  In this paper, we develop a pulsatile compartmental model of the Fontan
circulation and use it to explore the effects of a fenestration added to this
physiology. A fenestration is a shunt between the systemic and pulmonary veins
that is added either at the time of Fontan conversion or at a later time for
the treatment of complications. This shunt increases cardiac output and
decreases systemic venous pressure. However, these hemodynamic benefits are
achieved at the expense of a decrease in the arterial oxygen saturation. The
model developed this paper incorporates fenestration size as a parameter and
describes both blood flow and oxygen transport. It is calibrated to clinical
data from Fontan patients, and we use it to study the impact of a fenestration
on several hemodynamic variables. In certain scenarios corresponding to
high-risk Fontan physiology, we demonstrate the existence of an optimal
fenestration size that maximizes oxygen delivery to the systemic tissues.
