Simple equations to predict the effects of veno‐venous ECMO in decompensated Eisenmenger syndrome

Abstract

Adult patients with uncorrected congenital heart diseases and chronic intracardiac shunt may develop Eisenmenger syndrome (ES) due to progressive increase of pulmonary vascular resistance, with significant morbidity and mortality. Acute decompensation of ES in conditions promoting a further increase of pulmonary vascular resistance, such as pulmonary embolism or pneumonia, can precipitate major arterial hypoxia and death. In such conditions, increasing systemic oxygenation with veno‐venous extracorporeal membrane oxygenation (VV‐ECMO) could be life‐saving, serving as a bridge to treat a potential reversible cause for the decompensation, or to urgent lung transplantation. Anticipating the effects of VV‐ECMO in this setting could ease the clinical decision to initiate such therapeutic strategy. Here, we present a series of equations to accurately predict the effects of VV‐ECMO on arterial oxygenation in ES and illustrate this point by a case of ES decompensation with refractory hypoxaemia consecutive to an acute respiratory failure due to viral pneumonia.

Introduction

In case of refractory hypoxaemia due to intrapulmonary shunt (e.g. severe acute respiratory distress syndrome), veno‐venous extracorporeal membrane oxygenation (VV‐ECMO) is an option when other strategies have failed. ¹ VV‐ECMO improves systemic oxygenation by rising venous oxygen content, ² mitigating the consequences of venous admixture. ³ Physiologically, the same concept could apply to cardiac right‐to‐left shunt, such as in Eisenmenger syndrome (ES). The latter develops in patients with unrepaired congenital heart disease and chronic left‐to‐right shunt, with progressive increase in pulmonary vascular resistance and progression towards a predominant right‐to‐left shunt. ⁴ Although not classically considered in ES, VV‐ECMO could be life‐saving during acute decompensation as a bridge to recovery, surgery, or transplantation. ⁵ , ⁶ , ⁷ Anticipating the effects of VV‐ECMO in decompensated ES could ease the decision to initiate ECMO. We present simple equations that can be used for this purpose and illustrate our point by a case presentation. An Excel fill‐in spreadsheet (Supporting Information, Table S1 ) is provided with this report for solving all the relevant equations.

• 1. Calculation of the total (cardiac plus intrapulmonary) shunt fraction (F_shunt‐Tot)

$${\mathrm{F}}_{\text{shunt‐}\mathrm{Tot}}={\mathrm{Q}}_{\mathrm{s}}/{\mathrm{Q}}_{\mathrm{t}}=\left({\mathrm{C}}_{\mathrm{c}}{\mathrm{O}}_2-{\mathrm{C}}_{\mathrm{a}}{\mathrm{O}}_2\right)/\left({\mathrm{C}}_{\mathrm{c}}{\mathrm{O}}_2-{\mathrm{C}}_{\mathrm{v}}{\mathrm{O}}_2\right)$$ (1)

where Q_s: shunt flow; Q_t: systemic cardiac output; C_cO₂: pulmonary capillary O₂ content; C_aO₂: systemic arterial O₂ content; and C_vO₂: mixed venous O₂ content. The content equation is as follows: (1.39 × [haemoglobin] × SO₂) + (0.031 × PO₂).

• 2. Calculation of right ventricular oxygen content under VV‐ECMO (C_RVO₂)

$${\mathrm{C}}_{\mathrm{RV}}{\mathrm{O}}_2=\left[\left({\mathrm{Q}}_{\mathrm{EC}}/{\mathrm{Q}}_{\mathrm{t}}\right)\times {\mathrm{C}}_{\mathrm{EC}}{\mathrm{O}}_2\right]+\left[\left[1-\left({\mathrm{Q}}_{\mathrm{EC}}/{\mathrm{Q}}_{\mathrm{t}}\right)\right]\times {\mathrm{C}}_{\mathrm{cv}}{\mathrm{O}}_2\right]$$ (2)

where C_ECO₂: O₂ content in blood exiting the oxygenator; C_cvO₂: central O₂ content in venous blood bypassing the oxygenator; Q_EC: ECMO flow (assuming no recirculation); and Q_t: systemic venous return (= systemic cardiac output).

