Modeling and analysis of mechanisms underlying fMRI-based decoding of information conveyed in cortical columns

Multivariate machine learning algorithms applied to human functional MRI (fMRI) data can decode information conveyed by cortical columns, despite the voxel-size being large relative to the width of columns. Several mechanisms have been proposed to underlie decoding of stimulus orientation or the stimulated eye. These include: (I) aliasing of high spatial-frequency components, including the main frequency component of the columnar organization, (II) contributions from local irregularities in the columnar organization, (III) contributions from large-scale non-columnar organizations, (IV) functionally selective veins with biased draining regions, and (V) complex spatio-temporal filtering of neuronal activity by fMRI voxels. Here we sought to assess the plausibility of two of the suggested mechanisms: (I) aliasing and (II) local irregularities, using a naive model of BOLD as blurring and MRI voxel sampling. To this end, we formulated a mathematical model that encompasses both the processes of imaging ocular dominance (OD) columns and the subsequent linear classification analysis. Through numerical simulations of the model, we evaluated the distribution of functional differential contrasts that can be expected when considering the pattern of cortical columns, the hemodynamic point spread function, the voxel size, and the noise. We found that with data acquisition parameters used at 3 Tesla, sub-voxel supra-Nyquist frequencies, including frequencies near the main frequency of the OD organization (0.5 cycles per mm), cannot contribute to the differential contrast. The differential functional contrast of local origin is dominated by low-amplitude contributions from low frequencies, associated with irregularities of the cortical pattern. Realizations of the model with parameters that reflected best-case scenario and the reported BOLD point-spread at 3 Tesla (3.5mm) predicted decoding performances lower than those that have been previously obtained at this magnetic field strength. We conclude that low frequency components that underlie local irregularities in the columnar organization are likely to play a role in decoding. We further expect that fMRI-based decoding relies, in part, on signal contributions from large-scale, non-columnar functional organizations, and from complex spatio-temporal filtering of neuronal activity by fMRI voxels, involving biased venous responses. Our model can potentially be used for evaluating and optimizing data-acquisition parameters for decoding information conveyed by cortical columns.