In Silico Evaluation of a Self-powered Venous Ejector Pump for Fontan Patients

Purpose The Fontan circulation carries a dismal prognosis in the long term due to its peculiar physiology and lack of a subpulmonic ventricle. Although it is multifactorial, elevated IVC pressure is accepted to be the primary cause of Fontan's high mortality and morbidity. This study presents a self-powered venous ejector pump (VEP) that can be used to lower the high IVC venous pressure in single-ventricle patients. Methods A self-powered venous assist device that exploits the high-energy aortic flow to lower IVC pressure is designed. The proposed design is clinically feasible, simple in structure, and is powered intracorporeally. The device's performance in reducing IVC pressure is assessed by conducting comprehensive computational fluid dynamics simulations in idealized total cavopulmonary connections with different offsets. The device was finally applied to complex 3D reconstructed patient-specific TCPC models to validate its performance. Results The assist device provided a significant IVC pressure drop of more than 3.2 mm Hg in both idealized and patient-specific geometries, while maintaining a high systemic oxygen saturation of more than 90%. The simulations revealed no significant caval pressure rise (< 0.1 mm Hg) and sufficient systemic oxygen saturation (> 84%) in the event of device failure, demonstrating its fail-safe feature. Conclusions A self-powered venous assist with promising in silico performance in improving Fontan hemodynamics is proposed. Due to its passive nature, the device has the potential to provide palliation for the growing population of patients with failing Fontan. Supplementary Information The online version contains supplementary material available at 10.1007/s13239-023-00663-5.


Impact of aortic pulsatility and CFD model on the VEP performance
In order to investigate the impact of aortic pulsatility on the device performance, one case (VEP with 1 DO TCPC) was simulated using a pulsatile aortic pressure. A physiological aortic pressure waveform with a mean aortic pressure and pulse pressure of 51.1 mm Hg and 40 mm Hg, respectively, was considered for the aortic graft inlet boundary condition. The aortic graft total pressure was assigned as the boundary condition. Unsteady RANS with the same computational schemes described in the main text was utilized. A second-order temporal discretization with a time step of 1 ms was considered. A residual reduction of e-4 was considered for the inner iterations. Figure S1.1 depicts the temporal variations of the Fontan hemodynamics with a pulsatile aortic pressure. Table S1.1 compares the hemodynamic indices for time-averaged pulsatile and steady time-averaged aortic pressure boundary conditions. As it can be observed, the device performance strongly correlates with the mean flow characteristics thus showing the validity of a time-averaged aortic boundary condition. More importantly, this result reveals the ability of the VEP to significantly increase the pulmonary arterial pulsatility which is believed to improve the pulmonary vascular health and reduce the pulmonary vascular resistance. Moreover, to examine the impact of implemented CFD model on the time-averaged device and Fontan hemodynamic indices, the same physics was simulated using large eddy simulation (LES) CFD model with the settings similar to reference [1]. Figure S1.2 and Table S1.2 present the device performance and Fontan hemodynamic metrices for the two CFD models. No significant difference is observed between time-averaged values showing the validity of using Reynolds averaged turbulence models.  Figure S1.2. Impact of aortic pulsatility on the Device performance and Fontan hemodynamics using two CFD models.

FDA nozzle benchmark validation
The exhaustion of the aortic nozzle jet in the VEP resembles the flow physics of the FDA nozzle jet expansion; however, the presence of a cross-flow from the IVC side and its interaction with the aortic jet as well as the atrial discharge contributes to a more complex and turbulent flow characteristic with the possible earlier transition. Therefore, the FDA nozzle with a Reynolds number of 6500 was selected as the most relevant case to account for a more turbulent flow profile in VEP. Figure S2.1.1 represents the centerline velocity variation predicted by the CFD solver settings used in this study as well as the available experimental data in the literature [2]. Good agreement can be observed between the CFD predicted flow and the experimental data for both the centerline velocity and the jet breakdown location. Figure S2.1.1 Comparison of axial velocity from CFD simulation and the available PIV data along the centerline of the benchmark FDA nozzle. The CFD represents the same solver settings used to asses the venous ejector pump performance in this study. The experimental data (EXP) are the average values taken from a multi-laboratory study [2]. The error bars represent the standard deviation from the average.

Device-specific pressure validation
To assess and validate the pressure prediction accuracy of the employed computational fluid dynamics solver settings, an experimental validation was conducted in our laboratory ( Figure   S2.2.2). The VEP with throat and aortic nozzle diameters of 8 mm and 2.5 mm, respectively, and no atrial discharge was considered for this experiment. The protype was 3D printed using stereolithography (Form 3, Formlabs, Somerville, MI, USA). A magnetically coupled centrifugal pump (Xylem, Washington, USA) was used to generate steady flow to the IVC and aortic graft.
The flow into the IVC and aortic graft was adjusted using pinchcock tube clamp (Bochem instrumente GmbH, Weilburg, Germany) and was measured using clamp-on ultrasonic flowmeters   idealized and patient-specific models, respectively, as well as excellent systemic oxygen concentration in these patient groups. The beauty of the proposed design is its simplicity and the fact that it can be readily 3D printed using surgical and bio-compatible materials with ultra-low costs based on patient size in any clinical centers or research laboratories. However, we acknowledge that the full spectrum of the blood damage characteristics and thrombogenicity has to be investigated and studied in great details which we believe is beyond the purview of the present manuscript and requires a separate dedicated study. The most important aspect of the design is that if the two grafts (atrial discharge and aortic) that are the most susceptible parts to thrombus formation get completely occluded, the circulation returns to its TCPC pre-VEP conditions with the minimal damage to the patient as evident in the

Impact of respiration-induced pulsatility on the device performance
Although the caval flow in Fontan patients lacks pulsatility due to absence of a subpulmonary ventricle, respiration-induced pulsatility have been shown to be significant in these patient groups [3]. The pulsatility level is quantified using respiratory dependency (RD) parameter as [4]:  Previously discussed physiological aortic pressure waveform was used as the inlet boundary condition for the aortic graft inlet. Table S5.1 summarizes the time-averaged hemodynamic indices over one respiratory cycle. The first cycle of the simulations was ignored due to starting effects. Interestingly, the IVC pressure reduction efficiency of the VEP has a negative correlation with the respiration-induced pulsatility in which higher pulsatility levels resulted in lower IVC pressure and thus improved device performance. Therefore, the conclusions reached using no respirationinduced pulsatility in the manuscript are valid as the pulsatility improves the performance.

Details of CFD simulation data
In this section, the details of the computational results for all cases are reported.