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Clinical Critical Care

Relationship Between Hemoglobin Concentration and Extracorporeal Blood Flow as Determinants of Oxygen Delivery During Venovenous Extracorporeal Membrane Oxygenation

A Mathematical Model

Spinelli, Elena; Bartlett, Robert H. MD

Author Information
doi: 10.1097/MAT.0000000000000125


Extracorporeal membrane oxygenation (ECMO) allows the intensivist to manipulate determinants of oxygenation which are not possible during conventional mechanical ventilation. Many aspects of physiology need to be re-learned to use this technology to optimal advantage. This is a model of two of the critical variables, extracorporeal blood flow (ECBF) and hemoglobin (Hb) concentration, which is proposed as a learning tool to help understand the physiology of oxygen delivery during veno-venous ECMO (VV-ECMO).

The ultimate goal of VV-ECMO support in patients with hypoxemic respiratory failure is to achieve adequate systemic oxygen delivery (DO2) in relation to systemic oxygen consumption (VO2). During VV-ECMO, DO2 depends on both patient physiological variables (hemoglobin, cardiac output, native lung function) and parameters of ECMO support (ECBF and gas exchanges across the membrane oxygenator).

We developed a mathematical model to study the interaction between Hb and ECBF in determining oxygenation during VV-ECMO. The model is not intended for clinical management; however, it illustrates the physiological concepts which should be taken into account when transfusion and ECBF adjustment are considered to optimize oxygenation in patients on VV-ECMO.


The abbreviations used in this model are: Hb, hemoglobin; DO2, systemic oxygen delivery; VO2, systemic oxygen consumption; MO2, rate of oxygen provided by the ECMO system; Q, cardiac output; ECBF, extracorporeal blood flow; CaO2 (and SaO2), arterial oxygen content (and saturation); CECMOO2 (SECMOO2), oxygen content (and saturation) of the blood returning from the ECMO system; CvO2 (SvO2), oxygen content (and saturation) of the native venous return; CiO2 (SiO2), oxygen content (and saturation) of blood entering the membrane lung.

In order to simplify the relationships between oxygenation determinants during VV-ECMO, four assumptions are made.

We assume recirculation between drainage and infusion blood does not occur in the ECMO system. We assume there is no residual native lung function. We assume that there is no difference between the oxygen saturation of native venous return and the oxygen saturation of blood entering the ECMO system (SvO2 = SiO2). We ignore the amount of dissolved oxygen when calculating oxygen content. Oxygen content (CxO2) is therefore calculated as the product of Hb concentration, Hb oxygen saturation (SxO2), and a constant (k) representing the oxygen-binding capacity of Hb (1.38 ml/g).

Systemic oxygen delivery is the product of CaO2 and Q.

In this model, total native venous return flow divides into two flows at the level of the right atrium: venous flow which goes into the ECMO system (indicated as extracorporeal blood flow, ECBF) and venous flow which “shunts” the ECMO system and goes directly to the right ventricle. In the absence of recirculation, the sum of these two flows equals total native venous return flow, which in turn equals cardiac output.

CaO2 results from the weighted contribution of two blood flows mixing in the right ventricle (Figure 1): oxygenated blood returning from ECMO system (whose oxygen content is indicated as CECMOO2 and whose flow is ECBF) and de-oxygenated blood of the native venous return which does not pass through the ECMO circuit (whose oxygen content is indicated as CvO2 and whose flow is the difference between Q and ECBF).

Figure 1:
Schematic representation of the mixing of oxygenated blood returning from the ECMO system and deoxygenated blood of native venous return which shunts the ECMO system in the right ventricle. The arterial oxygen content results from the weighted contribution of the two mixing flows. ECMO, extracorporeal membrane oxygenation.

In the absence of recirculation and residual native lung function, the following relationship exists:

Ignoring the amount of dissolved oxygen, Equation 2 can be simplified as follows:

The fundamental concept is that the system reaches a steady-state, which is an equilibrium condition between DO2 and VO2.

