Functional analysis of Fontan energy dissipation

Abstract

We formalize the hydrodynamic energy dissipation in the total cavopulmonary connection (TCPC) using dimensional analysis and examine the effect of governing flow variables; namely, cardiac output, flow split, body surface area, Reynolds number, and certain geometric characteristics. A simplistic and clinically useful mathematical model of the dependence of energy dissipation on the governing variables is developed. In vitro energy loss data corresponding to six patients’ anatomies validated the predicted dependency of each variable and was used to develop a predictive, semi-empirical energy dissipation model of the TCPC. It is shown that energy dissipation is a cubic function of pulmonary flow split in the physiological range. Furthermore, non-dimensional energy dissipation, which is a measure of resistance of the connection, is dependent on Reynolds number and geometrical factors alone. Non-dimensional energy dissipation decreases with Reynolds number as Re −0.25 ( R 2>0.95). In addition, for high Reynolds numbers, within physiological exercise limits, dissipation strongly correlates to minimum PA area as a power law decay with an exponent of −5/4 ( R 2>0.88). This study presents a simple analytical form of energy dissipation rate in complex patient-specific TCPCs that accurately captures the effect of cardiac output, flow split, body surface area, Reynolds number, and pulmonary artery size within physiological limits. Further studies with larger sample sizes are necessary for incorporating finer geometrical parameters such as vessel curvatures and offsets.