Estimating cardiac output based on gas exchange during veno-arterial extracorporeal membrane oxygenation in a simulation study using paediatric oxygenators

Veno-arterial extracorporeal membrane oxygenation (VA-ECMO) therapy is a rescue strategy for severe cardiopulmonary failure. The estimation of cardiac output during VA-ECMO is challenging. A lung circuit (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\dot{\text{Q}}}$$\end{document}Q˙Lung) and an ECMO circuit (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\dot{\text{Q}}}$$\end{document}Q˙ECMO) with oxygenators for CO2 removal (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathop {\text{V}}\limits^{.}$$\end{document}V.CO2) and O2 uptake (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathop {\text{V}}\limits^{.}$$\end{document}V.O2) simulated the setting of VA-ECMO with varying ventilation/perfusion (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathop {\text{V}}\limits^{.}$$\end{document}V./\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\dot{\text{Q}}}$$\end{document}Q˙) ratios and shunt. A metabolic chamber with a CO2/N2 blend simulated \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathop {\text{V}}\limits^{.}$$\end{document}V.CO2 and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathop {\text{V}}\limits^{.}$$\end{document}V.O2. \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\dot{\text{Q}}}$$\end{document}Q˙ Lung was estimated with a modified Fick principle: \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\dot{\text{Q}}}$$\end{document}Q˙Lung = \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\dot{\text{Q}}}$$\end{document}Q˙ECMO × (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathop {\text{V}}\limits^{.}$$\end{document}V. CO2 or \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathop {\text{V}}\limits^{.}$$\end{document}V.O2Lung)/(\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathop {\text{V}}\limits^{.}$$\end{document}V.CO2 or \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathop {\text{V}}\limits^{.}$$\end{document}V.O2ECMO). A normalization procedure corrected \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathop {\text{V}}\limits^{.}$$\end{document}V.CO2 values for a \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathop {\text{V}}\limits^{.}$$\end{document}V./\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\dot{\text{Q}}}$$\end{document}Q˙ of 1. Method agreement was evaluated by Bland–Altman analysis. Calculated \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\dot{\text{Q}}}$$\end{document}Q˙Lung using gaseous \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathop {\text{V}}\limits^{.}$$\end{document}V.CO2 and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathop {\text{V}}\limits^{.}$$\end{document}V.O2 correlated well with measured \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\dot{\text{Q}}}$$\end{document}Q˙Lung with a bias of 103 ml/min [− 268 to 185] ml/min; Limits of Agreement: − 306 ml/min [− 241 to − 877 ml/min] to 512 ml/min [447 to 610 ml/min], r2 0.85 [0.79–0.88]). Blood measurements of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathop {\text{V}}\limits^{.}$$\end{document}V.CO2 showed an increased bias (− 260 ml/min [− 1503 to 982] ml/min), clinically not applicable. Shunt and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathop {\text{V}}\limits^{.}$$\end{document}V./\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\dot{\text{Q}}}$$\end{document}Q˙ mismatch decreased the agreement of methods significantly. This in-vitro simulation shows that \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathop {\text{V}}\limits^{.}$$\end{document}V.CO2 and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathop {\text{V}}\limits^{.}$$\end{document}V.O2 in steady-state conditions allow for clinically applicable calculations of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\dot{\text{Q}}}$$\end{document}Q˙Lung during VA-ECMO therapy.


Veno-arterial extracorporeal membrane oxygenation (VA-ECMO) therapy is a rescue strategy for
Shock states and lung failure are the most common reasons for admission to an intensive care unit. Both carry considerable morbidity and mortality and are amongst the leading causes of death in the developed world. Extracorporeal membrane oxygenation (ECMO) has gained widespread interest as a rescue therapy for severe pulmonary or circulatory failure and its use grows exponentially 1 .
