This paper presents a nonlinear model of human brain activity in response to visual stimuli according to Blood-Oxygen-Level-Dependent (BOLD) signals scanned by functional Magnetic Resonance Imaging (fMRI). A BOLD signal often contains a low frequency signal component (trend), which is usually removed by detrending because it is considered a part of noise. However, such detrending could destroy the dynamics of the BOLD signal and ignore an essential component in the response. This paper shows a model that, in the absence of detrending, can predict the BOLD signal with smaller errors than existing models. The presented model also has low Schwarz information criterion, which implies that it will be less likely to overfit the experimental data. Comparison between the various types of artificial trends suggests that the trends are not merely the result of noise in the BOLD signal.

Diffusion-weighted (DW)-functional magnetic resonance imaging (fMRI) is a recently reported technique for measuring neural activities by using diffusion-weighted imaging (DWI). DW-fMRI is based on the property that cortical cells swell when the brain is activated. This approach can be used to observe changes in water diffusion around cortical cells. The spatial and temporal resolutions of DW-fMRI are superior to those of blood-oxygenation-level-dependent (BOLD)-fMRI. To investigate how the DWI signal intensities change in DW-fMRI measurement, we carried out Monte Carlo simulations to evaluate the intensities before and after cell swelling. In the simulations, we modeled cortical cells as two compartments by considering differences between the intracellular and the extracellular regions. Simulation results suggested that DWI signal intensities increase after cell swelling because of an increase in the intracellular volume ratio. The simulation model with two compartments, which respectively represent the intracellular and the extracellular regions, shows that the differences in the DWI signal intensities depend on the ratio of the intracellular and the extracellular volumes. We also investigated the MPG parameters, b-value, and separation time dependences on the percent signal changes in DW-fMRI and obtained useful results for DW-fMRI measurements.