• 3. Calculation of systemic arterial oxygen content under VV‐ECMO (C_aO_2‐ECMO)

$${\mathrm{C}}_{\mathrm{a}}{\mathrm{O}}_{2\text{‐ECMO}}=\left({\mathrm{F}}_{\text{shunt‐}\mathrm{Tot}}\times {\mathrm{C}}_{\mathrm{RV}}{\mathrm{O}}_2\right)+\left[\left(1-{\mathrm{F}}_{\text{shunt‐}\mathrm{Tot}}\right)\times {\mathrm{C}}_{\mathrm{c}}{\mathrm{O}}_2\right]$$ (3)

C_aO_2‐ECMO is the sum of O₂ content in shunted blood and in non‐shunted blood exiting the lung. We assume no alveolo‐capillary diffusion impairment and equilibrium between alveolar (P_AO₂) and capillary O₂ pressures (P_CO₂). We also consider that the cardiac shunt accounts for the total shunt, because we cannot separate intracardiac from intrapulmonary shunt, and the contribution of intrapulmonary shunt to total shunt is limited in conditions of massive cardiac right‐to‐left shunt. We can still introduce a correction factor, assuming a certain percentage of intrapulmonary shunt (F_shunt‐Lung), and determine the O₂ content exiting the lungs (left atrium, C_LAO₂, Equation 4). The corrected fraction of cardiac shunt (F_{shunt‐Heart} = F_shunt‐Tot − F_shunt‐Lung) should be used to calculate C_aO_2‐ECMO (Equation 5).

$${\mathrm{C}}_{\mathrm{LA}}{\mathrm{O}}_2={\mathrm{C}}_{\mathrm{C}}{\mathrm{O}}_2-\left[{\mathrm{F}}_{\text{shunt‐Lung}}\times \left({\mathrm{C}}_{\mathrm{C}}{\mathrm{O}}_2-{\mathrm{C}}_{\mathrm{RV}}{\mathrm{O}}_2\right)\right]$$ (4)

$${\mathrm{C}}_{\mathrm{a}}{\mathrm{O}}_{2\text{‐ECMO}}=\left({\mathrm{F}}_{\text{shunt‐Heart}}\times {\mathrm{C}}_{\mathrm{RV}}{\mathrm{O}}_2\right)+\left[\left(1-{\mathrm{F}}_{\text{shunt‐Heart}}\right)\times {\mathrm{C}}_{\mathrm{LA}}{\mathrm{O}}_2\right]$$ (5)

• 4. Calculation of predicted S_aO₂ and P_aO₂ under VV‐ECMO

$${\mathrm{S}}_{\mathrm{a}}{\mathrm{O}}_2=\left[{\mathrm{C}}_{\mathrm{a}}{\mathrm{O}}_2-\left(0.031\times {\mathrm{P}}_{\mathrm{a}}{\mathrm{O}}_2\right)\right]/\left(1.39\times \mathrm{Hb}\right)$$ (6)

$${\mathrm{P}}_{\mathrm{a}}{\mathrm{O}}_2=\sqrt[3]{\frac{1}{2}\left(-y_N+\sqrt{{y_N}^2-h^2}\right)}+\sqrt[3]{\frac{1}{2}\left(-y_N-\sqrt{{y_N}^2-h^2}\right)}$$ (7)

where

$$\begin{array}{c}{h}^2=-500000\\ y_N=-23400s/\left(1-s\right)\end{array}$$

Hb: haemoglobin concentration (g/L).

We can use here a P_aO₂ of 70 mmHg to calculate dissolved oxygen (0.031 × P_aO₂, which is negligible). Equation 7 is the inverse Severinghaus equation, which yields S_aO₂ (s) from P_aO₂. ⁸

These equations help predict the effect of VV‐ECMO on arterial oxygenation in patients with significant cardiac right‐to‐left shunt. The following case illustrates this concept.

Case Report

The patient was a 61‐year‐old female, known for partial ES due to a non‐corrected doubly committed ventricular septal defect with bidirectional shunt and severe pulmonary arterial hypertension. She was treated with macitentan (10 mg/day) and oxygen (2 L/min). She was admitted after a 3 day history of increasing dyspnoea and low O₂ saturation (70–80%) despite increasing supplemental O₂. Electrocardiogram showed new onset atrial fibrillation, chest X‐Ray displayed a right lower lobe infiltrate, and a transthoracic echocardiography showed severe right‐to‐left shunt. Figure 1 shows echocardiographic morphological characteristics of the congenital pathology of the patient (Figure 1 A and 1 B ), as well as the baseline shunt analysis with colour Doppler M‐mode during routine examination (Figure 1 C ), and its worsening on admission (Figure 1 D ). Right heart catheterization was not performed at this acute phase.

Figure 1.