ECMO provides an extracorporeal support for functions of the lung and heart. It may serve as a bridge to recovery or long-term mechanical assist devices and transplantation. In a parallel connection to the patient's own circulation, veno-arterial ECMO drains venous blood from the patient into an extracorporeal membrane lung, where carbon dioxide is removed and hemoglobin in the red blood cells is oxygenated. The arterialized (oxygenated and decarboxylized) blood is pumped back into the patient's arterial system. It is a concept similar to the cardiopulmonary bypass in heart surgery ("heart-lung-machine"), where patients undergo extracorporeal circulation on a daily basis. ECMO however is suitable for long-term support 2 .
ECMO treatment is technically demanding. In a recent review, refinement of patient inclusion criteria, optimization of additional treatment strategies and weaning strategies were considered research fields of major importance for the ongoing improvement for patients on ECMO treatment 3 . The physiology of gas exchange and blood flow with two competing systems, the ECMO and the patient's own heart and lung in parallel connection, is incompletely understood 4 . The goal of the treatment is to maintain tissue perfusion and gas exchange in order www.nature.com/scientificreports/ to gain time for recovery of native cardiac output (i.e. blood flow through the lungs). The assessment of cardiac output under ongoing extracorporeal treatment and especially during weaning, i.e. the stepwise liberation from the extracorporeal support, is difficult and mainly based on expert opinion 5,6 . Novel experimental approaches including modified thermodilution exist 7 , but are not validated in a clinical setting. Timing and strategy for weaning ECMO are complex issues 5 , whereby early weaning is linked to a favorable outcome 1,8,9 . During this weaning procedure, where . V/Q mismatch is improving, we see the possibility of assessing pulmonary blood flow through gas exchange as a useful tool to support the clinician at the bedside.
Recently, we investigated the non-invasive estimation of native cardiac output during ECMO using an adaptation of the Fick principle and expiratory gas measurements 10 . By conceptually treating the ECMO circuit as a right-to-left shunt, we created a mathematical model yielding pulmonary blood flow (i.e. cardiac output) from ECMO blood flow and from measurements of carbon dioxide elimination and oxygen consumption ( . VO 2 and . VO 2 ) through the membrane lung and the natural lung. As the ventilation / perfusion ratio ( . V/Q ratio) has a major influence on the amount of CO 2 eliminated 11,12 , we additionally estimated a correction factor to account for the non-linearity in CO 2 elimination 10 .
To confirm our preliminary results and model, we built an in-vitro lung/ECMO simulator by adapting an experimental setup developed at the department of Anaesthesiology and Pain Medicine, University Hospital of Bern, Switzerland 13 . In vitro models have successfully been used to simulate aspects of ECMO therapy such as flow characteristics 14 , platelet activation 15 , delivering of therapeutic enzymes 16 or energy loss due to components of the circuit 17 .
The aim of this simulator study was to evaluate our modified Fick method under changing . V/Q ratios and shunt and to evaluate the influence of these on the accuracy of the method. Furthermore, we compared the carbon dioxide contents in the blood and gas phase and their relationship to respective blood flows. According to the 3R principles for replacement, reduction, and refinement of the use of animals in experimentation, an additional simulation of our preliminary data from a small proof-of-concept study before confirming it in a larger trial will allow us to refine our techniques and define the limiting factors for the method more clearly.

