  We develop two mathematical lumped parameter models for blood pressure
distribution in the Fontan blood flow circulation: an ODE based spatially
homogeneous model and a PDE based spatially inhomogeneous model. We present
numerical simulations of the cardiac pressure-volume cycle and study the effect
of pulmonary resistance on cardiac output. We analyze solutions of two
initial-boundary value problems for a non-linear parabolic partial differential
equation (PDE models) with switching in the time dynamic boundary conditions
which model blood pressure distribution in the cardiovascular system with and
without Fontan surgery. We also obtain necessary conditions for parameter
values of the PDE models for existence and uniqueness of non-negative bounded
periodic solutions.
