Closed-loop CFD Model of the Self-Powered Fontan Circulation for the Hypoplastic Left Heart Syndrome

The Fontan operation is the definitive step in creating a compatible circulation in SV patients. This type of procedure may fail due to the known decrease survival rate, and the inability of the systemic venous blood to pass through the lungs, which leads to further complications in the patient. To improve the Fontan circulation an injection jet shunt (IJS) from the single ventricle to the Fontan pulmonary arteries, is incorporated into the closed-loop circulation model to determine if the energy and momentum will effectively be transferred to the pulmonary artery circulation. Using ANSYS Fluent two models, a baseline and an IJS model, were compared in a steady state solution to determine the effectiveness of the IJS velocity outflow and energy transfer. After the analysis was performed it was determined that a vacuum pressure is created at the exit of the IJS, and that indeed the energy and momentum transfer to the pulmonary arteries, improves the Fontan circulation. INTRODUCTION Congenital heart disease (CHD) occurs in 1/150 newborn babies, 7.7% of whom have only a single chambered (single ventricle, SV) heart [1]. The complication of this physiological anomaly is responsible for a high mortality rate near 50% by age of 20. The Hypoplastic Left Heart Syndrome (HLHS) consists of patients that have an underdeveloped left heart. Their aorta and left ventricle are too small and septum did not mature correctly, as shown in Figure 1 [2]. The alternative to treat single-ventricle (SV) types of heart defects is surgical, by creating a compatible circulatory system [2]. This type of surgery is performed through a surgical staging process that leads to the Fontan circulation. This surgery allows venous blood to flow passively, without a pump, through the pulmonary arteries into the lungs. Even though this type of procedure seems as a solution for SV patients, it may fail due to the inability of the systemic venous blood to pass through the lungs, which leads to further complications of high systemic venous pressure and low cardiac output [1]. Due to the failures experienced with the Fontan circulation, researchers have suggested to incorporate an assisted mechanism that can help level the systemic circulation pressure and cardiac output by using a pump. Incorporating an external pump has complications, such as reliability of mechanical moving parts and thrombus formation [3]. Others have proposed developing a synthetic pump with ideal flow characteristics and without intravascular device complications, which seems to be an ideal solution but it is still under development [4]. As an alternative to the synthetic and external powered pump, this research proposes a modified Fontan loop circulation model, where an injection jet shunt (IJS) is positioned from the single ventricle to the pulmonary arteries directly. The objective is to determine if Figure 2: Sketch of "IJS" functionality [3] Figure 1: Difference between normal heart and HLHS heart [2] 1 Quintero et al.: Closed-loop CFD Model of the Self-Powered Fontan Circulation for Published by Scholarly Commons, 2016 2 incorporating an IJS from the single ventricle to the Fontan pulmonary arteries will effectively increase the energy and momentum transfer to improve the Fontan Circulation (i.e. increased pulmonary flow and decreased inferior caval pressure), shown in Figure 2. In order to demonstrate that the proposed IJS solution achieves most of the objectives of the idealized synthetic pump, a steady-flow analysis will be performed using computational fluid dynamics (CFD) with the ANSYS Fluent solver. This research paper seeks to present the methodology, mesh analysis, and fluid analysis to demonstrate the conceptual effectiveness of the surgical modification to the Fontan operation with the goal of preventing or treating the failing Fontan to increase the survival rate of the patients with SV. EQUATIONS The “injector jet” that is proposed works on a combination of the Venturi effect and direct momentum transfer. To demonstrate that the required energetics are achievable, we performed the following analytic calculation assuming a single orifice, or “nozzle”: If one wishes to reduce the gradient, (p), between the inferior vena cava (IVC) and atrium by an amount p by interposing a high velocity jet in the pulmonary artery (PA) flow direction, then the power provided by this jet must be Qpp + Qs(p), where Qs and Qp are the systemic and pulmonary blood flows, respectively [5]. The first term is the power required to drive the excess (jet) flow, and the second term is the supplemental power required to drive the baseline Fontan (venous) flow at the reduced IVC-atrial pressure gradient. The jet energy comes from the ventricle, producing a left-to-right “shunt fraction”, f = Qp/Qs. The jet power is thus (f-1)Qsv2, where v is the jet velocity. Setting this equal to the required power, we get is shown in Equation 1. (1) In cgs units, r = 1 and if pressure is in mmHg, we obtain Equation 2, below.