A computer implemented method for simulating microvascular networks from a vascular tree model to simulate tissue perfusion under various physiological conditions, the method comprising: receiving a patient-specific vascular model of a patient's anatomy, including a vascular network comprising one or more arteries, arterioles, or capillaries; receiving a patient-specific target tissue model in which a blood supply may be estimated; characterized in that the method further comprises: measuring patient-specific intensity variations per segment inside the target tissue; generating a perfusion attenuation map based on measured patient-specific intensity variations; determining, using a processor, associations between the arteries of the vascular network of the patient-specific vascular model and their corresponding perfusion territories in the target tissue using joint prior information and the perfusion attenuation map, joint prior information including at least one of: the spatial location of the vessels and/or the arteries, the geometry, the absence or presence of stenosis, and physiological constraints; generating and outputting, using a processor, a vascular tree model that extends to perfusion regions in the target tissue, using the determined associations between the arteries of the vascular network of the patient-specific vascular model and their corresponding perfusion territories in the target tissue; and simulating perfusion inside the target tissue using the vascular tree model, including calculating an estimation of the supplied blood to each area of the target tissue under a first physiological state, and calculating an estimation of the supplied blood to each area of the target tissue under a second physiological state. receiving a patient-specific vascular model of a patient's anatomy, including a vascular network comprising one or more arteries, arterioles, or capillaries; receiving a patient-specific target tissue model in which a blood supply may be estimated; characterized in that the method further comprises: measuring patient-specific intensity variations per segment inside the target tissue; generating a perfusion attenuation map based on measured patient-specific intensity variations; determining, using a processor, associations between the arteries of the vascular network of the patient-specific vascular model and their corresponding perfusion territories in the target tissue using joint prior information and the perfusion attenuation map, joint prior information including at least one of: the spatial location of the vessels and/or the arteries, the geometry, the absence or presence of stenosis, and physiological constraints; generating and outputting, using a processor, a vascular tree model that extends to perfusion regions in the target tissue, using the determined associations between the arteries of the vascular network of the patient-specific vascular model and their corresponding perfusion territories in the target tissue; and simulating perfusion inside the target tissue using the vascular tree model, including calculating an estimation of the supplied blood to each area of the target tissue under a first physiological state, and calculating an estimation of the supplied blood to each area of the target tissue under a second physiological state. measuring patient-specific intensity variations per segment inside the target tissue; generating a perfusion attenuation map based on measured patient-specific intensity variations; determining, using a processor, associations between the arteries of the vascular network of the patient-specific vascular model and their corresponding perfusion territories in the target tissue using joint prior information and the perfusion attenuation map, joint prior information including at least one of: the spatial location of the vessels and/or the arteries, the geometry, the absence or presence of stenosis, and physiological constraints; generating and outputting, using a processor, a vascular tree model that extends to perfusion regions in the target tissue, using the determined associations between the arteries of the vascular network of the patient-specific vascular model and their corresponding perfusion territories in the target tissue; and simulating perfusion inside the target tissue using the vascular tree model, including calculating an estimation of the supplied blood to each area of the target tissue under a first physiological state, and calculating an estimation of the supplied blood to each area of the target tissue under a second physiological state.