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Mathematical modelling of oxygenation under veno-venous ECMO configuration using either a femoral or a bicaval drainage



The bicaval drainage under veno-venous extracorporeal membrane oxygenation (VV ECMO) was compared in present experimental study to the inferior caval drainage in terms of systemic oxygenation.


Two mathematical models were built to simulate the inferior vena cava-to-right atrium (IVC → RA) route and the bicaval drainage-to-right atrium return (IVC + SVC → RA) route using the following parameters: cardiac output (QC), IVC flow/QC ratio, venous oxygen saturation, extracorporeal pump flow (QEC), and pulmonary shunt (PULM-Shunt) to obtain pulmonary artery oxygen saturation (SPAO2) and systemic blood oxygen saturation (SaO2).


With the IVC → RA route, SPAO2 and SaO2 increased linearly with QEC/QC until the threshold of the IVC flow/QC ratio, beyond which the increase in SPAO2 reached a plateau. With the IVC + SVC → RA route, SPAO2 and SaO2 increased linearly with QEC/QC until 100% with QEC/QC = 1. The difference in required QEC/QC between the two routes was all the higher as SaO2 target or PULM-Shunt were high, and occurred all the earlier as PULM-Shunt were high. The required QEC between the two routes could differ from 1.0 L/min (QC = 5 L/min) to 1.5 L/min (QC = 8 L/min) for SaO2 target = 90%. Corresponding differences of QEC for SaO2 target = 94% were 4.7 L/min and 7.9 L/min, respectively.


Bicaval drainage under ECMO via the IVC + SVC → RA route gave a superior systemic oxygenation performance when both QEC/QC and pulmonary shunt were high. The VV-V ECMO configuration (IVC + SVC → RA route) might be an attractive rescue strategy in case of refractory hypoxaemia under VV ECMO.


Veno-venous extracorporeal membrane oxygenation (VV-ECMO) has become the standard of care in cases of severe acute respiratory distress syndrome (ARDS) and extreme respiratory failure [1,2,3]. Even though the precise criteria for initiation of extracorporeal therapy are still debated, its efficacy in cases of refractory hypoxaemia has been largely demonstrated [3, 4]. However, VV-ECMO may fail to restore a satisfactory level of oxygen saturation despite a significant extracorporeal blood flow. Direct determinants of systemic oxygenation are nowadays well known: pulmonary shunt, effective extracorporeal blood flow, cardiac output, and theoretical value of mixed venous oxygen saturation (“SvO2”) [5, 6]. Thus, effective extracorporeal blood flow, which is directly determined by the extracorporeal settings and recirculation phenomena, is the cornerstone of blood reoxygenation under VV-ECMO. Two recirculation mechanisms have imperatively to be distinguished; the structural recirculation that mainly depends on the chosen extracorporeal route, and on the other hand the direct recirculation that depends on many technical factors (position, orientation, size, length and pattern of cannulas, extracorporeal pump flow, local impedance…) as physiological factors (cardiac output, cardiac rhythm, tricuspid regurgitations, venous impedance, intrathoracic pressure, blood volume status…). [7, 8]

Since a 20 years, the most commonly used extracorporeal route under VV-ECMO is the inferior vena cava-to-right atrium (IVC → RA) route, with two main configurations: femoro-jugular and femoro-femoral [2, 4]. This IVC → RA route is reputed simple and efficient [9]. However, despite extensive use, the IVC → RA route has two main limitations: the structural recirculation and the superior cava shunt (i.e., deoxygenated venous blood from superior vena cava [SVC] directly heading to pulmonary artery) [6,7,8]. These structural limits in relation to the reinfusion of reoxygenated blood in the superior vena cava (SVC) are inevitable when extracorporeal blood flow is higher than the blood flow into the IVC and cannot be avoided by a simple modification of cannulas position [6]. These two phenomena may explain extracorporeal therapy failures in cases of major pulmonary shunt.

