Estimating resting energy expenditure in critically ill patients: a retrospective exploratory comparison of predictive equations and Fick-derived Weir estimates in Italy

Antonio Romanelli; Alessandro Calicchio; Salvatore Palmese; Sabato Pascarella; Bruna Pisapia; Renato Gammaldi

doi:10.4266/acc.001300

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Original Article Nutrition Estimating resting energy expenditure in critically ill patients: a retrospective exploratory comparison of predictive equations and Fick-derived Weir estimates in Italy: Acute and Critical Care 2025;40(3):491-504.
DOI: https://doi.org/10.4266/acc.001300
Published online: August 29, 2025

Antonio Romanelli¹

, Alessandro Calicchio²

, Salvatore Palmese¹

, Sabato Pascarella¹

, Bruna Pisapia¹

, Renato Gammaldi¹

¹Department of Anesthesia and Intensive Care, AOU “San Giovanni di Dio e Ruggi d’Aragona,” Salerno, Italy

²Department of Anesthesia and Intensive Care, ASL “Napoli 2 Nord,” “Santa Maria delle Grazie” Hospital, Pozzuoli (Naples), Italy

Corresponding author: Antonio Romanelli Department of Anesthesia and Intensive Care, AOU “San Giovanni di Dio e Ruggi d’Aragona,” Largo Città d’Ippocrate, Salerno 84131, Italy Tel: +39-89-67-26-18 Email: antonioromanelli86@gmail.com

• Received: March 14, 2025 • Revised: July 15, 2025 • Accepted: August 4, 2025

This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/4.0/) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Abstract
INTRODUCTION
MATERIALS AND METHODS
RESULTS
DISCUSSION
KEY MESSAGES
NOTES
REFERENCES

This article has been corrected. See "Correction: Estimating resting energy expenditure in critically ill patients: a retrospective exploratory comparison of predictive equations and Fick-derived Weir estimates in Italy" in Volume 40 on page 642.

Abstract

Background
Resting energy expenditure (REE) estimation is crucial in critically ill patients. While indirect calorimetry (IC) is the gold standard, its limited availability often necessitates alternative methods. In this exploratory study, we compared the accuracy of the stress factor-corrected Harris-Benedict (cREE_HB) and weight-based (REE_WB) equations with the Weir equation (REE_W) using oxygen consumption (VO₂) and carbon dioxide production (VCO₂) estimated via the Fick principle.
Methods
We included patients admitted to the intensive care unit (ICU) between January and August 2024, and computed cREE_HB, REE_WB (22.5 kcal/kg/day), and REE_W. Agreement between methods was assessed through Bland-Altman analysis. Sensitivity and correlation analyses identified bias determinants. Multiple linear regression explored associations of REE_W with VO₂, VCO₂, and cardiac output (CO).
Results
The sample size consisted of 30 patients. No correlation was found between REE_W and cREE_HB (r=0.177, P=0.349) or REE_WB (r=-0.006, P=0.975). Compared to REE_W, cREE_HB underestimated REE (mean bias, –47.9 kcal), while REE_WB overestimated it (mean bias, +9.7 kcal). CREE_HB bias was associated with sex, height, body surface area (BSA), VO₂, and respiratory quotient (RQ); REE_WB bias was influenced by actual body weight, body mass index, BSA, VO₂, and RQ (all P<0.05). Multiple linear regression analysis showed that REE_W was influenced by VO₂ (P<0.001) and VCO₂ (P<0.001) but not by CO (P=0.164).
Conclusions
Predictive equations may not be interchangeable in ICU settings, leading to inaccurate metabolic assessments. Studies incorporating IC as a reference are needed to determine the most reliable approach for estimating REE and optimizing nutritional support in critical patients.
Key Words: Fick equation; Harris-Benedict; nutritional support; resting energy expenditure; Weir equation

INTRODUCTION

Estimating resting energy expenditure (REE) in critically ill patients is a key component for managing nutritional needs. Adequate nutrition has been shown to reduce complications, improve outcomes, and promote recovery in the intensive care unit (ICU) [1]. Guidelines recommend indirect calorimetry (IC) as the “gold standard” for determining REE [2]. IC accurately estimates REE, particularly in critically ill patients whose metabolic needs constantly shift. The method allows a tailored approach to nutritional management and ensures the appropriate amount of calories based on patient condition. The oxygen consumption (VO₂) and carbon dioxide production (VCO₂) obtained by IC are used in the Weir equation to determine REE [3]. However, IC use is often constrained by costs, technical difficulties, and the need for trained personnel. Moreover, IC measurements are generally performed over 1–2 hours per day and under controlled conditions, not accounting for daily variation [4,5].

As a result, predictive equations, such as the Harris-Benedict (HB) equation, are widely used as substitutes when IC is not available [6,7]. The HB formula relies on static variables such as age, gender, weight, and height to estimate caloric needs and is a convenient and accessible tool in clinical practice. Therefore, HB remains a commonly used reference in many institutions, including ours. However, its accuracy in critically ill patients has been debated [8,9]. Despite the development of stress-corrected versions of the original HB formula, critical illness is associated with profound alterations in metabolism due to inflammation, infection, organ failure, and mechanical ventilation, which are not adequately captured by static models. Consequently, reliance on predictive equations can result in significant discrepancies between estimated and actual REE, potentially leading to underfeeding or overfeeding, both associated with adverse clinical outcomes [10,11]. In recognition of these limitations, current guidelines also suggest the use of simple weight-based equations (such as 20–25 kcal/kg/day) to approximate caloric requirements when IC is unavailable [2]. While practical, this approach may further oversimplify the estimation of REE in metabolically heterogeneous ICU populations.

The Fick equation represents an interesting alternative to computing VO₂ and VCO₂ by relating cardiac output (CO) to the difference in the arterial-venous contents of O₂ and CO₂ obtained from blood gas analysis. This allows reliable VO₂ and VCO₂ estimations without resorting to the IC and overcomes the limits related to predictive or weight-based equations [12,13]. However, studies exploring this alternative approach and its relationship with the HB or weight-based equations are lacking [14].

The primary objective of this exploratory retrospective analysis was to assess the relationships between three methods for REE estimation in critically ill patients: the stress-factor-corrected HB, weight-based HB, and the Weir equations based on surrogate VO₂ and VCO₂ values calculated using the Fick method. As a secondary objective, we aimed to identify clinical and demographic variables influencing the bias between predictive and measured estimates. Finally, we investigated the associations between REE derived via the Weir-Fick method and key physiological parameters, including CO, VO₂, and VCO₂.

