Bayesian connective field modeling using a Markov Chain Monte Carlo approach

The majority of neurons in the human brain process signals from neurons elsewhere in the brain. Connective Field (CF) modelling is a biologically-grounded method to describe this essential aspect of the brain's circuitry. It allows characterizing the response of a population of neurons in terms of the activity in another part of the brain. CF modelling translates the concept of the receptive field (RF) into the domain of connectivity by assessing, at the voxel level, the spatial dependency between signals in distinct cortical visual field areas. Thus, the approach enables to characterize the functional cortical circuitry of the human cortex. While already very useful, the present CF modelling approach has some intrinsic limitations due to the fact that it only estimates the model's explained variance and not the probability distribution associated with the estimated parameters. If we could resolve this, CF modelling would lend itself much better for statistical comparisons at the level of single voxels and individuals. This is important when trying to gain a detailed understanding of the neurobiology and pathophysiology of the visual cortex, notably in rare cases. To enable this, we present a Bayesian approach to CF modeling (bCF). Using a Markov Chain Monte Carlo (MCMC) procedure, it estimates the posterior probability distribution underlying the CF parameters. Based on this, bCF quantifies, at the voxel level, the uncertainty associated with each parameter estimate. This information can be used in various ways to increase confidence in the CF model predictions. We applied bCF to BOLD responses recorded in the early human visual cortex using 3T fMRI. We estimated both the CF parameters and their associated uncertainties and show they are only weakly correlated. Moreover, we show how bCF facilitates the use of effect size (beta) as a data-driven parameter that can be used to select the most reliable voxels for further analysis. Finally, to further illustrate the functionality gained by bCF, we apply it to perform a voxel-level comparison of a single, circular symmetric, Gaussian versus a Difference-of-Gaussian model. We conclude that our bCF framework provides a comprehensive tool to study human functional cortical circuitry in health and disease.