Performance bounds for dynamic causal modeling of brain connectivity

The use of complex dynamical models have been proposed for describing the connections and causal interactions between different regions of the brain. The goal of these models is to accurately mimic the event-related potentials observed by EEG/MEG measurement systems, and are useful in understanding overall 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 the resulting estimates are used to analyze the strength and direction of the causal interactions between different brain regions. The usefulness of the parameter estimates 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 goal of this paper is to derive Cramér-Rao performance bounds for DCM estimates, and examine the behavior of the bounds under different operating conditions.