Chemical energy used to fuel the human body is directly provided by adenosine triphosphate, which is formed by the oxidation of carbohydrate, protein, and lipid. The stores of adenosine triphosphate in the body are small, but they are in a constant, high-volume, well-balanced state of formation and utilization. Indirect calorimetry measures the oxygen used and carbon dioxide produced when carbohydrate, protein, and lipid are oxidized to produce adenosine triphosphate. Therefore, it is the production of chemical energy that is indirectly measured by the gas-exchange parameters. Despite this, it is the convention to describe this quantity as energy expended. Therefore, we use the term energy expenditure to describe the amount of energy quantified by indirect calorimetry.

In any discussion of energy expenditure, it is important to define what level of energy expenditure is being considered. Basal metabolic rate or basal energy expenditure (BEE) is the energy used by the body at complete rest and in the postabsorptive state (absence of active nutritional intake for at least 4 to 6 hours). This measurement can be obtained reliably only in deep sleep. If such a measurement is made, BEE does take into account the effects of illness and stress. However, BEE often is taken to be a value calculated from a standardized equation that does not account for stress, such as the Harris-Benedict equation. Resting energy expenditure (REE) is obtained from an awake person at rest and includes the energy used at rest in the awake state plus the energy used to metabolize foodstuffs, also called diet-induced thermogenesis. It is expected to be approximately 10% greater than BEE [3, 4 and 5]. Total energy expenditure (TEE) is REE plus the energy used during activity. TEE and REE are closer in value for ICU patients than for patients in other settings because most ICU patients are bedridden. In most cases, we wish to know the 24-hour REE or TEE rather than the BEE.

Most indirect calorimetry systems use the modified de Weir equation to calculate energy expenditure. In its more complete form, this equation uses oxygen consumption ([V with dot above]o₂), carbon dioxide production ([V with dot above]CO₂), and nonprotein urinary nitrogen (UN):

Energy expenditure = 3.9([V with dot above]o₂) – ([V with dot above]CO₂) – 2.17(UN g/day)

The de Weir equation is not experimentally derived from measurements on humans but is mathematically derived. The derivation relies on the knowledge that (a) TEE is equal to the sum of the energy expended from the combustion of carbohydrate, fat, and protein; (b) the caloric equivalents of glucose (3.7 kcal per g), fat (9.5 kcal per g), and protein (4.1 kcal per g) are known; (c) the oxygen consumed and carbon dioxide produced in metabolizing each of these fuels is known; and (d) therefore, the equation for energy expenditure can be expressed in terms of oxygen consumption and carbon dioxide production by solving the system of equations that describes the stoichiometry of fuel combustion. The reader is referred to other sources for a complete derivation of the equation [6]. In practice, the amount of urea nitrogen in the urine is usually not measured because of the fact that its contribution to TEE is considered minimal.

The essential measurements of indirect calorimetry are the inspired and expired oxygen fractions (Fio₂ and FEO₂, respectively), carbon dioxide fractions, (FICO₂ and FEO₂, respectively) and minute ventilation. Oxygen consumption and carbon dioxide production can be calculated using similar equations, which
compute the difference between inspired (I) and expired (E) volumes:

Oxygen consumption = [V with dot above]o₂ = VI(Fio₂) – [V with dot above]E(FEO₂

Carbon dioxide production = [V with dot above]CO₂ = [V with dot above]E(FEco₂) – [V with dot above]I(FICO₂)

To avoid the need to measure the volumes of expiratory and inspiratory gases, techniques have been developed that preferentially measure only exhaled volumes and mathematically derive the inhaled volume. Any assumption that the volume exhaled is equal to the volume inhaled is erroneous whenever [V with dot above]CO₂ and [V with dot above]o₂ are not equal (i.e., RQ is not equal to 1) and becomes more erroneous as Fio₂ increases. A mathematic relationship of [V with dot above]E to [V with dot above]I called the Haldane transformation can be used to explain this phenomenon. It takes advantage of the fact that nitrogen is an essentially inert gas. Therefore,

Volume inspired ([V with dot above]I) × FEN₂ = volume expired ([V with dot above]E) × FEN₂

Rearranged, this reads

[V with dot above]I = [V with dot above]E × FEN₂/FIN₂

Because FIO₂ FIN₂ = 1 and FEO₂ + FECO₂ + FEN₂ = 1, FIN₂ = 1 – FIO₂

and

FEN₂ = 1 – FECO₂ – FEO₂

If we substitute back into the previous equation,

[V with dot above]I = [V with dot above]E × (1 – FECO₂ – FEO₂)/(1 – FIO₂)

As the inspired oxygen concentration increases, the denominator decreases and the difference between inspired and expired gas volume becomes greater. The Haldane equation can therefore be used to determine the value of [V with dot above]I without measuring inspired volume.

The use of the Haldane equation during indirect calorimetry leads to some important and practical technical considerations. Most significantly, the accuracy of the Haldane equation in estimating inspired volume, and thereby oxygen consumption and energy expenditure, depends greatly on the accuracy of measurement of FIO₂ and [V with dot above]E. Any error in measuring exhaled volumes or gas concentrations directly produces an error of a greater magnitude in the calculation of oxygen consumption, carbon dioxide production, and energy expenditure. At a minute ventilation of 10 L per minute and an inspired-to-expired oxygen concentration difference of 0.03, the oxygen consumption would be 300 mL per minute. If the FIO₂ was measured to be 0.46 instead of 0.45 and the FEO₂ remained at 0.42, the oxygen consumption would be 400 mL per minute, a 33% change. If the measured minute ventilation was 10.1 L per minute and the actual value was 10 L per minute, there would be an error in the oxygen consumption of 30 mL per minute, or 10%. To prevent such errors, the analysis system must be free of leaks, and extremely accurate sensors must be used. Because most oxygen sensors are less accurate at higher FIO₂, indirect calorimetry studies are usually limited to patients on 60% oxygen or less. Although some systems have provided accurate results in vitro with higher levels of oxygen, there have been no studies to date that prove the accuracy of any system above FiO2 60% in critically ill patients [7, 8]. The 2004 American Association of Respiratory Care guideline also confirms the limitation of FEO₂ to 0.6 [1].

Oxygen sensors in commercially available systems are either zirconium or differential paramagnetic sensors. The zirconium oxide sensor is coated with an oxygen-permeable substance. At temperatures of approximately 800°C, oxygen diffuses across this outer layer and an electrical signal that is proportional to the partial pressure of oxygen is created [2, 9]. Differential paramagnetic analyzers measure the difference in concentration of the gas between the inspiratory and expiratory lines. These analyzers typically have an accuracy of ± 0.02% and a response time of 130 msec or less. Essentially all available carbon dioxide analyzers are nondispersed infrared devices. A gas sample in the path of infrared energy creates an alteration in an electrical signal that is proportional to the concentration of carbon dioxide. These analyzers have an accuracy of ± 0.02% with a response time of 110 msec. Some systems measure inspired and expired carbon dioxide, and some measure only expired, assuming the inspired value to be negligible. Volume is calculated by measuring flow and integrating the result over time to obtain volume. Flow is usually either measured with a pneumotach or a mass flow sensor or generated by the device and kept constant in response to changes in ventilation.

Gas concentrations are measured using one of three techniques: mixing chamber, breath-by-breath, and dilution. All devices must have well-validated calibration procedures for essential components. Newer machines have automated much of this process.