Mathematical modeling of Fontan circulation provides theoretical insights into blood pressure distribution and the effect of pulmonary resistance on cardiac output.
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Theoretical Fontan models extend hemodynamic frameworks; hypothesis-generating without clinical validation.
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.
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Keener et al. (2018) studied this question.
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