- The four most famous equations for the estimation of metabolic requirements are the Harris-Benedict, Ireton-Jones, Fusco and Frankenfield equations.
- They each have specific indications.
- Harris-Benedict is the best known and is applicable equally well in all circumstances
- Ireton-Jones is mainly for ventilated burns patients
- Fusco formula is for the morbidly obese ICU patient
- Frankenfield formula was designed with sepsis and trauma in mind

Because the metabolic cart for indirect calorimetry is frequently a cumbersome pain in the arse to deploy, lazy people have developed arithmetical shortcuts which - to some extent - predict the energy requirements of critically ill patients without having to resort to precise measurements of their gas exchange volumes. In the past papers, Question 28 from the second paper of 2007 and Question 7 from the first paper of 2015 required some knowledge of these equations' strengths and weaknesses, but so far the college has not asked anything too indepth.

## The Harris-Benedict Equation

This formula was arrived at after numerous empirical experiments, from data collected by the Nutrition Laboratory of the Carnegie Institution, under the direction of Francis G. Benedict.

They published in 1918, and their equation (with some revisions) to this day remains the most commonly used method of estimating the basal metabolic rate.

This equation can also be adjusted to accomodate different, non-basal rates of metabolism - by simply multiplying it by a factor which estimates the increased energy demand.

For instance, if one is engaged in heavy exercise, on can multiply one's BMR value by 1.75-2.00.

Similarly, multipliers are available to reflect the fact that critically ill patients frequently have very abnormal energy requirements, owing to their state of critical illness (or in some cases the perverse treatments they are receiving).

Even after all these years, critics reluctantly agree that "*All of the variables used in the equations have sound physiologic basis for use in predicting BEE*"(basal energy expenditure).

## The Ireton-Jones Formula

This is a more recent formula than the Harris-Benedict, and it was devised specifically to estimate the deranged patterns of energy expenditure in ventilated burns patients.

This equation adjusts for the changes in metabolic demand due to mechanical ventilation, and makes special provisions for the hypercatabolic state of trauma and burns.

## The Fusco formula

The simplicity of this equation almost allows one to forgive that it mixes Imperial and scientific measurements. I suppose we are to be thankful that one's height is not measured in handspans instead.

This equation was developed with a view to estimate the energy requirements of obese patients, and to prevent their overfeeding in intensive care.

## The Frankenfield formula

This equation was developed with sepsis and trauma in mind.

The investigators had found that minute volume correlated with basal metabolic rate, and thus have factored it into their equation. Haemoglobin also features, and its difficult to explain why. The possibilities for multipliers are endless; the investigators found a coefficient which one can use to multiply their dobutamine dose, thereby factoring it into the BMR calculations. Ultimately, the authors are forced to admit that their regression equations "*probably apply only to severe trauma and sepsis*", and that "*other studies should be conducted to predict energy expenditure in other patient types*".

## A comparison of predictive formulae

A comparison of these predicitive equations with indirect calorimetry and the Fick method was performed. None except the Ireton-Jones and the Frankenfield equation were particularly good. In the end, analysis revealed that even those two best performers had a pretty poor correlation coefficient, suggesting that for any individual patient they would produce inaccurate results.

In short, predictive equations - though useful as vague estimates - can never be as good as direct measurements.

### References

LITFL has an excellent summary dedicated to indirect calorimetry. I stole a couple of their references.

Holdy, Kalman E. "Monitoring energy metabolism with indirect calorimetry: instruments, interpretation, and clinical application." *Nutrition in Clinical Practice* 19.5 (2004): 447-454.

Flancbaum, Louis, et al. "Comparison of indirect calorimetry, the Fick method, and prediction equations in estimating the energy requirements of critically ill patients." *The American journal of clinical nutrition* 69.3 (1999): 461-466.

Weir, JB de V. "New methods for calculating metabolic rate with special reference to protein metabolism." *The Journal of physiology* 109.1-2 (1949): 1.

McClave, Stephen A., Robert G. Martindale, and Laszlo Kiraly. "The use of indirect calorimetry in the intensive care unit." *Current Opinion in Clinical Nutrition & Metabolic Care* 16.2 (2013): 202-208.

Lev, Shaul, Jonathan Cohen, and Pierre Singer. "Indirect calorimetry measurements in the ventilated critically ill patient: facts and controversies—the heat is on." *Critical care clinics* 26.4 (2010): e1-e9.

Fraipont, Vincent, and Jean-Charles Preiser. "Energy Estimation and Measurement in Critically Ill Patients." *Journal of Parenteral and Enteral Nutrition* 37.6 (2013): 705-713.

Müller, Manfred J., et al. "World Health Organization equations have shortcomings for predicting resting energy expenditure in persons from a modern, affluent population: generation of a new reference standard from a retrospective analysis of a German database of resting energy expenditure."*The American journal of clinical nutrition* 80.5 (2004): 1379-1390.

Long, Calvin L., et al. "Metabolic response to injury and illness: estimation of energy and protein needs from indirect calorimetry and nitrogen balance."*Journal of Parenteral and Enteral Nutrition* 3.6 (1979): 452-456.

Frankenfield, David C., Eric R. Muth, and William A. Rowe. "The Harris-Benedict studies of human basal metabolism: history and limitations." *Journal of the American Dietetic Association* 98.4 (1998): 439-445.

Harris, J. Arthur, and Francis G. Benedict. "A biometric study of human basal metabolism." *Proceedings of the National Academy of Sciences of the United States of America* 4.12 (1918): 370.

Ireton-Jones, Carol S., et al. "Equations for the estimation of energy expenditures in patients with burns with special reference to ventilatory status."*Journal of Burn Care & Research* 13.3 (1992): 330-333.

Fusco, M. A., M. E. Mills, and L. D. Nelson. "Predicting caloric requirements with emphasis on avoiding overfeeding." *JPEN J Parenter Enteral Nutr* 19 (1995): 18S. This one is not available in fulltext.

Frankenfield, David C., et al. "Correlation between measured energy expenditure and clinically obtained variables in trauma and sepsis patients." *Journal of parenteral and enteral nutrition* 18.5 (1994): 398-403.

Frankenfield, David, Lori Roth-Yousey, and Charlene Compher. "Comparison of predictive equations for resting metabolic rate in healthy nonobese and obese adults: a systematic review." *Journal of the American Dietetic Association*105.5 (2005): 775-789.