Embodiments relate to non-invasively determining coronary circulation parameters during a rest state and a hyperemic state for a patient. The blood flow in the coronary arteries during a hyperemic state provides a functional assessment of the patient's coronary vessel tree. Imaging techniques are used to obtain an anatomical model of the patient's coronary tree. Rest boundary conditions are computed based on non-invasive measurements taken at a rest state, and estimated hyperemic boundary conditions are computed. A feedback control system performs a simulation matching the rest state utilizing a model based on the anatomical model and a plurality of controllers, each controller relating to respective output variables of the coronary tree. The model parameters are adjusted for the output variables to be in agreement with the rest state measurements, and the hyperemic boundary conditions are accordingly adjusted. The hyperemic boundary conditions are used to compute coronary flow and coronary pressure variables.