Chapter 12: Metabolic Measurements

Oxygen (O2) and Carbon Dioxide (CO2)
Water Vapor Pressure and Humidity
Air Flow
Differentially-based Metabolic Measurements
Metabolic Measurement System Design
Propane-based Calibration
Chemical Reactions of Combustion
Flow-thru Calorimetry for Metabolic Measures

Oxygen (O2) and Carbon Dioxide (CO2)

O2 and CO2 are present in both inspired and expired air flows. The concentrations of O2 or CO2 in a specific sample of gas are represented by their measured partial pressures in that sample. A variety of methods exist to measure the partial pressures of O2 and CO2. Typically, gas sensors will output the measured partial pressure as a gas concentration number, referenced to a percentage or part per million (ppm), in a specific sample of gas. Gas sensors are sensitive to ambient barometric pressure.

Ambient gas concentrations are:

O2 – 20.95%
CO2 – 0.04%
Nitrogen – 78.08%
Argon – 0.93%
Trace gasses – very close to 0%

For metabolic measurements, Nitrogen, Argon and all other trace atmospheric gasses are combined together as “metabolically inert” gas, grouped under the N2 heading. This inert gas amounts to a total gas concentration of 79.01% in ambient air.

Water Vapor Pressure and Humidity

Water vapor is present as a gas in both inspired and expired air flows. The concentration of water vapor in a specific sample of gas is represented by the partial pressure of water vapor in that sample. Water vapor partial pressure must be considered in any type of metabolic system because the presence of water vapor will change the relative partial pressures of oxygen and carbon dioxide in the inspired and expired air streams. Water vapor pressure, in a gas sample, can be determined if both the relative humidity and temperature of the gas sample are known.


Temperature is an important variable for metabolic measurements, primarily for the purpose of accurate determination of water vapor pressure. Water vapor pressure can be calculated from an expression combining relative humidity and associated temperature. Most relative humidity probes include a temperature sensor for this express reason.

Air Flow

Precise gas volumetric recordings are critical for metabolic measurements. Generally, gas volume recordings are estimated via the use of air flow transducers (pneumotachs). When integrating air flow measurement over time, volume can be determined. A variety of technical methods are available to measure air flow. No matter which method is employed, calibration is important. Calibration can be performed by using a fixed volume syringe (0.5 to 3 liter) and directing the syringe output through the air flow transducer. The air flow signal is integrated and then compared to the known syringe volume. Calibration factors can be used to adjust the air flow transducer output signal so its integrated result equals the known volume.

Another important factor is humidity. Expired breath is 100% saturated with water vapor. If the air flow transducer is held at a lower temperature than expired breath, then water will condense out of the expired air and may affect air flow transducer behavior. This phenomena is only a problem in metabolic systems that are solely sourced by expired air flow. Flow-through metabolic systems, because they incorporate a sizable fraction of ambient air in the expired flow, may not exhibit water condensation on the expired side.

Differentially-based Metabolic Measurements

All metabolic measurements are based on the gas concentration differences between inspired and expired air. The following concentrations require measurement or estimation for both inspired (ambient) and expired air:

carbon dioxide
barometric pressure
relative humidity

Metabolic systems often employ assumptions to simplify measurement requirements. For example, assuming a source of fresh air as intake, then certain gas concentrations are automatically known:

Oxygen concentration: 20.95%
Carbon Dioxide concentration: 0.04%

By measuring ambient temperature and relative humidity then inspired water vapor pressure (H20 gas concentration) can be calculated.

By measuring barometric pressure, then conversion to Standard Temperature Pressure (STP) can be performed.

On the expired side, it’s assumed that the air is saturated with water vapor, so the relative humidity is assumed to be 100%. Expired air temperature is at 37 deg C. This condition is known as Body Temperature Pressure Saturated (BTPS). If expired air cools on the way to being measured, the air stays saturated, but water vapor will condense out of the air flow. If the expired air cools to ambient temperature, the air’s condition is then referred to as Ambient Temperature Pressure, Saturated (ATPS). Expired breath is assumed saturated, but the temperature should be measured at the point of gas concentration sensing to determine the correct water vapor pressure.

Metabolic Measurement System Design

Typical Connections:

Non-rebreathing T-valve, input is ambient air
Output side is mixing chamber and gas sampling
Air flow measured on inspired side or expired side

Equipment Construction:

Awareness with respect to gas permeability of tubing materials is important. For example, silicone tubing has significantly higher oxygen, carbon dioxide and water vapor permeability, as compared to Polyvinyl Chloride (PVC) or Polyethylene (PE) tubing.

Air Flow Transducer:

The pneumotach (air flow transducer) needs to measure unidirectional, pulsed, air flow. Assuming transducer is used to measured expired air flow, then it needs to accommodate the 100% humidity in the stream. Often, air flow is measured on the inspired side to avoid the issues associated with condensing water vapor. However, some airflow transducers are insensitive to water condensation.