MATERIALS AND METHODS

For this explorative retrospective study, we enrolled patients admitted to the ICU from January to August 2024. Data were anonymously collected. The study was conducted following the International Conference on Harmonization Good Clinical Practice guidelines, the 2008 Declaration of Helsinki provisions, and the STrengthening the Reporting of OBservational studies in Epidemiology (STROBE) guideline. The local Ethics Committee (Campania 2) approved the study (ID 2025/3337) and waived the requirement for informed consent in view of its retrospective and observational nature. All patients were managed within the scope of routine clinical practice.

On admission, the following variables were collected: sex, age, height, weight, main comorbidities, reasons for ICU admission, Glasgow Coma Scale (GCS), Sequential Organ Failure Assessment (SOFA) Score, and Simplified Acute Physiology Score (SAPS) II [15-17]. Body mass index (BMI) and body surface area (BSA; using the Mosteller formula) were computed, and obesity was defined as BMI ≥30.0 kg/m².

Exclusion Criteria CriteriaThe exclusion criteria for REE computation were (1) need for vasopressors and inotropic agents within 48 hours before measurement; (2) fever or hypothermia within 48 hours before measurement; (3) use of neuromuscular blocking agents at the time of measurement due to patient–ventilator asynchrony not correctable by sedation alone; (4) continuous renal replacement therapy; (5) arrhythmia; and (6) unstable plethysmographic SpO₂ curve signal.

REE Computation

All patients were sedated and mechanically ventilated prior to measurement. Sedation protocols included continuous infusion of propofol and/or midazolam, combined with opioids (mainly remifentanil), as per institutional standards. The target level of sedation was a Richmond Agitation-Sedation Scale score between –2 and –3.

For every patient, we performed one computation. REE was computed using the HB, weight-based, and Weir equations. For HB REE (REE_HB) estimation, we used the following formula [6]:

Male REE=88.362+(13.397×weight (kg))+(4.799×height (cm))–(5.677×age)

Female REE=447.593+(9.247×weight (kg))+(3.098×height (cm))–(4.33×age)

When BMI < 30.0 kg/m², we used actual body weight (AcBW), while other cases used adjusted body weight (AdBW), computed as ideal body weight (IBW) plus 33.3% of the difference between AcBW and IBW [2,18]. The REE_HB was corrected (cREE_HB) by multiplying its value by a stress factor: 1.10 for elective surgery, 1.25 for complicated surgery, and 1.25–1.50 for sepsis or trauma conditions.

For weight-based REE (REE_WB) estimation, we assumed a caloric requirement of 22.5 kcal/kg/day, the midpoint of the guideline-recommended range of 20–25 kcal/kg/day [2]. The same body weight criteria (AcBW vs. AdBW) described above were applied for this calculation.

For Weir REE (REE_W) estimation, we used the following formula [3]:

REE_W=1.44×[(3.94×VO₂)+(1.11×VCO₂)]

For that, VO₂ and VCO₂ were indirectly estimated with the Fick Equation, using values obtained from blood gas analysis and hemodynamic monitoring [12,13].

Venous and arterial blood samples were obtained using a central venous line placed in the internal jugular or subclavian vein and an arterial catheter placed in the non-dominant side radial artery. Before sampling, 5 mL were discharged from the line. An in-situ blood gas analyzer analyzed venous and arterial samples (GEM PREMIER 5000). Hemoglobin (Hb) concentration was obtained by laboratory testing with a venous blood sample before REE measurement. The following parameters were noted: arterial (PaO₂) and venous partial O₂ pressure (PvO₂), venous (SvO₂) and arterial O₂ saturation (SaO₂), arterial (PaCO₂) and venous partial CO₂ pressure (PvCO₂), and blood bicarbonate (HCO₃^-) concentration.

Using these variables, we computed

Arterial O₂ content (CaO₂)=(SaO₂×Hb×1.34)+(PaO₂×0.03)

Venous O₂ content (CvO₂)=(SvO₂×Hb×1.34)+(PvO₂×0.03)

Venous CO₂ content (CvCO₂)=(PvCO₂×0.03)+venous HCO₃^-

Arterial CO₂ content (CaCO₂)=(PaCO₂×0.03)+arterial HCO₃^-

CO was computed using the minimally invasive estimated Continuous Cardiac Output (esCCO; Nihon Kohden) based on pulse wave transit time (PWTT) [19,20]. PWTT is defined as the period between the peak of the wave R of the ECG and the beginning of the ascending phase of the SpO₂ plethysmographic curve. The SpO₂ probe was placed on a finger, free from arterial and venous lines to avoid bias.

The VO₂ and VCO₂ were computed as

VO₂ (ml/min)=CO×(CaO₂–CvO₂)

VCO₂ (ml/min)=CO×(CvCO₂–CaCO₂)

Then, the respiratory quotient (RQ) was computed.

Statistical Analysis

Continuous variables were tested for normal distribution with the Shapiro-Wilk test and reported as mean±standard deviations (SDs) or medians, first and third quartiles (Q₁–Q₃), and ranges. Categorical variables were reported as absolute numbers and percentages (%). According to our primary aim, we analyzed the correlations between REE_W, cREE_HB, and REE_WB, with REE_W as the reference method. We computed the Pearson correlation coefficient (r) with a 95% CI. We performed simple linear regression analysis and calculated the coefficients of determination (R²). We performed Bland-Altman analysis and computed bias, upper and lower limits of agreements (uLoA and lLoA), and 95% CI [21].

Our secondary aim was to identify factors influencing bias, for which we performed a sensitivity analysis. For categorical variables (sex, obesity, and admission for trauma), the difference in bias value was evaluated with Student t-test (Welch test in the case of heteroscedasticity) or Mann-Whitney test when appropriate. For continuous variables (age, BMI, BSA, CO, PaO₂, PvO₂, PaCO₂, PvCO₂, SaO₂, SvO₂, arterial and venous HCO₃^–, Hb, CaO₂, CvO₂, CaCO₂, CvCO₂, VO₂, VCO₂, RQ), r or Spearman (ρ) coefficients, with 95% CI, were computed according to data distribution (evaluated with the Shapiro-Wilk test). The strength of the relationship was defined as very weak (r/ρ ≤0.1), weak (0.1 < r/ρ ≤0.3), moderate (0.3< r/ρ ≤0.5), strong (0.5< r/ρ ≤0.7), or very strong (r/ρ >0.7) [22].