Another extracorporeal route has been proposed to limit the phenomenon of structural recirculation and superior cava shunt: the bicaval drainage-to-right atrium return (IVC+SVC → RA) route [10]. The IVC+SVC → RA route may be performed using either a single dual-lumen cannula (e.g., Avalon Elite cannula, Getinge, Germany) or three separate single-lumen cannulas (VV-V configuration) [10,11,12]. Using bicaval drainage and a proximal extracorporeal return, the IVC+SVC → RA route should be considered as a serial configuration, which should theoretically reduce structural recirculation. More important, the superior caval shunt, which is the main factor responsible for refractory hypoxaemia under V-V ECMO, would be also reduced; this is not possible with the IVC → RA route [6]. However, despite a strong physiological rational to limit the superior caval shunt, evidences on the superiority of the IVC+SVC → RA route to reoxygenate systemic blood is lacking. Therefore, we wanted to compare the IVC → RA route with the IVC+SVC → RA route in terms of blood reoxygenation performance using a recently published ECMO mathematical model [6].

The main objective of present study was to compare the IVC → RA route (V−V configuration) to the IVC+SVC → RA route (VV−V configuration) using mathematical modelling (systemic oxygenation, required extracorporeal blood flow) and to identify clinical situations, where bicaval drainage might be a relevant strategy.


Physiological bases of the two models

Two mathematical models were built on XLSTAT 7.5.2 software (Addinsoft, New York) considering the presence of two central venous systems, the IVC and the SVC [6].

The main abbreviations used in our two models are as follows:

QC, cardiac output.

QSVC, blood flow in the superior vena cava.

QIVC, blood flow in the inferior vena cava.

kIVC, proportion of cardiac output coming from the inferior vena cava.

QEC, extracorporeal pump flow.

QEff, effective extracorporeal pump flow.

PULM-Shunt, proportion of flow crossing the pulmonary shunt.

“SVO2”, theoretical value of mixed venous blood oxygen saturation, which is the product of IVC, SVC and coronary sinus blood re-entering the heart. “SVO2” value could theoretically be assessed in absence of ECMO therapy in the pulmonary artery, but becomes unmeasurable under ECMO therapy.

SPAO2, blood oxygen saturation in the pulmonary artery.

SaO2, arterial blood oxygen saturation.

The first model uses one only site of extracorporeal drainage into the IVC (the IVC → RA route), the other uses two extracorporeal drainage sites into the IVC and the SVC (the IVC+SVC → RA route). These two models are based on blood flows continuity and integrate blood flow and oxygen saturation for each anatomic compartment (Fig. 1). The admixture of blood produced by the ECMO reinfusion in the RA was considered to be homogeneous in these models [12, 13]. To better apprehend structural phenomena induced by these configurations, no direct recirculation was considered in the two models, leading to ideal situations for each of them. The IVC+SVC → RA route was, moreover, considered as a serial design without any structural recirculation when QEC ≤ QC. When QEC/QC > 1, QEff was equal to QC and QEC could only increase due to structural recirculation.

Fig. 1
figure 1

Modelling of the IVC → RA and IVC + SVC → RA routes. IVC inferior vena cava, RA right atrium, SaO2 arterial blood oxygen saturation, SPAO2 pulmonary arterial blood oxygen saturation, SPREO2 blood oxygen saturation in the drainage cannula(s), SVC superior vena cava

The main equations for the two models are presented in the Additional file 1.

Modelling clinical situations

The settings for four parameters (kIVC, “SvO2”, QC, PULM-Shunt) were determined a priori for the two models to represent different clinical scenarios: kIVC constant and arbitrary defined at 0.67 [14, 15]; “SvO2” constant and arbitrary defined at 60%; QC constant and arbitrary defined at 5 or 8 L/min; PULM-Shunt ranging from 5 to 100% in steps of 5%. For each analysis, once these clinical conditions were defined, QEC was gradually increased to determine SaO2 for each route. The QEC value was expressed by the QEC/QC ratio in steps of 0.1 (ranging from 0 to 2).

Study design

The consequences of PULM-Shunt on SaO2 were first represented according to the value of SPAO2 to better understand this pathophysiological concept under VV-ECMO, as well as the SPAO2 objectives of extracorporeal therapy, knowing that SPAO2 is the “SvO2” in the absence of extracorporeal therapy. A specific analysis was also performed for different target levels of SaO2 (90%, 94%, 98%).

Oxygenation performance of ECMO therapy was also determined for each route according the QEC/QC ratio, which was proven to be a robust reflect of extracorporeal therapy (QEC component) on oxygenation while integrating physiological conditions and tissue needs (QC component). SPAO2 was thus obtained according to different “SvO2” levels, whereas SaO2 was obtained according to PULM-Shunt (“SvO2” constant at 60%).

