A method is provided for optimizing a contrast injection function for CT imaging. The method includes injecting, with an injector pump, a test bolus of a contrast agent into a subject. The method also includes computing, on a processor, an impulse enhancement function. The method also includes determining, on a processor, a target enhancement function for a region of interest. The method also includes determining, with a processor, a plurality of parameters for a functional form for a contrast injection function in a time domain. The method also includes determining for the contrast injection function a constraint. The method also includes determining, with a processor, particular values for the plurality of parameters, which satisfy the constraint and minimize a difference between a value of an enhancement function and the target enhancement function computed in the time domain at discrete time periods without use of a Fourier transform.