Materials and methods
The simulation consisted of two parallel circuits-one representing the ECMO blood flow with extracorporeal gas exchange, the other lung and heart-merged into the systemic circulation (Fig. 1). One circuit represents the human heart and the lung: It consisted of a micro-diagonal pump (DeltaStream DP-II, Medos, Stolberg, Germany), generating non-pulsatile flow, as the heart and an oxygenator (Oxy Lung QUADROX-i Pediatric Oxygenators; MAQUET, Hirrlingen, Germany) as the natural lung, including a blood flow bypass around the Oxy LUNG Figure 1. In-vitro lung/ECMO simulation. The in-vitro simulation consists of two parallel circuits (ECMO and lung) with the ability to shunt Oxy Lung . Blood samples could be drawn after Oxy ECMO (post membrane), after Oxy Lung (post lung), from the left atrium (LA), the aorta as well as the right atrium (RA). www.nature.com/scientificreports/ for the simulation of anatomical or functional right-to-left shunt. The second circuit, consisting of the same type of pump and oxygenators, represents the ECMO (Oxy ECMO ). Both oxygenators were operated at a fraction of inspired oxygen of 50% throughout the experiment. These two circuits (Lung and ECMO) were merged into one mixed flow, representing the Aorta and then guided into a simulated metabolic chamber. Here, over two oxygenators (Oxy VCO2/O2 , Terumo Capiox RX25R, Ann Arbor, MI, USA) carbon dioxide was introduced into the system and oxygen washed out with a nitrogen/carbon dioxide gas blend to ensure venous pCO 2 values between 50 and 80 mmHg and mixed venous saturations of 70-90%. Gas flows were regulated with high precision flow control valves (Vögtlin RED-Y, Basel-Land, Switzerland). Blood was collected in a venous, air-free, reservoir bag above the functional right atrium to ensure steady perfusate supply at different blood flow rates. Blood flows between the circuits and the shunt were regulated with simple flow restrictors (adjusting nuts). Priming volume of the system was approximately 2.2 L. It was filled with a mixture of discarded human red blood cells and lactated Ringer's solution in a ratio of 3:1 to reach a hemoglobin value of 8-10 g/L. 50-100 mmol of sodium bicarbonate were added to reach physiological pH values between 7.3-7.4 4 . Glucose 20% was added to keep glucose level above 5 mmol/l. Boluses of 5000 I. E. Heparin were added every 2-3 h to prevent clotting. The system was heated to 36.8 °C using a temperature control system (HCV, Type 20-602, Jostra Fumedica, Muri, Switzerland).

Measurements.
Exhaust P E CO 2 at the ECMO was measured using a standard side-stream capnometer (Vamos, Dräger, Lübeck, Germany) with a constant 200 ml/min side-stream flow and a measurement accuracy of ± 3.3 mmHg + 8% relative error, as specified by the manufacturer. After every experimental maneuver, blood gas samples were drawn at specified ports and analyzed with a point of care device (Cobas b 123, Roche Diagnostics, Basel, Switzerland). Blood flows were continuously measured using liquid flow meters (Levitronix, Zurich, Switzerland, Fig. 1). Sweep gas flows were set and recorded manually at the gas blenders for Oxy Lung and Oxy ECMO and digitally using flow control valves for Oxy .
Study protocol. Baseline. We aimed at a total flow of 2500 ml in the systemic circulation, measured after the metabolic chamber. At baseline, this flow was partitioned in 2000 ml/min running through the ECMO circuit and 500 ml/min running through the lung circuit. Aortal pCO 2 at baseline was aimed at 40 mmHg corresponding to a simulated CO 2 production of approximately 120-150 ml/min. In a clinical setting the pulmonary blood flow is unknown and establishing steady . V/Q or its prediction is not possible. Therefore, lung gas flow was kept constant at 1.5 l/min (F i O 2 50%) and remained unchanged during each experimental step.
Step one. From this baseline, multiple weaning trials were performed by 500-ml-wise reductions of ECMO blood flow with either a constant . V/Q ratio of 1 (gas flow matches blood flow; Fig. 2 Step 1a) or varying . V/Q ratios of 3, 1.5, 1 and 0.75 (constant gas flow of 1.5 l/min during reduction of blood flow; Fig. 2 Step 1b) on the ECMO and consecutive increases in lung blood flow 500 ml, matching the ECMO blood flow reduction. These maneuvers were repeated for shunt fractions of 0%, and 20% and 40%.
Step two. In a second step-in order to investigate the situation of limited venous return or limited cardiac function-lung blood flow was not directly regulated but was the indirect result of changing the venous pool at unchanged rotations per minute (RPM; Fig. 2, Step 2a). Cardiac limitation was simulated by adjusting the RPM of the Lung pump ( Fig. 2, Step 2b). For these second steps, shunt was kept constant at 0%.