Finally, the difference in required QEC to obtain the SaO2 targets (90%, 94%, 98%) between the IVC → RA and IVC+SVC → RA routes was calculated according to PULM-Shunt. These results were expressed using the QEC/QC ratio but also as crude values of QEC (L/min) to better reflect clinically current situations (QC = 5 and 8 L/min).


PULM-Shunt and extracorporeal therapy

For a given SPAO2, SaO2 was linearly and inversely associated with PULM-Shunt (Fig. 2). At the two extremes: SaO2 = 100% when PULM-Shunt = 0% and SaO2 = SPAO2 when PULM-Shunt = 100%. As expected, the higher the SPAO2, the higher the SaO2 was for a given PULM-Shunt, highlighting the direct influence of extracorporeal therapy.

When PULM-Shunt was low, a large range of SPAO2 values allowed to obtain an SaO2 target of 90% or more: with a PULM-Shunt = 20%, an SPAO2 value comprised between 50 and 90% allowed to obtain an SaO2 target between 90 and 98% (Fig. 2B). Corresponding boundaries values of SPAO2 for a PULM-Shunt = 40% were 75% and 95%.

In contrast, when PULM-Shunt was high, only a high SPAO2, close to 90%, allowed to obtain an SaO2 target of 90% or more: with a PULM-Shunt = 60%, an SPAO2 value comprised between 83 and 97% allowed to obtain an SaO2 target between 90 and 98%. Corresponding boundaries values of SPAO2 for a PULM-Shunt = 80% were 88% and 98% (Fig. 2B).

Oxygenation performance and extracorporeal routes

Using the IVC → RA route, SPAO2 increased linearly with QEC/QC until the threshold of 0.67. Beyond this threshold, the increase in SPAO2 rise was strongly reduced and reached a plateau (Fig. 3). SaO2 showed the same behaviour as SPAO2, with a value directly dependent on PULM-Shunt. Despite a clinically important QEC/QC, SaO2 < 94% may occur when PULM-Shunt is significant: QEC/QC = 0.6 with a PULM-Shunt > 35% for example, QEC/QC = 0.8 with a PULM-Shunt > 50%, or and QEC/QC = 1 with a PULM-Shunt > 60%.

In contrast, with the IVC+SVC → RA route, SPAO2 and SaO2 increased linearly with QEC/QC until it reached 1, corresponding to a value of 100%. With a QEC/QC > 0.86, SaO2 was ≥ 94% regardless of the importance of PULM-Shunt.

Comparison of the IVC → RA and IVC + SVC → RA routes

The higher the SaO2 target, the more the difference in required QEC between the two routes was observed for low values of PULM-Shunt: 80% for an SaO2 target of 90%, 45% for an SaO2 target of 94%, and 12% for an SaO2 target of 98%. Similarly, the higher the SaO2 target, the higher this difference was for a given PULM-Shunt (Fig. 4).

The difference in required QEC between the two routes for an SaO2 target of 90% could reach 1.0 L/min when QC = 5 L/min, and 1.5 L/min when QC = 8 L/min (Fig. 5). For an SaO2 target of 94%, this difference in required QEC could reach 4.7 L/min and 7.9 L/min, respectively. A target SaO2 of 98% could not be obtained with the IVC → RA route when PULM-Shunt was 28% or more.


Present study compared the oxygenation performance of the IVC → RA route versus the IVC+SVC → RA route using mathematical ECMO models. First, our work has demonstrated that a significant pulmonary shunt imposes a high SPAO2 to maintain physiological systemic oxygenation. Second, SaO2 under the IVC → RA route inevitably reaches a plateau despite increasing QEC, whereas SaO2 under the IVC+SVC → RA route increases linearly with QEC until 100%. The difference between these two routes occurs indeed in parallel with structural recirculation, corresponding to QEC > QIVC. Third, the present study highlights that the higher the SaO2 target, the earlier is the difference in required QEC/QC between the IVC → RA and IVC+SVC → RA routes, and the greater this difference for low pulmonary shunt. Our analysis has also revealed that several SaO2 levels cannot be obtained under the IVC → RA route when pulmonary shunt was high because of structural recirculation and superior caval shunt. Bicaval drainage could, therefore, be a part of a rescue therapy when pulmonary shunt induces refractory hypoxaemia under the IVC → RA route.

