Apparatus for assessing a patient with a vascular stenosis and/or dysfunction, the apparatus comprising: a catheter (200, 210, 230, 310, 502) having a distal region sized and shaped to be advanced into an arterial vessel, the catheter (200, 210, 230, 310, 502) comprising a lumen (212, 242, 312) for delivering a fluid into the arterial vessel; a pressure sensor (201, 208, 306, 508, 510, 804) disposed at the distal region of the catheter (200, 210, 230, 310, 502) to measure a pressure; a reference pressure sensor (526, 528, 530) configured to measure a reference pressure at a location proximal to the distal region; and a controller (518, 1502) operatively coupled to the reference pressure sensor (526, 528, 530) and the pressure sensor (201, 208, 306, 508, 510, 804), the controller (518, 1502) configured to: cause the fluid to be delivered at a first volumetric flow rate through the lumen (212, 242, 312) into the arterial vessel; measure a first arterial pressure in the arterial vessel while the fluid is delivered at the first volumetric flow rate; cause the fluid to be delivered at a second volumetric flow rate through the lumen (212, 242, 312) into the arterial vessel; measure a second arterial pressure in the arterial vessel while the fluid is delivered at the second volumetric flow rate; and determine an equipoise volumetric flow rate at which the pressure corresponds to the reference pressure. a catheter (200, 210, 230, 310, 502) having a distal region sized and shaped to be advanced into an arterial vessel, the catheter (200, 210, 230, 310, 502) comprising a lumen (212, 242, 312) for delivering a fluid into the arterial vessel; a pressure sensor (201, 208, 306, 508, 510, 804) disposed at the distal region of the catheter (200, 210, 230, 310, 502) to measure a pressure; a reference pressure sensor (526, 528, 530) configured to measure a reference pressure at a location proximal to the distal region; and a controller (518, 1502) operatively coupled to the reference pressure sensor (526, 528, 530) and the pressure sensor (201, 208, 306, 508, 510, 804), the controller (518, 1502) configured to: cause the fluid to be delivered at a first volumetric flow rate through the lumen (212, 242, 312) into the arterial vessel; measure a first arterial pressure in the arterial vessel while the fluid is delivered at the first volumetric flow rate; cause the fluid to be delivered at a second volumetric flow rate through the lumen (212, 242, 312) into the arterial vessel; measure a second arterial pressure in the arterial vessel while the fluid is delivered at the second volumetric flow rate; and determine an equipoise volumetric flow rate at which the pressure corresponds to the reference pressure. cause the fluid to be delivered at a first volumetric flow rate through the lumen (212, 242, 312) into the arterial vessel; measure a first arterial pressure in the arterial vessel while the fluid is delivered at the first volumetric flow rate; cause the fluid to be delivered at a second volumetric flow rate through the lumen (212, 242, 312) into the arterial vessel; measure a second arterial pressure in the arterial vessel while the fluid is delivered at the second volumetric flow rate; and determine an equipoise volumetric flow rate at which the pressure corresponds to the reference pressure.