The existence of a coupling between changes in neuronal activity, cerebral blood flow and blood oxygenation is well known. The explicit relationship between these systems, however, is complex and remains a subject of intense research. Here, we use direct electrophysiological recordings to predict blood flow and oxygenation changes measured with optical methods during parametric stimulation applied to the somatosensory cortex in rat brain. Using a multimodal model of the cerebral functional unit, we estimate a neuro-vascular and a neuro-metabolic transfer function relating the experimentally measured neural responses with the inputs to a vascular model predicting hemodynamic and blood oxygenation changes. We show that our model can accurately predict experimentally measured parametric hemodynamic evoked responses by using a single linear transfer function relationship with a reduced number of state parameters to relate the level of neural activity to evoked cerebral blood flow and oxygen metabolism changes. At the same time, we characterize the metabolic and vascular neural response functions and interpret their physiological significance.