Deconvolving BOLD activation in event-related designs for multivoxel pattern classification analyses

Abstract

Use of multivoxel pattern analysis (MVPA) to predict the cognitive state of a subject during task performance has become a popular focus of fMRI studies. The input to these analyses consists of activation patterns corresponding to different tasks or stimulus types. These activation patterns are fairly straightforward to calculate for blocked trials or slow event-related designs, but for rapid event-related designs the evoked BOLD signal for adjacent trials will overlap in time, complicating the identification of signal unique to specific trials. Rapid event-related designs are often preferred because they allow for more stimuli to be presented and subjects tend to be more focused on the task, and thus it would be beneficial to be able to use these types of designs in MVPA analyses. The present work compares 8 different models for estimating trial-by-trial activation patterns for a range of rapid event-related designs varying by interstimulus interval and signal-to-noise ratio. The most effective approach obtains each trial's estimate through a general linear model including a regressor for that trial as well as another regressor for all other trials. Through the analysis of both simulated and real data we have found that this model shows some improvement over the standard approaches for obtaining activation patterns. The resulting trial-by-trial estimates are more representative of the true activation magnitudes, leading to a boost in classification accuracy in fast event-related designs with higher signal-to-noise. This provides the potential for fMRI studies that allow simultaneous optimization of both univariate and MVPA approaches.

Figure 1

The model estimation approaches considered for obtaining trial-by-trial parameter estimates. Five of the approaches (least squares, two versions of ridge regression, partial least squares and support vector regression) used the design matrix shown on the top left, X_S. This design matrix contains a single regressor for each trial (in this case 10) in the run, where each regressor is an impulse function convolved with a double gamma HRF. The middle design corresponds to the Add6 model, which models each trial using an unconvolved boxcar function capturing the time point 6 seconds after the time of stimulus presentation. The last design illustrates the LS-S approach, where a trial-specific design matrix is used to obtain the activation estimate for that trial. The design matrices contain two regressors, one for the trial of interest plus a second that models all other trials simultaneously. So, X_T1 is the design to obtain the activation estimate for trial 1 and has a regressor modeling that trial and a second regressor modeling all other trials. The estimate for β₁ from this first design is the activation for trial 1. This process is repeated N times to obtain estimates for all trials. The bottom table lists the regularization parameters used, when needed.

Figure 2

Illustration of the double cross-validation that was used in the simulation study. The primary cross-validation was a leave-one-run-out CV across 3 runs, for the purposes of obtaining classification accuracy reflecting the ability of the trial-by-trial parameter estimates to predict task type. One fold of the primary cross-validation is illustrated here. It begins with the parameter selection CV, which is a 2-fold CV used to select the regularization parameters used in ridge regression, PLS and SVR. Once this 2-fold CV is carried out the trial-specific activations can be estimated for all 3 runs. Then the primary CV is carried out, training a classifier to predict trial type using 2 runs of data and then testing this model on the test data.

Figure 3

Accuracy results from simulation studies. Each simulation consisted of 500 iterations and 60 trials split randomly and evenly between two tasks. Each of the 12 sets of boxplots contain the results from the eight different models outlined in Figure 1 and arranged by decreasing levels of collinearity (left to right) and increasing noise (top to bottom). When the noise is lower (top 2 rows) the Add6 model performs the worst across all levels of collinearity. For low noise, high collinearity cases (upper left) the LS-S model outperforms all other models. The solid horizontal line indicates chance (50%), while the dashed line indicates accuracy significantly better than chance according to the binomial distribution.

Figure 4

Correlation of trial-by-trial parameter estimates with true parameter estimate value from simulation studies. The correlations between true and estimated trial activation magnitude were similar for β₁ and β₂ and hence are averaged for each simulation. The organization of the boxplots is similar to Figure 3 with collinearity decreasing from left to right across rows and noise increasing from top to bottom. Methods with weaker correlation between estimated activation and true activation magnitudes tended to have worse classification results.

Figure 5

Variability of the parameter estimates. For each simulation the variance of the parameter estimates across trials was calculated and variances were similar for β₁ and β₂, so they are averaged for each simulation. As expected the unregulated LS-A model has the highest variance, although in some cases the SVR parameter estimates are much more variable. The variability of LS-S is often similar to the other regulated approaches, but is found to be slightly larger than some of the regulated approaches in higher noise situations.

Figure 6

Classification accuracies from the real data analysis. The Add6 accuracy was significantly lower than LS-S (p=0.0002, uncorrected) and Add4–6 (p<0.0001, uncorrected).

Figure 7

Classification accuracies from the real data analysis separated by stimulus type. Note that the classification accuracy increase for LS-S and Add4–6 compared to the other methods, as shown in Figure 6, is mostly due to an increase in the classification accuracy of the mirrored words.