For the third objective, we analyzed the relationships of REE_W with CO, VO₂, and VCO₂. For each variable, normality was tested using the Shapiro-Wilk test to determine the appropriate correlation coefficient (r or ρ). Correlation coefficients were reported along with 95% CI and associated P-values. To further explore independent associations, we performed multiple linear regression analyses with REE_W as the dependent variable and CO, VO₂, and VCO₂ as explanatory variables. We calculated the standardized beta (β) coefficients, standard errors (SEs), and adjusted R². Multicollinearity was assessed using the variance inflation factor (VIF).

Statistical analysis was computed using R-Studio (R Core Team 2024; R Foundation for Statistical Computing, https://www.R-project.org/). All tests were performed with α=0.05. A P-value <0.05 was considered significant. Results are reported in tables and plots.

RESULTS

Descriptive Statistics

Our sample consisted of 30 patients (Table 1). Briefly, 24 patients (80.0%) were male, the mean age was 60.6 years (SD, 14.4), and the mean BMI was 26.1 kg/m² (SD, 5.3). Seven patients (23.3%) required ICU admission for trauma. The median GCS, SAPS II, and SOFA scores were 5.0, 65.0, and 11.0, respectively. The most common comorbidities were hypertension (18 patients, 60.0%), diabetes (6 patients, 20.0%), obesity (5 patients, 16.7%), and COPD (5 patients, 16.7%). REE_HB showed a mean of 1473.0 kcal (SD, 203.7; range, 1,052.0–1,796.0). The correction factor was applied in four patients (13.3%), and the REE_HB correction factor was 1.25 in three patients and 1.5 in one patient. The mean cREE_HB was 1533.0 kcal (SD, 257.5; range, 1,052.0– 2,055.0), that of the REE_W was 1581.0 kcal (SD, 160.6; range, 1,315.0–1 ,930.0), and that of the REE_WB was 1590.0 kcal (SD, 225.7; range, 1,012.0–1,935.0). Table 2 shows the results of the parameters used to compute REE_W.

Correlation and Bland-Altman Analysis

Thirty data pairs were obtained. There was no significant relationship between REE_W and cREE_HB (r=0.177; 95% CI, –0.196 to 0.505; R²=0.031, P=0.349) (Figure 1A) or REE_W and REE_WB (r=–0.006; 95% CI, –0.365 to 0.355; R²=0.000, P=0.975) (Figure 1B). The Bland-Altman analysis (Figure 1C) showed that cREE_HB underestimated REE compared to REE_W, with a mean bias of –47.9 kcal (SD, 278.3 kcal; 95% CI, –151.8 to 56.0 kcal), which was not significant (P=0.354). The values of uLoA and lLoA were 497.5 kcal (95% CI, 317.9 to 677.1 kcal) and –593.3 (95% CI, –772.9 to –413.7 kcal), respectively. In contrast, REE_WB (Figure 1D) overestimated REE compared to REE_W, with a mean bias of +9.7 kcal (SD, 277.8 kcal; 95% CI, –94.0 to 113.5 kcal), which was not significant (P=0.849). The respective values of uLoA and lLoA were 554.2 kcal (95% CI, 374.9 to 733.5 kcal) and –534.8 (95% CI, –714.0 to –355.5 kcal).

Sensitivity Analysis

Regarding bias between cREE_HB and REE_W, females and males showed a mean bias of –222.9 kcal (SD, 188.1 kcal) and –4.1 kcal (SD, 282.8 kcal), respectively, with statistically significant difference (Welch test P=0.043). Non-obese and obese patients showed a mean bias of –27.4 kcal (SD, 285.7 kcal) and –150.2 kcal (SD, 236.4 kcal), respectively, with no significance (Welch test P=0.343). Patients admitted to the ICU for trauma showed a mean bias of 99.1 kcal (SD, 205.7 kcal), while the bias for patients admitted to the ICU for other reasons was –92.6 kcal (SD, 285.6 kcal). Difference was not significant (Welch test P=0.071). Regarding bias between REE_WB and REE_W, no differences were noted for sex (mean±SD, –36.3±102.9 kcal in females vs. 21.2±307.1 kcal in males, Welch test P=0.453), obesity (mean±SD, 13.1±293.2 kcal in non-obese vs. –7.0±216.7 kcal in obese patients; Welch test P=0.864), and admission for trauma (mean±SD, –19.2±304.4 in patients admitted for other reasons vs. 104.7±139.8 kcal in patients admitted for trauma; Welch test P=0.147).

Table 3 showed the correlation coefficients between bias and continuous variables. Regarding bias between cREE_HB and REE_W, height, BSA, VO₂, and RQ showed significant relationships. BSA showed a strong positive relationship (r=0.513; 95% CI, 0.188 to 0.737; P=0.004) (Figure 2A), while height (r=0.429; 95% CI, 0.081 to 0.684; P=0.018) (Figure 2B) and RQ (ρ=0.409; 95% CI, 0.010 to 0.806; P=0.025) (Figure 2C) showed a moderate positive relationship. Despite AcBW showing a moderate positive relationship, the results were not significant (r=0.351; 95% CI, –0.011 to 0.631; P=0.057). Finally, VO₂ showed a moderate negative relationship (r=-0.436; 95% CI, –0.688 to –0.089; P=0.016) (Figure 2D).

Regarding bias between REE_WB and REE_W, AcBW, BMI, BSA, VO₂, and RQ showed significant relationships. Strong positive relationships were found for aBW (r=0.594; 95% CI, 0.299 to 0.787; P<0.001) (Figure 3A), BSA (r=0.660; 95% CI, 0.393 to 0.824; P<0.001) (Figure 3B), and RQ (r=0.581; 95% CI, 0.305 to 0.853; P<0.001) (Figure 3C), while VO₂ showed a strong negative relationship (r=–0.628; 95% CI, –0.806 to –0.347; P<0.001) (Figure 3D). BMI showed a moderate positive relationship with bias (r=0.402; 95% CI, 0.049 to 0.666; P=0.027) (Figure 3E). Despite PaO₂ showing a moderate negative relationship, the results were not significant (r=–0.337; 95% CI, –0.622 to 0.026; P=0.068).

