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).