Calculations and mathematical model
Blood flow calculations. Based on the ventilation/perfusion ( . V/Q ) concept from respiratory physiology, gas exchange of the native lung is proportional to its blood flow 18 . The Fick principle and mass balance equations (Formula A-C) allow the deduction of formula (1) 10,19 : c v−ao CO 2 is the difference between venous and aortal CO 2 content, c v−LA CO 2 is the difference between venous and left atrial CO 2 content, c v−pm CO 2 is the difference between venous and post membrane CO 2 content ( Fig. 1) 10 . By simultaneous measurement of exhaled CO 2 at the lung and pCO 2 at the ECMO gas outlet, respective fractions of carbon dioxide elimination ( . VCO 2, ECMO and . VCO 2, LUNG ) can be calculated with simple means 10 . They should equal the blood carbon dioxide content difference in the respective segment. Rearrangement of formula 1 (formula D-F) proposes a proportional relationship between carbon dioxide elimination and respective blood flows: VCO 2 is the product of the differences in CO 2 times the blood flow and formula 2 can therefore be simplified using the following assumptions: The approximation signs are necessary, as . VCO 2 is not only determined by the difference in veno-arterial CO 2 , but also by blood flow. As production and elimination are mathematical opposites, we use absolute values: The original Fick principle suggests that this deduction is also true for the oxygenation and O 2 elimination ( . VO 2 ), such as: V/Q ratio (Step a and b, respectively). Both manoeuvres were triplicated at 0%, 20% and 40% pulmonary shunt.
Step 2a and 2b. A second part investigated the effects of limiting venous return (Step a) or limited pump function (step b). Venous return was limited by incomplete transfer of the weaned ECMO blood flow to lung blood flow (25% and 50% reduction), leading to venous pooling of blood. Limited cardiac function was simulated by a constant RPM at the lung circuit.  VCO 2 is predominantly determined by ventilation 11 and thus does not correlate well with blood flow. This results in different venoarterial content differences across the ECMO and lung, which will introduce an error into Eqs. (3) and (4). As we aim to calculate blood flow through the lungs, we correct . VCO 2 values on the ECMO towards a . V/Q of 1 10 : The constant c was calculated from a venous blood gas sample [ c = σ CO 2 × R × T × (1 + K c )] as a function of temperature T, pH (K c ), CO 2 solubility ( σ CO 2 ) and the gas constant R 20 . The normalization essentially allows to calculate the

Calculations of shunt and its impact on blood flow calculations.
Pulmonary right-to-left shunt fraction was calculated as shunt blood flow divided by total lung flow. The relative error in blood flow calculations resulting from varying shunt was calculated as true blood flow minus calculated blood flow divided by true blood flow. Using the Berggren shunt equation with O 2 contents and CO 2 contents, we calculated the estimated shunt fractions.
The error produced by the shunt fraction is calculated as: Calculations of CO 2 and O 2 content and of . VCO 2 and . VO 2 . Blood CO 2 content (cCO 2 ) was calculated for each sampling port with the method of Dash 21,22 . O 2 content (CO 2 ) was calculated for each sampling port using formula (7) 24,25 . p < 0.05 was considered significant with two-tailed testing. Linear regression was performed using the least square fit method. Correlation coefficients were calculated using Pearson's square (r 2 ). The least significant change of a method was calculated according to standard methods 26 . Multiple linear regression was used to assess the relationship between . VCO 2 , blood flow and differences in CO 2 content.      Relationship between CO 2 content in blood, blood flow and . VCO 2 , Gas, calculated for Oxy ECMO and Oxy Lung .
. VCO 2, Blood is the product of the difference in CO 2 content (Delta cCO 2 ) and blood flow. Multiple linear regression shows a high significance between . VCO 2, Gas , . VCO 2, GasNorm and these components of . VCO 2, Blood with both high r 2 and significance ( Table 1, Fig. 6C,D). The multiple linear regression on . VCO 2GasNorm results in Delta cCO 2 being non-significant. VCO 2Gas (C) and . VCO 2GasNorm (D). Regression coefficients can be found in Table 1. Values from Oxy ECMO are blue while values from Oxy Lung are in orange color.