At the steady-state, the SvO2 is correlated to SaO2 by the VO2/DO2 ratio:

Substituting Equation 4 into Equation 3 and solving for ECBF, the following relationships are obtained (detailed mathematical steps in Supplemental Digital Content 1,

The rate of oxygen supply provided by the ECMO system (MO2) is:

In the absence of native lung function, the ECMO system is the only source of oxygen to the body. Therefore, the rate of oxygen supply provided by the ECMO system (MO2) equals the VO2 at the steady state.

To isolate the reciprocal effects of ECBF and Hb in determining SaO2, we assumed theoretical static conditions, representing an instant in time of a hypothetical patient on VV-ECMO: therefore, we designated cardiac output (Q = 6 L/min) and oxygen consumption (VO2 = 200 ml/min). We used Equation 5 to determine different combinations of Hb and ECBF which result in the same level of SaO2 in these conditions. We explored three different levels of SaO2: 90%, 80%, and 70%.

For each combination of Hb and ECBF, we calculated the corresponding DO2 (and VO2/DO2 ratio) according to Equation 1 and the resulting SvO2 according to Equation 4. Normal VO2/DO2 ratio is 0.2; we considered a VO2/DO2 ratio of 0.3 to be safe (some DO2 reserve) and a VO2/DO2 ratio of 0.5 to be critical (no DO2 reserve).

Equation 6 was applied to find out the different combinations of Hb and ECBF resulting in the same SvO2, maintaining the preset conditions defined above. We explored four different levels of SvO2: 75% (optimal, VO2/DO2 0.25); 70% (normal, VO2/DO2 0.3); 65% (the lower safe limit, VO2/DO2 0.35); and 50% (critical, VO2/DO2 0.5).

We calculated the variables over an Hb range of 5–15 g/dl and ECBF range of 2–6 L/min. Because we assume no recirculation, the model is valid for a range of ECBF values ranging from 0% to 100% of cardiac output.


For a given Q (6 L/min) and VO2 (200 ml/min), the same resultant SaO2 can be accomplished through different combinations of Hb and ECBF (Figure 2 and Table 1).

Table 1:
The Different Combinations of Hb and ECBF Resulting in the Same SaO2 Are Shown for Three Different Values of Resultant SaO2 (90%, 80%, and 70%)
Figure 2:
Relationship between Hb and ECBF in determining SaO2. The graph shows ECBF required to achieve a given SaO2 at variable concentrations of Hb in the test conditions. ECBF, extracorporeal blood flow; Hb, hemoglobin; SaO2, arterial oxygen saturation.

Despite the same value of SaO2, DO2 resulting from the different combinations of Hb and ECBF progressively decreases with decreasing Hb (Table 1). With an identical SaO2 of 70%, DO2 decreases from 869 ml/min (VO2/DO2 ratio 0.23) at Hb 15 g/dl to 406 ml/min (VO2/DO2 ratio 0.49) at Hb 7 g/dl. With a SaO2 of 90%, DO2 is 1118 ml/min (VO2/DO2 0.18) if Hb is 15 g/dl, but only 522 (VO2/DO2 0.38) if Hb is 7 g/dl. The different values of VO2/DO2 corresponding to the same SaO2 are reflected by different values of SvO2.

The combinations of Hb and ECBF which result in high VO2/DO2 (> 0.3) indicate a “suboptimal” steady-state characterized by low or no oxygen reserve (gray area in Table 1). Low values of SaO2 result in adequate oxygenation only when associated with high Hb levels: Hb ≥ 12 g/dl is required to achieve VO2/DO2 < 0.3 when SaO2 is 70%, whereas Hb ≥ 9 g/dl is enough when SaO2 is 90%.

