A wide range of statistical methods are available to analyze fMRI data. Some are more appropriate for task-based fMRI while others are more applicable to resting-state studies. The most commonly used ones are briefly described below.

**Correlation Analysis**

The degree of temporal synchrony between two time series

*X = x1, x2, x3*, … and*Y = y1, y2, y3,*… can be expressed by the*correlation coefficient (r)*calculated as
where
r = 0 implies no correlation, r = 1 perfect correlation, and = −1 perfect anti-correlation. Correlation methodology was one of the earliest techniques applied to task-based fMRI studies in the 1990s. In this setting Y was the time course of the fMRI signal from a single voxel while X was the expected hemodynamic response to a task or stimulus. Voxels with larger r-values had signals more highly correlated to the input and hence were considered relatively activated. |

Today correlation analysis is more commonly used for

*), where***resting-state fMRI (RS-fMRI***X*and*Y*are the MRI signals from two different voxels or brain regions. Here higher*r*-values reflect greater connectivity between pairs of areas and assist in neural network modeling.**General Linear Model (GLM)**

The

**is an extension of simple correlation and regression that has evolved into the workhorse technique for analysis of task/stimulus-based fMRI experiments over the last 25 years. GLM is the default method provided by all MR vendors in their clinical fMRI packages and is also widely available in third party software. Often expressed in matrix algebra form, the GLM can be written***General Linear Model (GLM)**=*

**Y***β0 + β1*

*+*

**X****1***β2*+ … +

**X****2**

**ε**This equation states that the

**fMRI signa***for a given voxel can be expressed as the sum of one or more experimental***l (Y)****design variables****(**, each multiplied by a*X1, X2*, …)*, plus a random***weighting factor (β1,***β2,*…)*. There is usually one***error term (ε)***Xi*for each type of stimulus or event presented to the subject. Most models also contain additional*Xi*"nuisance regressors" to account for motion or signal drift.Once the design variables (

*Xi*) and recorded signals (Y) have been loaded into the GLM, a least squares optimization procedure calculates values for the weighting factors (*β1,*) corresponding to each design variable. Because the data fit will not be perfect, small errors (*β2,*…*ε**i**), also called**, will be generated for each time point. Various statistical tools (such as***residuals***) can then be applied to explore other features of the data, such as the degree of correlation between variables, assessment of linearity, and comparisons between populations. The final output is usually a***t- and F-tests***overlaid on an anatomic image or template.***Statistical Parametric Map (SPM)****Independent Component Analysis (ICA)**

The goal of

*is to detect underlying patterns present in the fMRI signal without prior knowledge of the experimental task or shape of the hemodynamic response function. ICA is thus considered a “model free” method for***Independent Component Analysis (ICA)***, allowing identification of unknown independent signals that have been linearly mixed together. For example, ICA methods could be used extract individual voices, music, and noise elements from an audio mixture recorded at a cocktail party without prior knowledge of their sources or locations.***blind source signal separation**As applied to fMRI data, ICA may distinguish meaningful areas of correlated brain activation from random and semi-periodic physiological noise. Although ICA can be used in conjunction with GLM methods for task-based experiments, it has found its most widespread application for the analysis of resting-state fMRI data.

**Multi-Voxel Pattern Analysis (MVPA) and Networks**

**seeks to discover spatial patterns of fMRI activity corresponding to different experimental conditions. Such knowledge might allow us to decode mental states, such as what a person is thinking or feeling, merely by observing fMRI data.**

*Multi-Voxel (Multi-Variate) Pattern Analysis (MVPA)*Unlike ICA, MVPA is model-based, and a wide range of MPVA techniques are available depending on the needs of a particular experiment and the psychologic-physiologic questions to be answered. One aspect to be considered is the spatial scope of the analysis. The

*searchlight*

*approach*creates thousands of localized multivariate predictive models; while the

*whole*-

*brain*

*approach*develops a single predictive model across applied diffusely.

Because of the brain's extraordinary complexity, an important role for

*machine***has emerged -- the use of computer algorithms to discern complex patterns from empirical data for making models and decisions. This, in turn, has led to multiple methods of for expressing connectivity -- through graphs, network maps, and quantitative measures. The NIH-sponsored***learning**is an example of the importance of developing a public fMRI data base and processing algorithms for better understanding of brain connectivity.***Human Connectome Project**### Advanced Discussion (show/hide)»

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**References**

Haxby JV, Gobbini MI, Furey ML, et al. Distributed and overlapping representations of faces and objects in the ventral temporal cortex. Science 2001; 293:2425-30. (frequently credited as the first MVPA paper).

Mahmoudi A, Takerkart S, Regragui F, et al. Multivoxel pattern analysis for fMRI data: a review. Comput Math Methods Med 2012: article ID 961257:1-14.

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 description of ICA applied to fMRI).

Monti MM. Statistical analysis of fMRI time-series: a critical review of the GLM approach. Front Hum Neurosci 2011; 5(28):1-13, doi: 10.3389/fnhum.2011.00028

Poline J-B, Brett M. The general linear model and fMRI: Does love last forever? Neuroimage 2012; 62:871-880.

Sporns O, Tononi G, Kötter R. The Human Connectome: a structural description of the human brain. PLoS Comput Biol 2005; 1: 245-251.

Whitlow CT, Casanova R, Maldjian JA. Effect of resting-state functional MR imaging duration on stability of graph theory metrics of brain network connectivity. Radiology 2011; 259:516-524.