Blood vessel compliance is the amount of stretch that the blood vessels in veins or arteries have when they receive an increase in blood flow, and then that increase is diminished.  When you have an MRI part of the process, is to stimulate an increase of blood flow, reduce it and measure the elasticity of the vessels, to see how much they increased, and then how quickly they returned to their original or normal size.   As we age, this compliance or stretch is reduced and this can cause all kinds of health problems. Veins have a much higher compliance level because the walls of a vein are much thinner then artery walls.   If, as you age, the veins become too compliant or stretchy, a person can develop edema. Edema is an increase in the fluids of the bodies organs.  This is really an over-simplification of these terms, but it gives people an idea of why blood vessel compliance is an important factor in the well being of the human body.