Multiple Linear Regression Analysis

CO showed a weak positive non-significant relationship with REE_W (r=0.173; 95% CI, –0.200 to 0.502; P=0.361) (Figure 4A). In contrast, VO₂ and VCO₂ showed, respectively, a very strong (r=0.981; 95% CI, 0.959 to 0.991; P<0.001) (Figure 4B) and strong (r=0.650; 95% CI, 0.379 to 0.819; P<0.001) (Figure 4C) significant positive relationship with REE_W. Multiple linear regression analysis showed that REE_W was influenced by VO₂ (β=5.68, SE=0.02, P<0.001) and VCO₂ (β=1.55, SE=0.02, P<0.001) but not by CO (β=–0.59, SE=0.41, P=0.164). No relevant collinearity was observed (VIF for CO, VO₂, and VCO₂ was 1.12, 1.46, and 1.40, respectively). The overall model P-value was <0.001 with an adjusted-R²=0.999.

DISCUSSION

In this exploratory study, we compared two predictive approaches for estimating REE, the cREE_HB and REE_WB, with the REE_W equation using VO₂ and VCO₂ derived from the Fick method. Our findings suggest that both predictive methods showed limited correlation with REE_W. Although the corrected HB equation tended to underestimate REE and the weight-based approach slightly overestimated it, these differences were not significant. Nevertheless, Bland-Altman analysis revealed a wide LoA for both comparisons, highlighting a relevant degree of individual variability. These observations underline the importance of cautious interpretation when relying on predictive methods for REE assessment in ICU patients. Our results are consistent with prior literature highlighting the limitations of predictive equations for REE in critically ill, mechanically ventilated patients. Although IC is the gold standard for REE measurement, its limited availability often leads clinicians to rely on predictive methods [2].

Several studies have shown that these formulas can produce substantial inaccuracies. For instance, Zusman et al. [23] reported that predictive equations may deviate from measured REE by up to 60%, while De Waele et al. [24] emphasized that HB and Penn State formulas tend to either overestimate or underestimate REE, particularly in elderly or obese individuals. Hunter et al. [25] also found low correlations between measured and predicted REE values in ventilated patients. Interestingly, they proposed that predictive performance might improve by incorporating variables such as body composition and physiological stress markers.

In our study, we attempted to correct the HB equation by applying stress factors tailored to clinical condition. However, findings in the literature on this approach remain mixed. MacDonald and Hildebrandt [26] suggested a stress factor (e.g., 1.6) to achieve predictive equations sufficiently accurate for short-term use in ICU settings, while Japur et al. [27] reported that adjusted HB estimates were reasonably reliable. In contrast, Hunter et al. [25] did not confirm these results, further underscoring the inconsistency of outcomes.

Finally, systematic reviews and meta-analyses have reiterated the poor clinical performance of predictive equations compared to measured REE, particularly in heterogeneous ICU populations [8,9]. The inaccuracy stems in part from the use of weight as a proxy variable, which can be difficult to assess reliably in critically ill patients and is influenced by fluid shifts, edema, or muscle loss [28]. Consequently, these tools may lead to underfeeding or overfeeding, both associated with worsened clinical outcomes.

Consistent with current guidelines [2], in the absence of IC or VO₂/VCO₂ measurements, simple weight-based equations (such as 20–25 kcal/kg/day) may represent a pragmatic and widely available option. While less tailored, their ease of use explains their frequent application in clinical practice. In our analysis, we used an intermediate value (22.5 kcal/kg/day) within the recommended range. Interestingly, compared to REE_W, REE_WB showed a limited average bias, suggesting reasonable alignment at the population level. Despite this average agreement, Bland-Altman analysis demonstrated wide limits of agreement, indicating that individual predictions can vary substantially. These findings align with previous studies, which underline the over- or underestimation of REE weight-based equations depending on the population and clinical context. Rousseau et al. showed that the 30 kcal/kg/day formula significantly overestimated REE in post-ICU survivors, with measured REE averaging around 22.9 kcal/kg/day [29]. Conversely, Smetana et al. reported that the 25 kcal/kg/day equation tended to underestimate energy needs in critically ill stroke patients, especially in those with intracerebral hemorrhage or subarachnoid hemorrhage, whereas the 30 kcal/kg/day formula offered closer estimates to IC targets [30]. Altogether, these data support the notion use of weight-based equations should be tempered by awareness of their limitations despite their usefulness in the absence of more advanced techniques. Clinicians should interpret their outputs cautiously and consider clinical context, patient phenotype, and illness phase when applying them to guide nutritional strategies.

Several variables showed significant associations with the bias observed between estimated and measured REE for both cREE_HB and REE_WB equations. In both cases, BSA showed a strong positive correlation with the bias, suggesting that larger BSA may contribute to overestimation of REE when using simplified formulas. Our results are different from those of Pavlidou et al. [31], who evaluated the agreement between predicted REE and actual measurements from IC. Equations incorporating height, along with other variables like weight, age, and sex, provided more accurate predictions than those using only weight and gender. For both methods, RQ exhibited a positive correlation, while VO₂ showed a strong inverse correlation with bias, which is expected given its direct influence on the measured REE via the Weir formula. Saur et al. [32] showed that VO₂ measured during mild therapeutic hypothermia was lower than that predicted by HB estimation, requiring a corrective factor when HB is used without IC.

In addition, sex was a relevant factor, although its impact differed between the two methods. For cREE_HB, female patients showed a significantly greater underestimation of REE compared to males. These findings suggest that the HB equation may not accurately capture the metabolic needs of critically ill women. To the best of our knowledge, the relationship between sex and bias among REE estimated methods is not well investigated. Bias can be clinically relevant, as inaccurate caloric intake in female patients could result in inadequate nutritional support, potentially leading to poor outcomes [11,33]. Gender differences can be attributed to variations in body composition, particularly free-fat mass (FFM). Carrasco et al. [34] showed that REE tends to be lower in women than men due to lower FFM. Furthermore, predictive equations like HB often fail to account accurately for these differences, leading to incorrect estimates in REE for women and obese patients. Interestingly, while AcBW and BMI were significantly associated with bias in the REE_WB, their correlation with cREE_HB bias was weaker, and that of AcBW was not significant. This discrepancy may reflect the influence of structural differences in the equations, as weight plays a more central role in simplified formulas than in HB-based estimations corrected by stress factors.