Echocardiographic investigations. (A) Four‐chamber view showing a dilated, hypertrophied right ventricle and bi‐atrial dilation. (B) Parasternal short‐axis view at the level of the left ventricular outflow tract (LVOT) showing the doubly committed ventricular septal defect (VSD). (C) Colour Doppler M‐mode performed during a routine visit before current hospitalization, showing a bidirectional shunt with a left‐to‐right shunt in early and mid‐systole (yellow arrow) and a right‐to‐left shunt in late systole and in diastole (green arrows), as well as a pulmonary insufficiency (white arrow). (D) Colour Doppler M‐mode performed on admission, showing an increase in the duration of the right‐to‐left shunt (green arrows), relative to the left‐to‐right shunt (yellow arrow). LA, left atrium; LV, left ventricle; PV, pulmonary valve; RA, right atrium; RV, right ventricle; TV, tricuspid valve.

Sinus rhythm was restored by amiodarone, and antibiotic therapy was initiated with piperacillin–tazobactam. The clinical condition worsened, with refractory hypoxaemia in spite of 100% O₂ by high nasal flow (P_aO₂/F_iO₂ O₂: 35–50 mmHg). A nasopharyngeal smear was positive for rhinovirus, and thoracic computed tomography scan revealed bilateral posterior condensations (Figure 2 ). A diagnosis of acute hypoxaemic respiratory failure due to viral pneumonia with worsening pulmonary hypertension and decompensated ES was made. Pulmonary vasodilators (intravenous iloprost and oral sildenafil and macitentan) were introduced to reduce pulmonary vascular resistance, together with intravenous diuretics (furosemide) without any improvement. Mean systemic arterial blood pressure was maintained at values between 70 and 80 mmHg, using intravenous vasopressin (0.5–1.5 U/H) and norepinephrine (0.1–0.3 μg/kg/min). Intubation and mechanical ventilation were not considered, due to the risks of right ventricular failure and increased right‐to‐left shunting. Owing to the potential for partial reversibility (viral pneumonia), we opted for VV‐ECMO to improve systemic oxygenation.

Figure 2.

Radiological investigations. (A) Evolution of bilateral pneumonia on sequential chest X‐rays obtained under veno‐venous extracorporeal membrane oxygenation (VV‐ECMO) at Day 1, Day 7, Day 14, and 1 day after VV‐ECMO weaning. (B) Contrast‐enhanced computed tomography scans of the chest showing massive bilateral pneumonia and severe dilation of the pulmonary artery trunk at Day 2 and Day 14 of VV‐ECMO support. (C) Native computed tomography scan of the chest obtained at 6 months of follow‐up showing resolution of the bilateral pneumonia.

The calculated shunt was 0.69 (Table 1 ), using central venous O₂ saturation obtained from the right atrium as a surrogate of mixed venous O₂ saturation. ⁹ Cardiac output (Q_T) was not directly measured but was estimated using the Krovetz–Goldbloom equation of O₂ consumption ¹⁰ : VO₂ = [138.1 − (17.04 * ln_(age))] + (0.378 × HR), and the arteriovenous O₂ difference, C_(a‐v)O₂ (Q_T = VO₂/C_(a‐v)O₂). Estimated Q_T was 7.1 L/min, which was close to the latest Q_T determined by cardiac catheterization at steady state, several weeks before current hospitalization (8 L/min).

Table 1.

Equations used to predict arterial oxygen status following VV‐ECMO initiation under conditions of intracardiac right‐to‐left shunt

Basal condition (before ECMO)
Parameter	Measured	Calculated	Formula
PVO2	30
PaO2	37
PaCO2	40
SaO2	0.72
SVO2	0.56
Hb	151
FIO2	1
PB	710
PH2O	47
PAO2		613	PAO2 = [(PB − PH2O) × FIO2] − (PaCO2/RQ)
PCO2		613	PCO2 = PAO2
SCO2		1	SCO2 = 1
CCO2		228.3	CCO2 = (Hb × SCO2 × 1.39) + (PCO2 × 0.031)
CaO2		152.2	CaO2 = (Hb × SaO2 × 1.39) + (PaO2 × 0.031)
CVO2		118.4	CVO2 = (Hb × SVO2 × 1.39) + (PVO2 × 0.031)
Fshunt‐Tot		0.69	Fshunt‐Tot = (CCO2 − CaO2)/(CCO2 − CVO2)

