Investigating the nonlinearity of fMRI activation data

Functional magnetic resonance imaging (fMRI) is a widely used method of neuroimaging, but there is still much debate on the preferred method of analyzing these functional images. Nonlinear time series methods have improved in their usefulness in analyzing deterministic, nonlinear systems, and the feasibility of their application to fMRI data should be investigated. It is insufficient to state that their use in fMRI data analysis is justified by the fact that the brain is known to be a nonlinear system. The method of surrogate data allows us to verify that the data are nonlinear and to conclude that we may proceed with these advanced techniques. We tested fMRI motor activation data using the maximal Lyapunov exponent, nonlinear prediction errors, and Hurst exponent as test statistics, and found that there is satisfactory evidence to conclude that fMRI data are nonlinear. The results of these tests suggest that the mechanics of the hemodynamic response to neuronal activation may be more completely understood by the application of nonlinear time series analysis.