Neuronal activity-induced changes in vascular tone and oxygen consumption result in a dynamic evolution of blood flow, volume, and oxygenation. Functional neuroimaging techniques, such as functional magnetic resonance imaging, optical imaging, and PET, provide indirect measures of the neural-induced vascular dynamics driving the blood parameters. Models connecting changes in vascular tone and oxygen consumption to observed changes in the blood parameters are needed to guide more quantitative physiological interpretation of these functional neuroimaging modalities. Effective lumped-parameter vascular balloon and Windkessel models have been developed for this purpose, but the lumping of the complex vascular network into a series of arterioles, capillaries, and venules allows only qualitative interpretation. We have therefore developed a parallel vascular anatomical network (VAN) model based on microscopically measurable properties to improve quantitative interpretation of the vascular response. The model, derived from measured physical properties, predicts baseline blood pressure and oxygen saturation distributions and dynamic responses consistent with literature. Furthermore, the VAN model allows investigation of spatial features of the dynamic vascular and oxygen response to neuronal activity. We find that a passive surround negative vascular response ("negative BOLD") is predicted, but that it underestimates recently observed surround negativity suggesting that additional active surround vasoconstriction is required to explain the experimental data.