Spring 2020 – Adaptive Mathematical Model for Hypoplastic Left Heart Syndrome

Hypoplastic left heart syndrome (HLHS) is characterized by malformations of the left ventricle and manifests itself as decreased ventricular contractility and increased diastolic stiffness. It is unknown whether associated abnormalities of the vasculature are a cause or effect of HLHS, because there is no accepted HLHS animal model. Mathematical models of HLHS are likewise limited. The conventional practice of solving model equations numerically requires a large number of parameter values to be assumed a priori, and thus results only pertain to a narrow window of fetal development. Therefore, the purpose of the present work is to derive general algebraic formulas predicting diastolic stiffness to test the hypothesis that HLHS emerges from adaptation in response to abnormal vascular properties. First an existing closed-loop model of the fetal circulation was assumed, consisting of two ventricles and seven resistances to blood flow through the systemic, pulmonary, and placenta circulations, as well as the ductus arteriosus and foramen ovale. Then we made the novel assumption that blood volume was controlled to make systemic pressure a regulated constant. Adaptation was characterized by assuming that diastolic stiffness is inversely proportional to end-diastolic wall stress. Unlike conventional approaches, model equations were linearized and solved algebraically. The resulting formulas predict that the left ventricle does indeed adapt to abnormal vasculature consistent with HLHS. Furthermore, the algebraic formulas remain valid over different developmental stages, and yield insights without assuming parameter values that cannot be measured in human fetuses.