Because SaO2 does not adequately indicate the oxygenation state, we applied the model to define the relationship between Hb and ECBF using the resultant SvO2 instead of SaO2 (Figure 3). At progressive levels of anemia, higher ECBF is required to maintain a given level of SvO2. To maintain optimal SvO2 (75%), ECBF ranges from 3.9 L/min at Hb 15 g/dl to 5.8 L/min at Hb 10 g/dl are required. To maintain SvO2 at 65%, ECBF ranges from 2.8 L/min at Hb 15 g/dl to 5.9 L/min at Hb 7 g/dl are required. For each level of SvO2, we identified an Hb value which would require an ECBF equal to 100% CO to establish the desired SvO2. For each level of SvO2, this is the Hb concentration below which the increase in ECBF cannot compensate the anemia to maintain target SvO2 (asterisks in Figure 3).

Figure 3:
Relationship between Hb and ECBF at different levels SvO2. The graph shows ECBF required to achieve a given SvO2 at variable concentrations of Hb in the test conditions. The maximal SvO2 which can be achieved at 6 L/min ECBF (100% of Q) at various levels of Hb is identified by asterisks. ECBF, extracorporeal blood flow; Hb, hemoglobin; Q, cardiac output; SvO2, oxygen saturation in the native venous return.

Below Hb 10 g/dl, ECBF increase cannot provide enough oxygen delivery to achieve a SvO2 of 75%, and lower SvO2 (higher VO2/DO2) must be accepted. Given the assumptions of this model, if the goal of clinical management is to maintain SvO2 higher than 70%, the lowest Hb which can be compensated by maximal ECBF is 8 g/dl. At the critical low level of SvO2 65%, the lowest Hb which can be compensated is 7 g/dl.

Figure 4 is a comprehensive overview of the possible combinations of Hb and ECBF and the corresponding oxygenation state as defined by both SaO2 and VO2/DO2 ratio.

Figure 4:
Relationship between VO2/DO2, Hb, ECBF, and SaO2 in test condition. For each level of VO2/DO2 ratio (y axis), the different combinations of Hb and ECBF can be found at the intersection between Hb curve (colored lines) and the corresponding VO2/DO2 gridline. The resultant SaO2 is between the two values indicated by the adjacent dashed gray lines. Asterisks indicate the lowest achievable VO2/DO2 ratio for each Hb level, corresponding to ECBF 6 L/min and SaO2 100%. Typical VV-ECMO conditions are described in the green box. ECBF and Hb are managed to maintain VO2/DO2 between 0.25 and 0.35, accepting SaO2 between 80% and 90%. The extremes are ECBF 3 L/min and Hb 12 g/dl resulting in SaO2 80% (point A) and ECBF 4.5 L/min Hb 8 resulting in SaO2 90% (point B). DO2, systemic oxygen delivery; ECBF, extracorporeal blood flow; Hb, hemoglobin; SaO2, arterial oxygen saturation; VO2, systemic oxygen consumption; VV-ECMO; veno-venous extracorporeal membrane oxygenation.


The aim of this study was to provide a theoretical basis for a rational approach to strategies implemented to optimize oxygen delivery in patients on VV-ECMO.

We developed a simplified mathematical model to isolate the reciprocal effects of Hb and ECBF in determining the oxygenation state during VV-ECMO under static theoretical conditions.

This choice was dictated by two considerations. First, Hb reduction is common during the acute phase of critical diseases,1–3 and anemia occurs frequently in patients undergoing VV-ECMO, as a consequence of the application of restrictive transfusion practice to this population4,5 in which bleeding and high transfusion requirement are recognized.6,7 Second, Hb and ECBF are the main determinants of DO2 which can be manipulated in patients on VV-ECMO.

Four variables affect the oxygenation state and determine SaO2 and SvO2 during total VV-ECMO support: VO2,Q, Hb, and ECBF. These variables are therefore the possible targets for therapeutic maneuvers performed to optimize the balance between oxygen demand and supply. VO2 reduction can be pursued through the application of deep sedation, paralysis, and hypothermia. However, this strategy contrasts with the goal of minimal sedation and spontaneous breathing during ECMO support for respiratory failure.8–10 Increase in cardiac output could be difficult to achieve in patients with concomitant cardiac dysfunction, and the use of inotropic drugs is not devoid of side effects. Therefore, in clinical practice, Hb and ECBF represent the two variables which are preferentially adjusted to achieve adequate DO2 during VV-ECMO.

