It recently has been demonstrated that magnetic resonance imaging can be used to map changes in brain hemodynamics produced by human mental operations. One method under development relies on blood oxygenation level-dependent (BOLD) contrast: a change in the signal strength of brain water protons produced by the paramagnetic effects of venous blood deoxyhemoglobin. Here we discuss the basic quantitative features of the observed BOLD-based signal changes, including the signal amplitude and its magnetic field dependence and dynamic effects such as a pronounced oscillatory pattern that is induced in the signal from primary visual cortex during photic stimulation experiments. The observed features are compared with the results of Monte Carlo simulations of water proton intravoxel phase dispersion produced by local field gradients generated by paramagnetic deoxyhemoglobin in nearby venous blood vessels. The simulations suggest that the effect of water molecule diffusion is strong for the case of blood capillaries, but, for larger venous blood vessels, water diffusion is not an important determinant of deoxyhemoglobin-induced signal dephasing. We provide an expression for the apparent in-plane relaxation rate constant (R2*) in terms of the main magnetic field strength, the degree of the oxygenation of the venous blood, the venous blood volume fraction in the tissue, and the size of the blood vessel.