Abstract: 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 si(t) for voxels (i) of said region of interest at a series of time values (t) 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 si(t) for said signal strength and an arterial input function v(t), determining values for the tissue residue function ri(t) for each said voxel; and optionally generating an image of said region of interest from the determined values of ri(t); the improvement comprising generating from si(t) a voxel specific arterial function vi(t) and using said voxel specific arterial function to determine the values of the tissue residue function ri(t).