Because of the limitations of this mathematical model, the reported relationships are not intended to predict real clinical conditions. First of all, the model simulates an arbitrary steady-state, which occurs only for an instant in any critically ill patients. The dynamic adaptations to changes in parameters of oxygenation are not predictable, and a steady-state is required for the purpose of isolating the variables of Hb and ECBF. Because cardiac output and oxygen consumption are assumed to be constant, the model does not describe the effects of changing Hb and ECBF in patients, but simply illustrates the different combinations of Hb and ECBF resulting in the same SaO2 or SvO2 under theoretical static conditions. The assumptions of the model also limit its ability to reflect patient state. We assumed no recirculation, a condition that requires optimal cannula position. We assumed no residual native lung function, which commonly occurs during early ECMO support for respiratory failure as a consequence of both acute disease and protective ventilator settings. We also assume that there is no difference between SvO2 and SiO2, a condition which is respected only if the end of the drainage cannula draws blood from both the superior and inferior vena cava (or directly from the right atrium) and recirculation is absent. We ignored the amount of dissolved oxygen when calculating oxygen content. This introduces a significant error in the calculation of outlet oxygen content, where the dissolved oxygen can account for up to 10% of total content.

Despite these considerations, the application of this mathematical model clarifies some provocative physiologic concepts potentially relevant to the management of patients on VV-ECMO. As expected, a decrease in Hb requires an increase in ECBF to maintain SaO2. More importantly, despite the same value of SaO2, the DO2 resulting from the different combinations of Hb and ECBF progressively decreases with decreasing Hb. Although SaO2 is commonly used to target VV-ECMO support in clinical practice,4,11 this model demonstrates that SaO2 is a poor indicator of oxygen delivery adequacy. Indeed, the same level of SaO2 can correspond to very different values of DO2 and VO2/DO2 ratio, depending on Hb. In normal physiology, DO2 adjusts to metabolic rate to maintain a VO2/DO2 ratio of 0.2–0.3 (only 20–30% of the oxygen delivered is used). When DO2 decreases, VO2 can be initially maintained through the increase in oxygen extraction rate (higher VO2/DO2), but when a critical DO2 threshold is reached, VO2 decreases and the patient is in a state of supply dependency. Metabolism changes from aerobic to anaerobic pathways, and organ function becomes impaired. There is not a universal threshold for critical DO2,12–14 but experimental studies report that supply dependency occurs when VO2/DO2 is greater than 0.415; we arbitrarily considered VO2/DO2 < 0.3 to be the safe limit, extrapolating this value from the normal physiology and from studies addressing hemodynamic optimization in high-risk patients.16,17 Independently of the values used to define critical and optimal DO2, our model demonstrates that the use of SaO2 to assess oxygenation can be misleading and that DO2 should be used as the parameter to evaluate the efficacy of different therapeutic maneuvers at improving oxygenation.

When improvement of DO2 is needed in patients on VV-ECMO, the risks and benefits of transfusion must be balanced against the risks and benefits of ECBF increase.

The benefit of transfusion is good oxygen delivery at lower ECBF. The risks of transfusion include volume overload, immunologic response disorders, acute lung injury and infections. Three large observational studies demonstrated an association between transfusions and mortality.1,2,18 One randomized controlled trial19 showed that lower transfusion thresholds could be acceptable and even beneficial in acutely ill patients, leading to the spread of restrictive transfusion strategies.20 However, the generalizability of the results of this trial has been questioned, and the debate about transfusion strategies is still open.21 In the meantime, efforts are underway to improve transfusion safety, including avoiding use of old blood22,23 and leukoreduction.24–26 Indeed, the results from more recent studies demonstrate a reduction of mortality associated with transfusions in critically ill patients.3,27,28

