Article Text

Original article
A new predictive equation for oxygen consumption in children and adults with congenital and acquired heart disease
  1. Michael D Seckeler,
  2. Russel Hirsch,
  3. Robert H Beekman III,
  4. Bryan H Goldstein
  1. The Heart Institute, Cincinnati Children's Hospital Medical Center, Cincinnati, Ohio, USA
  1. Correspondence to Dr Michael D Seckeler, Department of Pediatrics (Cardiology), The University of Arizona, 1501 N. Campbell Ave, PO Box 245073, Tucson, AZ 85724, USA; mseckeler{at}


Objective To develop a new predictive equation for oxygen consumption (VO2) in children and adults with congenital and acquired heart disease.

Methods We retrospectively reviewed data from 502 consecutive patients (age 0–59 years) undergoing cardiac catheterisation with measured VO2 (M-VO2) and compared M-VO2 with VO2 from the LaFarge equations (LF-VO2) in patients <3 years (Group 1) and ≥3 years (Group 2). Factors associated with inaccurate LF-VO2 were used to develop a new predictive equation, which was prospectively validated in 100 consecutive patients (age 0–59 years).

Results LF-VO2 was inaccurate in 42% of Group 1 (n=201) and 13% of Group 2 (n=301). Multivariable predictors of inaccurate LF-VO2 included age (OR 0.41, p=0.01) and single ventricle anatomy (OR 2.98, p=0.03) in Group 1 and anaemia (OR 0.84, p<0.001) in Group 2. Critical illness was borderline significant in both groups. The new predictive equation for VO2:Embedded Image

Intraclass correlation between M-VO2 and the new predictive equation was good (r=0.53), whereas LF-VO2 was not (r=0.17). Bland-Altman analysis comparing M-VO2 with the new equation and with LF-VO2 demonstrated superiority of the new equation (mean bias 2.5 mL/min/m2 vs −5.0 mL/min/m2; limits of agreement −51.6, 56.5 vs −82.1, 72).

Conclusions VO2 derived from the LaFarge equations is frequently inaccurate, particularly in younger patients, and will lead to erroneous haemodynamic calculations. We developed and prospectively validated a new VO2 predictive equation for use in patients of all ages with congenital and acquired heart disease.

Statistics from


An accurate haemodynamic evaluation is critical to the management of paediatric patients with congenital and acquired heart disease, including those with congenital heart disease (CHD) needing intervention, pulmonary hypertension, myocarditis, cardiomyopathy and those awaiting or following cardiac transplantation. Cardiac index (CI) can be measured with thermodilution (TDCI), but only in patients without intracardiac shunts or significant right-heart valvar regurgitation.1 ,2 For patients with these lesions, which are common in CHD, CI must be calculated using the Fick equation.3 Oxygen consumption (VO2), the numerator in the Fick equation, has historically been cumbersome to measure in clinical settings. Therefore, most catheterisation laboratories estimate VO2 using predictive equations, most commonly those published by LaFarge and, less commonly, those from Lundell or Bergstra.4–6

The LaFarge equations were derived nearly 50 years ago, when neonates and infants were not often studied invasively, single ventricle heart disease was infrequently palliated, percutaneous interventions were non-existent, and general anaesthesia was rarely employed during catheterisations.4 ,7 ,8 Therefore, it may be inappropriate to estimate VO2 from the LaFarge equations in the current era of interventional congenital cardiac catheterisation in complex patient populations. In fact, recent work has shown that the predictive equations for VO2 can be inaccurate, especially for younger patients with CHD and those receiving general anaesthesia with positive pressure ventilation.9–15 There are likely other factors associated with inaccurate VO2 assumptions, but these have not been yet identified.9–13 Moreover, recently published survey data demonstrate that a majority of congenital cardiac catheterisation labs use the LaFarge equations to derive VO2 during catheterisation procedures on patients of all ages (including infants and neonates), despite the derivation data set for those equations only including children ≥3 years of age.7

Currently, children with complex CHD generally undergo early surgical intervention, often as neonates, and frequently require diagnostic catheterisation and catheter-based interventions as part of their management.16 ,17 Ascertainment of highly accurate invasive haemodynamic data in the CHD and acquired heart disease populations is crucial for medical and surgical decision making. It is therefore necessary to have accurate VO2 data readily available, whether directly measured or accurately predicted. Recent advances in technology have allowed for easier real-time acquisition of measured VO2 (M-VO2) during catheterisation. While measuring VO2 on a case-by-case basis would eliminate the need to assume VO2, this requires the purchase of new and expensive equipment, and is therefore unlikely to be broadly adopted in clinical practice. Therefore, in this study of patients with acquired heart disease and CHD undergoing cardiac catheterisation, we sought to identify factors associated with an inaccurately assumed VO2 using the LaFarge equations, and more importantly, to develop and validate a new VO2 predictive equation for use in patients of all ages in the contemporary congenital cardiac catheterisation laboratory.