Other Methodologies:

If expired air is sampled, after flowing through temperature equalizing and Nafion (gas drying) tubing, then BTPS can’t be assumed. Nafion tubing will reduce the expired air humidity level to ambient conditions, assuming proper lengths and diameters of Nafion tubing are chosen for the given sampled flow rate. In this case, expired sampled air is considered to be at ATP, with its WVP to be at ambient. Any additional water vapor, contributed by the subject, is assumed removed from the sample stream. Furthermore, both inspired and expired sample streams are assumed to be at ambient temperature and WVP. Given equivalent temperatures and WVP amounts on both inspired side and expired side, it’s not necessary to measure either parameter to determine a corrected CO2 or O2 measurement, when considering a differential measure. This is because both Nitrogen and Water Vapor amounts will be identical on inspired and expired side. The only differences will be in the relative concentrations (partial pressures) of CO2 and O2.

Propane-based Calibration

Metabolic measurement systems are best calibrated via “Propane Test”. A Propane Test is accomplished by efficiently burning propane, using a small torch, that has been placed on a precision scale capable of measuring with 10mg resolution or better. Assuming sufficiently available oxygen, propane combustion produces threemolecules of CO2 for each five molecules of O2 consumed. Accordingly, the Respiratory Exchange Ratio (RER) mimicked by optimal propane combustion is 3/5 or 0.600.

The RER for humans can vary from 0.6 to 1.2, with typical values of roughly 0.8. A diet of fat will result in an RER of roughly 0.7, while a diet of carbohydrate will result in an RER of about 1.0. For a short time, under periods of strenuous exercise, it’s possible for subjects to have RERs greater than 1.0. This is because CO2 produced by skeletal muscle increases. In this circumstance, more CO2 is being expired than O2 consumed.

Chemical Reactions of Combustion

With sufficient O2 present, propane (C3H8) combusts (burns) to produce CO2 and H2O. The chemical reaction is:

1 of C3H8 + 5 of O2 = 3 of CO2 + 4 of H2O + combustion heat
1 propane molecule + 5 oxygen molecules =
3 carbon dioxide molecules + 4 water molecules + heat

With insufficient O2 present, propane combustion produces CO2, H2O and CO (carbon monoxide). The chemical reaction is:

1 of C3H8 + 4.5 of O2 = 2 of CO2 + 4 of H2O + 1 of CO + combustion heat
1 propane molecule + 4.5 of oxygen molecules =
2 carbon dioxide molecules + 4 water molecules + 1 carbon monoxide molecule + heat

The production of CO indicates incomplete combustion, so it can be helpful to have a carbon monoxide detector incorporated into metabolic measuring systems, when calibrating with propane.

All metabolic measurement systems are concerned with inspired and expired gas volumes. Metabolic systems operate via the estimation, or direct measurement, of differential gas volumes of oxygen (O2), carbon dioxide (CO2) and water vapor. The estimation, or direct measurement, of gas volumes are concerned with the concentrations of O2, CO2 and water vapor on inspiration and expiration.

Because all gases are combined in any measurement volume, specific gas volumes are calculated by measuring that gas concentration in a known measurement volume. Measurement volumes are typically determined by measuring air flow and integrating the flow to obtain the associated volume of gas over a certain time period.

Typically, metabolic measurement systems separate inspired and expired airflows via a non-rebreathing “T” valve. With these valves, inspired air enters the nose/mouth and into lungs via the inspiration port on the “T valve. Expired air from the lungs is exhausted through the expiration port on the “T” valve.

A flow transducer can be situated, on the inspiration port, to measure inspiratory flow and used to determine inspiratory air volume. Alternatively, a flow transducer can be situated on the expiration port, to measure expiratory flow and used to determine expiratory air volume. In addition, using the Haldane transformation, the expiratory volume can be calculated from the inspiratory volume, or vice versa, because the amount of nitrogen (N2) is unchanged.

Flow-thru Calorimetry for Metabolic Measures

In this circumstance inspired air to the chamber is at ATP. Expired air from the chamber (ATPe) is usually nearly at ATP, but at perhaps slightly higher temperature and higher relative humidity (water vapor pressure).

Fractional CO2 Concentration in Inspired Air: FiCO2
Fractional O2 Concentration in Inspired Air: FiO2
Fractional N2 Concentration in Inspired Air: FiN2
Fractional H2O Concentration in Inspired Air: FiH2O

Where: FiCO2 + FiO2 + FiN2 + FiH2O = 1 (ATP)

Fractional CO2 Concentration in Expired Air: FeCO2
Fractional O2 Concentration in Expired Air: FeO2
Fractional N2 Concentration in Expired Air: FeN2
Fractional H2O Concentration in Expired Air: FeH2O

Where: FeCO2 + FeO2 + FeN2 + FeH2O = 1 (ATPe)

FiH2O and FeH2O are forced to zero when inspired air at ATP and expired air at ATPe are converted to STPD.