ECBF increase also carries several risks. Because ECBF is limited by drainage cannula size, large-sized (29–30 Fr) and additional drainage cannulas are required for high flow during VV-ECMO.5,29 Mismatch between required ECBF and cannula size results in excessive negative pressure on the drainage side, which can cause cavitation and hemolysis, and high pressure on the infusion side, which carries the risk of blowout. The attempt to overcome flow limitation can translate into the need to increase intravascular volume; besides the demonstrated negative impact of positive fluid balance in patients with acute lung injury,30 the consequent hemodilution further compromises DO2, resulting in a vicious circle.

The present mathematical model illustrates the physiological concepts which should be taken into account when transfusion and ECBF management are considered to optimize oxygenation in patients on VV-ECMO.


By illustrating the physiology of oxygen delivery during VV-ECMO support, this model may serve as a learning tool and could provide a theoretical basis for a rational approach to strategies implemented to optimize oxygenation in patients on VV-ECMO.


1. Vincent JL, Baron JF, Reinhart K, et al.ABC (Anemia and Blood Transfusion in Critical Care) Investigators. Anemia and blood transfusion in critically ill patients. JAMA. 2002;288:1499–1507
2. Corwin HL, Gettinger A, Pearl RG, et al. The CRIT study: Anemia and blood transfusion in the critically ill—Current clinical practice in the United States. Crit Care Med. 2004;32:39–52
3. Sakr Y, Lobo S, Knuepfer S, et al. Anemia and blood transfusion in a surgical intensive care unit. Crit Care. 2010;14:R92
4. Brodie D, Bacchetta M. Extracorporeal membrane oxygenation for ARDS in adults. N Engl J Med. 2011;365:1905–1914
5. Schmidt M, Tachon G, Devilliers C, et al. Blood oxygenation and decarboxylation determinants during venovenous ECMO for respiratory failure in adults. Intensive Care Med. 2013;39:838–846
6. Butch SH, Knafl P, Oberman HA, Bartlett RH. Blood utilization in adult patients undergoing extracorporeal membrane oxygenated therapy. Transfusion. 1996;36:61–63
7. Ang AL, Teo D, Lim CH, Leou KK, Tien SL, Koh MB. Blood transfusion requirements and independent predictors of increased transfusion requirements among adult patients on extracorporeal membrane oxygenation—A single centre experience. Vox Sang. 2009;96:34–43
8. Fuehner T, Kuehn C, Hadem J, et al. Extracorporeal membrane oxygenation in awake patients as bridge to lung transplantation. Am J Respir Crit Care Med. 2012;185:763–768
9. Crotti S, Lissoni A, Tubiolo D, et al. Artificial lung as an alternative to mechanical ventilation in COPD exacerbation. Eur Respir J. 2012;39:212–215
10. MacLaren G, Combes A, Bartlett RH. Contemporary extracorporeal membrane oxygenation for adult respiratory failure: Life support in the new era. Intensive Care Med. 2012;38:210–220
11. Hemmila MR, Rowe SA, Boules TN, et al. Extracorporeal life support for severe acute respiratory distress syndrome in adults. Ann Surg. 2004;240:595–605
12. van Woerkens EC, Trouwborst A, van Lanschot JJ. Profound hemodilution: What is the critical level of hemodilution at which oxygen delivery-dependent oxygen consumption starts in an anesthetized human? Anesth Analg. 1992;75:818–821
13. Shibutani K, Komatsu T, Kubal K, Sanchala V, Kumar V, Bizzarri DV. Critical level of oxygen delivery in anesthetized man. Crit Care Med. 1983;11:640–643
14. Ronco JJ, Fenwick JC, Tweeddale MG, et al. Identification of the critical oxygen delivery for anaerobic metabolism in critically ill septic and nonseptic humans. JAMA. 1993;270:1724–1730
