Time Series Analysis

Inferences about functional connectivity can be made from analyses of time series data. The underlying assumption is that correlations between brain activity in different brain regions indexes connectivity between them. These correlations are calculated over vectors of activation values across a period of time.

When doing these analyses on MRI data, we must define the regions from which these time series will be drawn, and then extract the time series for each region that will be entered into the analysis. The time series vectors are saved into a flexibly interpretable file (e.g., plaintext) that can be read into some other software suitable for operating over sets of numbers (e.g., R, MATLAB, Excel).

FreeSurfer

Surface Parcellation and Functional Analysis

The first precondition for these analyses in surface space is that the anatomical data must be processed in FreeSurfer, and a functional analysis must be run on the BOLD data.

The brain regions from which the time series are drawn can be defined any number of ways. One way of defining these regions has been to use anatomical region definitions. Because different anatomical regions vary greatly in size, we have been using the Lausanne 2008 parcellation scheme to divide the cortex into roughly 1000 regions of comparable size. The second precondition for this analysis is to define your regions of interest. Any definition method that has been documented is allowable, though at this point, instructions exist on this wiki for the Lausanne 2008 parcellation scheme.

Detrending

The second step is to detrend your functional data, which is to remove a linear signal drift from your data.

Over the course of a run, there can be a linear drift in the signal in different regions of the brain. There are many possible causes for this that have nothing to do with any interesting aspect of your data -- in other words, this linear drift is a nuisance artifact because it introduces spurious correlations between two unrelated time series.

You can see this for yourself in a quick experiment you could whip up in Excel: take two vectors of 100 randomly generated numbers (e.g., randbetween(1,99)). They should be uncorrelated. Now add 1, 2, 3, ... , 99, 100 to the values in each vector. This simulates a linear trend in the data. You shouldn't be surprised to find that the two vectors are now highly and positively correlated!

See Detrending for details on how to detrend the functional data prior to time series extraction.

Extract Timecourse Data to Text File

The third step is to extract the timeseries data from the brain regions that you wish to include in your network.

Thus far, this lab has focused on functional networks across cortical regions in surface space (i.e., ignoring subcortical regions). Details describing how to extract these data in surface space using FreeSurfer can be found here.

SPM

Steps for SPM data have not been implemented yet.

Functional Connectivity

One application of time series analysis is to generate functional connectivity matrices. Our lab explores different approaches of producing, analyzing and using these matrices, but a (relatively) quick and dirty way of producing a connectivity matrix is to calculate the cross-correlation between each pair of regions in the data. A simple Pearson correlation is a special case of the more general cross-correlation, with a lag of 0.