Single ventricle malformations are complex congenital heart defects which require a three-stage surgical treatment, starting from the very first days of life, to separate the systemic and pulmonary circulations, and restore the serial circuit occurring in normal patients. The final surgery results in a total cavopulmonary connection (TCPC), where both the superior and the inferior vena cava are connected to the right pulmonary artery. Several clinical and computational studies have been done to optimize the geometry of the TCPC, with the aim of minimizing energy losses and improving surgical outcomes. To date, only few modeling studies have taken into account respiration and exercise as important factors to quantify the performance of a Fontan geometry. The objective of this work is to test the dependence of fluid dynamic variables and energy efficiency on respiration in patient-specific models of Fontan circulation, when subjected to exercise tests.|A closed-loop multiscale approach was used, including a simple respiration model that modulates the extravascular pressures in the thoracic and abdominal cavities, to generate physiologic time-varying flow conditions. A lumped parameter network (LPN) representing the whole circulation was coupled to a patient-specific 3D finite volume model of the preoperative bidirectional cavo-pulmonary anastomosis (BCPA) with detailed pulmonary anatomy. Subsequently, three virtual TCPC alternatives were coupled to the LPN and investigated in terms of both local and global hemodynamics. In particular, a T-junction of the venae cavae to the pulmonary arteries, a design with an offset between the venae cavae and a Y-graft design were compared under exercise conditions.|Results showed that the BCPA model is able to realistically capture oscillations due to both cardiac and respiratory effects, when compared to the venous Doppler velocity tracings acquired preoperatively on the patient.|The differences in hemodynamics between the three investigated TCPC options were minimal and similar to those obtained without inclusion of respiratory effects. Hence, the three surgical options result to be equivalent according to the analyzed parameters. Moreover, although the simulation of the Fontan circulation with a respiratory model requires a longer computational time, the developed framework allows for a more physiologic method to incorporate respiratory effects that was not possible using other methods.