The veno-arterial extracorporeal membrane oxygenation (VA-ECMO) support is a widely adopted procedure to provide oxygenated blood support in patients who underwent cardiac shock. Nevertheless, many pitfalls are linked with its usage, such as the risk of left ventricle (LV) afterload increase caused by the retrograde flow when VA-ECMO flow support is excessive [1]. The right balance between vessel perfusion and LV loading resides mainly in the clinician expertise. Numerical approaches represent a valid tool to investigate cardiovascular fluid dynamics [2,3] and they might be adopted to explore the afterload - perfusion balance in this context. The current work presents a computational study to define a correlation between ECMO level and both systemic pressure and arterial perfusion. The morphological data from CT imaging of a patient-specific aorta, including supra-aortic vessels, coronaries, renal and iliac arteries, was adopted. A set of computational fluid dynamic (CFD) simulations was defined. In particular, the healthy status plus three cardiac shock cases (mild, medium and severe) were simulated by reducing the healthy cardiac output. For each case, different levels of VA-ECMO support were simulated (0 - 6 l/min) by imposing a flow at left iliac vessel. The CFD results were processed to evaluate the systemic afterload and perfusion of arteries. A linear trend of the perfusion as a function of ECMO level support was successfully validated. Additionally, the minimum level of VA-ECMO support to grant the perfusion of all arteries and causing the minimum possible afterload increase was individuated and fitted with a linear model against different levels of cardiogenic shock. The results achieved represent a first significant step towards a prediction tool to assess the best level of VA-ECMO support in cardiac shock cases, in order to grant vessel perfusion and avoid unwanted and unnecessary pressure increases.