Characterization of Post-Operative Hemodynamics Following the Norwood Procedure Using Population Data and Multi-Scale Modeling

FIGURE 1. Anatomical configuration after the (A) stage I Norwood procedure and (B) stage II Bidirectional Glenn (Migliavacca et al., 2002).

FIGURE 2. Modeling approach used to reconstruct anatomy of representative HLHS patient geometry at two time-points–post-S1 and pre-S2. Anatomy was constructed from (A) patient-specific MRI data that was then (B) scaled to match literature-based morphological data for both time-points (Machii and Becker, 1997; Mahle et al., 1998; Malec et al., 2003; Fiore et al., 2011; Bellsham-Revell et al., 2013; Aiyagari et al., 2014). The slight degree of tapering at each anastomosis of the shunt can be observed.

FIGURE 3. (A) The 3D-0D multi-domain framework utilized to simulate hemodynamics in both post-S1 and pre-S2 models. The geometry corresponding to the pre-S2 model is shown. Outlets with “W” correspond to a Windkessel boundary condition (B). Outlet with “H” corresponds to the heart model boundary condition. (B) 0D heart model coupled to the ascending aorta inlet face. A plot of time-varying elastance to model the contraction and relaxation of the right ventricle (RV) is included. (C) Three-element Windkessel model representing the distal vasculature applied to all outlets. Abbreviations: L, inductor; D, diode; RPA, right pulmonary artery; LPA, left pulmonary artery; P, pressure; Q, flow; RV, right ventricle; RA, right atrium; Rp, proximal resistance; Rd, distal resistance; C, compliance; AVV, atrioventricular valve; NAoV, neo-aortic valve. Calibrated LPN parameter values are listed in Table 4.

FIGURE 4. (A) Reconstructed geometry with volume-rendering of MRA data and three different PC-MRI planes. (B) Plot of dynamic luminal area changes and percent luminal area changes at the ascending aorta, transverse arch and descending aorta PC-MRI planes. (C) Material properties applied to both the post-S1 and pre-S2 models. Stiffness values were calculated based on patient-specific pressure measurements and dynamic luminal area changes measured from MRI data (Hirai et al., 1989).

FIGURE 5. Left: Comparison of simulated results (red) and literature-based clinical data (blue) of hemodynamic indices for post-S1 and pre-S2 models. All indices were matched within 10% of literature values. Right: Volume renders of FSI simulations velocity maps.

FIGURE 6. Simulated pulsatile flow waveforms at all boundaries of the 3D domain for both post-S1 (orange) and pre-S2 (blue) models. All outflows are plotted as positive and all inflows are plotted as negative. Note that three different y-axis scales have been used: one for the descending aorta, another for the ascending aorta and a third for the remainder of the outlets. A volume rendering of velocity magnitude for the pre-S2 model is shown during peak-systole (t = 0.21 s).

FIGURE 7. Simulated pulsatile pressures at all boundaries of the 3D domain for both post-S1 (orange) and pre-S2 (blue) models. Arrows indicate whether pressure increased or decreased from post-S1 to pre-S2. Note that two different y-axis scales have been used: one for the LPA and RPA, and a second for the remainder of the outlets. A pressure coloring on the surface of the pre-S2 model is shown during peak-systole (t = 0.21 s).

FIGURE 8. Velocity streamlines for both post-S1 and pre-S2 models during peak systole (t = 0.21 s). Disturbed flow patterns are prominent at the mBTTs-PA anastomosis and propagate throughout the PAs. Surface plots of WSS (center) in the PAs are presented for both models. There are concentrations of high WSS where the mBTTs flow impacts the wall of the PA. The WSS experienced in the PAs slightly increases during the interim period between stage I and II. Finally, velocity profiles at the mBTTs, LPA, and RPA (bottom) and their corresponding time average and peak systolic Reynolds numbers. High Reynolds numbers (>2,000) are indicative of turbulence and can be seen within the mBTTs and PAs. These Reynolds numbers increase from post-S1 to pre-S2.

FIGURE 9. Top: The various isotropic linear finite element meshes generated for the mesh-independence analysis for both Post-S1 and Pre-S2 models. Finer meshes are generated by incrementally decreasing the global element size (L). Bottom: Results from the mesh independence analysis. Flow at the LPA and RPA are plotted for both Post-S1 and Pre-S2 at each mesh size–coarse (orange), fine (blue), and very fine (green). As seen in each plot, there is little alteration in mean flow values in the PAs and the high-frequency oscillation is present in all cases.

FIGURE 10. The evolution of hemodynamic indices from ∼7 days of age at post-S1 to ∼5 months of age at pre-S2.