AbstractTo fully characterize the activity patterns on the cerebral cortex as measured with fMRI, the spatial scale of the patterns must be ascertained. Here we address this problem by constructing steerable bandpass filters on the discrete, irregular cortical mesh, using an improved Gaussian smoothing in combination with differential operators of directional derivatives. We demonstrate the utility of the algorithm in two ways. First, using modelling we show that our algorithm yields superior results in numerical precision and spatial uniformity of filter kernels compared to the most widely adopted approach for cortical smoothing. An important interim insight hereby was that the effective scales of information differ from the nominal filter sizes applied to extract them, and thus need to be calculated separately to compare different algorithms on par. Second, we applied the algorithm to an fMRI dataset to assess the scale and pattern form of cortical encoding of information about visual objects in the ventral visual pathway. We found that filtering by our method improved the detection of discriminant information about experimental conditions over previous methods, that the level of categorization (subordinate versus superordinate) of objects was differentially related to the spatial scale of fMRI patterns, and that the spatial scale at which information was encoded increased along the ventral visual pathway. In sum, our results indicate that the proposed algorithm is particularly suited to assess and detect scale-specific information encoding in cortex, and promises further insight into the topography of cortical encoding in the human brain.
Stochastic Lévy differential operators and Yang–Mills equations