After approval from the Institutional Review Board, we identified consecutive patients that underwent catheterisation with general anaesthesia and measurement of VO2 at a single-centre academic quaternary-care children's hospital between February 2011 and May 2013. Since February 2011, it has been standard practice in our catheterisation laboratory to measure VO2 in any patient under general anaesthesia with an artificial airway in place. Measurement of VO2 is acquired using the D-lite and Pedi-lite flow sensors (Datex-Ohmeda Division, Instrumentarium Corp, Helsinki, Finland) which attach inline to an artificial airway, have a sidestream sampling port for gas analysis and spirometry and have been in clinical use for over 20 years.18 ,19 They are accurate for tidal volume ranges of 150–2000 mL (D-lite) and 15–300 mL (Pedi-lite) and introduce minimal additional dead space.20 The flow sensors are connected to the GE CARESCAPE B850 Monitor with E-CAiOV Airway Module (GE Healthcare, Milwaukee, Wisconsin, USA) and use continuous gas sampling and a paramagnetic oxygen sensor to provide breath-by-breath analysis of expired air, including measurement of VO2.11 ,19 Our group has previously validated the use of the D-lite and Pedi-lite sensors and CARESCAPE monitor for acquisition of accurate M-VO2 to determine cardiac output by the Fick equation in children <3 years of age undergoing catheterisation.7 A detailed description of the procedural methodology was published previously.7

Assumed VO2 was calculated using the LaFarge equations (LF-VO2),4 the most common predictive equations for VO2 used in contemporary catheterisation laboratories.7 A greater than 20% difference between LF-VO2 and M-VO2 defined an inaccurate LF-VO2. This cut-off was chosen as clinically relevant given the direct relationship between VO2, CI and pulmonary vascular resistance (PVR), and the accepted variance in those measurements during catheterisation.21 Patients were stratified by age for analysis into two groups (Group 1: <3 years old and Group 2: ≥3 years old), as the LaFarge equations have not been validated for children <3 years of age. Factors evaluated for association with an inaccurate LF-VO2 included: age (years), weight (kilograms), body surface area (BSA) (kilograms/m2), heart rate (beats per minute), haemoglobin (grams/dL), clinical status (critically ill versus not critically ill) and cardiac diagnosis. Critical illness was defined by patient location at the time of the procedure (critically ill=intensive care unit admission; not critically ill=outpatient, general or cardiac step-down unit admission). Cardiac diagnoses were stratified into nine predetermined categories (table 1).

Table 1

Characteristics of the 502 patients in the baseline analysis

Continuous normally distributed data were compared using paired t tests, non-normally distributed data were compared with Mann-Whitney U tests and categorical data were compared using χ2 tests. A p value ≤0.05 was considered statistically significant. Simple and multiple logistic regressions were used to identify factors associated with an inaccurate LF-VO2. Pearson's correlation coefficient and Bland-Altman analysis were used to assess the accuracy of LF-VO2 compared with M-VO2.22

A linear regression model for estimating VO2 was developed using data from the retrospective derivation data set, incorporating significant predictors from the regression models; univariate predictors were considered for inclusion in the new predictive model if they had a p value ≤0.1. The new model was then prospectively validated against M-VO2 in the next 100 consecutive patients (whose data were not used to derive the new model), using intraclass correlation coefficient and Bland-Altman analysis. In addition, M-VO2 from the validation data set was compared with VO2 derived from the LaFarge and Lundell equations.6 These comparisons were made across the validation data set overall and in subgroups stratified by age (<3 years old and ≥3 years old). The Lundell equations were included in the analysis of the validation data set because they were derived from a data set similar to that used in the current study (patients <3 years of age were included). Statistical analyses were performed using IBM SPSS Statistics V.21.0 (IBM Corporation, Armonk, New York, USA).