According to our results, static predictive equations can determine under- or overestimations of REE, especially at the extremes of “normal” distributions curve of physical and metabolic characteristics. The Weir equation is better suited to capturing the dynamic energy requirements of patients with highly variable metabolic activity. This is particularly important in the ICU, where metabolic demands can change rapidly in response to stressors such as sepsis, trauma, and mechanical ventilation. We calculated VO₂ and VCO₂ using the Fick principle. Although current nutritional guidelines [2] recommend the use of data derived from pulmonary artery catheter (PAC) measurements to estimate VO₂ more accurately, this approach is not always feasible in clinical practice due to its invasive nature, limited availability, and patient-specific contraindications. In our cohort, PAC was not routinely used, and data acquisition relied on less invasive methods compatible with standard monitoring. While this limitation may introduce a source of variability, previous evidence supports the validity of this approach. Ong et al. [35] demonstrated that combining Fick-derived VO₂ and VCO₂ with the Weir equation allowed a reasonably accurate estimation of REE in critically ill patients undergoing venovenous extracorporeal membrane oxygenation for whom IC was not feasible. This pragmatic choice reflects the balance between methodological rigor and real-world applicability, particularly in the heterogeneous ICU setting.

In our study, VO₂ and VCO₂ were significant and influential predictors of REE_W. These findings have substantial implications for clinical practice. The strong relationships of VO₂ and VCO₂ with REE_W indicate that real-time assessment with the Fick equation is highly effective for accurately determining patient energy needs. Contrary to the findings of the literature, CO did not show a significant relationship. Studies highlighted the interconnectedness of CO and REE. Brown and Pearson [36] demonstrated a positive correlation between CO and VO₂, providing an early foundation for understanding how variations in CO impact metabolic demands. Peyton [37] further elaborated on the effects of changes in CO, particularly in the context of hemodynamic alterations, on CO₂ elimination, confirming that CO₂ variations can reflect real CO changes. In our study, the hemodynamic stability and the reduced VO₂ related to the use of sedative drugs could partly explain the lack of correlation between CO and REE. According to our findings, given the minimal contribution of CO to the prediction of REE, relying on VO₂ and VCO₂ as primary indicators for caloric needs may lead to better-informed decisions regarding nutritional support and energy supplementation. In our study, CO was computed with esCCO, a less invasive alternative to the traditional thermodilution method. Several studies have demonstrated a moderate to strong correlation between esCCO and thermodilution or PAC-derived CO, with correlation coefficients ranging from 0.6 to 0.84 depending on the clinical setting [38,39]. However, the agreement in absolute values remains variable, with reported biases up to ±1.2 L/min and percentage errors between 18% and 69%. [40,41] While esCCO may underestimate CO in unstable patients or during hemodynamic shifts, it is generally considered suitable for trend monitoring, particularly in hemodynamically stable conditions or when invasive methods are contraindicated [42].

This study presents several strengths. First, to our knowledge, it is among the few analyses to directly compare REE estimated via the corrected HB equation, a standardized weight-based approach, and the Weir equation derived from Fick-based VO₂ and VCO₂ measurements in a homogeneous cohort of sedated, mechanically ventilated ICU patients. Second, we applied a comprehensive sensitivity analysis to explore patient-specific factors influencing estimation bias, offering novel insights into the performance of predictive formulas across physiological profiles. Third, the method we adopted relies solely on routinely available arterial and central venous blood gas analyses and is feasible even in settings lacking access to advanced monitoring techniques such as PAC or IC.

However, some limitations should be acknowledged. First, we did not directly compare our results with IC, the gold standard for measuring REE. Therefore, our findings should be interpreted cautiously. Second, the retrospective design introduced potential biases, and the small sample size limited the generalizability of the findings, especially on factors influencing bias. Prospective studies allow more controlled data collection and potentially more accurate results, leading to more robust conclusions. Third, the study population may not fully represent all critically ill patients. Specifically, although CO was not significant, its role in specific subpopulations, such as patients with heart failure or severe hemodynamic instability, may be more pertinent. Further studies are needed to explore how CO and other hemodynamic factors influence REE. Fourth, the study relied on a static model, which may not adequately capture the dynamic changes in metabolism in critically ill patients. Variations in patient conditions, treatments, or metabolic stress can affect energy demands. A model that adjusts dynamically over time may yield more accurate predictions. Future research should investigate how time-dependent variables can enhance the model responsiveness to evolving clinical conditions.

In conclusion, our study highlights the limitations of predictive equations in accurately estimating REE in critically ill patients and raises questions about their interchangeability when IC is unavailable. In contrast, the Weir equation, applied using VO₂ and VCO₂ estimates derived from the Fick method, offers a more customized and dynamic assessment of metabolic demands. This approach benefits from integration of real-time physiological variables and reflects the fluctuating metabolic state of ICU patients more accurately than static formulas. Notably, it requires only data obtained from standard arterial and central venous blood gas analysis and is a minimally invasive and widely applicable alternative even in the absence of advanced monitoring systems. Further research with larger cohorts is needed to refine this method and evaluate its accuracy across phases of critical illness. Incorporating comparisons with IC will also be essential to confirm the clinical validity of VO₂ and VCO₂ estimates derived from the Fick principle.

KEY MESSAGES

▪ Accurate estimation of resting energy expenditure (REE) is crucial for optimizing nutrition in critically ill patients; while indirect calorimetry (IC) remains the reference standard, it is often unavailable in daily practice.

▪ The stress factor-corrected Harris-Benedict and weight-based equations showed limited agreement with the Weir equation-based results when oxygen consumption (VO₂) and carbon dioxide production (VCO₂) are derived using the Fick method.

▪ Furthermore, several factors influenced bias among methods, impacting the accuracy of predictions.

▪ The use of the Weir equation with minimally invasive Fick-derived gas exchange measurements may offer a more individualized and feasible alternative for estimating REE at the bedside when IC is not accessible.

NOTES

CONFLICT OF INTEREST

No potential conflict of interest relevant to this article was reported.

FUNDING

None.

ACKNOWLEDGMENTS

None.