Haldane Transformation

Concentration of Nitrogen (N2) is the same in inspired and expired air

Vi*FiN2 = Ve*FeN2

Ve = Vi * (1 – FiCO2 – FiO2) / (1 – FeCO2 – FeO2)


Fi*CO2 = 0.0004
Fi*O2 = 0.2095

Ve = Vi * (0.7901) / (1- FeCO2 – FeO2)

VO2 = ViO2 – VeO2
VO2 =(Vi*FiO2)-(Ve*FeO2)

VCO2 = VeCO2 – ViCO2
VCO2 =(Ve*FeCO2)-(Vi*FiCO2)

To precisely measure FeO2 and FeCO2, use the following methodology:

FeO2 = 0.2095 – delta O2
FeCO2 = 0.0004 + delta CO2


delta O2 = O2 ambient – O2 expired
delta CO2 = CO2 expired – CO2 ambient

In this fashion, any drift in gas analyzer is removed from calculation. To measure ambient gas concentration levels, mixing chamber is flushed with environmental air.

Measured Barometric Pressure: Pb (kPa)
Standard Barometric Pressure: 101.3 (kPa)
Standard Temperature: 273 deg K
Ambient Temperature: Ta (deg C)

ViSTPD = ViATP * (273 / (273 + Ta)) * ((Pb – PH2O) / 101.3)
Vis = ViSTPD
Ves = VeSTPD

Gas sensing modules measure the partial pressure of the gas of interest. The partial pressure of the gas is a function of the following factors:

1. ambient pressure in the gas sensor volume
2. partial pressures of other gases in the sensor volume

Generally, the ambient pressure is simply the ambient barometric pressure. Partial pressure calculations need to factor in the water vapor differences between inspired and expired air flows. Correct gas concentration measurements, due to PH2O, where PH2O is measured in both inspired and expired air flows. This is important because the subject in the chamber is generating additional water vapor pressure as compared to ambient water vapor pressure.

Correction factor for water vapor partial pressure:

O2 corrected = (O2 measured) * (Pb/(Pb – PH2O))
CO2 corrected = (CO2 measured) * (Pb/(Pb – PH2O))

Delta measurements:

delta O2 = (O2 ambient – O2 expired)
delta CO2 = (CO2 expired – CO2 ambient)

Ves = Vis * (0.7901) / (1- FeCO2 – FeO2)
Ves = Vis * (0.7901) / (1- (0.0004+delta CO2) – (0.2095-delta O2))

VO2 = (Vi*FiO2)-(Ve*FeO2)
VO2 = (Vi*0.2095) – (Ve*(0.2095-delta O2))

VCO2 = (Ve*FeCO2)-(Vi*FiCO2)
VCO2 = (Ve*(0.0004+delta CO2)) – (Vi*0.0004)

Respiratory Exchange Ratio


Weir Equation

Energy Expenditure (kcal/min) = [(VO2 * 3.941) + (VCO2 * 1.11)]
Per day: RMR (kcal) = [(VO2) (3.941) + (VCO2)(1.11)] * 1440 minutes
24 hours * 60 minutes = 1440 minutes/day


ATP = Ambient (Atmospheric) Temperature and Pressure
ATPS = Ambient (Atmospheric) Temperature and Pressure, Saturated
BTPS = Body Temperature and Pressure, Saturated
STPD = Standard Temperature and Pressure, Dry
Ta = Temperature (ambient) in deg C
Pb = Barometric Pressure (ambient)
PH20 = Water Vapor Pressure (WVP – ambient)
Inspired Volume: Vi
Expired Volume: Ve
Standard Temperature: 273 deg K (0 deg C)
Standard Pressure: 760 mmHg (at sea level)
Body Expired Air Temperature: 37 deg C
Body Expired Water Vapor Pressure at 37 deg C: 47mmHg (saturated)

If flow measurements are performed on the inspired side, then air at Ambient Temperature Pressure (ATP), can be converted to SPTD by:

ViSTPD = ViATP * (273 / (273 + Ta)) * ((Pb – PH20) / 760)

If flow measurements are performed on the expired side, with no expired gas cooling to ambient, then gas at Body Temperature and Pressure, Saturated (BTPS), can be converted to SPTD by:

VeSTPD = VeBTPS * (273 / (273 + 37)) * ((Pb – 47) / 760)

So assuming Pb is at sea level (760mm Hg) then:

VeSTPD = VeBTPS * (0.8262)

WVP calculation, assuming 100% RH:

Water Vapor Pressure (kPa), for Ta ranges from 10 – 40 deg C, assuming air is saturated with water vapor.

PH2O = 0.42013 + 0.07985*Ta – 0.000751*Ta^2 + 0.000078*Ta^3