Appendices

Calculation of Oxygen Consumption

Calculation of oxygen consumption is a relatively simple process that involves subtracting the amount of oxygen exhaled from the amount of oxygen in-haled:

The volume of O₂ inspired (I) is computed by multiplying the volume of air inhaled per minute (V̇_I) by the fraction (F) of air that is made up of oxygen. Room air is 20.93% O₂. Expressed as a fraction, 20.93% becomes .2093 and is symbolized as F_IO₂. When we exhale, the fraction of O₂ is lowered (i.e., O₂ diffuses from the lung to the blood) and the fraction of O₂ in the expired (E) gas is represented by F_EO₂. The volume of expired O₂ is the product of the volume of expired gas (V̇_E) and F_EO₂. Equation (1) can now be symbolized as:

The exercise values for F_IO₂, F_EO₂, V̇_I, and V̇_E for a subject are easily measured in most exercise physiology laboratories. In practice, F_IO₂ is not generally measured but is assumed to be a constant value of .2093 if the subject is breathing room air. F_EO₂ will be determined by a gas analyzer, and V̇_I and V̇_E can be measured by a number of different laboratory devices capable of measuring airflow. Note that it is not necessary to measure both V̇_I and V̇_E. This is true because if V̇_I is measured, V̇_E can be calculated (and vice versa). The formula used to calculate V̇_E from the measurement of V̇_I is called the “Haldane transformation” and is based on the fact that nitrogen (N₂) is neither used nor produced in the body. Therefore, the volume of N₂ inhaled must equal the volume of N₂ exhaled:

Therefore, V̇_I can be computed if V̇_E, F_IO₂, and F_EO₂ are known. For example, to solve for V̇_I:

Likewise, if V̇_I was measured, V̇_E can be computed as:

The values for F_IN₂ and F_EN₂ are obtained in the following manner. If the subject is breathing room air, F_IN₂ is considered to be a constant .7904. The final remaining piece to the puzzle is F_EN₂. Recall that the three principal gases in air are N₂, O₂, and CO₂ and the sum of their fractions must add up to 1.0 (i.e., F_ECO₂ + F_EO₂ + F_EN₂ = 1.0). Therefore, F_EN₂ can be computed by subtracting the sum of F_ECO₂ and F_EO₂ from 1 (i.e., F_EN₂ = 1 − (F_ECO₂ + F_EO₂)). Because the expired fractions of O₂ and CO₂ will be determined by gas analyzers, F_EN₂ can then be calculated.

Calculation of Carbon Dioxide Production

The volume of carbon dioxide produced (V̇CO₂) can be calculated in a manner similar to $V˙O2$. That is, the volume of CO₂ produced is equal to:

or

The steps in performing this calculation are the same as in the computation of $V˙O2$. That is, V̇_E and V̇_I must be measured (or calculated) and the fraction of expired carbon dioxide (F_ECO₂) must be determined by a gas analyzer. Similar to F_IO₂, the fraction of inspired carbon dioxide (F_ICO₂) is considered to be a constant value of .0003.

Standardization of Gas Volumes

By convention, $V˙O2$ or V̇CO₂ are expressed in liters · min⁻¹ and standardized to a reference condition called “STPD.” STPD is an acronym for “standard temperature pressure dry.” In a similar manner, pulmonary ventilation is expressed in liters · min⁻¹ and standardized to a reference standard called BTPS, an acronym for “body temperature pressure saturated.” The purpose of these reference standards is to allow comparison of gas volumes measured in laboratories throughout the world, which may vary in ambient temperature and barometric pressures. Standardization of gas volumes to a specified temperature and pressure is necessary because gas volume is dependent upon both temperature and pressure. For instance, a given number of gas molecules will occupy a greater volume at a higher temperature and lower pressure than at a lower temperature and higher pressure. This means that a fixed number of gas molecules would change volume as a function of the ambient temperature and barometric pressure. This poses a serious problem to researchers trying to make comparisons of respiratory gas exchange, because temperature and pressures vary day by day and vary from one laboratory to another. By standardizing temperature and pressure conditions for gases, the scientist or technician knows that two equal volumes of gas contain the same number of molecules. For these reasons, respiratory gases must be corrected to a reference temperature and volume.

Before we begin a discussion of “how to” calculate gas volume corrections, it is necessary to introduce two important gas laws. The first, called “Charles’s Law,” states that the relationship between temperature and gas volume is directly proportional. That is, the gas volume is directly related to temperature, so that increasing or decreasing the temperature of a gas (at a constant pressure) causes a proportional volume increase or decrease, respectively. This relationship is expressed mathematically in the following way:

The units for temperature in equation (8) are the Kelvin (K) or Absolute (A) scale, where 0° C = 273° K [i.e., 20° C = (273° + 20°) = 293° K]. In using Charles’s Law for gas temperature corrections, we rearrange equation (8) to solve for V₂:

Let’s leave Charles’s Law for the moment and introduce a second gas law known as Boyle’s Law. Boyle’s Law states that at a constant temperature, the number of gas molecules in a given volume varies inversely with the pressure and is represented mathematically in the following equation:

Again, rearranging equation (10) to solve for V₂:

Pressure in equations (10) and (11) is expressed in mm Hg or Torr. Note that when respiratory gases are corrected for pressure differences, a correction is often made for water vapor, even though water vapor pressure is dependent only upon temperature (because respiratory gas is saturated with water vapor). When the gas volume is to be corrected to “0” water vapor pressure or “dried” as in STPD, the vapor pressure of water (PH₂O) at the ambient temperature is subtracted from the ambient or initial pressure (P₁) in Boyle’s Law as follows:

We can now combine Charles’s Law and Boyle’s Law (complete with water vapor correction) into one equation for STPD and BTPS conditions. Let’s consider the STPD correction first.

