Nonlinear aspects of the BOLD response in functional MRI

Functional magnetic resonance imaging (fMRI) using blood oxygenation level-dependent (BOLD) contrast has progressed rapidly and is commonly used to study function in many regions of the human brain. This paper introduces a method for characterizing the linear and nonlinear properties of the hemodynamic response. Such characterization is essential for accurate prediction of time-course behavior. Linearity of the BOLD response was examined in the primary visual cortex for manipulations of the stimulus amplitude and duration. Stimuli of 1, 2, 4, and 8 s duration (80% contrast) and 10, 20, 40, and 80% contrast (4 s duration) were used to test the hemodynamic response. Superposition of the obtained responses was performed to determine if the BOLD response is nonlinear. The nonlinear characteristics of the BOLD response were assessed using a Laplacian linear system model cascaded with a broadening function. Discrepancies between the model and the observed response provide an indirect measure of the nonlinearity of the response. The Laplacian linear system remained constant within subjects so the broadening function can be used to absorb nonlinearities in the response. The results show that visual stimulation under 4 s in duration and less than 40% contrast yield strong nonlinear responses.