Handling Complexity in Oxygen Delivery in the Univentricular Circulation
To the Editor:
Barnea et al present an important analysis1 of pulmonary-to-systemic flow balance (Qp:Qs) and total systemic oxygen delivery (Do2) in patients with complete mixing of blood.
We feel that they are too modest about the analytical utility of their equations. A central theme of their work is the relationship between Do2 and its determinants: metabolic rate (V̇o2), pulmonary venous oxygen content (Cpvo2), pulmonary blood flow (Qp), systemic blood flow (Qs), and cardiac output (CO)=Qp+Qs. They present the following equation relating these parameters, which appeared too complex2 to proceed to algebraic maximization of Do2 in the general case, and hence the authors were obliged to perform computer modeling for a few individual cases: However, we would like to add the observation that this relationship may be expressed more simply, with each relevant variable appearing only once: From this, one can readily deduce that for maximization of Do2, the chosen value of pulmonary blood flow should be: Qp for max Do2=, and the fraction of blood sent to the lung should be (Qp/CO)=.
Applying values of V̇o2 (0.009 L · min−1 · kg−1), CO (0.30 L · min−1 · kg−1), and Cpvo2 (0.184 l O2/L blood), we obtain a target Qp of 0.12 L · min−1 · kg−1, or a Qp/CO of 40%.
The clinical significance of this for a clinician aiming to maximize Do2 is that if cardiac output rises in proportion to metabolism (V̇o2/CO ratio conserved) in the recovery period after surgery, then the target Qp:Qs balance remains constant, whereas if the rise in cardiac output fails to match that in metabolism, then one would have to divert progressively larger fractions of that cardiac output to the lungs.
The final comment we have is that it is far from clear that total oxygen delivery is the most important quantity to maximize, because it disregards the fact that oxygen of different saturations (and hence partial pressures) is of different metabolic utility in protecting tissue from hypoxic damage. Nevertheless, we support this analytical approach to developing a theoretical basis for our clinical choices in these difficult and unstable patients. We contend that these relationships are not as complex and unfathomable as they may seem at first, and further analyses may give yet more useful additions to the clinician’s armory of rules of thumb.
- Copyright © 1999 by American Heart Association
We thank Drs Francis, Davies, and Coats for their thoughtful comments. The perioperative management of children with hypoplastic left heart syndrome (HLHS) presents a challenge. Given the small patient size and precarious hemodynamics, it is difficult to make measurements. For this reason, we developed a simple model to predict systemic oxygen delivery. In our first article, we used this model to demonstrate that maximal oxygen delivery occurs at a pulmonary-to-systemic flow ratio (Qp/Qs) ≤1.R1 In our second study, we examined the efficacy of arterial and mixed venous oxygen saturations and indexes derived from these blood gases to monitor system oxygen delivery.R2
We are delighted that our article stimulated you and your colleagues to reformulate the basic equations. Obviously, there are many different ways to express these relationships. You expressed the pulmonary artery blood flow at maximal systemic oxygen delivery as a function of cardiac output, whole-body oxygen consumption, and pulmonary venous oxygen capacity. We plotted this relationship: pulmonary artery blood flow versus cardiac output. Similar to our first study, for maximal systemic oxygen delivery, the Qp/Qs ratio was <1. As cardiac output increases, pulmonary blood flow increases, but not in a linear fashion. Thus, Qp/Qs continues to decrease. There is no one value of Qp/Qs for maximal oxygen delivery.
Your assumption that cardiac output and whole-body oxygen consumption would increase proportionally is too restrictive. Clearly, changes in oxygen extraction occur in these patients. Also, most HLHS patients suffer from depressed ventricular function and a high Qp/Qs after surgery. Thus, in most patients, the problem is too much, and not too little, pulmonary blood flow.
Again, we are glad of your interest. For our last article,R2 we solved the basic equations and plotted the results in Excel. This spreadsheet (in Excel for PC) is available free of charge. Just send an e-mail message to Dr Barnea (firstname.lastname@example.org), and he will send you a copy. We hope that you, other clinicians, and investigators will try this demonstration. We are all looking for the best way to monitor these patients and save lives.R1 R2 R3 R4
Barnea O, Austin EH, Richman B, Santamore WP. Balancing the circulation: theoretic optimization of pulmonary/systemic flow ratio in hypoplastic left heart syndrome. J Am Coll Cardiol. 1994;24:1376–1381.
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.
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.