Variations in local neural activity are accompanied by rapid, focal changes in cerebral blood flow and volume. While a range of observations have shown that dilation occurs in cerebral arteries, there is conflicting evidence about the significance of volume changes in post-arteriole vessels. Here, we reconcile the competing observations using a new mathematical model of the hemodynamic response. First, we followed a 'top down' approach, without constraining the model, but using experimental observations at progressively more detailed scales to ensure physiological behaviour. Then, we blocked dilation of post-arteriole vessels, and predicted observations at progressively more aggregated scales (a 'bottom up' approach). Predictions of blood flow, volume, velocity, and vessel diameter changes were consistent with experimental observations. Interestingly, the model predicted small, slow increases in capillary and venous diameter in agreement with recent in vivo data. Blocking dilation in these vessels led to erroneous volume predictions. The results are further evidence that arteries make up the majority of blood volume increases during brief functional activation. However, dilation of capillaries and veins appears to be increasingly significant during extended stimulation. These are important considerations when interpreting results from different neurovascular imaging modalities. (C) 2012 Elsevier Inc. All rights reserved.