A mathematical model of transitional circulation toward biventricular repair in hypoplastic left heart syndrome

Although the traditional surgical approach for left hypoplastic heart syndrome is to perform staged, palliative procedures as a single ventricle lesion, certain anatomical subsets of patients are candidates for a 2-ventricle repair either as a primary or as a staged procedure. The pulmonary blood flow (Q(P))/systemic blood flow (Q(S)) range necessary to optimize systemic oxygen delivery (DO(2)) and systemic venous oxygen saturation has been delineated for patients undergoing conventional interventions as a single ventricle physiology where the left ventricle is assumed to make no contribution to systemic cardiac output. However, in the transitional circulations created during staging to a 2-ventricle repair, the left ventricle does contribute to cardiac output. The Q(P)/Q(S) at which systemic DO(2) and systemic venous oxygen saturation are optimized in the latter circulations has not yet been evaluated. Using computer modeling, we investigated parameters to optimize systemic oxygen delivery.

We designed model circulations after both modified stage I operation and modified bidirectional Glenn shunt with Sano shunt, which are transitional circulations created during staging to a 2-ventricle repair. Mathematical equations were derived to describe DO(2) in both models. Using a computer and an Excel spreadsheet, we used the equations to examine the relationships between DO(2) and arterial oxygen saturation (Sao(2)), venous oxygen saturation (SvO(2)), SaO(2) - SvO(2), Q(P)/Q(S), and the oxygen excess factor SaO(2)/(SaO(2) - SvO(2)).

In both circulations, SaO(2) or SvO(2) alone does not accurately predict DO(2) or Q(P)/Q(S). The relationships between these variables are further altered by the degree of systemic cardiac output supplied by the left ventricle. To the contrary, DO(2) demonstrates the linear relationship with the oxygen excess factor Sao(2)/(Sao(2) - Svo(2)) irrespective of the degree of systemic cardiac output supplied by the left ventricle.

Commonly obtained clinical values such as SaO(2) and SvO(2) alone are not accurate assessments of DO(2) or Q(P)/Q(S). Therefore, these cannot be used in isolation to guide perioperative therapy.