Presentation on theme: "FMRI Methods Lecture 10 – Using natural stimuli. Reductionism Reducing complex things into simpler components Explaining the whole as a sum of its parts."— Presentation transcript:
Reductionism Reducing complex things into simpler components Explaining the whole as a sum of its parts Duck behavior is the sum of its automatically behaving parts. Descartes 1662
Vision Decompose visual experience into: Locations in visual field Contrast Orientation Spatial frequency Direction of motion Categories – objects, faces, houses
Visual experiment Change a stimulus attribute in a controlled manner and see how the neural response changes (easy to do!). Repeat many times and average.
Visual system Different neurons in different visual system areas process specific components: Spatial receptive field Contrast and spatial frequency sensitivity Color sensitivity Selectivity for orientation, direction of motion, visual category. Temporal dependence, adaptation.
Natural stimulus Despite the complexity of the stimulus: 1.Categorical visual areas maintain selectivity. 2.Responses are similar across different subjects. 3.Reverse engineering works: can go from brain to stimulus. 4.Or map multiple areas at once by breaking down the stimulus into visual components (e.g. retinotopic mapping).
Temporal receptive windows Hasson et. al. J Neurosci. 2008
Temporal receptive windows Do the neurons care about the momentary stimulus being presented, or about its context within a certain temporal history…
Temporal receptive windows Scrambling the movie at different segment lengths. Inter-subject correlation in some cortical areas depended on the temporal continuity of the movie.
In autism Individuals with autism show weak inter-subject correlations Hasson et. al. Aut. Res. 2009
In autism Individual variability, but group averages were similar…
Data driven multivariate analyses Our variables are voxels We assume that voxel fMRI measurements represent a sum of separate linear components (separate brain processes) that are mixed in some unknown way. Find a mathematical criteria to separate the data into meaningful components: Principle component analysis (PCA) Independent component analysis (ICA) Clustering algorithms: K means, spectral clustering, etc…
1.Normalize the data (% sig change). 2.Find the direction with largest variability (1 st component). Data are most correlated along this direction…. 3.Add its orthogonal direction (2 nd component). Principal component analysis In two dimensions PCA is a way of representing the data in components that are orthogonal (dot product = 0, correlation = 0), while ordering them by the amount of variability that they explain.
fMRI data has as n by m dimensions (n voxels and m time-points). Perform PCA on the temporal dimensions. Principal component analysis Num voxels Num TRs
One way of computing a PCA is using singular value decomposition (SVD): Computing the components Data = U * S * V T Eigenvectors n by n matrix Eigenvalues n by n matrix n by m matrix n = num of trs m = num of voxels n by m matrix
Data structure If the data is correlated, it will have components (eigenvectors) that will explain a large part of the variability… Reduce the dimensionality of the data? Variance
Spatio-temporal components Brain areas that work together will be correlated in time The weighting of a particular component in the different voxels: The dot product of a voxels weights and the components matrix will give the original voxels timecourse
Principle component analysis Are orthogonality and variability explained good criteria for separating independent brain processes? How many simultaneous processes are there? Are they correlated in time? Reliability across scans and subjects? Typically more than one PCA solution…. Has mostly been used for dimensionality reduction (good for compressing data).
Independent component analysis A different algorithm that separates components such that they are statistically independent. Pr(A B) = Pr(A) * Pr(B) Cov(X,Y) = 0 Independent variables are uncorrelated, but not all uncorrelated variables are independent… They need to have a joint distribution fulfilling:
Good for separating audio Two microphones: Microphone 1Microphone 2 Two sources: Source 1Source 2
Good for cleaning EEG data Spatially consistent sparse processes.
Independent component analysis And with fMRI free viewing movie data:
Independent component analysis Things to think about: 1.You decide how many independent components to split the data into (arbitrary choice). 2.Reliability across scans and subjects. 3.How can we tell whether the components are biologically meaningful?