Accuracy of the Bernoulli Equation for Estimation of Pressure Gradient Across Stenotic Blalock–Taussig Shunts: An In Vitro and Numerical Study

Abstract. Accurate assessment of the pressure gradient (PG) across a modified Blalock–Taussig (mBT) shunt is important in planning for staging to a cavopulmonary anastomosis for many patients with cyanotic congenital heart disease. The mBT shunt Doppler velocity has been used in the simplified echo Bernoulli equation to predict this PG with variable results. The purpose of this investigation is to provide analysis of the flow dynamics through stenotic mBT shunts and to assess the accuracy of Doppler techniques in determining PGs and the presence and location of stenosis. Three-dimensional models of mBT shunts were created, with and without stenosis. In vitro and computational fluid dynamic flow experiments were carried out. In vitro experiments demonstrated that the Doppler-measured PG underestimated catheter-measured PG in the mBT shunt with diffuse stenosis. In nonstenotic mBT and those that had outlet and inlet stenosis, the Doppler-measured PG showed underestimation of catheter PG at low PG and generally improved estimation at higher PG. In the mBT shunt model with inlet stenosis, there was slight overestimation at higher PG. Numerical simulations provide an ``observation window'' into events occurring in and around mBT shunts showing that the hemodynamics vary significantly. Changing hemodynamic processes are at work through stenotic mBT shunts causing variations in overestimation and underestimation of catheter-measured PG using the simplified echo Bernoulli equation. Our results have relevance to the assessment of patients with mBT shunts, helping to explain some of the discrepancies that investigators have found in the past.