Blood flow is distributed through the heart muscle via a system of vessels forming the coronary circulation. The perfusion of the myocardium can be hampered by atherosclerosis creating localized obstructions in the epicardial vessels or by microvascular disease. In early stages of the disease, these impediments to blood flow are offset by dilation of the resistance vessels, which normally compensates for a decrease in perfusion pressure or increased metabolism. However, this dilatory reserve can become exhausted, which in general occurs first at the deeper layers of the heart wall where intramural vessels are subjected to compressive forces related to heart contraction. In the catheterization laboratory, guide wires of 0.33 mm diameter are available that are equipped with a pressure and flow velocity sensor at the tip, which can be positioned distal to the stenosis. These signals provide information about the impediment of the stenosis on coronary flow and allow for the evaluation of the status of the microcirculation. However, the interpretation of these signals is strongly model-dependent and therefore it is of paramount importance to develop realistic models reflecting the anatomy and unique physiology of the coronary circulation.