Beta-blockade in V-V ECMO,Critical Care

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Beta-blockade in V-V ECMO
Critical Care ( IF 15.1 ) Pub Date : 2024-04-25 , DOI: 10.1186/s13054-024-04923-1
Aravind K. Bommiasamy , Bishoy Zakhary , Ran Ran

To the Editor,

We read with great interest Staudacher et al.’s illustrative cases of beta-blocker therapy on V-V ECMO [1]. The authors’ 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 beta-blockade for a patient completely dependent on V-V 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 beta-blockade. Second, that the membrane lung is well functioning such that the post-membrane lung blood oxygen saturation (${S}_{m}{{\text{O}}}_{2}$) is 100%. Third, that the patient’s lungs are non-functional and contribute no oxygenation to the blood. Finally, given the relatively small contribution of dissolved oxygen to total oxygen content, we ignore 0.03 × ${P}_{m}{O}_{2}$ in the calculation to simplify the math. With these assumptions in place, the arterial saturation on V-V ECMO equation simplifies to Eq. (1):

$$\begin{gathered} S_{a} O_{2} = \frac{EF}{{CO}} \times S_{m} O_{2} + S_{v} O_{2} \left( {1 - \frac{EF}{{CO}}} \right) + 0.03 \times P_{m} O_{2} \hfill \\ S_{a} O_{2} = \frac{EF}{{CO}} + S_{v} O_{2} \left( {1 - \frac{EF}{{CO}}} \right) \hfill \\ \end{gathered}$$(1)

Equation 1: Patient arterial oxygen saturation on V-V ECMO simplified

If we rewrite Eq. (1), we get Eq. (2) [2]:

$$S_{a} O_{2} = \frac{{EF + S_{v} O_{2} \left( {CO - EF} \right)}}{CO}$$(2)

Equation 2: Patient arterial oxygen saturation rewritten

Likewise, if we rewrite the Fick equation, we get Eq. (3):

$$S_{a} O_{2} = S_{v} O_{2} + \frac{{VO_{2} }}{13.4 \times Hgb \times CO}$$(3)

Equation 3: Fick’s Equation solved for ${S}_{a}{O}_{2}$

Equating Eqs. (2) and (3), then solving for S_vO₂, we get Eq. (4):

$$S_{v} O_{2} = 1 - \frac{{VO_{2} }}{13.4 \times Hgb \times EF}$$(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 V-V 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 V-V ECMO, then, are ${VO}_{2}$, Hgb, and EF as seen in Eq. (4).

Finally, we explore the effect of beta-blockers 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 DO₂ equation:

$$DO_{2} = 13.4 \times Hgb \times CO \times S_{a} O_{2}$$(5)

Equation 5: Oxygen delivery simplified

Combining Eq. (3) with Eq. (5):

$$\begin{gathered} DO_{2} = 13.4 \times Hgb \times CO \times \left( {S_{v} O_{2} + \frac{{VO_{2} }}{13.4 \times Hgb \times CO}} \right) \hfill \\ \quad \quad \; = 13.4 \times Hgb \times CO \times S_{v} O_{2} + VO_{2} \hfill \\ \end{gathered}$$(6)

Equation 6: ${DO}_{2}$ with relation to ${S}_{v}{O}_{2}$

Lastly, combining Eq. (6) with Eq. (4):

$$DO_{2} = 13.4 \times Hgb \times CO \times \left( {1 - \frac{{VO_{2} }}{13.4 \times Hgb \times EF}} \right) + VO_{2}$$(7)

Equation 7: ${DO}_{2}$ on V-V ECMO expressed independent of ${S}_{a}{O}_{2}$ and ${S}_{v}{O}_{2}$

This final equation expresses delivery of oxygen on V-V ECMO as dependent only on hemoglobin, cardiac output, ECMO effective blood flow rate, and the body’s consumption of oxygen. Introducing beta-blocker 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 beta-blocker 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 (6–8 ml/100 g/min). At maximal inotropy and chronotropy, however, myocyte oxygen consumption could become a nontrivial factor and beta-blocker 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 V-V ECMO as it effectively reduces DO₂.

