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Abstract Objective(s) The Fontan procedure is a common palliative intervention for sufferers of single ventricle congenital heart defects that results in an anastomosis of the venous return to the pulmonary arteries called the total cavopulmonary connection (TCPC). In patients with palliated single ventricular heart defects, the Fontan circulation passively directs systemic venous return to the pulmonary circulation in the absence of a functional sub-pulmonary ventricle. Therefore, the Fontan circulation is highly dependent on favourable flow and energetics, and minimal energy loss is of great importance. The majority of in vitro studies, to date, employ a rigid TCPC model. Recently, few studies have incorporated flexible TCPC models, without the inclusion of commercially available conduits used in these surgical scenarios. Method The methodology set out in this study successfully utilizes patient-specific phantoms along with the corresponding flowrate waveforms to characterise the flow haemodynamic performance of extracardiac Gore-Tex conduits. This was achieved by comparing a rigid and flexible TCPC models against a flexible model with an integrated Gore-Tex conduit. Results The flexible model with the integrated Gore-Tex graft exhibited greater levels of energy losses when compared to the rigid walled model. With this, the flow fields showed greater levels of turbulence in the complaint and Gore-Tex models compared to the rigid model under ultrasound analysis. Conclusion This study shows that vessel compliance along with the incorporation of Gore-Tex extracardiac conduits have significant impact on the flow haemodynamics in a patient-specific surgical scenario.