Mathematical analysis of hemoglobin target in univentricular parallel circulation

Objective: The hemoglobin threshold for a decision to transfuse red blood cells in univentricular patients with parallel circulation is unclear. A pediatric expertise initiative put forth a "weak recommendation" for avoiding reflexive transfusion beyond a hemoglobin of 9 g/dL. We have created a mathematical model to assess the impact of hemoglobin thresholds in patients with parallel circulation.

Methods: A univentricular circulation was mathematically modeled. We examined the impact on oxygen extraction ratios and systemic and venous oxygen saturations by varying hemoglobin levels, pulmonary to systemic blood flow ratios, and total cardiac output.

Results: Applying a total cardiac index of 6 L/m²/min, oxygen consumption of 150 mL/min/m², and a Q_p/Q_s ∼ 1, we found a hemoglobin level of 9 g/dL would lead to severe arterial (arterial oxygen saturation <70%) and venous (systemic venous oxygen saturation <40%) hypoxemia. To operate above the critical oxygen economy boundary (systemic venous oxygen saturation ∼40%) and maintain arterial oxygen saturation >70% would require either increasing the cardiac index to ∼ 9 L/m²/min or increasing the hemoglobin to greater than 13 g/dL. Further, we found a greater improvement in arterial and venous saturation arises when hemoglobin is augmented from levels below 12 g/dL.

Conclusions: Based on our model, a hemoglobin level of 9 g/dL would require a constricted set of features to sustain arterial saturations >70% and systemic venous saturations >40% and would risk unfavorable oxygen economy with elevations in oxygen consumption. Further prospective clinical studies are needed to delineate the impact of restrictive transfusion practices in univentricular circulation.