the invention provides , in a method of perfusion magnetic resonance imaging of a region of interest in a vascularized animal subject , said method comprising administering a contrast agent bolus into the vascular system of said subject ; determining the magnetic resonance signal strength s i for voxels of said region of interest at a series of time values over a period from before contrast agent arrival in said region of interest to at least the end of the first pass of said contrast agent through said region of interest ; from the determined values s i for said signal strength and an arterial input function v , determining values for the tissue residue function r i for each said voxel ; and optionally generating an image of said region of interest from the determined values of r i ; the improvement comprising generating from s i a voxel specific arterial function v i and using said voxel specific arterial function to determine the values of the tissue residue function r i .