Under VV‐ECMO
Parameter	Measured	Calculated	Formula
FSO2	0.8
QEC	4.5
PECO2	400
SECO2	1
QT	7
CECO2		222.3	CECO2 = (Hb × SECO2 × 1.39) + (PECO2 × 0.031)
CRVO2		185.2	CRVO2 = [(QEC/QT) × CECO2] + [(1 − (QEC/QT)) × CcvO2]
CaO2 ECMO		198.5	CaO2 ECMO = (Fshunt‐Tot × CRVO2) + [(1 − Fshunt‐Tot) × CCO2]
SaO2 ECMO	0.93 (actual)	0.94 (predicted)	SaO2 ECMO = [(CaO2 ECMO − 0.031 × PaO2)]/(Hb × 1.39)
PaO2	67 (actual)	69 (predicted)	Inverse Severinghaus equation

Under VV‐ECMO: intrapulmonary shunt 10% (Fshunt‐Lung: estimated fraction of Fshunt‐Tot)
Parameter	Measured	Calculated	Formula
Intracardiac shunt (Fshunt‐Heart)		0.59	Fshunt‐Heart = Fshunt‐Tot − Fshunt‐Lung
CLAO2 ECMO		224	CLAO2 = CCO2 − [Fshunt‐Lung × (CCO2 − CRVO2)]
CaO2 ECMO		201	CaO2 = (Fshunt‐Heart × CRVO2) + [(1 − Fshunt‐Heart) × CLAO2]
SaO2 ECMO	0.93 (actual)	0.95	SaO2 ECMO = [(CaO2 ECMO − 0.031 × PaO2)]/(Hb × 1.39)
PaO2	67 (actual)	74	PaO2 ECMO = inverse Severinghaus equation

Under VV‐ECMO: intrapulmonary shunt 20% (Fshunt‐Lung: estimated fraction of Fshunt‐Tot)
Parameter	Measured	Calculated	Formula
Intracardiac shunt (Fshunt‐Heart)		0.49	Fshunt‐Heart = Fshunt‐Tot − Fshunt‐Lung
CLAO2 ECMO		219.7	CLAO2 = CCO2 − [Fshunt‐Lung × (CCO2 − CRVO2)]
CaO2 ECMO		202.7	CaO2 = (Fshunt‐Heart × CRVO2) + [(1 − Fshunt‐Heart) × CLAO2]
SaO2 ECMO	0.93 (actual)	0.96	SaO2 ECMO = [(CaO2 ECMO − 0.031 × PaO2)]/(Hb × 1.39)
PaO2	67 (actual)	79	PaO2 ECMO = inverse Severinghaus equation

Under VV‐ECMO: intrapulmonary shunt 30% (Fshunt‐Lung: estimated fraction of Fshunt‐Tot)
Parameter	Measured	Calculated	Formula
Intracardiac shunt (Fshunt‐Heart)		0.39	Fshunt‐Heart = Fshunt‐Tot − Fshunt‐Lung
CLAO2 ECMO		215.4	CLAO2 = CCO2 − [Fshunt‐Lung × (CCO2 − CRVO2)]
CaO2 ECMO		203.5	CaO2 = (Fshunt‐Heart × CRVO2) + [(1 − Fshunt‐Heart) × CLAO2]
SaO2 ECMO	0.93 (actual)	0.96	SaO2 ECMO = [(CaO2 ECMO − 0.031 × PaO2)]/(Hb × 1.39)
PaO2	67 (actual)	81	PaO2 ECMO = inverse Severinghaus equation

C_aO₂ (mL/L), arterial oxygen content; C_aO_{2 ECMO} (mL/L), arterial oxygen content under ECMO support; C_CO₂ (mL/L), pulmonary capillary oxygen content; C_CVO₂ (mL/L), central O₂ content in venous blood bypassing the oxygenator; C_ECO₂ (mL/L), ECMO outflow oxygen content; C_LAO_2ECMO (mL/L), left atrium oxygen content under ECMO; C_RVO₂ (mL/L), right ventricular oxygen content; C_VO₂ (mL/L), mixed venous oxygen content; F_IO₂, inspired fraction of oxygen; F_{shunt‐Heart}, intracardiac shunt fraction; F_shunt‐Lung, intrapulmonary shunt fraction; F_shunt‐Tot, total shunt fraction (intracardiac + intrapulmonary); F_sO₂, fraction of sweep gas oxygen delivered by ECMO; Hb (g/L), haemoglobin concentration; P_aCO₂ (mmHg), arterial partial pressure of carbon dioxide; P_AO₂ (mmHg), alveolar partial pressure of oxygen; P_aO₂ (mmHg), arterial partial pressure of oxygen; P_B (mmHg), barometric pressure; P_CO₂ (mmHg), pulmonary capillary partial pressure of oxygen; P_ECO₂ (mmHg), ECMO outflow partial pressure of oxygen; PH₂O (mmHg), partial pressure of water vapour; P_VO₂ (mmHg), central venous partial pressure of oxygen; Q_EC (L/min), ECMO flow; Q_T (L/min), cardiac output; RQ, respiratory quotient (default value assumed to be 0.8); S_aO_{2 ECMO}, arterial oxygen saturation under ECMO support; S_aO₂, arterial oxygen saturation; S_CO₂, pulmonary capillary oxygen saturation; S_ECO₂, ECMO outflow oxygen saturation; S_VO₂, mixed venous oxygen saturation; VV‐ECMO, veno‐venous extracorporeal membrane oxygenation.

