Nonlinear analysis of BOLD signal: biophysical modeling, physiological states, and functional activation.

There is an increasing interest in exploiting the biophysical plausible models to investigate the physiological mechanisms that underlie observed BOLD response. However, most existing studies do not produce reliable model parameter estimates, are not robust due to the linearization of the nonlinear model, and do not perform statistics test to detect functional activation. To overcome these limitations, we developed a general framework for the analysis of fMRI data based on nonlinear physiological models. It performs system dynamics analysis to gain meaningful insight, followed by global sensitivity analysis for model reduction which leads to better system identifiability. Subsequently, a nonlinear filter is used to simultaneously estimate the state and parameter of the dynamic system, and statistics test is performed to derive activation maps based on such model. Furthermore, we investigate the change of the activation maps of these hidden physiological variables with experimental paradigm through time as well.