Understanding the pulmonary shunt and clinical implications

The expression of pulmonary shunt as a simple percentage may appear abstract in clinical practice, especially in cases of heterogeneous ARDS or unsystematized alveolar damage. Definition of pulmonary shunt indeed is not only defined by the volume of aerated lung/alveolar collapse, but rather by the percentage of pulmonary blood circulation that will not be oxygenated through the lung; two theoretical flows into the pulmonary venous return may thus be distinguished: reoxygenated blood (SO2 = 100%) and deoxygenated blood (SO2 = SPAO2). This definition includes redistribution of the pulmonary circulation, as well as anatomic and functional pulmonary shunts [17, 18]. In clinical practice without ECMO therapy, SPAO2 and “SvO2” are logically equal [19]. Pulmonary shunt is simply accessible with SaO2, when the value of “SvO2” is known (SaO2 = 100 × (1 − PULM-Shunt) + “SvO2” × PULM-Shunt).

Under VV-ECMO, the “SvO2” becomes a theoretical value translating cellular extraction that cannot be measured. Moreover, the relationship between PULM-Shunt and SaO2 becomes more complex, because it is strongly influenced by the variations of SPAO2 induced by extracorporeal support (Fig. 2). Effects of VV-ECMO on oxygenation may indeed be simply summarized by an increase in SPAO2, which, combined with the PULM-Shunt, directly determines SaO2. For these reasons, we focused the first part of our analysis on the inter-relationship between these determinants. Thus, our work demonstrates innovatively that for a low PULM-Shunt, a large range of SPAO2 values will generate a physiological SaO2; in other words, a large range of QEC values will generate a physiological SaO2. In contrast, in the case of significant PULM-Shunt, only a high SPAO2 target obtained by high QEC will allow an acceptable SaO2 to be maintained. In this case, a small reduction in SPAO2 may induce a strong decrease in systemic oxygenation, highlighting the importance of extracorporeal rheological conditions in the most critical situations (Fig. 2). The present analysis allows, therefore, better understanding of the interactions between ECMO therapy and the clinical pulmonary situation. In addition, Fig. 2 shows that a high SPAO2 generated by ECMO could mask significant pulmonary impairment, which will not be visible on SaO2. This observation explains why the SaO2 target under ECMO therapy should not be maximal to better understand the clinical worsening and the status of alveolar recruitment.

Fig. 2
figure 2

Relationship between SaO2 and SPAO2 according to pulmonary shunt. When lung function is optimal (PULM-Shunt=0%), SaO2 is equal to 100% regardless the SPAO2 value. In contrast when residual lung function is null (PULM-Shunt=100%), SaO2 is equal to SPAO2. Between these two clinical status, the relationship SaO2 * PULM-Shunt is linear with a slope that directly depends on SPAO2. The SPAO2 value is the final consequence of ECMO therapy in term of oxygenation. PULM-Shunt pulmonary shunt, SaO2 arterial blood oxygen saturation, SPAO2 pulmonary arterial blood oxygen saturation

Structural recirculation and extracorporeal routes

Direct recirculation under VV-ECMO is well known by clinicians, unlike structural recirculation, which is less understood [7, 20, 21]. However, structural recirculation is inevitable under the IVC → RA route when QEC exceeds QIVC. [6] The direct consequence is that effective QEC, extracorporeal blood well oxygenated, becomes lower than the set QEC. In parallel, the superior cava shunt caused by the admixture of extracorporeal reinfusion in SVC will favour hypoxaemia despite a high value of QEC. All these mechanisms are intrinsic and inevitable limits of this route that cannot be reduced by any repositioning of cannulas. Thus, refractory hypoxaemia is possible using the IVC → RA route when the pulmonary shunt is massive despite optimized ECMO therapy (Fig. 3) [22]. This has been demonstrated by our “ideal” model that does not integrate direct recirculation. Other routes such as to right atrium-to-inferior vena cava were also proposed, but they showed a higher rate of structural recirculation [9, 12, 23]. In contrast, the IVC+SVC → RA route using bicaval extracorporeal drainage behaves like a serial design, without structural recirculation and with a QEff close to the QEC. The direct consequence is that the superior cava shunt may be reduced allowing systemic oxygenation to be maintained in the case of a massive PULM-Shunt (Fig. 3). Three conclusions can thus be drawn from the comparison between IVC → RA and IVC+SVC → RA routes. First, the difference between these two routes in terms of oxygenation is mainly observable when PULM-Shunt is severe (Fig. 4). Second, this difference of performance is higher when SaO2 target and/or PULM-Shunt are high. Third, the IVC+SVC → RA route becomes superior only when structural recirculation occurs under IVC → RA route.

