Estimation of Oxygen Delivery in Newborns With a Univentricular Circulation
To the Editor:
The article by Barnea et al1 entitled “Estimation of Oxygen Delivery in Newborns With a Univentricular Circulation” provides an interesting mathematical analysis of tissue oxygen delivery.
However, their interpretation of Equation 5 (Equation 1 below) is misleading. They conclude that systemic oxygen delivery (Do2) is a complex function of cardiac output (CO). This is not strictly true, because replacement of Qs+Qp (systemic plus pulmonary blood flow) by CO (their Equation 3, Equation 2 below) in the first part of Equation 1 yields Equation 3 below, because the term CO cancels itself out. Thus, Do2 is dependent on the systemic blood flow and on the reciprocal of the shunt ratio Qp/Qs and not on CO, as they deduce.
- Copyright © 1999 by American Heart Association
Barnea O, Santamore WP, Rossi A, Salloum E, Chien S, Austin EH. Estimation of oxygen delivery in newborns with a univentricular circulation. Circulation. 1998;98:1407–1413.
We thank Dr Poullis for his interest and are glad that our articles are stimulating new ideas.R1 R2 In our initial mathematical analysis, we developed an equation (Equation 1 in Dr Poullis’ letter) that related systemic oxygen delivery to cardiac output, the ratio of pulmonary to systemic blood flow (QP/QS), the oxygen content in pulmonary venous blood, and whole body oxygen consumption. Each of these variables can be independently changed. For example, cardiac output can be changed without the necessity of altering QP/QS.
By making a substitution of variables, Dr Poullis develops another equation (Equation 3 in his letter). This equation presents systemic oxygen delivery as a function of systemic blood flow (QS), QS/QP, the oxygen content in pulmonary venous blood, and whole body oxygen consumption. Although the equation is mathematically valid, the conclusion that systemic oxygen delivery is not a function of cardiac output is invalid. Dr Poullis includes QS/QP ratio and Qs as 2 independent variables. This, of course, is not the case. In Dr Poullis’ equation, QS/QP cannot be changed without altering Qs, and Qs cannot be changed without altering QS/QP. Dr Poullis’ equation also begs the question, how does QS change? Without changing QS/QP, QS can only change by changing cardiac output. Therefore, in his equation, systemic oxygen delivery is a function of cardiac output as well, only here cardiac output is implicit and hidden behind QS.
Although there are many ways to express these equations, the goal should be kept in mind: the perioperative management of children with hypoplastic left heart syndrome. Given the small patient size and precarious hemodynamics, it is difficult to make measurements. For this reason, we developed a simple model to evaluate the ability of blood gases–derived indexes to monitor systemic oxygen delivery.R1 R2 This mathematical analysis awaits clinical studies to find the best way to monitor these patients and save lives.R3 R4
Barnea O, Santamore WP, Rossi AF, Salloum E, Chien S, Austin EH III. Estimation of oxygen delivery in newborns with a univentricular circulation. Circulation. 1998;98:1407–1413.
Tweddell JS, Hoffman GM, Fedderly RT, Ghanayem NS, Kampine JM, Berger S, Litwin SB. Patients at risk for low systemic oxygen delivery following the Norwood procedure for hypoplastic left heart syndrome (HLHS). Circulation. 1998;98(suppl I):I-689. Abstract.