study 4 / 28

Modeling fMRI data Predicted response Overview Introduction Haemodynamic Reponse Function (HRF) Modeling fMRI data Blood oxygen level dependent (BOLD) signal Predicted response GLM Model Overview The predicted response Inference on fMRI data The TSM ICP Bayesian Model Data Analysis & Results Conclusion Figure: Obtaining the predicted response at a voxel. Source: FSL Course (http://fsl.fmrib.ox.ac.uk/fslcourse/) 5 / 28

Modeling fMRI data GLM Model Overview Introduction Modeling fMRI data Predicted response GLM Model Overview Inference on fMRI data The TSM ICP Bayesian Model Data Analysis & Results Conclusion Figure: The GLM framework at each voxel. Source: FSL Course (http://fsl.fmrib.ox.ac.uk/fslcourse/) 6 / 28

Modeling fMRI data Contrast maps Overview Introduction Modeling fMRI data Predicted response GLM Model Overview Inference on fMRI data The TSM ICP Bayesian Model Data Analysis & Results Conclusion Figure: Generation of contrast maps. Source: FSL Course (http://fsl.fmrib.ox.ac.uk/fslcourse/) 7 / 28

Modeling fMRI data Overview Introduction Modeling fMRI data Predicted response GLM Model Overview Inference on fMRI data The TSM ICP Bayesian Model Data Analysis & Results Conclusion Figure: Typical steps for image processing (Source: Karl Friston, SPM workshop (May 2011)) 8 / 28

Inference on fMRI data Thresholding Overview What features to infer on? Introduction Voxel Modeling fMRI data Clusters Predicted response GLM Model Overview Inference on fMRI data The TSM ICP Bayesian Model Data Analysis & Results Conclusion Figure: Choosing an appropriate threshold for inference. (Source: Presentation, RFT for Dummies - Part 1 (2009), Lea Firmin and Anna Jafarpour) 9 / 28

Inference on fMRI data: Multiple testing problem Definition and corrections Overview Hypothesis testing in neuroimaging: Multiple testing problem Introduction Modeling fMRI data Measures of error: Predicted response GLM Model Overview Familywise Error Rate (FWE) Inference on fMRI data Bonferroni correction The TSM ICP α corr = α F W E / ( n Tests ) Bayesian Model Data Analysis Random Field theory & Results Conclusion p vox ( t ) ≈ R (4 ln(2)) 3 / 2 e ( − t 2 / 2) ( t 2 − 1) ((2 π ) 2 ) No. of Resels R = V/ ( FWHM x FWHM y FWHM z ) Permutation testing 10 / 28

Inference of fMRI data RFT assumptions Overview Introduction RFT assumptions: Modeling fMRI data Spatial smoothness of fMRI signal is constant across the Predicted response GLM Model brain Overview Inference on the autocorrelation function is a squared exponential fMRI data The TSM Eklund et al: Real resting-state data and random task group ICP Bayesian Model analyses to compute empirical family-wise error rates for the Data Analysis fMRI software packages SPM,FSL, and AFNI & Results Conclusion High false-positive rates in established methods for cluster-wise inference spatial autocorrelation in the data violates the assumption squared exponential assumption of RFT 11 / 28

An alternative approach Overview Introduction Modeling fMRI data Predicted response GLM Model Overview A trend surface model proposed by Heurtas et. al. (2017) Inference on fMRI data employing the instantaneous connectivity parcellation (ICP) The TSM (van Oort et al 2016). ICP Bayesian Model Data Analysis & Results Conclusion 12 / 28

The Trend Surface Model (TSM) ICP Overview Instantaneous Correlation Parcellation Introduction (van Oort et al. 2016) Modeling fMRI data Top-down parcellation Predicted response Known large-scale ROI → functionally homogenous GLM Model Overview sub-regions based on temporal signature Inference on fMRI data The TSM ICP Bayesian Model Data Analysis & Results Conclusion Figure: Simulated time courses using simple sinusoid, transients and Gaussian noise, as presented in Van Oort et al. “Human brain parcellation using time courses of instantaneous correlations” NeuroImage (2017) 13 / 28

