On tests of activation map dimension for fMRI-based studies of learning

Methodology for linking fMRI BOLD signal distributional changes associated with paradigm-related learning remains needed. Herein we consider settings where task related activation may be present before and after learning, yet the distribution of activated voxels changes. For context, consider the study of a motor learning task performed in scanner twice prior to and after a training session compared with a control motor task of equal difficulty occurring twice but without training. Current methodology would likely use random effect statistical parametric mapping to test the interaction of training on task. However, this approach suffers from considering estimated voxel-level activation or change in activation in isolation. In contrast, learning may evidence itself in changes in activation distribution , i.e. the distribution of intensities of BOLD response to the paradigm. The use of the analyses of lower dimensional subspaces of fMRI task-based activation maps provides our starting framework for such analysis. This manuscript investigates tests of dimension for the study of learning, particularly motor learning. The proposed methods consider the distribution of activation maps and tests the dimension of activation distribution between a trained and untrained tasks. If the BOLD signal is identical between the tasks (up to noise) the activation distribution should be one dimensional. The proposed analysis formally tests dimension in this setting. The methodology is formally developed and evaluated via simulation.Our investigation includes a large scale simulation study of brain activation maps, motivated by a study of motor learning in healthy adults. Our simulation results demon- strate that the study of linear dimension reduction using the singular value decompo- sition in a framework similar to Zarahn (2002) is able to capture specific instances of learning effects. The method is illustrated on the motivating data set