Fig. 3
figure 3

Oxygenation performance of the IVC → RA and IVC + SVC → RA routes. Beyond QEC/Qc = 1 using the IVC+SVC → RA route, QEff reaches the Qc value and cannot increase further. QEC increases then due to structural recirculation. IVC inferior vena cava, PULM-Shunt pulmonary shunt, QEC extracorporeal pump flow, QEff effective extracorporeal pump flow, QC cardiac output, RA right atrium, SaO2 arterial blood oxygen saturation, SPAO2 pulmonary arterial blood oxygen saturation, “SvO2 mixed venous blood oxygen saturation, SVC superior vena cava

Fig. 4
figure 4

Required QEC to reach target SaO2. IVC inferior vena cava, PULM-Shunt pulmonary shunt, QEC extracorporeal pump flow, QC cardiac output, RA right atrium, SaO2 arterial blood oxygen saturation, SVC superior vena cava

Clinical indications of bicaval drainage

Our study explores, therefore, the clinical situations, where the IVC+SVC → RA route may be superior to the IVC → RA route in terms of blood reoxygenation. The performances of these two routes may be considered as comparable in the absence of structural recirculation (i.e., QEC < QIVC) or when PULM-Shunt is moderate. In the case of refractory hypoxaemia, the first step of management should be an increase in the QEC/QC ratio, either increasing QEC and/or decreasing QC (β-blockers, sedation, etc.…) [24, 25]. However, the change of QEC/QC ratio may also increase direct recirculation leading to an uncertain result. Furthermore, ELSO recommendations consider that as SaO2 around 85% could be an acceptable clinical value [26]. Anyway, in the presence of significant structural recirculation under IVC → RA route, the IVC+SVC → RA route appears to be superior in terms of systemic oxygenation. These assumptions are only valuable if direct recirculation phenomenon does not increase with the change of route. Our analysis supports thus that, in the case of refractory hypoxaemia, the IVC+SVC → RA route should be used when other optimization measures have failed. It is nevertheless important to understand that its added value depends on the target SaO2. Differences are particularly visible for high target of SaO2 (Fig. 4); the reduction in QEC using bicaval drainage may rapidly reach 1–2 L/min, which may make a real difference in clinical practice (Fig. 5). Moreover, several SaO2 targets will not be attainable with the IVC → RA route, because required QEC is too high.

Fig. 5
figure 5

Reduction in required QEC from the IVC → RA route to the IVC + SVC → RA route. IVC inferior vena cava, PULM-Shunt pulmonary shunt, QEC extracorporeal pump flow, QC cardiac output, RA right atrium, SaO2 arterial blood oxygen saturation, SVC superior vena cava

