We have developed a MATLAB toolbox for performing FC analyses which includes many of the most commonly-used approaches researchers have utilized to date for the identification of condition-dependent functional interactions between fMRI time-series obtained from two or more brain regions [Biswal et al., 1995
, Rissman et al., 2004
, Salvador et al., 2005
, Siegle et al., 2007
]. The approaches are either bivariate or multivariate methods defined in time or frequency domains that emphasize distinct features of relationships among the time-series. An optional pre-smoothing step is also implemented which allows empirically-derived temporal smoothing of the data before performing FC analyses. The FC toolbox enables ease of comparison and greater flexibility for choosing among FC measures, and may potentially lead to a greater understanding of the precise nature of FC relationships manifested in a given dataset. The simulation results illustrated that using multiple FC measures could effectively detect and classify regional associations and provide more information about the type of FC than any single measure. We have developed an initial classification tree based on the simulation results; to the extent that the included relationships are of interest, other researchers can utilize this tree to discover which pattern of connectivity may exist in their data. If other relationships are of interest, it is easy to expand this tree using additional simulated data - the simulated data we used are freely available on the web along with the code used to simulate the data, in concert with the toolbox (http://groups.google.com/group/fc-toolbox
Other simulation results illustrated that the temporal smoothing procedure we have implemented is robust to high levels of noise in fMRI responses. Addtionally, it was found that using a smoothing procedure which explicitly models autocorrelated noise or pre-whitening fMRI responses before smoothing is crucial for detecting inter-regional relationships if the noise is in fact autocorrelated, especially when data exhibit low SNR.
We applied these methods to an fMRI study to determine FC between dACC(BA32) and DLPFC(BA9) during a digit sorting task. We found strong relationships between these two ROIs. Relationships between the regions were 1) heterogeneous across subjects, 2) related to task, and 3) more complex than would have been detected using simple zero-order statistics such as correlation. Following the classification tree () 27 of 32 subjects were classified to relationship 6, 8 and 10 (). This indicated that the most common FC relationship in the sample involved a higher peak response in dACC(BA32) in response to a higher peak response in DLPFC(BA9). But some subjects displayed a prolongation of response in dACC(BA32) in response to a higher peak response in DLPFC(BA9). These relationships were not trivial, and certainly were more complex than would be revealed by zero-order correlation alone. At the most basic level, we can conclude that in this study, the dACC(BA32) and DLPFC(BA9) were strongly related among nearly all subjects - this point would not have been possible without using multiple connectivity measures. Future research is necessary to suggest whether the different observed patterns of relationships have psychological and biological importance, e.g., whether subjects with different patterns of connectivity differed in other important ways such as their performance.
The toolbox is flexible, taking brain activity data as inputs but also able to accept peripheral physiological measures (i.e., blood pressure, heart rate, etc.) into the FC function, with the requirement that all time-series inputs should be on the same resolution. An interpolation function is available in this toolbox that would allow time courses with different resolutions to be applied that are thereafter altered to be on the same resolution as the fMRI time courses. Furthermore, this toolbox could be implemented for determining whole brain network structure in which, instead of doing FC analysis between ROIs, researchers could do FC analysis between each pair of voxels over the whole brain.
We plan future work in several areas. First, an important question not addressed in the smoothing step is the estimation of the autocorrelation in the noise. We intend to implement an improved smoothing step which estimates the autocorrelation as well as smoothing in a future version of the toolbox. Second, the simulation studies implemented in this paper only considered direct relationships between two regions; multivariate relationships involving three or more regions are, of course, important. We intend to perform further simulations involving more than two regions to examine the behavior of these algorithms under indirect regional associations. Finally, our simulation studies only included 11 distinct patterns of inter-regional connectivity; since there may be many more types of connectivity relationships in actual data, results obtained from our classification tree may be misleading. However, we have used this limited set of patterns to demonstrate some possible associations, and to show that for understanding plausible relationships it may be useful to compute multiple FC measures. Moreover, the website for this toolbox is open to the public so that users can provide information on this issue. Specifically, we have created an area in which new empirical or simulated datasets can be uploaded with known relationships. We plan to update the classification tree regularly based on these data.