Bayesian Linear Regression Overview Introduction Modeling fMRI data Basis functions: subnetworks obtained from ICP Predicted response GLM Model Find a linearly weighted sum of these basis functions Overview Inference on fMRI data M The TSM � y s = w m φ m ( x ) + ǫ s (1) ICP Bayesian Model m =1 Data Analysis where & Results - M is the total no. of basis functions, ǫ s ∼ N (0 , β − 1 ) , β is Conclusion the noise precision - w s = [ w 1 ,s , . . . , w M,s ] T is an M dimensional weight vector of regression coefficients 14 / 28

Overview Introduction Modeling fMRI data Predicted response GLM Model p ( Y , Φ , W , Λ α , β | θ β , θ α ) = p ( β | θ β ) p ( Λ α | θ α ) Overview Inference on S (2) fMRI data � p ( y s | X , β, w s ) p ( w s | Λ α ) The TSM ICP s =1 Bayesian Model Data Analysis - Φ is a V × M matrix of basis functions and Y is a V × S & Results matrix of the neuroimaging data for all subjects. Conclusion - W = [ w 1 , . . . , w N ] is an M × S weight matrix, with prior p ( w s | α ) = N ( w s | 0 , Λ − 1 α ) . Λ α is the precision matrix with α = [ α 1 , . . . , α m ] T as hyperparameters. 15 / 28

Overview Introduction Modeling - The precision matrix is assigned a Wishart prior fMRI data Predicted response p ( Λ α | θ α ) = Wish( Λ α | N, P ) , N is degrees of freedom and P GLM Model is the precision of the prior. Overview Inference on fMRI data The TSM - The noise precision has a Gamma prior ICP p ( β | θ β ) = Gamma( β | a, b ) where a, b are the shape Bayesian Model Data Analysis coefficients. & Results Conclusion - Spatial correlations between basis functions by allowing off-diagonal entries in Λ α 16 / 28

Data Analysis The Data Overview Introduction 1. Resting state fMRI data (used as null data) from the 1000 Modeling Functional Connectomes project - Cambridge dataset fMRI data Predicted response GLM Model 198 healthy controls (75 M,123 F), 18–30 y.o. Overview Inference on 3T scanner, 119 time points, 72 × 72 × 47 voxels fMRI data The TSM ICP 2. Task fMRI data from the Human Connectome Project (500 Bayesian Model Subjects release) Data Analysis & Results 100+ unrelated healthy subjects Conclusion 3T scanner Four tasks: Working memory, Gambling, Emotion and Language tasks 17 / 28

Results: Specificity Specificity of the TSM Overview Introduction Modeling fMRI data Predicted response GLM Model Overview How well does TSM detect false positives? Inference on fMRI data The TSM ICP Bayesian Model Randomized box-design: ∼ 6 % false positive rate Data Analysis & Results Conclusion 18 / 28

Results: Specificity Overview Introduction Modeling fMRI data Predicted response GLM Model Overview Inference on fMRI data The TSM ICP Bayesian Model Data Analysis & Results Conclusion Figure: False positive rate from the TSM using pruned principle components, in comparison with results obtained by Eklund et al. (2016) for the softwares FSL, SPM and AFNI for cluster defining threshold (CDT) values of p=0.001 and p=0.01 19 / 28

Results: Sensitivity Sensitivity of the TSM Overview Introduction Modeling fMRI data How well does TSM detect task activation? Predicted response GLM Model Overview 1000 groups of N=20 subjects selected randomly (without Inference on fMRI data replacement) from 100+ subjects in each of the four tasks The TSM from the Human Connectome Project task fMRI data ICP Bayesian Model One sample t-test; random group shows significant result Data Analysis if atleast one parcel is significant (FWE) & Results Conclusion An ICP parcel that is significant in atleast 50% of random group analysis is considered to be activated 20 / 28