AUTHOR CONTRIBUTIONS

Conceptualization: AC. Methodology: AR, AC, SP (Salvatore Palmese), SP (Sabato Pascarella), BP. Formal analysis: AR, AC, SP (Salvatore Palmese), BP. Data curation: AR. Visualization: AC, SP (Salvatore Palmese), SP (Sabato Pascarella), BP. Project administration: RG. Funding acquisition: RG. Writing - original draft: AR, AC, SP (Salvatore Palmese), SP (Sabato Pascarella), BP, RG. Writing - review & editing: AR, AC, SP (Salvatore Palmese), SP (Sabato Pascarella), BP, RG. All authors read and agreed to the published version of the manuscript.

Figure 1.

(A, B) Scatter plots with regression line (red dashed line) and 95% CI (grey area) for Weir resting energy expenditure (REE_W) respectively compared to resting energy expenditure computed with the corrected Harris-Benedict equation (cREE_HB) and weight-based REE (REE_WB). (C, D) The Bland-Altman plots for bias between Harris-Benedict and Weir (C), and weight-based and Weir (D). The blue, red, and green areas represent the 95% CI, for bias, lower limit of agreement, and upper limit of agreement, respectively.

Figure 2.

Scatter plots for bias (defined as the difference between resting energy expenditure computed with the corrected Harris-Benedict equation [cREE_HB] and Weir resting energy expenditure [REE_W]) and body surface area (BSA) (A), height (B), respiratory quotient (RQ) (C), and oxygen consumption (VO₂) (D). The red dashed line represents the regression line, while the grey area is the 95% CI.

Figure 3.

Scatter plots for bias (defined as the difference between weight-based REE [REE_WB] and Weir resting energy expenditure [REE_W]) and actual body weight (AcBW) (A), body surface area (BSA) (B), respiratory quotient (RQ) (C), oxygen consumption (VO₂) (D), and body mass index (BMI) (E). The red dashed line represents the regression line, while the grey area is the 95% CI.

Figure 4.

Scatter plots for cardiac output (CO) (A), oxygen consumption (VO₂) (B), and carbon dioxide production (VCO₂) (C), with the regression line (red dashed line) and 95% CI (grey area). REE_W: resting energy expenditure computed with the Weir equation.

Table 1.

Sample characteristics (n=30)

Variable	Value	Range
Age (yr)	60.6±14.4	20–89
Sex, male	24 (30.0)	-
Height (cm)	169.4±8.0	155.0–190.0
Actual body weight (kg)	74.4±13.4	45.0–100.0
BMI (kg/m²)	26.1±5.3	16.5–40.8
BSA (m²)	1.8±0.2	1.5–2.1
BMI/BSA (kg/m⁴)	14.1±2.3	9.9–20.9
Admission for trauma	7 (23.3)	-
GCS	5.0 (4.0–7.0)	3.0–13.0
SAPS II	65.0 (55.0–78.0)	34.0–106.0
SOFA score	11.0 (8.0–13.0)	6.0–18.0
Hypertension	18 (60.0)	-
Diabetes	6 (20.0)	-
Obesity	5 (16.7)	-
COPD	5 (16.7)	-
Congestive heart failure	3 (10.0)	-
Arrhythmia	3 (10.0)	-
Seizure	3 (10.0)	-
Myocardial infarction	2 (6.7)	-
Cerebral vascular disease	2 (6.7)	-
Solid tumor	2 (6.7)	-
Neurodegenerative disease	2 (6.7)	-
Liver disease	1 (3.3)	-
Chronic kidney disease	1 (3.3)	-
Drug or alcohol addiction	1 (3.3)	-
Hematological disease	1 (3.3)	-
Mood disorder	1 (3.3)	-

Values are presented as mean±standard deviation, number (%), or median (first-third quartile). Continuous variables were tested for normal distribution with the Shapiro-Wilk test (α=0.05).

BMI: body mass index; BSA: body surface area; GCS: Glasgow Coma Scale; SAPS: Simplified Acute Physiology Score; SOFA: Sequential Organ Failure Assessment; COPD: chronic obstructive pulmonary disease.

Table 2.

Blood gas analysis and hemodynamic parameters

Variable	Value	Range
CO (L/min)	6.1±1.1	4.2–8.7
PaO₂ (mm Hg)	113.0±26.3	71.0–180.0
PvO₂ (mm Hg)	50.0±6.4	37.0–65.0
PaCO₂ (mm Hg)	39.1±4.6	28.0–48.0
PvCO₂ (mm Hg)	45.5±5.3	35.0–58.0
SaO₂ (%)	99.7 (99.0–100.0)	95.0–100.0
SvO₂ (%)	73.9 (70.5–76.7)	60.0–80.5
Arterial HCO₃^– (mmol/L)	25.4±6.0	14.5–41.0
Venous HCO₃^– (mmol/L)	28.9±5.9	18.7–43.6
Hemoglobin (g/dl)	9.8 (9.0–10.6)	8.0–16.5
CaO₂ (ml/dl)	13.5 (12.5–14.8)	11.2–22.7
CvO₂ (ml/dl)	9.9 (9.1–10.8)	7.4–16.3
CaCO₂ (ml/dl)	26.5±6.1	15.5–42.3
CvCO₂ (ml/dl)	30.2±6.0	19.9–45.1
VO₂ (ml/min)	220.9±24.7	176.3–268.6
VCO₂ (ml/min)	215.1±23.1	159.0–265.9
RQ	1.0 (0.9–1.0)	0.8–1.2

Values are presented as mean±standard deviation or median (first-third quartile). Continuous variables were tested for normal distribution with the Shapiro-Wilk test (α=0.05).

CO: cardiac output; PaO₂: arterial partial O₂ pressure; PvO₂: venous partial O₂ pressure; PaCO₂: arterial partial CO₂ pressure; PvCO₂: venous partial CO₂ pressure; SaO₂: arterial O₂ saturation; SvO₂: venous O₂ saturation; HCO₃^-: blood bicarbonate; CaO₂: arterial O₂ content; CvO₂: venous O₂ content; CaCO₂: arterial CO₂ content;

CvCO₂: venous CO₂ content; VO₂: oxygen consumption; VCO₂: carbon dioxide production; RQ: respiratory quotient.

Table 3.