Technical considerations for the VV-V configuration

Bicaval drainage can be realized as soon as implantation of ECMO using a dual-lumen cannula via the SVC and positioned across the RA [27]. However, a bicaval dual-lumen cannula imposes large diameters (≥ 27 Fr) to obtain an acceptable QEC and its position is reputed instable. Furthermore, direct recirculation may widely increase in cases of moderate shifting [11]. Finally, this kind of device may hardly be proposed as second step when clinical situation remains critical, because a change of configuration at this phase would be too risky. A second option could be to use a multi-staged interrupted drainage cannula upon ECMO implantation [28]. However, this configuration requires transatrial cannulation, which may be technically challenging during its placement. Furthermore, as dual-lumen cannula, repartition between superior and inferior drainage is not known and probably strongly varies with several factors (i.e., QEC, local impedance, drainage pressure, cannula size…). Finally, a cannula change in case of critical situation does not appears without risk. A third option is the use of a triple cannulation, the VV-V ECMO configuration: two drainage cannulas (IVC and SVC) and one reinfusion cannula (RA) [10]. VV-V ECMO allows a choice of optimal and sufficient diameters for each cannula and a better precision and stability of their positioning. Superior/inferior drainage ratio may be adjusted by cannulas mobilization and external compression of the tubing to favour one or the other of the drainages to limit direct recirculation. Moreover, this attractive configuration may be proposed as a stepwise procedure if the IVC → RA route has failed (Fig. 5). For example, conversion from the femoro-jugular V-V configuration to a VV-V configuration is easy, keeping the two cannulas previously placed as drainage cannulas and repositioning a third cannula for the return of extracorporeal blood into the RA (Fig. 6). An accurate positioning in the RA and a single-stage design are, however, indispensable to limit direct recirculation. In addition to the reduction in the superior cava shunt and optimization of the QEff, this configuration would also allow improvement in the impedance of venous blood drainage and maximal pump flow [10]. We strongly believe that this sequenced strategy of extracorporeal respiratory support is the most appropriate way to adapt to the clinical needs of patients and their delayed worsening; a gradual response when necessary! However, prospective studies must be done to prove the safety and efficacy of this kind of strategy.

Fig. 6
figure 6

Changing the configuration from VV ECMO to VV-V ECMO. After clamping the 2 initial cannulas, tubings can be cut in conserving some length. An Y-piece connector is then positioned to reunite these 2 tubings. This Y-piece is also connected to the drainage tubing of ECMO system. Oxygenator used in V-V configuration may be conserved or changed if its performance is too altered. All tubings must be totally purged of air before connection. A complementary tubing may be necessary on return line between ECMO system and returning cannula if oxygenator is conserved. Once totally purged of air, returning cannula may be connected to the ECMO system and VV-V extracorporeal circulation may be started. In our experience, the femoral/jugular couples (29Fr–55 cm)/(22Fr–15 cm) and (27Fr–61 cm)/(20Fr–15 cm) have good balance in term of drainage, with flow percentages frequently comprised between 60%/40% and 70%/30%, respectively

Potential limitations of the present study

First, direct recirculation was not considered in our analysis. A bad positioning of a cannula may indeed significantly increase recirculation phenomena, especially under the IVC+SVC → RA route or when QEC is high. Furthermore, the heart cycle and tricuspid valve closure may reinforce these phenomena. Thus, behaviour of VV-V configuration, more at risk of direct recirculation and more dependent from cannula positioning, could be less efficient in term of oxygenation than the ideal model used in our works. However, it seems to us essential to understand the differences in structural recirculation according to different extracorporeal routes to identify the limitations and disadvantages of each ECMO configuration. Second, our IVC+SVC → RA model was built as previously detailed without any structural recirculation when QEC ≤ QC. This simulates obviously an ideal situation that in clinical conditions depends on many parameters, such as position of each cannulas, theirs patterns, their diameters, local impedances, and thoracic or abdominal pressures. In clinical practice, a structural recirculation may exist under IVC+SVC → RA route, which logically alters performance of this configuration. Third, our model did not consider the influence of dissolved oxygen in the reoxygenated blood. A strong increase in the partial pressure of oxygen (e.g., oxygen fraction crossing the oxygenator close to 100%) may increase the mass of oxygen transferred into the extracorporeal circulation by increasing the mass of dissolved oxygen. However, we assume that this analysis bias exists similarly for each route and has a modest influence on the SaO2 [29, 30]. Anyway, to better understand structural recirculation phenomena, it appears more relevant to apprehend extracorporeal oxygenation determinants without mechanisms of solubility of gases. Fourth, pulmonary shunt may vary during the respiratory cycle or by a change in the airway pressure level by modifying West’s lung zones [31]. Many clinical factors influencing the pulmonary shunt could indeed be integrated into the model. However, we believe that this simplified approach offers a global understanding of the clinical situation and balance between lung and extracorporeal oxygenation, which is the central question during VV-ECMO management.


