.where r = 0 implies no correlation, r = 1 perfect correlation, and = −1 perfect anti-correlation.
It is possible to perform this calculation for all pairs of voxels in the data set, resulting in over 200,000 comparisons. More frequently a "seed" is chosen (a predetermined voxel, cluster, or small anatomic region) and comparison made to similar seeds in the data set. A seed correlation matrix (shown left) may be constructed, where higher r-values reflect greater connectivity between paired regions. High-correlation areas can also be displayed as "blobs" overlaid on co-registered anatomic images.
The ICA algorithm begins by constructing a matrix (Y) of all the observed fMRI data. Each column of Y contains sequential time points for a single voxel; each row of Y is the fMRI signal at a certain time point for organized by space (all the voxels). After some pre-processing to normalize means and variances, Y is decomposed into the product of two matrices (T and S), where T is a matrix of time courses and S is a matrix of spatial components. The values in T and S are iteratively adjusted to determine a decomposition that maximizes statistical independence (typically between rows of S). The resultant independent component signals can then be color-coded and overlaid on an anatomic image (above).
Advanced Discussion (show/hide)»
Meaningful resting-state fMRI data lies in the frequency range of approximately 0.01 − 0.1 Hz. By comparison, respiratory fluctuations produce aliased signals in the range of 0.1 − 0.3 Hz, while cardiac pulsations produce signals in the range of 0.8 − 1.3 Hz. Thus physiological noise is a much greater problem for RS-fMRI than for task-based studies.
Barkhof F, Haller S, Rombout SARB. Resting-state functional MR imaging: a new window to the brain. Radiology 2014; 272:29-49. (good recent review)
Beckman CF. Modelling with independent components. NeuroImage 2012; 62: 891-901.
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Calhoun VD, Adali T, Hasen LK, et al. ICA of functional MRI data: an overview. 4th International Symposium on Independent Component Analysis and Blind Signal Separation, Nara, Japan, 2003:281-288.
Chen JE, Glover GH. Functional magnetic imaging methods. Neuropsychol Rev 2015; 25:289-313.
Hyvärinen A, Oja E. Independent component analysis: algorithms and applications. Neural Networks 2000; 13:411-413. (provides mathematical details of matrix decomposition and optimization for ICA)
Lee MH, Smyser CD, Shimony JS. Resting-state fMRI: a review of methods and clinical applications. AJNR Am J Neuroradiol 2013; 34:1866-72. (good recent review)
McKeown MJ, Makeig S, Brown GG, et al. Analysis of fMRI data by blind separation into independent spatial components. Hum Brain Mapping 1998; 6:160-188 (first use of ICA for fMRI data, actually a task-based experiment, not RS-fMRI)
Power JD, Schlaggar BL, Petersen SE. Studying brain organization via spontaneous fMRI signal. Neuron 2014; 84:681-696. (Good recent review)
Rosazza C, Minati L, Ghielmetti F, et al. Functional connectivity during resting-state functional MR imaging: study of the correspondence between independent component analysis and region-of-
interest-based methods. AJNR Am J Neuroradiol 2012; 33:180–87. (little difference between correlation and ICA methods for normal adults RS-fMRI analysis)
Van Dijk et al. Intrinsic functional connectivity as a tool for human connectomics: theory, properties, and optimization. J Neurophysiol. 2010; 103:297-321.
How do you statistically analyze fMRI data?
What is meant by resting state fMRI? How is it used?