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Yi Chen, Radoslaw M. Cichy and John-Dylan Haynes Bernstein Center for Computational Neuroscience Berlin & Charité – Universitätsmedizin Max-Planck-Institute for Human Cognitive and Brain Sciences, Leipzig 25/11/2011 Berlin. Multi-Scale Mapping Of fMRI Information On The Cortical Surface: - PowerPoint PPT Presentation

Yi Chen, Radoslaw M. Cichy and John-Dylan Haynes

Bernstein Center for Computational Neuroscience Berlin & Charit Universittsmedizin Max-Planck-Institute for Human Cognitive and Brain Sciences, Leipzig 25/11/2011 BerlinMulti-Scale Mapping Of fMRI Information On The Cortical Surface:A Graph Wavelet Based Approach

Pattern Recognition?Haxby et al. Science, 2001Multivariate Pattern Analysis of fMRI Signal

Spatial Range of MVPA MethodsHaxby et al., Science, 2001 Haynes & Rees, Nature Rev. Neurosci, 2006 Kriegeskorte et al., PNAS, 2007Whole brainSearchlight techniqueROI-based Searchlight technique affords unbiased, spatially localized information detection.GlobalLocal

The fMRI Signal in SpaceInformation carried by the fMRI signals resides in the convolved cortical sheets.Jin & Kim, Neuroimage, 2008 3D searchlight methods do not take this structural complexity of the brain into account.The brain has a complex structure:3D searchlight

Yi Chen - this and the next together introduce the surface searchlight stuff

Cortical Surface-based SearchlightChen et al., NeuroImage, 2011Surface-based searchlight respects local geometry3D searchlight neglects local geometrySearchlight on cortical surface mesh

Application: Decoding Object CategoryObject categories:Trumpets vs Chairs vs BoatsChen et al., NeuroImage, 2011

Surface-based vs 3D MethodChen et al., NeuroImage, 2011 3D method deteriorates spatial specificity Surface-based method observes local structureFusiform gyrusCollateral sulcusFusiform gyrusCollateral sulcus Surface-based method localizes fMRI information more precisely

Multiscale Organization of Brain FunctionOcular dominance and orientation preference columnsRetinotopic maps Object selective regions Hierarchical organization with increasing spatial scale Knowing the spatial scale of patterns is crucial for understanding the brains functional organizationYacoub et al., PNAS, 2008 Wandell, Encyclopedia Neurosci., 2007

Multiscale Analysis Wavelet TransformWavelets, or little waves, are families of spatially local, band-passing filters: Information specific to different scales can be extracted with waveletsFine scale informationFine scale waveletLarge scale waveletOutput:Large scale informationTransformHackmack and Haynes, in prep.Scale up

Wavelets on regular gridWavelets on irregular meshVaries on translation Translation invariant On an irregular mesh, wavelet transform cannot be directly implementedWavelets on Irregular Mesh

Another Way to Look at Discrete Fourier TransformProjecting a signal onto the space spanned by these eigenvectors is thus computationally equivalent to its Discrete Fourier Transform (DFT):

Manipulating the transform coefficients and exploiting the unitary property of U, we can implement filters on the frequency domain. The filtered signal is given by:

Discrete Laplacian:where K is a symmetric matrix, its eigenvectors, when sorted non-decreasingly w.r.t. eigenvalues:The diagonal matrix contains the Impulse Response function of the designed filter.Taubin SIGGRAPH '95For a signal x defined on a one-dimensional, regular and circular field, we have:

Biyikoglu et al., Laplacian Eigenvectors of Graphs, 2007 Hammond et al., Applied & Comp. Harmonic Analysis, 2009Implementing Wavelets via Graph LaplacianEigenspectrumFreq. Response Wavelets on irregular mesh can then be defined on the eigenspectral domain: Generalized graph Laplacian H:

Multiscale Analysis on Irregular Mesh Fine scale informationFine scale waveletLarge scale waveletOutputsLarge scale informationTransform Spectral graph wavelets can be used to achieve multiscale analysis on irregular meshes

Anisotropic Filters on Cortical SurfaceFine scaleLarge scaleVerticalHorizontal Anisotropic filters are possible by using different geometric schemes for the graph Laplacian

Multiscale Analysis of Object Categories/ExemplarsCichy et al., Cerebral Cortex, 20112-step procedure:

BOLD estimates were sampled onto the cortical surface & transformed with spectral graph wavelets

At each scale, the outputs from the filter banks were taken as feature vectors for classification

Scale Differentiated Analysis of Exemplar and Category EncodingLarge ScaleFine ScaleCategoriesExemplars Categories are preferentially encoded in large scale and exemplars in fine scale z-score

Summary Cortical surface-based method respects natural geometry of the brain improves spatial specificity of MVPA Multi-scale analysis on the cortical surface can extract information from fMRI signals at different scales using spectral graph wavelets shows that object categories and exemplars are encoded in different spatial scales in the ventral visual stream The combination of surface-based technique and multi-scale information mapping promises a better understanding of human brain function

AcknowledgementsFernando RamirezNEUROCUREKerstin Hackmack

Appendix

Spectral Graph Wavelets & Fast AlgorithmHammond et al., Applied & Comp. Harmonic Analysis, 2009 For filter with compact spatial support, its impulse response function defined on eigenspectral domain needs to be continuously differentiable. Wavelet functions are defined by a family of dilated versions of a single function (mother wavelet). Mother wavelet needs to meet the admissibility condition.

Fast algorithm is possible by approximating the wavelet function on eigenvalue domain with truncated orthogonal polynomials (e.g. Chebyshev polynomial), and calculating the eigenspace projection with recursive sparse matrix vector multiplications (Sect.6, Hammond et al., 2009). Note, however, by adopting above fast algorithm, the dilation of mother wavelet is now carried on the eigenvalue domain, rather than the eigenvalues rank/index domain.

Multiscale Analysis on Regular GridFine scale waveletLarge scale waveletOutputsTransform

Objects were rotating with randomly changing axis. Subjects were performing a Landolt-C task