Our mathematical modelling has allowed us to compare the differences between the IVC → RA and IVC+SVC → RA routes in terms of oxygenation performance. The usual IVC → RA route generates inevitably a structural recirculation and a superior cava shunt, which may lead to refractory hypoxaemia in extreme cases. The IVC+SVC → RA route would not suffer from these structural limitations. The present study suggests, therefore, that the VV-V ECMO configuration might be an attractive therapeutic option when VV-ECMO does not allow sufficient oxygenation, provided that the configuration change is not associated with a significant increase of direct recirculation.

Availability of data and materials

The data sets used and analyzed are during the current study are available from the corresponding author on reasonable request.


  1. Papazian L, Aubron C, Brochard L et al (2019) Formal guidelines: management of acute respiratory distress syndrome. Ann Intensive Care 13:69

    Article  Google Scholar 

  2. Schmidt M, Pham T, Arcadipane A et al (2019) Mechanical ventilation management during extracorporeal membrane oxygenation for acute respiratory distress syndrome. An international multicenter prospective cohort. Am J Respir Crit Care Med 200:1002–1012

    Article  CAS  Google Scholar 

  3. Peek G, Mugford M, Tiruvoipati R, et al., CESAR trial collaboration (2009) Efficacy and economic assessment of conventional ventilatory support versus extracorporeal membrane oxygenation for severe adult respiratory failure (CESAR): a multicentre randomised controlled trial. Lancet 374: 1351–1363.

  4. Combes A, Hajage D, Capellier G et al (2018) EOLIA Trial Group, REVA, and ECMONet: extracorporeal membrane oxygenation for severe acute respiratory distress syndrome. N Engl J Med 378:1965–1975

    Article  Google Scholar 

  5. Schmidt M, Tachon G, Devilliers C et al (2013) Blood oxygenation and decarboxylation determinants during venovenous ECMO for respiratory failure in adults. Intensive Care Med 39:838–846

    Article  CAS  Google Scholar 

  6. Charbit J, Deras P, Courvalin E et al (2021) Structural recirculation and refractory hypoxemia under femoro-jugular veno-venous extracorporeal membrane oxygenation. Artif Organs 45:893–902

    Article  CAS  Google Scholar 

  7. Abrams D, Bacchetta M, Brodie D (2015) Recirculation in venovenous extracorporeal membrane oxygenation. ASAIO J 61:115–121

    Article  CAS  Google Scholar 

  8. Togo K, Takewa Y, Katagiri N et al (2015) Impact of bypass flow rate and catheter position in veno-venous extracorporeal membrane oxygenation on gas exchange in vivo. J Artif Organs 18:128–135

    Article  CAS  Google Scholar 

  9. Rich P, Awad S, Crotti S, Hirschl R, Bartlett R, Schreiner R (1998) A prospective comparison of atrio-femoral and femoro-atrial flow in adult venovenous extracorporeal life support. J Thorac Cardiovasc Surg 116:628–632

    Article  CAS  Google Scholar 

  10. Ichiba S, Peek G, Sosnowski A, Brennan K, Firmin R (2000) Modifying a venovenous extracorporeal membrane oxygenation circuit to reduce recirculation. Ann Thorac Surg 69:298–299

    Article  CAS  Google Scholar 

  11. Van Heijst A, van der Staak F, de Haan A et al (2001) Recirculation in double lumen catheter veno-venous extracorporeal membrane oxygenation measured by an ultrasound dilution technique. ASAIO J 47:372–376

    Article  Google Scholar 

  12. Broman M, Frenckner B, Bjällmark A, Broomé M (2015) Recirculation during veno-venous extra-corporeal membrane oxygenation—a simulation study. Int J Artif Organs 38:23–30

    Article  CAS  Google Scholar 

  13. Messaı E, Bouguerra A, Harmelin G, Di Lascio G, Cianchi G, Bonacchi M (2013) A new formula for determining arterial oxygen saturation during venovenous extracorporeal oxygenation. Intensive Care Med 39:327–334

    Article  Google Scholar 

  14. Coleridge J, Hemingway A (1958) Partition of the venous return to the heart. J Physiol 142:366–381

    Article  CAS  Google Scholar 

  15. Mohiaddin R, Wann S, Underwood R, Firmin D, Rees S, Longmore D (1990) Vena caval flow: assessment with cine MR velocity mapping. Radiology 177:537–541

    Article  CAS  Google Scholar 

  16. Murray J, Matthay M, Luce J, Flick M (1988) An expanded definition of the adult respiratory distress syndrome. Am Rev Respir Dis 138:720–723