Not applicable.

V-V ECMO:: Veno-venous extracorporeal membrane oxygenation
$DO_{2}$ :: Patient oxygen delivery
$S_{a} O_{2}$ :: Patient arterial oxygen saturation
$EF$ :: ECMO flow rate
$S_{m} O_{2}$ :: Post-oxygenator oxygen saturation
$VO_{2}$ :: Patient oxygen consumption
$Hgb$ :: Hemoglobin
$P_{m} O_{2}$ :: Partial pressure of oxygen post-oxygenator

Staudacher DL, Wengenmayer T, Schmidt M. Beta-blockers in refractory hypoxemia on venovenous extracorporeal membrane oxygenation: a double-edged sword. Crit Care. 2023;27(1):360.
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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):327–34.
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Authors and Affiliations

Division of Pulmonary and Critical Care Medicine, Oregon Health and Science University, Portland, OR, USA
Aravind K. Bommiasamy & Bishoy Zakhary
Department of Emergency Medicine Critical Care Section, Oregon Health and Science University, Portland, OR, USA
Ran Ran

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AKB, BZ, and RR have contributed in all parts in producing the manuscript. All authors read and approved the final manuscript.

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Correspondence to Aravind K. Bommiasamy.

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Bommiasamy, A.K., Zakhary, B. & Ran, R. Beta-blockade in V-V ECMO. Crit Care 28, 139 (2024). https://doi.org/10.1186/s13054-024-04923-1

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Received: 09 April 2024
Accepted: 20 April 2024
Published: 25 April 2024
DOI: https://doi.org/10.1186/s13054-024-04923-1

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中文翻译：

VV ECMO 中的 β 阻断

致编辑，

我们饶有兴趣地阅读了 Staudacher 等人关于 VV ECMO β 受体阻滞剂治疗的说明性案例 [1]。作者的出色工作提醒我们不要关注容易测量的动脉血氧饱和度（${S}_{a}{O}_{2}$），而应该关注生理上更重要的变量——输送氧气（${DO}_{2}$ )。在此，我们从生理学和数学上证明，完全依赖 VV ECMO 的患者的 β 阻断总是会减少${DO}_{2}$，无论其对${S}_{a}{O} 的影响如何_{2}$。

为了从数学上说明这个概念，必须做出一些合理的假设。首先，ECMO 有效血流量 (EF) 处于膜肺的正常操作参数范围内，并且在 β 阻断期间保持恒定。其次，膜肺功能良好，膜后肺血氧饱和度（${S}_{m}{{\text{O}}}_{2}$）为100%。第三，患者的肺部没有功能，无法为血液提供氧合。最后，考虑到溶解氧对总氧含量的贡献相对较小，我们在计算中忽略 0.03 × ${P}_{m}{O}_{2}$以简化数学计算。有了这些假设，VV ECMO 方程上的动脉饱和度就简化为方程： (1):

$$\begin{聚集} S_{a} O_{2} = \frac{EF}{{CO}} \times S_{m} O_{2} + S_{v} O_{2} \left( {1 - \frac{EF}{{CO}}} \right) + 0.03 \times P_{m} O_{2} \hfill \\ S_{a} O_{2} = \frac{EF}{{CO}} + S_{v} O_{2} \left( {1 - \frac{EF}{{CO}}} \right) \hfill \\ \end{聚集}$$ (1)

公式 1：简化的 VV ECMO 患者动脉血氧饱和度

如果我们重写方程。 (1)，我们得到方程。（二）[2]：

$$S_{a} O_{2} = \frac{{EF + S_{v} O_{2} \left( {CO - EF} \right)}}{CO}$$ (2)

方程 2：改写患者动脉血氧饱和度

同样，如果我们重写菲克方程，我们得到方程：（3）：

$$S_{a} O_{2} = S_{v} O_{2} + \frac{{VO_{2} }}{13.4 \times Hgb \time CO}$$ (3)

方程 3：菲克方程求解${S}_{a}{O}_{2}$

等式(2) 和 (3)，然后求解 S _v O ₂，我们得到方程：（4）：

$$S_{v} O_{2} = 1 - \frac{{VO_{2} }}{13.4 \times Hgb \times EF}$$ (4)

