A sensor for determining native cardiac output of a beating heart, comprising: an intravascular blood pump having a cannula, a rotor configured to be rotated within a blood vessel and pump blood through the cannula, and a drive mechanism configured to impart power to turn the rotor; a pressure sensor operationally positioned proximal or distal to the blood pump and configured to detect pressure within the blood vessel arising at least in part from the pumping of blood within the vessel; and a controller being electrically coupled to the pressure sensor and configured to detect signals from the pressure sensor indicative of blood pressure, and configured to calculate native cardiac output based on a non-linear model that correlates cardiac output to vascular resistance and compliance, characterized in that the controller is configured to: detect a first aortic pressure wave of the heart reflecting a plurality of beats of the heart, each reflected beat including a dicrotic notch; apply hemodynamic support to the heart at a first pumping rate during a first beat of the plurality of beats; adjust the hemodynamic support to the heart during a second beat of the plurality of beats by providing a second pumping rate to the heart during the second beat after its dicrotic notch; detect second aortic pressure wave of the heart during the second beat; compare the second aortic pressure wave to a portion of the first aortic pressure wave corresponding to the second beat to detect a change in the second aortic pressure wave and identify resistance and compliance of the aorta; and determine native cardiac output of the heart based on a non-linear transfer function programmed within the software, the transfer function relating cardiac output to aortic resistance and compliance. an intravascular blood pump having a cannula, a rotor configured to be rotated within a blood vessel and pump blood through the cannula, and a drive mechanism configured to impart power to turn the rotor; a pressure sensor operationally positioned proximal or distal to the blood pump and configured to detect pressure within the blood vessel arising at least in part from the pumping of blood within the vessel; and a controller being electrically coupled to the pressure sensor and configured to detect signals from the pressure sensor indicative of blood pressure, and configured to calculate native cardiac output based on a non-linear model that correlates cardiac output to vascular resistance and compliance, characterized in that the controller is configured to: detect a first aortic pressure wave of the heart reflecting a plurality of beats of the heart, each reflected beat including a dicrotic notch; apply hemodynamic support to the heart at a first pumping rate during a first beat of the plurality of beats; adjust the hemodynamic support to the heart during a second beat of the plurality of beats by providing a second pumping rate to the heart during the second beat after its dicrotic notch; detect second aortic pressure wave of the heart during the second beat; compare the second aortic pressure wave to a portion of the first aortic pressure wave corresponding to the second beat to detect a change in the second aortic pressure wave and identify resistance and compliance of the aorta; and determine native cardiac output of the heart based on a non-linear transfer function programmed within the software, the transfer function relating cardiac output to aortic resistance and compliance. detect a first aortic pressure wave of the heart reflecting a plurality of beats of the heart, each reflected beat including a dicrotic notch; apply hemodynamic support to the heart at a first pumping rate during a first beat of the plurality of beats; adjust the hemodynamic support to the heart during a second beat of the plurality of beats by providing a second pumping rate to the heart during the second beat after its dicrotic notch; detect second aortic pressure wave of the heart during the second beat; compare the second aortic pressure wave to a portion of the first aortic pressure wave corresponding to the second beat to detect a change in the second aortic pressure wave and identify resistance and compliance of the aorta; and determine native cardiac output of the heart based on a non-linear transfer function programmed within the software, the transfer function relating cardiac output to aortic resistance and compliance.