STPD Correction

Gas volumes measured in the laboratory under room conditions of temperature and pressure are expressed as “ambient temperature pressure and saturated” (ATPS). This means that the gas volume is not a standardized volume but rather a volume that is subject to the ambient conditions of temperature and pressure. As previously stated, because ATPS conditions may vary from laboratory to laboratory, there is a need to correct $V˙O2$ and V̇CO₂ volumes to the reference volume, STPD. Correcting a volume to STPD requires the standardization of temperature to 0° C (273° K), pressure to 760 mm Hg (sea level), and a correction for vapor pressure. For simplicity we will divide the gas correction procedure into two parts: (1) temperature and (2) pressure correction.

Step 1: Temperature Correction

Let’s consider the temperature correction first. For this correction, we use equation (9) (Charles’s Law):

where:

• V₂ = volume corrected to standard temperature (V_ST)

• V₁ = ATPS volume (V_ATPS)

• T₁ = absolute temperature in ambient surroundings (273° K + T_a° C)

• where: T_a = ambient temperature

• T₂ = absolute standard temperature (273° K)

Therefore, correcting an ATPS gas volume to V_ST is performed using the following equation:

Step 2: Barometric Pressure and Water Vapor Pressure Correction

To correct for barometric pressure and vapor pressure, we use equation (12), where:

• V₁ = volume ATPS

• V₂ = volume corrected to standard pressure and dry (V_SPD)

• P₁ = ambient barometric pressure in mm Hg

• P₂ = standard barometric pressure (760 mm Hg)

• PH₂O = partial pressure of water vapor at ambient temperature (see Table A.1 for a list of vapor pressures at various ambient temperatures)

Therefore, when correcting V_SPD from ATPS volumes, the following equation is used:

At this point we are ready to combine both the temperature correction factor equation (13) and the pressure and vapor pressure correction factor equation (14) into one equation and compute one single STPD correction factor. Combining equations (13) and (14) we arrive at:

Let’s consider a sample problem to illustrate correction of ATPS volumes to STPD volumes.

Given:

• V_ATPS = 90.0 liters

• Laboratory temperature = 21° C

• Ambient barometric pressure = 742 mm Hg

• H₂O vapor pressure at 21° C (from Table A.1) = 18.7 mm Hg

Using the above sample conditions and equation (15), the STPD correction would be as follows:

It is important to point out that if inspired gas volumes are measured and the relative humidity of the inspired gas is not 100%, then equation (15) must be modified by multiplying the relative humidity (RH) of the inspired gas (expressed as a fraction) by the partial pressure of water vapor at ambient temperature (e.g., if RH = 80%, then use .8 × PH₂O).

BTPS Correction

As previously mentioned, all ventilatory volumes are corrected to BTPS conditions. This correction procedure is similar to the STPD correction procedure with two exceptions: (1) Standard temperature is 310°K instead of 273°K (e.g., 310° = 273°K + 37°C [normal core temperature]). This correction is necessary because body temperature is usually greater than ambient temperature and results in an increase in gas volume. (2) The partial pressure of vapor pressure at body temperature is subtracted from P₁ in equation (14). This correction is necessary because the partial pressure of water vapor at body temperature is generally greater than PH₂O at ambient conditions (i.e., at 37° the PH₂O = 47 mm Hg).

Therefore, correcting from ATPS to BTPS would involve the following equation:

Let’s consider a sample calculation of converting V_ATPS to V_BTPS using the following conditions:

• Laboratory temperature = 20° C

• Ambient barometric pressure = 752 mm Hg

• PH₂O at 20° C = 17.5 mm Hg

• V_ATPS = 60 liters

Therefore:

Problems

1. Calculate $V˙O2$ and V̇CO₂ given:

   • V̇_E (ATPS) = 100 liters · min⁻¹

   • F_EO₂ = .1768

   • F_ECO₂ = .0351

   • Assume F_IO₂ = .2093 and F_ICO₂ = .0003

   • Ambient temperature = 21° C

   • Barometric pressure = 749 mm Hg

2. Calculate the respiratory exchange ratio (R) from $V˙O2$ and V̇CO₂ values computed in question 1.

3. Calculate V_BTPS and V_STPD given:

   • V_ATPS = 45.3 liters

   • Laboratory temperature = 19° C

   • Ambient barometric temperature = 746 mm Hg

   • Body temperature = 37° C

Answers

1. $V˙O2$ = 2.73ℓ · min⁻¹

   V̇CO₂ = 3.54ℓ · min⁻¹

2. R = 1.15

3. V_BTPS = 50.19 liters

4. V_STPD = 40.65 liters

Appendix B: Dietary Reference Intakes: Estimated Energy Requirements

Appendix C: Dietary Reference Intakes: Vitamins

Appendix D: Dietary Reference Intakes: Minerals and Elements

Appendix E: Percent Fat Estimate for Men: Sum of Triceps, Chest, and Subscapula Skinfolds

Appendix F: Percent Fat Estimate for Women: Sum of Triceps, Abdomen, and Suprailium Skinfolds