Identification and validation of effective connectivity networks in functional magnetic resonance imaging using switching linear dynamic systems

Dynamic connectivity networks identify directed interregional interactions between modeled brain regions in neuroimaging. However, problems arise when the regions involved in a task and their interconnections are not fully known a priori. Objective measures of model adequacy are necessary to validate such models. We present a connectivity formalism, the Switching Linear Dynamic System (SLDS), that is capable of identifying both Granger-Geweke and instantaneous connectivity that vary according to experimental conditions. SLDS explicitly models the task condition as a Markov random variable. The series of task conditions can be estimated from new data given an identified model providing a means to validate connectivity patterns. We use SLDS to model functional magnetic resonance imaging data from five regions during a finger alternation task. Using interregional connectivity alone, the identified model predicted the task condition vector from a different subject with a different task ordering with high accuracy. In addition, important regions excluded from a model can be identified by augmenting the model state space. A motor task model excluding primary motor cortices was augmented with a new neural state constrained by its connectivity with the included regions. The augmented variable time series, convolved with a hemodynamic kernel, was compared to all brain voxels. The right primary motor cortex was identified as the best region to add to the model. Our results suggest that the SLDS model framework is an effective means to address several problems with modeling connectivity including measuring overall model adequacy and identifying important regions missing from models.