Fontan circulations are surgical strategies to treat infants born with single ventricle physiology. Clinical and mathematical definitions of Fontan failure are lacking, and understanding is needed of parameters indicative of declining physiologies. Our objective is to develop lumped parameter models of two-ventricle and single-ventricle circulations. These models, their mathematical formulations and a proof of existence of periodic solutions are presented. Sensitivity analyses are performed to identify key parameters. Systemic venous and systolic left ventricular compliances and systemic capillary and pulmonary venous resistances are identified as key parameters. Our models serve as a framework to study the differences between two-ventricle and single-ventricle physiologies and healthy and failing Fontan circulations.

中文翻译：

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双心室和健康和失败的心外 Fontan 循环的集总参数模型。

Fontan 循环是治疗天生单心室生理婴儿的手术策略。缺乏 Fontan 衰竭的临床和数学定义，需要了解指示生理机能下降的参数。我们的目标是开发双心室和单心室循环的集总参数模型。介绍了这些模型、它们的数学公式和周期性解的存在证明。执行敏感性分析以确定关键参数。全身静脉和收缩左心室顺应性以及全身毛细血管和肺静脉阻力被确定为关键参数。我们的模型作为一个框架来研究双心室和单心室生理与健康和失败的 Fontan 循环之间的差异。