    Article  CAS  Google Scholar 

  17. Cruz J, Metting P (1987) Understanding the meaning of the shunt fraction calculation. J Clin Monit 3:124–134

    Article  CAS  Google Scholar 

  18. Berggren S (1942) The oxygen deficit of arterial blood caused by nonventilating parts of the lung. Acta Physiol Scand 4:1–92

    Article  Google Scholar 

  19. Reinhart K, Kuhn H, Hartog C, Bredle D (2004) Continuous central venous and pulmonary artery oxygen saturation monitoring in the critically ill. Intensive Care Med 30:1572–1578

    Article  Google Scholar 

  20. Frenckner B, Broman M, Broomé M (2018) Position of draining venous cannula in extracorporeal membrane oxygenation for respiratory and respiratory/circulatory support in adult patients. Crit Care 22:163

    Article  CAS  Google Scholar 

  21. Xie A, Yan T, Forrest P (2016) Recirculation in venovenous extracorporeal membrane oxygenation. J Crit Care 36:107–110

    Article  Google Scholar 

  22. Nunes L, Mendes P, Hirota A et al (2014) ECMO Group: severe hypoxemia during veno-venous extracorporeal membrane oxygenation: exploring the limits of extracorporeal respiratory support. Clinics 69:173–178

    Article  Google Scholar 

  23. Kolla S, Awad S, Rich P, Schreiner R, Hirschl R, Bartlett R (1997) Extracorporeal life support for 100 adult patients with severe respiratory failure. Ann Surg 226:544–564

    Article  CAS  Google Scholar 

  24. Montisci A, Maj G, Zangrillo A, Winterton D, Pappalardo F (2015) Management of refractory hypoxemia during venovenous extracorporeal membrane oxygenation for ARDS. ASAIO J 61:227–236

    Article  CAS  Google Scholar 

  25. Guarracino F, Zangrillo A, Ruggeri L et al (2012) β-Blockers to optimize peripheral oxygenation during extracorporeal membrane oxygenation: a case series. J Cardiothorac Vasc Anesth 26:58–63

    Article  CAS  Google Scholar 

  26. Tonna J, Abrams D, Brodie D, Greenwood J, Rubio MS, Jose A, Usman A, Fan E (2021) Management of adult patients supported with venovenous extracorporeal membrane oxygenation (VV ECMO): guideline from the extracorporeal life support organization (ELSO). ASAIO J 67:601–610

    Article  CAS  Google Scholar 

  27. Badu B, Cain M, Durham L (2020) A dual-lumen percutaneous cannula for managing refractory right ventricular failure. ASAIO J 66:915–921

    Article  Google Scholar 

  28. Broman L, Wittberg L, Westlund C (2019) Pressure and flow properties of cannulae for extracorporeal membrane oxygenation II: drainage (venous) cannulae. Perfusion 34:65–73

    Article  Google Scholar 

  29. Hills B (1972) Diffusion and convection in lungs and gills. Respir Physiol 14:105–114

    Article  CAS  Google Scholar 

  30. Butler J, Tsuda A (2011) Transport of gases between the environment and alveoli—theoretical foundations. Compr Physiol 1:1301–1316

    Article  Google Scholar 

  31. West J, Dollery C, Naimark A (1964) Distribution of blood flow in isolated lung; relation to vascular and alveolar pressures. J Appl Physiol 19:713–724

    Article  CAS  Google Scholar 

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Authors and Affiliations



J.C. prepared the draft of the study and conducted the modelling. E.C., G.D., P.D., C.M. and H.W. performed figures and annexes. J.C. wrote the article, which was revised by T.L. and X.C. All authors are physicians that regularly implement and manage ECMO therapy in their daily practice. All authors read and approved the final manuscript.

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Correspondence to Jonathan Charbit.

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Supplementary Information

Additional file 1.

Mathematical Basis of Model 1: the IVC→RA Route. Mathematical basis of Model 2: the IVC+SVC→RA Route.

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Charbit, J., Courvalin, E., Dagod, G. et al. Mathematical modelling of oxygenation under veno-venous ECMO configuration using either a femoral or a bicaval drainage. ICMx 10, 10 (2022).

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