Discussion
Our simulation of two competing blood circuits (ECMO and lung) with a deoxygenation and carboxylation unit (metabolic chamber) was able to reach physiologically representative parameters regarding gas exchange and blood content of carbon dioxide and oxygen. The blood flows in this experiment are adequate for the pediatric oxygenators and the simulated . VO 2 . As the main result, we could calculate simulated pulmonary blood flow with high accuracy and precision and correlations using . VCO 2, GasNorm and . VO 2, Blood values. This confirms our main hypothesis that gas exchange may be used for blood flow calculations in extracorporeal circuits. The underlying physiological principles and mass conservation show that CO 2 production and O 2 consumption must be in equilibrium in two competing systems with two circuits and oxygenators, which allows calculation of blood flow within certain limits 10 . The mass balance equations do not necessarily pose a need for the calculation with absolute values as suggested by Eqs. (3) and (4). The absolute values make the interpretation of results easier, since they cancel out directional (I. E. elimination or production) effects of gas exchange on the direction of calculated blood flow, as we have previously published 10 . The accuracy of these flow calculations is impaired by high shunt and . V/Q mismatch. Shunted blood will not participate in gas exchange and is therefore not detected by our method. We showed that the simulated pulmonary shunt has a linear relationship to the difference in CO 2 content as it does with O 2 content. This shunt contributes to inaccuracy in our model. A shunt of 100%, which is possible upon initiation of ECMO therapy, would therefore produce a calculated blood flow of 0 ml/min. The linear regressions of Fig. 5A,B estimate an error of 86.7% and 107.2% respectively for an assumed shunt of 100%, which confirms this assumption. In the three-compartment model of the lung 27 , shunt or venous admixture is seen as the cause of hypoxemia, while excessive dead space ventilation with exhaustion of respiratory reserves explains hypercapnia 27 . Our results indicate that increased arterial pCO 2 could be caused by shunt as well, when the alveolar minute ventilation stays constant, as it would be the case during controlled mechanical ventilation.
Blood flow through the oxygenator and . VCO 2, Gas and . VO 2, Blood show a strong correlation. Mass conservation implies that Eqs. (3) and (4) are only true if two prerequisites are met: First, the inflow content into both circuits needs to be equal and second, the difference in gas content across the lung and the ECMO must be the same. If . V/Q ratio at the ECMO and the lung are not equal, the second prerequisite is not met due to the influence of ventilation on the veno-arterial content difference 11,12 . Therefore, the best result using carbon dioxide based calculations is achieved with . VCO 2, GasNorm for both lung and ECMO, where content differences are normalized for inequalities introduced by ventilation 10 . High . V /Q will lead to an overestimation of pulmonary blood flow and low . V/Q will lead to an underestimation (Fig. 5C). The differences in the blood contents of CO 2 or O 2 share a relationship with . VCO 2 and . VO 2 in the gas phase, which represents the physiological background to replace the blood content used in the original Fick description with . VCO 2 and . VO 2 in the gas phase (formula 3 and 4). The slope of the grids in Fig. 6C represent the proportionality between the differences in blood gas content and . VCO 2, Gas . Both models for the simple as well as the normalized gas measurement show high goodness of fit. The model for . VCO 2Gas shows the delta in CO 2 content as well as blood flow as significant determinants whereas after the normalization, only blood flow remains as a significant factor. If blood flow remains steady, different . VCO 2 values will result from different ventilation settings, i.e. varying . V/Q ratios are traversed. This results in varying blood CO 2 content differences for the same blood flow. As a side note, this may have a major effect on v-a PCO 2 gradients, which are proposed for monitoring of the microcirculation 28 .
The normalization shown in Fig. 6D discards the effect of the difference in CO 2 content and fully reestablishes the relationship in Eqs. (3) and (4). This improves the accuracy of our blood flow estimations, since varying . V/Q ratios are corrected for and the normalization reestablishes equal differences in gas content across the ECMO and the lung. This method for normalization was previously described 10 .
