Controlled Comparison of Simulated Hemodynamics Across Tricuspid and Bicuspid Aortic Valves

Abstract

Bicuspid aortic valve is the most common congenital heart defect, affecting 1–2% of the global population. Patients with bicuspid valves frequently develop dilation and aneurysms of the ascending aorta. Both hemodynamic and genetic factors are believed to contribute to dilation, yet the precise mechanism underlying this progression remains under debate. Controlled comparisons of hemodynamics in patients with different forms of bicuspid valve disease are challenging because of confounding factors, and simulations offer the opportunity for direct and systematic comparisons. Using fluid–structure interaction simulations, we simulate flows through multiple aortic valve models in a patient-specific geometry. The aortic geometry is based on a healthy patient with no known aortic or valvular disease, which allows us to isolate the hemodynamic consequences of changes to the valve alone. Four fully-passive, elastic model valves are studied: a tricuspid valve and bicuspid valves with fusion of the left- and right-, right- and non-, and non- and left-coronary cusps. The resulting tricuspid flow is relatively uniform, with little secondary or reverse flow, and little to no pressure gradient across the valve. The bicuspid cases show localized jets of forward flow, excess streamwise momentum, elevated secondary and reverse flow, and clinically significant levels of stenosis. Localized high flow rates correspond to locations of dilation observed in patients, with the location related to which valve cusps are fused. Thus, the simulations support the hypothesis that chronic exposure to high local flow contributes to localized dilation and aneurysm formation.

Appendix

We conducted a convergence study to evaluate the sensitivity of the velocity fields, flow and pressure waveforms, and integral metrics to changes in simulation resolution. We selected the bicuspid case with left/right coronary cusp fusion for the study, as we wanted a bicuspid case to evaluate the amount of stenosis caused by geometric changes to the valve as compared with resolution. We ran otherwise identical simulations with fluid resolutions of $\Delta x = 0.1, 0.075, 0.05$ and 0.0375 cm, where $\Delta x = 0.05$ cm is the fluid resolution used throughout the study.

Precise convergence is difficult to achieve in these flows for a variety of numerical and physical reasons. First, the IB method effectively thickens the structure due to $\delta$-function based, diffuse-interface coupling. This coupling makes the effective orifice area and thus resistance to forward flow resolution-dependent. Further, the boundary conditions at the outlet are determined in a coupled manner with flow through the valve. Resistance due to the flow-averaging force is also dependent on flow rate. Additionally, the Reynolds number of such flows is in an inertial, potentially transitional, and thus physically unstable regime, which makes precise pointwise agreement in velocity fields impossible.

We see agreement, despite these limitations, between the resolutions in velocity fields, waveforms and integral metrics, as shown in Fig. 7. Qualitative trends in the velocity fields are consistent across all resolutions. The flow fields show increasing detail with resolution, as expected given the potentially transitional Reynolds number of the flow. At the coarsest resolution, the jet appears narrower when leaving the valve orifice, indicating insufficient resolution. At the finest two resolutions, the jets, regions of reverse flow and regions of recirculation are qualitatively similar.

On the two finest resolutions, $\Delta x = 0.05$ and 0.0375 cm, the total cumulative flows are 170.7 and 173.2 mL, respectively, a relative change of 1.4%, and these simulations show sustained pressure gradients above 18 and 15 mmHg, respectively. Thus, the two finest resolutions show similar flow rates and levels of stenosis. With $\Delta x = 0.1$ and 0.075 cm the total flow is 148.9 and 119.8 mL, respectively, and these simulations show sustained pressure gradients above 25 and 30 mmHg, respectively. We conclude that the two more coarse resolutions are under-resolved.

The integral metric curves show identical trends on the two finest resolutions. The values of $I_{1}$, $I_{2}$ and $I_{\text {R}}$ are very similar at the two finest scales. At the coarsest resolution, $\Delta x = 0.1$ cm, the values of $I_{1}$ are elevated relative to other cases, $I_{2}$ shows subtly different trends and elevated values, especially at slice 3, from finer resolution. We conclude that the most coarse resolution, which we do not use elsewhere, is inadequate to evaluate such metrics. For all metrics that show agreement at the finer scales, the values do not precisely agree pointwise in time because of the unsteady nature of the flow, which also causes the non-smooth appearance of the curves.

Thus, we believe that our conclusions throughout this work would be consistent with our selected resolution of $\Delta x = 0.05$ cm or increased resolution of 0.0375 cm. We consider results with $\Delta x = 0.05$ cm to be well-resolved and use this resolution throughout the study.

Fig. 7

Convergence study with the bicuspid valve with LC/RC fusion and varying resolution. a Fluid velocity, vertical component and velocity normal to five selected slices. The color scheme is identical to that of Fig. 2. b Flow and pressure waveforms. c Values of integral metrics (values of $I_{1}$ above 2.6 in the $\Delta x = 0.1$ cm case are truncated).