A Patient-based Computational Model that Predicts Pressure Drop in Supravalvar Aortic Stenosis in Patients with Williams Syndrome
Assessment of supravalvar aortic stenosis (SVAS) severity in Williams syndrome (WS) is often complicated by the discrepancy in pressure drops obtained via peak-instantaneous Doppler and peak-to-peak cardiac catheterization measurements. With SVAS, static pressure in the left ventricle is converted to kinetic energy, maximal at the vena contracta, some of which is recovered through pressure energy and some of which is lost through thermal energy and deformation. The phenomenon of pressure recovery (PR) is distance-dependent relative to the area of stenosis. We hypothesized that PR explains the discrepancy in catheterization and echocardiographic data, and sought to analyze this using a computational model developed from patient data.
We reviewed all pre-intervention echocardiograms in WS patients with SVAS cared for at our center and measured the aortic annulus, sinotubular junction, and peak Doppler gradients. We used these data to develop a computational model for PR in the setting of variable degrees of SVAS assuming a fixed flow rate of 6 L/min. The model is based on solving the Navier-Stokes equations and considers steady-state flow through an idealized SVAS geometry. Pressure is computed along the centerline of the cavity.
We analyzed 91 echocardiograms in 26 children (65% male) with WS (median age at scan: 0.89 years, IQR: 0.3-2.4 and median echocardiograms: 2, IQR: 1.3-5.8). Median peak SVAS Doppler gradient was 27 mmHg (IQR: 14-49). The model demonstrated more extreme pressure drops and later PR at increasing severity of SVAS. (Figure)
Using patient-derived anatomic data, our computational model of SVAS shows distance to PR depends on the degree of stenosis. Our model explains the discrepancy between Doppler and catheter-derived gradients and highlights the importance the distance from SVAS plays in variations in catheter-based measurements. This model could be used to predict the expected difference between Doppler and catheter-derived pressure drops.