Lumped parameter models for two-ventricle and healthy and failing extracardiac Fontan circulations

Matthew G Doyle; Marina Chugunova; S Lucy Roche; James P Keener

doi:10.1093/imammb/dqab012

Lumped parameter models for two-ventricle and healthy and failing extracardiac Fontan circulations

Math Med Biol. 2021 Dec 15;38(4):442-466. doi: 10.1093/imammb/dqab012.

Authors

Matthew G Doyle¹, Marina Chugunova², S Lucy Roche³, James P Keener⁴

Affiliations

¹ Department of Mechanical and Industrial Engineering and Division of Vascular Surgery, University of Toronto, Toronto, ON M5S 1A1, Canada.
² Institute of Mathematical Sciences, Claremont Graduate University, Claremont, CA 91711, USA.
³ Division of Cardiology, Peter Munk Cardiac Centre, University Health Network, Toronto, ON M5S 1A1, Canada.
⁴ Department of Mathematics, University of Utah, Salt Lake City, UT 84112, USA.

PMID: 34534322
DOI: 10.1093/imammb/dqab012

Abstract

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.

Keywords: Fontan procedure; failing Fontan circulation; lumped parameter models; single-ventricle circulation; two-ventricle circulation.