In vitro measurement of hepatic flow distribution in Fontan vascular conduits: Towards rapid validation techniques

Fontan operation is the last stage of single-ventricle surgical reconstructions that connects superior and inferior vena cava (SVC, IVC) to the pulmonary arteries. The key design objectives in total cavopulmonary connections (TCPC) are to achieve low power loss (PL) and balanced hepatic flow distribution (HFD). Computational fluid dynamics (CFD) played a pivotal role in pre-surgical design of single-ventricle patients. However, the clinical application of current CFD techniques is limited due to their complexity, high computational time and untested accuracy for HFD prediction. This study provides a performance assessment of computationally low-cost steady Reynolds-Averaged Navier-Stokes (RANS) k-ɛ turbulent models for simulation of Fontan hemodynamics. The performance is evaluated based on prediction accuracy for three clinically important Fontan hemodynamic indices: HFD, PL and total pulmonary flow split (TPFS). For this purpose, a low-cost experimental technique is developed for rapid quantification of Fontan performance indices. Experiments and simulations are performed for both an idealized and a complex 3D reconstructed patient-specific TCPC. Time-averaged flow data from phase contrast MRI was used as the boundary conditions for the patient-specific model. For the idealized model, different SVC/IVC flow ratios corresponding to different cardiac outputs and Reynolds' numbers were examined. This study revealed that steady RANS k-ɛ models are able to estimate the Fontan hemodynamic indices with acceptable accuracy within minutes. Among these, standard k-ɛ two-layer was found to deliver the best agreement with the in vitro data with an average error percentage of 1.7, 2.0 and, 3.9 for HFD, TPFS and, PL, respectively for all cases.