Peripheral veno-arterial extra corporeal membrane oxygenation (VA-ECMO) is an established technique for short-to-medium support of patients with severe cardiac failure. However, in patients with concomitant respiratory failure, the residual native circulation will provide deoxygenated blood to the upper body, and may cause differential hypoxemia of the heart and brain. In this paper, we present a general computational framework for the identification of differential hypoxemia risk in VA-ECMO patients. A range of different VA-ECMO patient scenarios for a patient-specific geometry and vascular resistance were simulated using transient computational fluid dynamics simulations, representing a clinically relevant range of values of stroke volume and ECMO flow. For this patient, regardless of ECMO flow rate, left ventricular stroke volumes greater than 28 mL resulted in all aortic arch branch vessels being perfused by poorly-oxygenated systemic blood sourced from the lungs. The brachiocephalic artery perfusion was almost entirely derived from blood from the left ventricle in all scenarios except for those with stroke volumes less than 5 mL. Our model therefore predicted a strong risk of differential hypoxemia in nearly all situations with some residual cardiac function for this combination of patient geometry and vascular resistance. This simulation highlights the potential value of modelling for optimising ECMO design and procedures, and for the practical utility for personalised approaches in the clinical use of ECMO.