The model for perfusion images calls for a "delta" function -- in other words, all the contrast material would appear at one point in time (still, the amount is proportional to flow) and disappear.

It takes time to inject contrast material, and because the body mixes contrast with blood, the true input function is more like a bell curve. If this function can be sampled, the effects of it not being a true delta function can be corrected, using a process called "convolution".

The common method of correction is to measure a vessel and use its intensity profile as a model of the input function.

While this sounds reasonable, the effects of flow-related turbulence on signal intensity is a confounding factor that is difficult to correct. This assumption is more valid for a modality like CT where turbulence does not affect signal intensity.