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Betablockade in VV ECMO
Critical Care volumeÂ 28, ArticleÂ number:Â 139 (2024)
To the Editor,
We read with great interest Staudacher et al.â€™s illustrative cases of betablocker therapy on VV ECMO [1]. The authorsâ€™ excellent work reminds us not to focus on the easily measured arterial oxygen saturation (\({S}_{a}{O}_{2}\)) but rather on the much more physiologically important variable of delivered oxygen (\({DO}_{2}\)). Herein, we demonstrate physiologically and mathematically that betablockade for a patient completely dependent on VV ECMO will always decrease \({DO}_{2}\) irrespective of its effect on \({S}_{a}{O}_{2}\).
To illustrate this concept mathematically, there are some reasonable assumptions that must be made. The first is that ECMO effective blood flow rate (EF) are within normal operational parameters of the membrane lung and remain constant during betablockade. Second, that the membrane lung is well functioning such that the postmembrane lung blood oxygen saturation (\({S}_{m}{{\text{O}}}_{2}\)) is 100%. Third, that the patientâ€™s lungs are nonfunctional and contribute no oxygenation to the blood. Finally, given the relatively small contribution of dissolved oxygen to total oxygen content, we ignore 0.03 Ã— \({P}_{m}{O}_{2}\) in the calculation to simplify the math. With these assumptions in place, the arterial saturation on VV ECMO equation simplifies to Eq.Â (1):
Equation 1: Patient arterial oxygen saturation on VV ECMO simplified
If we rewrite Eq.Â (1), we get Eq.Â (2) [2]:
Equation 2: Patient arterial oxygen saturation rewritten
Likewise, if we rewrite the Fick equation, we get Eq.Â (3):
Equation 3: Fickâ€™s Equation solved for \({S}_{a}{O}_{2}\)
Equating Eqs.Â (2) and (3), then solving for S_{v}O_{2}, we get Eq.Â (4):
Equation 4: Determinants of \({S}_{v}{O}_{2}\)
Therefore, we find that though \({S}_{v}{O}_{2}\) is traditionally dependent on CO, this is not necessarily true on VV ECMO. Its covariates, CO and \({S}_{a}{O}_{2}\), cancel out in the idealized scenario proposed above. The only determinants of \({S}_{v}{O}_{2}\) on VV ECMO, then, are \({VO}_{2}\), Hgb, and EF as seen in Eq.Â (4).
Finally, we explore the effect of betablockers on delivered oxygen (\({DO}_{2}\)) with the specific question, does the increase in \({S}_{a}{O}_{2}\) triumph over the reduction in CO or vis versa?
Simplifying the DO_{2} equation:
Equation 5: Oxygen delivery simplified
Combining Eq.Â (3) with Eq.Â (5):
Equation 6: \({DO}_{2}\) with relation to \({S}_{v}{O}_{2}\)
Lastly, combining Eq.Â (6) with Eq.Â (4):
Equation 7: \({DO}_{2}\) on VV ECMO expressed independent of \({S}_{a}{O}_{2}\) and \({S}_{v}{O}_{2}\)
This final equation expresses delivery of oxygen on VV ECMO as dependent only on hemoglobin, cardiac output, ECMO effective blood flow rate, and the bodyâ€™s consumption of oxygen. Introducing betablocker therapy, then, irrespective of its effect on \({S}_{a}{O}_{2}\), reduces delivery of oxygen through reduction of cardiac output if Hgb, EF, and \({VO}_{2}\) remains constant. While it is conceivable that betablocker therapy could reduce \({VO}_{2}\) by decreasing myocyte oxygen consumption, thereby increasing \({DO}_{2}\), this effect is unlikely in normal physiologic ranges because myocyte oxygen consumption is typically only 10% of total body oxygen consumption (6â€“8Â ml/100Â g/min). At maximal inotropy and chronotropy, however, myocyte oxygen consumption could become a nontrivial factor and betablocker therapy may have utility as an antihypertensive agent in the tachycardic patient. For the vast majority of cases, however, beta blockade is not indicated during VV ECMO as it effectively reduces DO_{2}.
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Abbreviations
 VV ECMO:

Venovenous extracorporeal membrane oxygenation
 \(DO_{2}\) :

Patient oxygen delivery
 \(S_{a} O_{2}\) :

Patient arterial oxygen saturation
 \(EF\) :

ECMO flow rate
 \(S_{m} O_{2}\) :

Postoxygenator oxygen saturation
 \(VO_{2}\) :

Patient oxygen consumption
 \(Hgb\) :

Hemoglobin
 \(P_{m} O_{2}\) :

Partial pressure of oxygen postoxygenator
References
Staudacher DL, Wengenmayer T, Schmidt M. Betablockers in refractory hypoxemia on venovenous extracorporeal membrane oxygenation: a doubleedged sword. Crit Care. 2023;27(1):360.
Messai E, Bouguerra A, Harmelin G, Di Lascio G, Cianchi G, Bonacchi M. A new formula for determining arterial oxygen saturation during venovenous extracorporeal oxygenation. Intensive Care Med. 2013;39(2):327â€“34.
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Bommiasamy, A.K., Zakhary, B. & Ran, R. Betablockade in VV ECMO. Crit Care 28, 139 (2024). https://doi.org/10.1186/s13054024049231
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DOI: https://doi.org/10.1186/s13054024049231