This table presents measured and calculated values at baseline, in a patient with massive intracardiac right‐to‐left shunt due to decompensated Eisenmenger syndrome. Knowing ECMO flow, cardiac output and calculated shunt fraction allows to accurately predict the arterial oxygen saturation after VV‐ECMO initiation. The calculated predicted P_aO₂ value is obtained using the inverse solution of the Severinghaus equation (see text). The bottom of the table indicates the predicted values of arterial oxygenation taking into consideration intrapulmonary shunt contributing 10%, 20%, or 30% of total shunt.

Using this value of Q_T, we predicted that ECMO flow of 4.5 L/min with a delivered sweep gas O₂ fraction of 0.8–1.0 (producing a post‐membrane PO₂ of 300–500 mmHg ¹¹ ) would result in a S_aO₂ of 0.94 and P_aO₂ of 69 mmHg (Equation 7). The actual values of S_aO₂ and P_aO₂ after ECMO initiation at these settings were 0.93 and 67 mmHg, agreeing well with predicted values. Considering some degree of intrapulmonary shunt did not significantly modify the results (predicted S_aO₂ increased by 0.01–0.02) (Table 1 ).

The clinical condition improved, allowing weaning from VV‐ECMO after 29 days. FiO₂ was progressively reduced to 0.28 (2 L/min O₂ flow), with maintenance of arterial O₂ saturation between 80% and 85%, corresponding to the patient's usual values. She was discharged from the intensive care unit after 40 days, from the hospital after 61 days, and was in stable condition at a follow‐up visit 6 months after discharge.

Discussion

In the case presented here, decompensation of ES occurred in the context of an acute viral pneumonia, with some potential for reversibility. Treating refractory hypoxaemia with positive pressure ventilation in this setting would likely worsen the shunt fraction and precipitate cardiovascular collapse. In such conditions, VV‐ECMO appeared as the only viable strategy as a bridge to recovery, giving time to treat the reversible components and preventing the complications of major hypoxaemia. The effects of VV‐ECMO on systemic oxygenation in this setting could be accurately predicted by the use of relatively simple equations, which can be solved easily using a fill‐in Excel spreadsheet (Table S1 ). The ability to predict the influence of VV‐ECMO on oxygenation even before its insertion adds an important clinical value, not only by providing significant help in the decision process but also by determining in advance the optimal settings of VV‐ECMO for best expected results. Moreover, it is worth to underscore that the equations detailed in this report refer to fundamental principles of gas exchange, oxygen content, and shunt physiology. Therefore, they might also be considered to predict the effects of VV‐ECMO in other clinical conditions associated with significant right‐to‐left shunt (both intracardiac and intrapulmonary) and refractory hypoxaemia, an assumption that will require further validation studies.

Conflict of interest

None declared.

Funding

This work was supported in part by the ‘Emma Muschamp Foundation’, Lausanne, Switzerland, to J.B.

Author contributions

J.B., L.P., and L.L. were involved in the design and the implementation of the work and in the analysis and interpretation of the results. J.B., L.P., and L.L. wrote the first draft of the manuscript with the contribution of D.A. and T.R. D.A., T.R., P.Y., J.D.A., A.R., O.P., and M.R. contributed to the analysis and interpretation of the results and critically revised the manuscript. All authors approved the final version of the manuscript.

Ethical statement

The patient's informed consent has been obtained for this publication.

Supporting information

Table S1. Supporting Information

Bonnemain, J. , Auberson, D. , Rutz, T. , Yerly, P. , Aubert, J.‐D. , Roumy, A. , Pantet, O. , Rusca, M. , Liaudet, L. , and Piquilloud, L. (2021) Simple equations to predict the effects of veno‐venous ECMO in decompensated Eisenmenger syndrome. ESC Heart Failure, 8: 1637–1642. 10.1002/ehf2.13253.