Power dissipation associated with surgical operations' hemodynamics: Critical issues and application to the total cavopulmonary connection

The issue of the correct determination of the mechanical power dissipated by the blood flow in the circulatory system is very important. This parameter is particularly critical when the patient's circulation has to overcome structural impairments, such as, e.g., in the case of only one functional ventricle. The surgical palliation of such a condition, which is a relatively common form of congenital heart disease, calls for an optimization of the new connection's hydrodynamics. Starting from the general formulation of the energy dissipation rate in a given control volume, this paper discusses the critical assumptions of the formula usually employed to assess the power dissipation in complex connections, such as the total cavopulmonary connection (TCPC). A new formula is derived, in which the mean elevation of the outlet and inlet sections is shown to be relevant, through the use of the piezometric pressure. Moreover, the flow profile at the boundary of the control volume is also important, since the usual approach implicitly assumes that the flow is perfectly flat: this assumption is doubtful, especially in the venous return (as in the TCPC). In the experimental part of the study, the power dissipation was measured in a physical model of the TCPC, and a large difference was found between the usual method and the proposed one, especially at low regime (85% relative difference, at 1.5 l/min total cardiac output). The proposed approach should be adopted in order to improve the accuracy of the hydrodynamical performance's assessment of surgical connections (e.g., TCPC) or implantable devices (e.g., valved conduit).