Validation of a Mathematical Model of Bidirectional Glenn Circulation With Aortopulmonary Collaterals and the Implications for Q_P/Q_S Calculation

Objectives: A mathematical model of the oxygen delivery kinetics of the bidirectional Glenn (BDG) shunt circulation incorporating aortopulmonary collateral (APC) flow was created. The model was used to characterize oxygen delivery and compare modeled data to actual patient data obtained using cardiac magnetic resonance imaging (MRI) and catheterization. In addition, cardiac MRI and catheterization assessment of pulmonary blood flow in the presence of APC flow were compared.

Design: Mathematical model and retrospective data analysis of patients who underwent cardiac MRI and catheterization. The mathematical model is based on the concept that APC flow to the lungs is recirculated pulmonary venous blood flow, which does not contribute to systemic oxygen delivery.

Setting: Single-center, university teaching hospital.

Participants: The study included 98 patients with BDG shunt undergoing cardiac MRI and cardiac catheterization.

Measurements and main results: In the absence of APC flow, the pulmonary blood flow to systemic blood flow ratio (Qp/Qs) calculated using cardiac catheterization data closely matched that obtained with cardiac MRI. In the presence of APC flow, Qp/Qs calculated using cardiac catheterization data systematically underestimated values obtained with cardiac MRI. A mathematical model of BDG shunt oxygen delivery incorporating variable APC flow was created. The model provided reasonable prediction of actual patient data for arterial blood oxygen, superior vena cava oxygen saturation, and oxygen delivery obtained at the time of cardiac catheterization in patients.

Conclusion: The oxygen delivery kinetics of a BDG shunt incorporating variable APC flow can be modeled mathematically. Model output can be used to predict blood oxygen saturation after coil embolization of APC flow in the cardiac catheterization laboratory.