Algorithms and Bounds for Dynamic Causal Modeling of Brain Connectivity

Abstract—Recent advances in neurophysiology have led to the development of complex dynamical models that describe the con-nections 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 func-tionality. 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 re-gions. The usefulness of these parameters in this process will de-pend on how accurately they can be estimated, which in turn will depend on noise, the sampling rate, number of data samples col-lected, 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 algo-rithms against the theoretical performance limits under a variety of circumstances. The influence of noise and sampling rate will be explicitly investigated. Index Terms—Brain connectivity, dynamic causal modeling, EEG, MEG. I