An apparatus and method for the determination of the flow, the coronary reserve and relative coronary reserve of a specific coronary artery. The apparatus and method employ a three-dimensional model (50) providing the volume of a segment of the artery at a plurality of points in time, and disclose various options (56) for determining the arterial flow through the artery segment during one or more heart beat cycles or parts thereof. The determination of the coronary reserve (62) and relative coronary reserve (64) follow from the volume (54) and the flow through the artery. Alternatively, the coronary reserve is determined directly from a velocity profile relating to one or more fixed artery segments and the three-dimensional model.