Correlation coefficients

Variable	Bias between cREE_HB and REE_W		Bias between REE_WB and REE_W
Variable	Results (95% CI)	P-value	Results (95% CI)	P-value
Age	–0.315 (–0.606 to 0.051)	0.090	0.029 (–0.335 to 0.385)	0.879
Height	0.429 (0.081 to 0.684)	0.018	0.260 (–0.110 to 0.567)	0.165
Actual body weight	0.351 (–0.011 to 0.631)	0.057	0.594 (0.299 to 0.787)	<0.001
BMI	0.116 (–0.255 to 0.457)	0.541	0.402 (0.049 to 0.666)	0.027
BSA	0.513 (0.188 to 0.737)	0.004	0.660 (0.393 to 0.824)	<0.001
Cardiac output	0.149 (–0.223 to 0.483)	0.432	0.114 (–0.257 to 0.456)	0.548
PaO₂	–0.121 (–0.461 to 0.250)	0.523	–0.337 (–0.622 to 0.026)	0.068
PvO₂	0.172 (–0.200 to 0.501)	0.363	–0.040 (–0.394 to 0.325)	0.833
PaCO₂	0.170 (–0.203 to 0.499)	0.369	0.180 (–0.192 to 0.508)	0.340
PvCO₂	0.077 (–0.291 to 0.425)	0.687	–0.024 (–0.381 to 0.339)	0.898
SaO₂ (%)^a)	0.045 (–0.381 to 0.470)	0.815	–0.089 (–0.525 to 0.348)	0.639
SvO₂ (%)^a)	0.127 (–0.290 to 0.543)	0.503	0.040 (–0.315 to 0.395)	0.834
Arterial HCO₃^–	0.038 (–0.327 to 0.393)	0.841	–0.131 (–0.469 to 0.240)	0.490
Venous HCO₃^–	0.025 (–0.339 to 0.381)	0.897	–0.163 (–0.494 to 0.210)	0.390
Hemoglobin^a)	–0.299 (–0.680 to 0.086)	0.109	–0.277 (–0.713 to 0.161)	0.138
CaO₂^a)	–0.292 (–0.686 to 0.106)	0.118	–0.272 (–0.717 to 0.174)	0.145
CvO₂^a)	–0.228 (–0.639 to 0.186)	0.226	–0.258 (–0.663 to 0.150)	0.169
CaCO₂	0.033 (–0.331 to 0.389)	0.862	–0.127 (–0.466 to 0.245)	0.504
CvCO₂	0.011 (–0.350 to 0.370)	0.952	–0.157 (–0.490 to 0.215)	0.407
VO₂	–0.436 (–0.688 to –0.089)	0.016	–0.628 (–0.806 to –0.347)	<0.001
VCO₂	–0.141 (–0.477 to 0.231)	0.458	–0.148 (–0.483 to 0.224)	0.434
RQ^a)	0.409 (0.010 to 0.806)	0.025	0.581 (0.305 to 0.853)	<0.001

The table showed the correlation coefficients between multiple variables and bias, defined as the differences between cREE_HB and REE_W and between cREE_HB and REE_WB.

cREE_HB: resting energy expenditure computed with the corrected Harris-Benedict equation; REE_W: resting energy expenditure computed with the Weir equation; REE_WB: resting energy expenditure computed with the weight-based formula; BMI: body mass index; BSA: body surface area; PaO₂: arterial partial O₂ pressure; PvO₂: venous partial O₂ pressure; PaCO₂: arterial partial CO₂ pressure; PvCO₂: venous partial CO₂ pressure; SaO₂: arterial O₂ saturation; SvO₂: venous O₂ saturation; HCO₃^-: blood bicarbonate; CaO₂: arterial O₂ content; CvO₂: venous O₂ content; CaCO₂: arterial CO₂ content; CvCO₂: venous CO₂ content; VO₂: oxygen consumption; VCO₂: carbon dioxide production; RQ: respiratory quotient.

^a)The relationship was explored by computing the Spearman correlation coefficient.

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Estimating resting energy expenditure in critically ill patients: a retrospective exploratory comparison of predictive equations and Fick-derived Weir estimates in Italy

Acute Crit Care. 2025;40(3):491-504. Published online August 29, 2025

DOI: https://doi.org/10.4266/acc.001300

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Correction: Estimating resting energy expenditure in critically ill patients: a retrospective exploratory comparison of predictive equations and Fick-derived Weir estimates in Italy

Estimating resting energy expenditure in critically ill patients: a retrospective exploratory comparison of predictive equations and Fick-derived Weir estimates in Italy

Figure 1. (A, B) Scatter plots with regression line (red dashed line) and 95% CI (grey area) for Weir resting energy expenditure (REEW) respectively compared to resting energy expenditure computed with the corrected Harris-Benedict equation (cREEHB) and weight-based REE (REEWB). (C, D) The Bland-Altman plots for bias between Harris-Benedict and Weir (C), and weight-based and Weir (D). The blue, red, and green areas represent the 95% CI, for bias, lower limit of agreement, and upper limit of agreement, respectively.

Figure 2. Scatter plots for bias (defined as the difference between resting energy expenditure computed with the corrected Harris-Benedict equation [cREEHB] and Weir resting energy expenditure [REEW]) and body surface area (BSA) (A), height (B), respiratory quotient (RQ) (C), and oxygen consumption (VO2) (D). The red dashed line represents the regression line, while the grey area is the 95% CI.

Figure 3. Scatter plots for bias (defined as the difference between weight-based REE [REEWB] and Weir resting energy expenditure [REEW]) and actual body weight (AcBW) (A), body surface area (BSA) (B), respiratory quotient (RQ) (C), oxygen consumption (VO2) (D), and body mass index (BMI) (E). The red dashed line represents the regression line, while the grey area is the 95% CI.

Figure 4. Scatter plots for cardiac output (CO) (A), oxygen consumption (VO2) (B), and carbon dioxide production (VCO2) (C), with the regression line (red dashed line) and 95% CI (grey area). REEW: resting energy expenditure computed with the Weir equation.

Figure 1.

Figure 2.

Figure 3.

Figure 4.

