Functional connectivity through nonlinear modeling: An application to the rat hippocampus

Implementation of neuroprosthetic devices requires a reliable and accurate quantitative representation of the input-output transformations performed by the involved neuronal populations. Nonparametric, data driven models with predictive capabilities are excellent candidates for these purposes. When modeling input-output relations in multi-input neuronal systems, it is important to select the subset of inputs that are functionally and causally related to the output. Inputs that do not convey information about the actual transformation not only increase the computational burden but also affect the generalization of the model. Moreover, a reliable functional connectivity measure can provide patterns of information flow that can be linked to physiological and anatomical properties of the system. We propose a method based on the Volterra modeling approach that selects distinct subsets of inputs for each output based on the prediction of the respective models and its statistical evaluation. The algorithm builds successive models with increasing number of inputs and examines whether the inclusion of additional inputs benefits the predictive accuracy of the overall model. It also explores possible second-order (inter-modulatory) interactions among the inputs. The method was applied to multi-unit recordings from the CA3 (input) and CA1 (output) regions of the hippocampus in behaving rats, in order to reveal spatiotemporal connectivity maps of the input-output transformation taking place in the CA3-CA1 synapse.