Optimization of Shunt Placement for the Norwood Surgery using Multi-Domain Modeling

An idealized systemic-to-pulmonary shunt anatomy is parameterized and
coupled to a closed loop, lumped parameter network (LPN) in a
multidomain model of the Norwood surgical anatomy. The LPN approach is
essential for obtaining information on global changes in cardiac output
and oxygen delivery resulting from changes in local geometry and
physiology. The LPN is fully coupled to a custom 3D finite element
solver using a semi-implicit approach to model the heart and downstream
circulation. This closed loop multidomain model is then integrated with a
fully automated derivative-free optimization algorithm to obtain
optimal shunt geometries with variable parameters of shunt diameter,
anastomosis location, and angles. Three objective functions: (1)
systemic; (2) coronary; and (3) combined systemic and coronary oxygen
deliveries are maximized. Results show that a smaller shunt diameter
with a distal shunt-brachiocephalic anastomosis is optimal for systemic
oxygen delivery, whereas a more proximal anastomosis is optimal for
coronary oxygen delivery and a shunt between these two anatomies is
optimal for both systemic and coronary oxygen deliveries. Results are
used to quantify the origin of blood flow going through the shunt and
its relationship with shunt geometry. Results show that coronary artery
flow is directly related to shunt position.