Baseline data set

Characteristics of the 502 consecutive patients in the derivation data set are shown in table 1. The data set included a broad range of paediatric and adult subjects, with age and weight ranging from 0 years to 59 years and 2.8 kg to 122 kg, respectively. M-VO2 was lower than LF-VO2 in Group 1 (165.9 mL/min/m2 vs 187 mL/min/m2, p<0.001) and higher than LF-VO2 in Group 2 (145.9 mL/min/m2 vs 140.5 mL/min/m2, p<0.001). The rate of inaccurate LF-VO2 was substantially greater in Group 1 compared with Group 2 (42% vs 13%, p<0.001). LF-VO2 had a weak negative correlation with M-VO2 in Group 1 (r=−0.315, p<0.001; figure 1A) and a strong positive correlation in Group 2 (r=0.593, p<0.001; figure 1B), suggesting reasonable accuracy of the LaFarge equation in patients ≥3 years of age but not in younger patients. Bland-Altman analysis revealed the inaccuracy of LF-VO2 compared with M-VO2 in Group 1 (mean bias −21.1 mL/min/m2, 95% limits of agreement −103.9, 61.8; figure 2A). In Group 2, however, LF-VO2 was found to be highly accurate (mean bias 5.4 mL/min/m2, 95% limits of agreement −35.5, 46.3; figure 2B). Multiple logistic regression identified younger age and single ventricle anatomy in Group 1 and anaemia in Group 2 as significant predictors of an inaccurate LF-VO2; critical illness was of borderline significance in both groups (table 2).

Table 2

Results of simple and multiple logistic regression analyses to identify factors associated with an inaccurate LaFarge VO2 for each group

Figure 1

Correlation plots of measured VO2 versus LaFarge derived VO2 for Group 1 (<3 years old) (A) and Group 2 (≥3 years old) (B) from the baseline data set. There is a weak negative correlation between measured VO2 and LaFarge VO2 in Group 1 and a strong positive correlation in Group 2. VO2, oxygen consumption.

Figure 2

Bland-Altman plots comparing measured VO2 with LaFarge derived VO2 for Group 1 (A) and Group 2 (B) from the baseline data set. LaFarge VO2 is less accurate in Group 1 (larger mean bias and wider limits of agreement) than in Group 2 when compared with measured VO2. VO2, oxygen consumption.

New predictive equation

The univariate predictors tested for use in the new predictive model of VO2 were: age, weight, BSA, heart rate, haemoglobin level, critical illness and single ventricle anatomy (dichotomous variables; each given a value of 1 for yes or 0 for no). BSA was found to be collinear with age and weight, and was not included in the final model. The addition of heart rate and haemoglobin level added to the complexity of the model without improving its accuracy so were not included in the final model. Therefore, the final predictive equation for VO2 was defined as:Embedded Image

Validation data set

The 100 consecutive patients in the validation data set (age 0–59 years, weight 3–85 kg) were not significantly different from the patients in the derivation data set (table 3). As shown in table 4, the new predictive equation generated the highest intraclass correlation coefficient for the validation cohort overall. Bland-Altman analysis, shown in online supplementary figure S1 (left column), demonstrated superiority of the new predictive equation (mean bias 2.3 mL/min/m2, 95% limits of agreement −51.7, 56.2) compared with VO2 derived from the LaFarge (mean bias −5.0 mL/min/m2, 95% limits of agreement −82.1, 72.0) and Lundell (mean bias −11.8 mL/min/m2, 95% limits of agreement −71.9, 48.2) predictive equations in the overall validation data set.

Table 3

Characteristics of the patients in the derivation and validation data sets

Table 4

Intraclass correlation coefficients for the three predictive equations within the validation data set

In the subgroup of children <3 years old (n=41), the intraclass correlation was best for the Lundell equations, acceptable for the new equation and poor for LaFarge (table 4). Bland-Altman analysis showed that the new and Lundell equations were comparably accurate (mean bias −1.32 mL/min/m2 vs 0.61 mL/min/m2, 95% limits of agreement −65.4, 62.8 vs −65.2, 66.4), whereas LF-VO2 was inaccurate (mean bias −23.3 mL/min/m2, 95% limits of agreement −119.84, 73.2) (see online supplementary figure S1, middle column).

