Balancing the circulation in hypoplastic left heart syndrome

A mathematical model based on oxygen flow was developed to study the effects of pulmonary to systemic flow ratios (Q(P)/Q(S)) on systemic oxygen availability. The model suggests that Q(P)/Q(S) = 1 is the safest ratio that would provide the largest safety margin in either low cardiac output or low pulmonary oxygenation conditions. The optimal value of Q(P)/Q(S) that will result in maximum oxygen availability is smaller than unity and depends on several circulatory parameters such as cardiac output, maximal oxygen capacity, level of pulmonary oxygenation, and oxygen consumption. The values of these parameters also dictate the permissible range of Q(P)/Q(S) beyond which abrupt oxygen deficiency ensues. Decreased pulmonary resistance resulting in increased pulmonary flow may eventually result in Q(P)/Q(S) that is beyond the vital range.