Estimating resting energy expenditure in critically ill patients: a retrospective exploratory comparison of predictive equations and Fick-derived Weir estimates in Italy

Variable	Value	Range
Age (yr)	60.6±14.4	20–89
Sex, male	24 (30.0)	-
Height (cm)	169.4±8.0	155.0–190.0
Actual body weight (kg)	74.4±13.4	45.0–100.0
BMI (kg/m²)	26.1±5.3	16.5–40.8
BSA (m²)	1.8±0.2	1.5–2.1
BMI/BSA (kg/m⁴)	14.1±2.3	9.9–20.9
Admission for trauma	7 (23.3)	-
GCS	5.0 (4.0–7.0)	3.0–13.0
SAPS II	65.0 (55.0–78.0)	34.0–106.0
SOFA score	11.0 (8.0–13.0)	6.0–18.0
Hypertension	18 (60.0)	-
Diabetes	6 (20.0)	-
Obesity	5 (16.7)	-
COPD	5 (16.7)	-
Congestive heart failure	3 (10.0)	-
Arrhythmia	3 (10.0)	-
Seizure	3 (10.0)	-
Myocardial infarction	2 (6.7)	-
Cerebral vascular disease	2 (6.7)	-
Solid tumor	2 (6.7)	-
Neurodegenerative disease	2 (6.7)	-
Liver disease	1 (3.3)	-
Chronic kidney disease	1 (3.3)	-
Drug or alcohol addiction	1 (3.3)	-
Hematological disease	1 (3.3)	-
Mood disorder	1 (3.3)	-

Variable	Value	Range
CO (L/min)	6.1±1.1	4.2–8.7
PaO₂ (mm Hg)	113.0±26.3	71.0–180.0
PvO₂ (mm Hg)	50.0±6.4	37.0–65.0
PaCO₂ (mm Hg)	39.1±4.6	28.0–48.0
PvCO₂ (mm Hg)	45.5±5.3	35.0–58.0
SaO₂ (%)	99.7 (99.0–100.0)	95.0–100.0
SvO₂ (%)	73.9 (70.5–76.7)	60.0–80.5
Arterial HCO₃^– (mmol/L)	25.4±6.0	14.5–41.0
Venous HCO₃^– (mmol/L)	28.9±5.9	18.7–43.6
Hemoglobin (g/dl)	9.8 (9.0–10.6)	8.0–16.5
CaO₂ (ml/dl)	13.5 (12.5–14.8)	11.2–22.7
CvO₂ (ml/dl)	9.9 (9.1–10.8)	7.4–16.3
CaCO₂ (ml/dl)	26.5±6.1	15.5–42.3
CvCO₂ (ml/dl)	30.2±6.0	19.9–45.1
VO₂ (ml/min)	220.9±24.7	176.3–268.6
VCO₂ (ml/min)	215.1±23.1	159.0–265.9
RQ	1.0 (0.9–1.0)	0.8–1.2

Variable	Bias between cREE_HB and REE_W		Bias between REE_WB and REE_W
Variable	Results (95% CI)	P-value	Results (95% CI)	P-value
Age	–0.315 (–0.606 to 0.051)	0.090	0.029 (–0.335 to 0.385)	0.879
Height	0.429 (0.081 to 0.684)	0.018	0.260 (–0.110 to 0.567)	0.165
Actual body weight	0.351 (–0.011 to 0.631)	0.057	0.594 (0.299 to 0.787)	<0.001
BMI	0.116 (–0.255 to 0.457)	0.541	0.402 (0.049 to 0.666)	0.027
BSA	0.513 (0.188 to 0.737)	0.004	0.660 (0.393 to 0.824)	<0.001
Cardiac output	0.149 (–0.223 to 0.483)	0.432	0.114 (–0.257 to 0.456)	0.548
PaO₂	–0.121 (–0.461 to 0.250)	0.523	–0.337 (–0.622 to 0.026)	0.068
PvO₂	0.172 (–0.200 to 0.501)	0.363	–0.040 (–0.394 to 0.325)	0.833
PaCO₂	0.170 (–0.203 to 0.499)	0.369	0.180 (–0.192 to 0.508)	0.340
PvCO₂	0.077 (–0.291 to 0.425)	0.687	–0.024 (–0.381 to 0.339)	0.898
SaO₂ (%)^a)	0.045 (–0.381 to 0.470)	0.815	–0.089 (–0.525 to 0.348)	0.639
SvO₂ (%)^a)	0.127 (–0.290 to 0.543)	0.503	0.040 (–0.315 to 0.395)	0.834
Arterial HCO₃^–	0.038 (–0.327 to 0.393)	0.841	–0.131 (–0.469 to 0.240)	0.490
Venous HCO₃^–	0.025 (–0.339 to 0.381)	0.897	–0.163 (–0.494 to 0.210)	0.390
Hemoglobin^a)	–0.299 (–0.680 to 0.086)	0.109	–0.277 (–0.713 to 0.161)	0.138
CaO₂^a)	–0.292 (–0.686 to 0.106)	0.118	–0.272 (–0.717 to 0.174)	0.145
CvO₂^a)	–0.228 (–0.639 to 0.186)	0.226	–0.258 (–0.663 to 0.150)	0.169
CaCO₂	0.033 (–0.331 to 0.389)	0.862	–0.127 (–0.466 to 0.245)	0.504
CvCO₂	0.011 (–0.350 to 0.370)	0.952	–0.157 (–0.490 to 0.215)	0.407
VO₂	–0.436 (–0.688 to –0.089)	0.016	–0.628 (–0.806 to –0.347)	<0.001
VCO₂	–0.141 (–0.477 to 0.231)	0.458	–0.148 (–0.483 to 0.224)	0.434
RQ^a)	0.409 (0.010 to 0.806)	0.025	0.581 (0.305 to 0.853)	<0.001

Table 1. Sample characteristics (n=30)

Values are presented as mean±standard deviation, number (%), or median (first-third quartile). Continuous variables were tested for normal distribution with the Shapiro-Wilk test (α=0.05).

BMI: body mass index; BSA: body surface area; GCS: Glasgow Coma Scale; SAPS: Simplified Acute Physiology Score; SOFA: Sequential Organ Failure Assessment; COPD: chronic obstructive pulmonary disease.

Table 2. Blood gas analysis and hemodynamic parameters

Values are presented as mean±standard deviation or median (first-third quartile). Continuous variables were tested for normal distribution with the Shapiro-Wilk test (α=0.05).

CvCO₂: venous CO₂ content; VO₂: oxygen consumption; VCO₂: carbon dioxide production; RQ: respiratory quotient.

Table 3. Correlation coefficients

The table showed the correlation coefficients between multiple variables and bias, defined as the differences between cREE_HB and REE_W and between cREE_HB and REE_WB.

The relationship was explored by computing the Spearman correlation coefficient.