In the subgroup of patients ≥3 years old (n=59), intraclass correlation was best for the new equation followed by the LaFarge and Lundell equations, respectively (table 4). Bland-Altman analysis showed that the new and LaFarge equations were comparably accurate (mean bias 4.8 mL/min/m2 vs 7.7 mL/min/m2, 95% limits of agreement −40.8, 50.3 vs −38.1, 53.5), whereas the Lundell equation was not highly accurate (mean bias −20.5 mL/min/m2, 95% limits of agreement −69.7, 28.8) (see online supplementary figure S1, right column).

Predicted VO2 derived using the new predictive equation, stratified by single ventricular or biventricular physiology and clinical status, is shown in tables 5 and 6.

Table 5

Predicted oxygen consumption (mL/min/m2) by age and weight for not critically ill (top) and critically ill (below) patients with single ventricle anatomy

Table 6

Predicted oxygen consumption (mL/min/m2) by age and weight for not critically ill (top) and critically ill (below) patients with two ventricle anatomy


In this large single-centre study of children and adults undergoing cardiac catheterisation with direct measurement of VO2, we demonstrated that the LaFarge equations were frequently inaccurate in children and adults with acquired heart disease and CHD. Several factors, particularly young age and single ventricle anatomy, were found to be associated with an inaccurate VO2 predicted by the LaFarge equations. Using these factors, we derived a new predictive equation for VO2 in patients of all ages with acquired heart disease and CHD and prospectively validated the new equation in an independent sample of 100 consecutive patients. Our new equation was shown to be more accurate for patients of all ages as compared with two VO2 predictive equations currently in use across the continuum of childhood and adult heart disease.

Our study is not unique in identifying inaccuracies with predicted VO2 derived from the LaFarge equations. Multiple prior studies in patients with CHD have shown inaccuracies in VO2 derived from predictive equations, including the LaFarge equations and others.9–13 However, the present study may be unique in identifying specific factors associated with an inaccurate predicted VO2 using the LaFarge equations. The risk factors identified in this study are biologically plausible, as they are markers of substantial perturbations from the ‘normal’ physiological state. Anaemia is frequently associated with an increased heart rate as a means to augment cardiac output and normalise oxygen delivery to the tissues. As the LaFarge equations use age and heart rate to predict VO2, an elevated heart rate for age due to anaemia (in contrast to a situation with increased cardiac output and tissue oxygen delivery, such as hyperthyroidism) would likely lead to an overestimate of VO2. Critical illness may also have effects on heart rate, along with intended or unintended iatrogenic effects on cardiac output, tissue oxygen supply and demand and lead to inaccurate VO2 predicted by the LaFarge equations. Patients with functional single ventricle anatomy have been shown to have lower measured VO2 and diminished cardiac output compared with similar children with biventricular circulation, so it is not surprising that VO2 measured during catheterisation is lower than would be predicted with the LaFarge equations.10 ,23–25

As shown in table 4 and online supplementary figure S1, the inaccuracy of VO2 from the LaFarge equations in the validation data set is largely driven by its inaccuracy in patients <3 years old, a group for which the equation was neither derived nor validated. Moreover, the LaFarge equations were developed when infants and high-risk single ventricle patients did not undergo catheterisation. Despite these important limitations, the LaFarge equations remain one of the most commonly used VO2 predictive equations in catheterisation laboratories today.7 Analyses of VO2 derived from the Lundell equations show that they perform at least as well as our new VO2 predictive equation in patients <3 years of age. However, the Lundell equations are less accurate than the new and LaFarge equations for patients ≥3 years old. Our new VO2 predictive equation performs well in patients of all ages and can serve as a single predictive equation for use in all patients with acquired heart disease and CHD who undergo invasive haemodynamic evaluation.

It is interesting to note that despite the use of general anaesthesia for all patients in this study, the LaFarge equations, which were derived from patients who were sedated, were quite accurate for patients ≥3 years of age in our data set. This finding might suggest that, while the method of airway management and anaesthesia can affect the VO2,14 ,15 the near exclusive use of general anaesthesia for catheterisation procedures in our study population is not likely to be the primary source of inaccuracies found in the predicted VO2 data in younger children.

