Appraisal of partial anomalous pulmonary venous drainage through a lumped-parameter mathematical model: a new pathophysiological proof of concept.

Objectives: Haemodynamic determinants of the ratio between pulmonary and systemic flow (Qp/Qs) in partial anomalous pulmonary venous return (PAPVR) are still not fully understood. Indeed, among patients with the same number of lung segments draining anomalously, a great variability is observed in terms of right ventricular overload. The aim of this study was to test the hypothesis that the anatomic site of drainage, affecting the total circuit impedance, independently influences the magnitude of shunt estimated by Qp/Qs. A zero-dimensional lumped parameter mathematical model was developed and validated on a sample of patients.

Methods: We developed a zero-dimensional lumped parameter model, using time-varying elastances for heart chambers, RLC Windkessel circuits for the systemic and pulmonary circulations. Patients were categorized into vena cava (VC) type (including left drainage to anomalous vein) and right atrium (RA) type. The mathematical model is a system of ordinary differential equations that are numerically solved by means of the ode15s solver in the MATLAB environment.

Results: The model showed an increase of Qp/Qs with the increase of the number of anomalous veins. With the same number of anomalous veins, Qp/Qs was lower in patients with anomalous drainage to the VC as compared with RA. The validation sample consisted of 49 patients (27, 55% females). As predicted by the model, patients with PAPVR with VC type displayed a lower invasive and cardiac magnetic resonance Qp/Qs as compared with drainage to RA: 1.4 (1.2-1.7) and 1.45 (1.25-1.6) versus 2 (1.75-2.1) and 1.9 (1.6-2), P < 0.05. After stratifying for number of lung territories, a lower Qp/Qs was measured in patients with VC PAPVR as compared with RA.

Conclusions: In patients with PAPVR, the site of anomalous drainage modulates the Qp/Qs. According to the model, this effect is mediated by the post-capillary impedance of the circuit and significantly decreases with the increase of pulmonary vascular resistances.