Assessing the State Space of the Brain with fMRI: An Integrative View of Current Methods

Abstract

Systems biology has gained substantial benefit from the application of systems modeling in engineering sciences. In general, methods as employed for construction and simulation of technical devices and buildings are applicable to modeling of biological systems. A number of modeling approaches originally derived from different areas such as engineering, econometrics and genetics have been adapted to functional brain imaging datasets in the recent years. However, despite a number of analogies, the complexities of brain systems might be much higher than those observed in technical systems. A dynamical system can be described as a state space in which a certain state of the system is specified by a single point. Varying states of the system over time can be described by a trajectory of states. Different modeling algorithms focus on certain aspects of this state space. The covariance of the state-space variables can be examined by correlational analysis (targeting normalized covariance) and principal component analysis. One of the principle aims in any systems identification approach is to identify parameters of the state matrix, i.e. the rules of transitions between different states of the system. Dynamic approaches with temporal information include the full state space model, vector autoregressive model and dynamic causal modeling. Structural equation modeling focuses on the instantaneous relationship between functional nodes. Directional analysis strategies are available in temporal and frequency domain. Depending on general assumptions as to how neuronal representation is established, the approaches present complementary information about the underlying neuronal interactions. The present article attempts to provide an integrative overview of the most established models and methods which are currently being applied for modeling dynamic brain systems.