A contrast medium injector for injecting a patient with contrast medium for a CT scan is programmed to provide an injection protocol that is a representation of an ideally defined exponential curve with an initial injection rate decaying at an exponential rate. This has been found to produce a uniform vascular enhancement for the scanning of a patients blood vessels. The particular exponential decay coefficient which has been found to be optimal is directly proportional to the cardiac output divided by the patients weight and is approximated at 0.01 for a typical human.