FILM - Voxelwise Timeseries Analysis

In FMRI statistical analysis there are problems with accounting for temporal autocorrelation (the intrinsic smoothness in each voxel's timeseries). Unless this is correctly accounted for, the timeseries analysis is at best inefficient (in terms of sensitivity to true activation) and at worst statistically invalid. Commonly, techniques have utilised temporal filtering strategies to either shape these autocorrelations, or remove them. Shaping, or ``colouring'', attempts to negate the effects of not accurately knowing the intrinsic autocorrelations by imposing known autocorrelation via further smoothing. Removing the autocorrelation, or ``prewhitening'', gives the best linear unbiased estimator, if the autocorrelation can be accurately estimated.

Figure 1: Relative efficiency when using prewhitening or colouring for dealing with temporal autocorrelation, for four different types of regressor (SE = single-event, ISI = inter-stimulus interval)

In [43] we demonstrated that when using block designs, colouring can be used with minimal loss of efficiency. However, as shown in figure 1, for single-event designs with randomized intervals, jittering or just very short intervals, colouring is much less efficient and hence prewhitening is desirable. It had previously been suggested that sufficiently accurate estimates of the autocorrelation are currently not available to give prewhitening acceptable accuracy [18]. To overcome this, we developed the following methodology for accurate voxelwise autocorrelation estimation. Firstly, high-pass filtering needs to be performed as a preprocessing step to remove the worst of the large-scale, non-stationary components and low frequency noise. Secondly, we investigated various methods of initial estimation (and regularisation) of the autocorrelation coefficients, finding that applying a Tukey taper to the raw estimates (to smoothly ``roll off'' higher lags) gave the best results. Thirdly, spatial smoothing of the resulting autocorrelation estimates was found to be important in reducing bias further. The autocorrelation was found to vary considerably between matter types (with higher autocorrelation in the grey matter than in white). Therefore, we apply non-linear spatial smoothing [32] to the autocorrelation coefficients, only smoothing within matter type.

Using the above approach we were able to demonstrate close to zero bias at probability levels as low as $0.00001$ [43]. We thus obtain optimally efficient estimation of the model parameters, giving greater sensitivity to activation than if colouring were used. Furthermore, even with this more flexible model, we are able to find the autocorrelation function at a voxel level, i.e., do not need to rely, in order to obtain robustness, on relatively inaccurate global estimation. This approach has been implemented as FILM (FMRIB's Improved Linear Model), the time-series modelling tool used within FEAT.