A mixed-effects, spatially varying coefficients model with application to multi-resolution functional magnetic resonance imaging data.

Spatial resolution plays an important role in functional magnetic resonance imaging studies as the signal-to-noise ratio increases linearly with voxel volume. In scientific studies, where functional magnetic resonance imaging is widely used, the standard spatial resolution typically used is relatively low which ensures a relatively high signal-to-noise ratio. However, for pre-surgical functional magnetic resonance imaging analysis, where spatial accuracy is paramount, high-resolution functional magnetic resonance imaging may play an important role with its greater spatial resolution. High spatial resolution comes at the cost of a smaller signal-to-noise ratio. This begs the question as to whether we can leverage the higher signal-to-noise ratio of a standard functional magnetic resonance imaging study with the greater spatial accuracy of a high-resolution functional magnetic resonance imaging study in a pre-operative patient. To answer this question, we propose to regress the statistic image from a high resolution scan onto the statistic image obtained from a standard resolution scan using a mixed-effects model with spatially varying coefficients. We evaluate our model via simulation studies and we compare its performance with a recently proposed model that operates at a single spatial resolution. We apply and compare the two models on data from a patient awaiting tumor resection. Both simulation study results and the real data analysis demonstrate that our newly proposed model indeed leverages the larger signal-to-noise ratio of the standard spatial resolution scan while maintaining the advantages of the high spatial resolution scan.