An injection system includes an injector for injecting a fluid into a patient and a controller in operative communication with the injector for control thereof. The controller controls a diagnostic injection of the fluid based upon at least one mathematical model individualized to the patient. The model(s) are determined by collecting data corresponding to a time response curve resulting from at least one test injection of the fluid into the patient. The time response curve represents a response of a region of interest of the patient over time due to the fluid passing therethrough. An imaging system having such an injection system is also disclosed, as is a system for effecting a medical procedure. A method of delivering such a fluid to a patient using such an injection system is also disclosed, as is a method of modeling propagation of such a fluid in a patient.
