Contrast enhancement is a key component of computed tomography (CT) imaging and offers opportunities for optimization. The design and optimization of techniques, however, require orchestration with the scan parameters and, further, a methodology to relate contrast enhancement and injection function. We used such a methodology to develop a method, the analytical inverse method, to predict the required injection function to achieve a desired contrast enhancement in a given organ by incorporation of a physiologically based compartmental model. The method was evaluated across 32 different target contrast enhancement functions for aorta, kidney, stomach, small intestine, and liver. The results exhibited that the analytical inverse method offers accurate performance with error in the range of 10% deviation between the predicted and desired organ enhancement curves. However, this method is incapable of predicting the injection function based on the liver enhancement. The findings of this study can be useful in optimizing contrast medium injection function as well as scan timing to provide more consistency in the way contrast-enhanced CT examinations are performed. To our knowledge, this work is one of the first attempts to predict the contrast material injection function for a desired organ enhancement curve.