An apparatus for quantifying a cardiac output of a patient operably connected to an extracorporeal blood oxygenation circuit; the extracorporeal blood oxygenation circuit having a venous line withdrawing blood from a circulatory system of the patient, a blood oxygenator, a pump, and an arterial line returning oxygenated blood to a venous portion of the circulatory system; the apparatus comprising: a controller configured to connect to one of the blood oxygenator and the pump, the controller configured to calculate a cardiac output of the patient based on: (i) a measured flow rate of oxygenated blood from the extracorporeal blood oxygenation circuit, (ii) a first arterial carbon dioxide content or surrogate of the first arterial carbon dioxide content and a first carbon dioxide content or surrogate of the first carbon dioxide content of the blood delivered to the patient circulatory system measured during a first flow rate of sweep gas through the blood oxygenator in the extracorporeal blood oxygenation circuit; and (iii) a second arterial carbon dioxide content or surrogate of the second arterial carbon dioxide content and a second carbon dioxide content or surrogate of the second carbon dioxide content of the blood delivered to the patient circulatory system measured during a second flow rate of sweep gas through the blood oxygenator in the extracorporeal blood oxygenation circuit. the extracorporeal blood oxygenation circuit having a venous line withdrawing blood from a circulatory system of the patient, a blood oxygenator, a pump, and an arterial line returning oxygenated blood to a venous portion of the circulatory system; the apparatus comprising: a controller configured to connect to one of the blood oxygenator and the pump, the controller configured to calculate a cardiac output of the patient based on: (i) a measured flow rate of oxygenated blood from the extracorporeal blood oxygenation circuit, (ii) a first arterial carbon dioxide content or surrogate of the first arterial carbon dioxide content and a first carbon dioxide content or surrogate of the first carbon dioxide content of the blood delivered to the patient circulatory system measured during a first flow rate of sweep gas through the blood oxygenator in the extracorporeal blood oxygenation circuit; and (iii) a second arterial carbon dioxide content or surrogate of the second arterial carbon dioxide content and a second carbon dioxide content or surrogate of the second carbon dioxide content of the blood delivered to the patient circulatory system measured during a second flow rate of sweep gas through the blood oxygenator in the extracorporeal blood oxygenation circuit. (i) a measured flow rate of oxygenated blood from the extracorporeal blood oxygenation circuit, (ii) a first arterial carbon dioxide content or surrogate of the first arterial carbon dioxide content and a first carbon dioxide content or surrogate of the first carbon dioxide content of the blood delivered to the patient circulatory system measured during a first flow rate of sweep gas through the blood oxygenator in the extracorporeal blood oxygenation circuit; and (iii) a second arterial carbon dioxide content or surrogate of the second arterial carbon dioxide content and a second carbon dioxide content or surrogate of the second carbon dioxide content of the blood delivered to the patient circulatory system measured during a second flow rate of sweep gas through the blood oxygenator in the extracorporeal blood oxygenation circuit.