﻿ Equations for VO2
 Respirometry:  Equations for VO2 File Edit Respirometry Analyze View Script Window Special
Equations used for computing exchange rates are derived in part from Depocas and Hart (1957; J.  Appl.  Physiol.  10:388-392), Hill (1972, J.  Appl.  Physiol.  33:261-263) and Withers (1977, J.  Appl.  Physiol.  42:120-123); others I derived myself.  If you want to see a (relatively) simple example of deriving an equation for VO2, look at this page.

The following symbols are used: FR = flow rate, V = exchange rate for the gas in question (oxygen, CO2, or water vapor), STP = factor for converting to standard conditions of temperature and pressure, Fi = input fractional concentration, Fe = excurrent fractional concentration, RQ = respiratory quotient.

 Note: if you have already done the STP correction to the a fixed flow rate or flow rate data in a separate channel -- for example, if you measured flow with a mass flow controller with STP-corrected output, or if you used the STP converter in the OUTPUT menu and saved the results-- make sure the temperature and pressure are set to 0 °C and 760 torr, respectively.

 ONE MORE CAUTION:  the algorithms used here are appropriate for most -- BUT NOT ALL -- respirometry systems.  Check to make sure your system exactly matches the conditions outlined below.

For VO2, the calculations depend on the position of the flowmeter and whether (and where) water vapor and CO2 are absorbed.  Flow rate (FR) through the metabolism chamber is best measured upstream from the chamber in most cases.  If you need to humidify the air stream, the best arrangement is to use an upstream flow meter, with the air dried before it enters the flow meter and then re-humidified between the flow meter and the chamber.  For accurate calculations it is also necessary to remove water vapor and helpful to scrub CO2 from the air stream downstream from the animal chamber, before O2 content is measured.

 If both CO2 and water are scrubbed and the flowmeter is upstream from the chamber (Mode 1): VO2 = STP * (FiO2 - FeO2) * FR / (1 - FeO2) If both CO2 and water are scrubbed and the flowmeter is downstream (Mode 3; Mask mode 1 uses the same equation after correction of flowrate for incurrent water vapor content): VO2 = STP * (FiO2 - FeO2) * FR / (1 - FiO2) These are the simplest and most accurate ways to compute VO2

For some flow configurations you need to know RQ for accurate calculation of VO2 , or you must have a previously computed channel containing VCO2 in ml/min, or have data on %CO2 in excurrent air (expressed as the difference from incurrent CO2 concentration).  If the animal is metabolizing carbohydrate, RQ is 1.0; if it metabolizes fat the RQ is about 0.7; if it metabolizes protein the RQ is about 0.8.  Mixed diets yield intermediate RQ.  If you don't know RQ or diet, the potential error is minimized if you use the default RQ of 0.85 (see Gessaman and Nagy 1988).  Also, you should be aware that there are situations where the CO2/O2 ratio can exceed 1.0 (for example, if the animal is depositing fat).

 CAUTION:   If you are using the 'calculate from %CO2' or 'calculate from VCO2' modes, you need to exactly synchronize the oxygen and CO2 channels in time.   This is especially important in serial configuration (first read CO2, then read O2) because the two analyzers are not 'looking' at the gas stream simultaneously (the lag correction option in the EDIT menu can usually fix this problem).   Note that if your subject's metabolism is changing rapidly, this may not be possible even if you split your sample gas stream and read O2 and CO2 in parallel, as the response times of different gas analyzers are usually unequal.   For example, the response time of a typical CO2 analyzer is seconds, while some O2 analyzers (like those from Applied Electrochemistry) respond in milliseconds.

 In 'calculate from constant RQ' mode: If the flowmeter is upstream and CO2 is not removed from the excurrent air stream at any point (Mode 2): VO2 = STP * (FiO2 - FeO2) * FR / (1 - FeO2 * (1 - RQ))If the flowmeter is downstream and CO2 is not scrubbed from the excurrent air stream prior to flow measurement but IS removed prior to oxygen measurement (Mode 4 or Mask Modes 2 and 4): VO2 = STP * (FiO2 - FeO2) * FR / (1 - FiO2 + RQ * (FiO2 - FeO2))If the flowmeter is downstream and CO2 is not removed from the excurrent air stream at any point (Mode 5 or Mask Modes 3 or 5): VO2 = STP * (FiO2 - FeO2) * FR / (1 - FiO2 * (1 - RQ)) In 'calculate from VCO2' mode: If the flowmeter is upstream and CO2 is not removed from the excurrent air stream at any point (Mode 2): VO2 = STP * ((FiO2 - FeO2) * FR - FeO2* VCO2) / (1 - FeO2)If the flowmeter is downstream and CO2 is not scrubbed from the excurrent air stream prior to flow measurement but IS removed prior to oxygen measurement (Mode 4 or Mask Modes 2 and 4): VO2 = STP * ((FiO2 - FeO2) * FR + VCO2 * (FeO2 - FiO2)) / (1 - FiO2)If the flowmeter is downstream and CO2 is not removed from the excurrent air stream at any point (Mode 5 or Mask Modes 3 or 5): VO2 = STP * ((FiO2 - FeO2) * FR - FiO2 * VCO2)/ (1 - FiO2) In 'calculate from % CO2' mode: If the flowmeter is upstream and CO2 is not removed from the excurrent air stream at any point (Mode 2): VO2 = STP * FR * ((FiO2 - FeO2) - FeO2* (FeCO2 - FiCO2)) / (1 - FeO2)If the flowmeter is downstream and CO2 is not scrubbed from the excurrent air stream prior to flow measurement but IS removed prior to oxygen measurement (Mode 4 or Mask Modes 2 and 4); note that this mode is sensitive to whether CO2 is scrubbed from the incurrent air stream: VO2 = STP * FR * ((FiO2 - FeO2) - FiO2 * (FeCO2 - FiCO2) + FeO2 * FeCO2) / (1 - FiO2)If the flowmeter is downstream and CO2 is not removed from the excurrent air stream at any point (Mode 5 or Mask Modes 3 or 5): VO2 = STP * FR * ((FiO2 - FeO2) - FiO2 * (FeCO2 - FiCO2))/ (1 - FiO2)