Detection of Spatial Connectivity via fMRI Data AnalysisPlanRelevant PapersBackground of fMRIDetection of fMRI ResponseSignificant TechniquesSelf-Organizing MappingSlide 8Slide 9Slide 10Slide 11Slide 12Canonical Correlation AnalysisSlide 14Slide 15Slide 16Slide 17Slide 18SOM vs. CCAImportanceDetection of Spatial Connectivity via fMRI Data AnalysisRamesh M. SingaComputer Integrated Surgery II, 600.4461 March 2001Plan•Spatial cognition•Deficient areas•Complex fMRI data analysisRelevant Papers•Ngan, S-C, Hu, X. Analysis of Function Magnetic Resonance Imaging Data Using Self-Organizing Mapping With Spatial Connectivity. Magnetic Resonance in Medicine 41:939-946 (1999). •Friman, O., et al. Detection of Neural Activity in Functional MRI Using Canonical Correlation Analysis Analysis. Magnetic Resonance in Medicine 45:323-330 (2001)•Andrade, A. Detection of Activation Using Cortical Surface Mapping. Human Brain Mapping 12:79-93 (2001).•Gold, S. et al. Functional MRI Statistical Software Packages: A Comparative Analysis. Human Brain Mapping 6:73-84 (1998).Background of fMRI•Noninvasive mapping of human cortical function (without agents) •BOLD contrast•Δ Deoxyhemoglobin alterations in MR signal•Correlation between neuronal activity and MR signal changesDetection of fMRI Response•Not trivial process response is few percent•Current and general approaches:– Explicit prior knowledge of activation time course and MRI response–Calculate correlation between assumed MRI form and measured dataTechniques not appropriate for unknown responses or complicated neural responses…univariate methods considers single pixels separatelySignificant TechniquesTwo appropriate techniques explored:• Self-Organizing Mapping•Canonical Correlation AnalysisSelf-Organizing Mapping•Groups image pixels together based on the similarity of their intensity •Intensity hyperspace a time course with n time points represented by one point in this n-dimensional hyperspace•Resulting hyperspace is partitioned into clusters based on proximity of input dataSelf-Organizing Mapping•SOM trained iteratively by pixel time courses selected randomly from the measured data•Training consists of –Finding node whose pattern has the best match to time course of training pixel (winner node)–Modifying winner node and four closest neighbors in neuron map by moving their associated feature vectors closer to the pixel time course. –Modification diminished until stable SOM converges–Neighboring nodes with similar feature patterns group together to form clusters.Self-Organizing Mapping•Able to identify features in data that are not so prominent•Facilitates merging of nodes to form super clusters and visualize high-dimensional data setsSelf-Organizing Mapping•Modified SOM based on spatial connectivity of activation sites pixel connectivity•Take size of connected region into account in thresholding improve detectability of low-contrast regions and reduce noise •Training process of basic SOM followed by image segmentation technique called probabilistic relaxation•Calculate probability pixel i belongs to node k and determine probability pixel i belongs to node k with likelihood that pixel i neighbors belong to node kSelf-Organizing Mapping•Locations of activation corresponding to neuronal activities cluster with finite spatial extent (rather than isolated sites)•Improvement in performance with varied factors of contrast level and signal pattern of artificial activation•Suboptimal in detecting isolated activated pixelsTop: modified SOM. Bottom: Standard SOM.Self-Organizing Mapping•How to improve modified SOM–Optimize computation speed –Employ batch SOM algorithm–Discard fixed network topologyCanonical Correlation Analysis•Extension of univariate correlation analysis•Multidimensional technique combines subspace modeling of hemodynamic response and use of spatial dependencies •Assumes a number of image slices are acquired at N subsequent time points in each pixel in each image slice a timeseries of length N is obtained•Search for pixels whose timeseries have a component that has a small signal increase during task performanceCanonical Correlation Analysis•Consider region of pixels to use the spatial relationship between pixels x-variable with timeseries x(t)•Set of basis-functions act as y-variable and span the signal subspace, denoted γ, which represent the range of hemodynamic response•Seek linear combinations of canonical variates, X,Y, so they correlate the most X=wx1x1+...wxmxm=wxTxY=wyy1+...wymym=wyTy•linear combination coefficients wx and wy, correlation ρCanonical Correlation Analysis•CCA finds the linear combination coefficients which give the largest correlation between X(t) and Y(t)•Linear combinations of pixel timeseries X(t)=wxTx(t) and basis-function Y(t)=wyTy(t) found so correlation between X(t) and Y(t) is the largest achievable valueCanonical Correlation Analysis•Largest canonical correlation analysis coefficient qualitative measure of how well the timeseries in the 3x3 neighborhood corresponded to the optimal signal Y(t)•Large correlation high degree of similarity•Low correlation not possible to find signal in the signal subspace that had similarity to timecourse in the neighborhoodCanonical Correlation Analysis•Will not fail to detect highly localized activations a single pixel•Larger activated regions than true neurological sense•Postprocessing step rejects spurious activated pixels Y(t) falls outside valid region of γCanonical Correlation Analysis•How to improve CCA–Method for obtaining statistical significance of the effect of postprocessing process –Method to reduce enlargements of activated regions caused when a vessel is encountered, which gives strong and spatially compact BOLD signalsSOM vs. CCA•Potentially faster than CCA•Uses similarity of time courses of pixels to cluster groups•Excellent experimental performance•Uses thresholding for modified version•Potentially more refined than SOM•Combines subspace modeling of hemodynamic response with use of spatial relationships in data•Excellent experimental performance•Detection not only based on thresholdingImportance•CCA appears to be a method a better alternative than SOM•However, both techniques useful in detecting and mapping spatial connectivity•Need to