Accurate invasive haemodynamic data is of importance in the evaluation of many patients with complex cardiovascular physiology, congenital and acquired. Such evaluations are often required to assess indications for intervention, preoperative risk stratification, determination of surgical or transplantation candidacy and modification of vasoactive medication regimens. In the case of single ventricle patients being considered for (further) staged surgical palliation, highly accurate invasive haemodynamic data is critical. In the absence of a subpulmonary ventricle following superior cavopulmonary anastomosis and Fontan completion, these patients require low PVR for adequate pulmonary blood flow, systemic preload and cardiac output. An inverse relationship has been shown between PVR and systemic preload, CI and mechanical efficiency after the Fontan procedure.26 ,27 Fakler et al found that compared with similar patients with biventricular anatomy, Fontan-palliated single ventricle patients had lower VO2.10 In the present study, we found that VO2 derived from existing predictive equations is often inaccurate in single ventricle patients of all ages and after any stage of surgical palliation. Use of an inaccurate assumed VO2 in this patient population could lead to falsely increased estimates of pulmonary blood flow and falsely low calculated PVR. Such an error may inappropriately permit a single ventricle patient to proceed to further staged surgical palliation when a more accurate assessment of PVR might otherwise preclude their candidacy, or at least potentially alter preoperative and perioperative medical management in a high-risk patient. Accurate haemodynamic data ought to improve the efficacy of catheterisation as a tool for preoperative risk assessment in the single ventricle population and others.

Given the importance of accurate haemodynamic assessments in children with acquired heart disease and CHD undergoing catheterisation, direct measurement of VO2 should be the gold standard. This is especially true in patients with factors that we found to be associated with inaccurate predicted VO2. However, the additional expense of the necessary technology makes this an unrealistic expectation for many catheterisation laboratories. Moreover, the development and validation of a new predictive equation specifically for use in patients of all ages with acquired heart disease and CHD, including those with single ventricle physiology and critical illness, may mitigate the need for direct measurement of VO2. We believe that use of this new VO2 predictive equation and tables published here will improve the accuracy of routinely measured invasive haemodynamic data in patients with acquired heart disease and CHD without investment in additional technology or adoption of significant changes in clinical practice.

This study has several important limitations. First, the study was performed at a single centre, which may introduce local biases. However, the inclusion of a large number of catheterisation procedures by multiple providers across a broad spectrum of patients with acquired heart disease and CHD, preoperative and postoperative, should serve to reduce this impact. Second, there are several published equations for VO2 estimation that were not analysed in this study. We chose to focus only on the LaFarge and Lundell predictive equations as these have the greatest penetration in clinical practice today.7 Third, in order to measure VO2 in this study, all patients had an artificial airway in place and most, but not all, received positive pressure ventilation during the catheterisation. This may limit the generalisability of the new VO2 predictive equation to those patients undergoing catheterisation with general anaesthesia, as patients without an artificial airway in place were not studied. This distinction may have a substantial impact on VO2. Direct non-invasive measurement of VO2 in a sedated patient cohort would allow for validation of this new equation in that setting.

In this large single-centre study of cardiac catheterisation and VO2 in acquired heart disease and CHD, we demonstrated the inaccuracy of the LaFarge predictive equations for VO2 and developed and prospectively validated a new predictive equation for VO2 in patients of all ages with acquired heart disease and CHD. Use of the new VO2 predictive equation should improve the accuracy of invasively derived haemodynamic measures.

Key messages

  • What is known on this subject?

  • Oxygen consumption (VO2) is a critical value for calculating systemic and pulmonary blood flow during congenital cardiac catheterisations. Given the expense and difficulty with direct measurement of VO2, this value is typically derived from predictive equations. These equations have been shown to be inaccurate in multiple studies of paediatric patients with congenital heart disease.

  • What might this study add?

  • This study again highlights the inaccuracy of the most commonly used predictive equations for VO2 in clinical practice. We then developed and prospectively validated a new equation for VO2 for use in children and adults with congenital and acquired heart disease.

  • How might this impact on clinical practice?

  • By making more accurate VO2 data available and easy to obtain without the additional cost of new equipment, we hope that the quality of haemodynamic data obtained during congenital catheterisations will improve, leading to improved outcomes for patients. The reference tables provided can be easily incorporated into routine practice in the catheterisation lab.


Supplementary materials

  • Supplementary Data

    This web only file has been produced by the BMJ Publishing Group from an electronic file supplied by the author(s) and has not been edited for content.

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  • Contributors All listed authors are responsible for this research and have participated in the design, data collection, analysis, writing and revising of the manuscript and have given final approval.

  • Funding The Burleigh Family Fund provided funds to purchase the GE CARESCAPE B850 Monitor.

  • Competing interests None.

  • Ethics approval Cincinnati Children’s Hospital Medical Center Institutional Review Board.

  • Provenance and peer review Not commissioned; externally peer reviewed.

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