Algorithms and Bounds for Dynamic Causal Modeling of Brain Connectivity

Recent advances in neurophysiology have led to the development of complex dynamical models that describe the connections and causal interactions between different regions of the brain. These models are able to accurately mimic the event-related potentials observed by EEG/MEG measurement systems, and are considered to be key components for understanding brain functionality. In this paper, we focus on a class of nonlinear dynamic causal models (DCM) that are described by a set of connectivity parameters. In practice, the DCM parameters are inferred using data obtained by an EEG or MEG sensor array in response to a certain event or stimulus, and then used to analyze the strength and direction of the causal interactions between different brain regions. The usefulness of these parameters in this process will depend on how accurately they can be estimated, which in turn will depend on noise, the sampling rate, number of data samples collected, the accuracy of the source localization and reconstruction steps, etc. The goals of this paper are to present several algorithms for DCM parameter estimation, derive Cramér-Rao performance bounds for the estimates, and compare the accuracy of the algorithms against the theoretical performance limits under a variety of circumstances. The influence of noise and sampling rate will be explicitly investigated.