Such a normalization seems unnecessary for . VO 2 , as oxygen is primarily transported by binding to hemoglobin (formula 7). As long as post oxygenator saturation reaches 100%, . VO 2 is independent of . V/Q ratio and represents blood flow, thus the difference and gas content across the ECMO and the lung are the same. Only if hemoglobin were to become incompletely saturated, ventilation would have an influence on . VO 2 . An increase in F i O 2 will correct this phenomenon, unless a functional shunt exists 29 .
Blood flow calculations for . VCO 2, Blood are not reliable because there is no normalization applied and calculating the CO 2 blood content can be challenging, since mathematical models do not represent the underlying physical chemistry completely 30,31 . Gas measurements are easily done and calculating . VCO 2 from exhaust capnography is simple, readily available and reliable 32 . The multiple linear regression shows a strong relationship between . VCO 2Gas and . VCO 2Blood , which proves the underlying physiological principle. In our previously published animal series with this new method 10 , we used the differences in . VCO 2 and blood flow during weaning, as the experimental setup did not allow to reach a steady state. In the present simulation study-using a highly controllable environment-such a steady state could be reached quickly. Therefore, we validated our method using these steady state conditions rather than differences in gas change during weaning. We interpret the small content differences in the . VCO 2, Blood and . VO 2, Blood at the metabolic chamber and the lung and membrane contents as limits of the calculation models rather than expressions of non-steady state.
Transferring our findings to a clinical setting would imply that the estimations of pulmonary blood flow during ECMO weaning are possible using F i O 2 , exhaust pCO 2 /pO 2 , . Venous pH, ECMO blood flow, ECMO ventilation, lung alveolar ventilation and lung dead space. The two latter parameters are readily available using volumetric capnography 33,34 , and all of these parameters can easily be measured in an intensive care unit where ECMO therapy is performed. Our method is limited by high shunt and . V/Q mismatch, which we can only partially correct for. In a clinical setting, the . V/Q ratio at the lung would remain unknown, but . VCO 2Gas at the lung might be corrected using alternative estimations of . V/Q . Multiple approaches exist such as MIGET 35 , electrical impedance tomography and positron emission tomography 36  www.nature.com/scientificreports/ use. High precision measurements of gas exchange at the lung might increase the precision of our approach 37 . We would therefore suggest that our method will have the most benefit during ECMO weaning, when in general the patient's . V/Q mismatch has improved. This study has multiple limitations: Firstly, we calculate simulated pulmonary blood flow using a high fidelity in-vitro simulation and the transfer to a clinical setting might be limited. Secondly, we have not performed gaseous measurements of . VO 2 . However, from a physiological point of view these should correlate well with measurements of . VO 2 in the blood phase. Thirdly, our calculations of VCO 2, Blood show a high bias and wide limits of agreement with . VCO 2, Gas . This is in contrast to recent findings 38 , where . VCO 2, Blood correlated well with . VCO 2, Gas . In our model, this mismatch may be owed to the fact that we used a red cell suspension and not whole blood. The missing serum fraction may have influenced the content calculation 31 . Figure 6 suggests that the differences could also be caused by . V/Q mismatch and shunt, because calculations excluding shunt shows its influence on these differences. Fourthly, the here proposed method assesses the heart and lung function of a patient simultaneously as a functional unit. If during ECMO weaning the cardiac output assessed with our method is not sufficient, further diagnosis should help clarifying the underlying pathophysiology. In case of weaning failure due to left and right ventricular dysfunction, valvular dysfunction, incomplete filling or insufficient venous return echocardiography as well as pulmonary catheterization should be considered 5 .

Conclusions
This in-vitro study explored the relationships between blood gas content (CO 2 and O 2 ), blood flow and the elimination of these gases. We show that gas exchange during ECMO weaning might help in predicting the pulmonary blood flow. Our method could easily be transferred into a clinical setting, but would be limited if there are high shunts of blood in the lung or a high . V/Q mismatch.