15. Hirschl RB, Heiss KF, Cilley RE, Hultquist KA, Housner J, Bartlett RH. Oxygen kinetics in experimental sepsis. Surgery. 1992;112:37–44
16. Kern JW, Shoemaker WC. Meta-analysis of hemodynamic optimization in high-risk patients. Crit Care Med. 2002;30:1686–1692
17. Rivers E, Nguyen B, Havstad S, et al.Early Goal-Directed Therapy Collaborative Group. Early goal-directed therapy in the treatment of severe sepsis and septic shock. N Engl J Med. 2001;345:1368–1377
18. Gong MN, Thompson BT, Williams P, Pothier L, Boyce PD, Christiani DC. Clinical predictors of and mortality in acute respiratory distress syndrome: Potential role of red cell transfusion. Crit Care Med. 2005;33:1191–1198
19. Hébert PC, Wells G, Blajchman MA, et al. A multicenter, randomized, controlled clinical trial of transfusion requirements in critical care. Transfusion Requirements in Critical Care Investigators, Canadian Critical Care Trials Group. N Engl J Med. 1999;340:409–417
20. Hébert PC, Fergusson DA, Stather D, et al.Canadian Critical Care Trials Group. Revisiting transfusion practices in critically ill patients. Crit Care Med. 2005;33:7–12
21. Deans KJ, Minneci PC, Suffredini AF, et al. Randomization in clinical trials of titrated therapies: Unintended consequences of using fixed treatment protocols. Crit Care Med. 2007;35:1509–1516
22. Lacroix J, Hébert P, Fergusson D, et al.ABLE Study Group. The Age of Blood Evaluation (ABLE) randomized controlled trial: Study design. Transfus Med Rev. 2011;25:197–205
23. Steiner ME, Assmann SF, Levy JH, et al. Addressing the question of the effect of RBC storage on clinical outcomes: The Red Cell Storage Duration Study (RECESS) (Section 7). Transfus Apher Sci. 2010;43:107–116
24. Hébert PC, Fergusson D, Blajchman MA, et al.Leukoreduction Study Investigators. Clinical outcomes following institution of the Canadian universal leukoreduction program for red blood cell transfusions. JAMA. 2003;289:1941–1949
25. King KE, Shirey RS, Thoman SK, Bensen-Kennedy D, Tanz WS, Ness PM. Universal leukoreduction decreases the incidence of febrile nonhemolytic transfusion reactions to RBCs. Transfusion. 2004;44:25–29
26. Blumberg N, Zhao H, Wang H, Messing S, Heal JM, Lyman GH. The intention-to-treat principle in clinical trials and meta-analyses of leukoreduced blood transfusions in surgical patients. Transfusion. 2007;47:573–581
27. Vincent JL, Sakr Y, Sprung C, Harboe S, Damas PSepsis Occurrence in Acutely Ill Patients (SOAP) Investigators. . Are blood transfusions associated with greater mortality rates? Results of the Sepsis Occurrence in Acutely III Patients study. Anesthesiology. 2008;108:31–39
28. Park DW, Chun BC, Kwon SS, et al. Red blood cell transfusions are associated with lower mortality in patients with severe sepsis and septic shock: A propensity-matched analysis. Crit Care Med. 2012;40:3140–3145
29. Davies A, Jones D, Bailey M, et al.Australia and New Zealand Extracorporeal Membrane Oxygenation Influenza I Investigators. Extracorporeal membrane oxygenation for 2009 influenza A(H1N1) acute respiratory distress syndrome. JAMA. 2009;302:1888–1895
30. Wiedemann HP, Wheeler AP, Bernard GR, et al.National Heart, Lung, Blood Institute Acute Respiratory Distress Syndrome Clinical Trials Network. National Heart, Lung, Blood Institute Acute Respiratory Distress Syndrome Clinical Trials Network. Comparison of two fluid-management strategies in acute lung injury. N Engl J Med. 2006;354:2564–2575

extracorporeal membrane oxygenation; oxygen delivery; hemoglobin; transfusion; mixed-venous oxygen saturation

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