方程 4：${S}_{v}{O}_{2}$的行列式

因此，我们发现虽然${S}_{v}{O}_{2}$传统上依赖于CO，但在 VV ECMO 上却不一定如此。它的协变量CO和${S}_{a}{O}_{2}$在上面提出的理想化场景中相互抵消。那么，VV ECMO 上${S}_{v}{O}_{2}$的唯一决定因素是${VO}_{2}$、Hgb 和 EF，如等式 1 所示。（4）。

最后，我们探讨了 β 受体阻滞剂对输送氧气 ( ${DO}_{2}$ ) 的影响，并提出了具体问题，${S}_{a}{O}_{2 }$战胜二氧化碳减排，还是反之亦然？

简化 DO ₂方程：

$$DO_{2} = 13.4 \times Hgb \times CO \times S_{a} O_{2}$$ (5)

方程式 5：简化的氧气输送

结合方程。 (3) 与等式。（5）：

$$\begin{收集} DO_{2} = 13.4 \times Hgb \times CO \times \left( {S_{v} O_{2} + \frac{{VO_{2} }}{13.4 \times Hgb \次 CO}} \right) \hfill \\ \quad \quad \; = 13.4 \times Hgb \times CO \times S_{v} O_{2} + VO_{2} \hfill \\ \end{聚集}$$ (6)

方程 6：${DO}_{2}$与${S}_{v}{O}_{2}$的关系

最后，结合方程。 (6) 与等式。（4）：

$$DO_{2} = 13.4 \times Hgb \times CO \times \left( {1 - \frac{{VO_{2} }}{13.4 \times Hgb \times EF}} \right) + VO_{2} $$ (7)

方程 7： VV ECMO 上的${DO}_{2}$独立于${S}_{a}{O}_{2}$和${S}_{v}{O }_{2}$

最终方程表示 VV ECMO 上的氧气输送仅取决于血红蛋白、心输出量、ECMO 有效血流量和身体的氧气消耗。那么，引入 β 受体阻滞剂治疗，无论其对${S}_{a}{O}_{2}$ 的影响如何，如果 Hgb、EF 和${ VO}_{2}$保持不变。虽然可以想象β受体阻滞剂治疗可以通过减少心肌细胞耗氧量来减少${VO}_{2}$ ，从而增加${DO}_{2}$，但这种效果在正常生理范围内不太可能因为肌细胞耗氧量通常仅为全身耗氧量（6-8 毫升/100 克/分钟）的 10%。然而，在最大正性肌力和变时性时，肌细胞耗氧量可能成为一个重要因素，β-受体阻滞剂治疗可能可作为心动过速患者的抗高血压药物。然而，对于绝大多数情况，VV ECMO 期间并不需要 β 阻滞，因为它可以有效减少 DO ₂。

不适用。

VV ECMO：: 静脉-静脉体外膜氧合
$DO_{2}$ :: 患者供氧
$S_{a} O_{2}$ :: 患者动脉血氧饱和度
$EF$：: ECMO流量
$S_{m} O_{2}$ :: 氧合器后氧饱和度
$VO_{2}$ :: 患者耗氧量
\（血红蛋白\）：: 血红蛋白
$P_{m} O_{2}$ :: 充氧器后氧分压

Staudacher DL，Wengenmayer T，Schmidt M。β受体阻滞剂治疗静脉体外膜氧合难治性低氧血症：一把双刃剑。危重护理。 2023；27(1):360。
文章 PubMed PubMed Central Google Scholar
Messai E，Bouguerra A，Harmelin G，Di Lascio G，Cianchi G，Bonacchi M。用于确定静脉体外氧合期间动脉氧饱和度的新公式。重症监护医学。 2013；39(2)：327–34。
文章 CAS PubMed 谷歌学术

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俄勒冈健康与科学大学肺科和重症监护医学科，美国俄勒冈州波特兰
Aravind K. Bommiasamy 和 Bishoy Zakhary
俄勒冈健康与科学大学急诊医学系重症监护科，美国俄勒冈州波特兰
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