Abstract
This paper is concerned with the mathematical modeling of a severe and common congenital defect called hypoplastic left heart syndrome (HLHS). Surgical approaches are utilized for palliating this heart condition; however, a brain white matter injury called periventricular leukomalacia (PVL) occurs with high prevalence at or around the time of surgery, the exact cause of which is not known presently. Our main goal in this paper is to study the hemodynamic conditions under which HLHS physiology may lead to the occurrence of PVL. A lumped parameter model of the HLHS circulation has been developed integrating diffusion modeling of oxygen and carbon dioxide concentrations in order to study hemodynamic variables such as pressure, flow, and blood gas concentration. Results presented include calculations of blood pressures and flow rates in different parts of the circulation. Simulations also show changes in the ratio of pulmonary to systemic blood flow rates when the sizes of the patent ductus arteriosus and atrial septal defect are varied. These changes lead to unbalanced blood circulations and, when combined with low oxygen and carbon dioxide concentrations in arteries, result in poor oxygen delivery to the brain. We stipulate that PVL occurs as a consequence.
Highlights
Hypoplastic left heart syndrome (HLHS) is a congenital heart defect (CHD) in which the left side of the heart is severely underdeveloped
The pressure values of the different sections of the heart through the two contraction cycles are consistent with a heart that has a blockage/defect of the left ventricle as in patients with hypoplastic left heart syndrome, where the right ventricle is responsible for circulating blood to the lungs as well as throughout the body
The goal of this paper has been to develop a lumped parameter model of HLHS, a fairly common congenital heart disease. The need for this physical modeling comes from our ultimate goal to predict and prevent one of the consequences of this abnormal circulation, namely, a form of brain injury called periventricular leukomalacia (PVL)
Summary
Hypoplastic left heart syndrome (HLHS) is a congenital heart defect (CHD) in which the left side of the heart is severely underdeveloped. Without early surgical palliation HLHS is universally fatal [1]. HLHS results from a failure of the aortic or mitral valve to form. Lack of antegrade flow through the valves causes insufficient growth of both the left ventricle and the ascending aortic arch. Underdevelopment of the left ventricle-aorta complex resulting in critical aortic valve stenosis or aortic valve atresia with an intact ventricular septum is the most recognized form of HLHS. All right sided cardiac structures are larger than normal including the right atrium, pulmonary artery, and pulmonary valve [2]
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