Modeling the hepatic arterial flow in living liver donor after left hepatectomy and postoperative boundary condition exploration

Preoperative and postoperative hepatic perfusion is modeled with one-dimensional (1-D) Navier-Stokes equations. Flow rates obtained from ultrasound (US) data and impedance resulted from structured trees are the inflow and outflow boundary condition (BC), respectively. Structured trees terminate at the size of the arterioles, which can enlarge their size after hepatectomy. In clinical studies, the resistance to pulsatile arterial flow caused by the microvascular bed can be reflected by the resistive index (RI), a frequently used index in assessing arterial resistance. This study uses the RI in a novel manner to conveniently obtain the postoperative outflow impedance from the preoperative impedance. The major emphasis of this study is to devise a model to capture the postoperative hepatic hemodynamics after left hepatectomy. To study this, we build a hepatic network model and analyze its behavior under four different outflow impedance: (a) the same as preoperative impedance; (b) evaluated using the RI and preoperative impedance; (c) computed from structured tree BC with increased radius of terminal vessels; and (d) evaluated using structured tree with both increased radius of root vessel, ie, the outlets of the postoperative hepatic artery, and increased radius of terminal vessels. Our results show that both impedance from (b) and (d) give a physiologically reasonable postoperative hepatic pressure range, while the RI in (b) allows for a fast approximation of postoperative impedance. Since hemodynamics after hepatectomy are not fully understood, the methods used in this study to explore postoperative outflow BC are informative for future models exploring hemodynamic effects of partial hepatectomy.