A computer-implemented method for estimating patient-specific values of perfusion of blood at locations in target tissue of a patient, the method comprising: receiving a patient-specific tissue model of said target tissue of the patient and a patient-specific vessel model of a vascular network supplying blood to the target tissue; receiving or calculating one or more patient-specific parameters at locations in said patient-specific vessel model and/or in said patient-specific tissue model, said patient-specific parameters comprising one or more medical image characteristics of the target tissue or of the vascular network, anatomical characteristics of the target tissue or vascular network, estimated perfusion territories within said target tissue, estimated blood supply to the target tissue, and/or estimated blood flow to the target tissue, as well as, optionally, one or more of patient characteristics, disease burden characteristics, and/or electromechanical measurements of the patient; determining an estimate of perfusion at locations in the target tissue, in one or more physiological states, using the patient-specific parameters at said locations in said patient-specific vessel model and/or tissue model and a machine learning algorithm trained, using a database, to map said patient-specific parameters at locations in patient vessel and/or target tissue models to perfusion at said locations, said database being a database of patients with known perfusion characteristics and containing said one or more of the patient-specific parameters at locations in the vessel and/or target tissue models of said patients with known perfusion characteristics, and measured perfusion data at those locations; and outputting the estimate of the perfusion of blood to an electronic display; the method further comprising: estimating one or more virtual perfusion images designed to simulate a SPECT or PET scan of the patient in one or more physiological states using the estimated perfusion of blood, wherein the estimation is performed by modeling contrast agent in the concentrations given by the perfusion estimates for the patient; and outputting the one or more virtual perfusion images to an electronic storage medium. receiving a patient-specific tissue model of said target tissue of the patient and a patient-specific vessel model of a vascular network supplying blood to the target tissue; receiving or calculating one or more patient-specific parameters at locations in said patient-specific vessel model and/or in said patient-specific tissue model, said patient-specific parameters comprising one or more medical image characteristics of the target tissue or of the vascular network, anatomical characteristics of the target tissue or vascular network, estimated perfusion territories within said target tissue, estimated blood supply to the target tissue, and/or estimated blood flow to the target tissue, as well as, optionally, one or more of patient characteristics, disease burden characteristics, and/or electromechanical measurements of the patient; determining an estimate of perfusion at locations in the target tissue, in one or more physiological states, using the patient-specific parameters at said locations in said patient-specific vessel model and/or tissue model and a machine learning algorithm trained, using a database, to map said patient-specific parameters at locations in patient vessel and/or target tissue models to perfusion at said locations, said database being a database of patients with known perfusion characteristics and containing said one or more of the patient-specific parameters at locations in the vessel and/or target tissue models of said patients with known perfusion characteristics, and measured perfusion data at those locations; and outputting the estimate of the perfusion of blood to an electronic display; the method further comprising: estimating one or more virtual perfusion images designed to simulate a SPECT or PET scan of the patient in one or more physiological states using the estimated perfusion of blood, wherein the estimation is performed by modeling contrast agent in the concentrations given by the perfusion estimates for the patient; and outputting the one or more virtual perfusion images to an electronic storage medium. estimating one or more virtual perfusion images designed to simulate a SPECT or PET scan of the patient in one or more physiological states using the estimated perfusion of blood, wherein the estimation is performed by modeling contrast agent in the concentrations given by the perfusion estimates for the patient; and outputting the one or more virtual perfusion images to an electronic storage medium.