﻿ Respirometry: VCO2 equations
 Respirometry:  Equations for VCO2 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 VCO2, you need to know RQ, or you must have data on oxygen content or consumption.  If you don't know RQ or diet, use the default RQ of 0.85, which usually produces results with an error of <5%.  Alternately, you can use a previously-computed channel containing VO2 in ml/min, or have data on %O2 in excurrent air (in difference from incurrent O2 concentration).  The equations (which assume gas is dry when FeCO2 is measured) are as follows:

 CAUTION:   If you are using the 'calculate from %O2' or 'calculate from VO2' 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 from the chamber (Mode 1 or Mask Mode 1): VCO2 = STP * (FeCO2 - FiCO2) * FR / (1 - FeCO2 * (1-(1/RQ)))If the flowmeter is downstream from the chamber and CO2 is not scrubbed prior to flow measurement (Mode 2): VCO2 = STP * (FeCO2 - FiCO2) * FR / (1 - FiCO2 * (1-(1/RQ)))If the flowmeter is downstream and CO2 is scrubbed prior to flow measurement (Mode 3 or Mask Mode 2): VCO2 = STP * (FeCO2 - FiCO2) * FR / (1 - FeCO2 + FiCO2/RQ)If you are using a mask and the flowmeter is immediately downstream from the animal, and water is scrubbed prior to CO2 measurement (Mask Mode 3): VCO2 = STP * (FeCO2 - FiCO2) * FR / (1 - FiCO2 * (1 + 1/RQ)) In 'calculate from VO2' mode: If the flowmeter is upstream from the chamber (Mode 1): VCO2 = STP * (FR * (FeCO2 - FiCO2) - FeCO2* VO2) / (1 - FeCO2)If the flowmeter is downstream from the chamber and CO2 is not scrubbed prior to flow measurement (Mode 2 or Mask Mode 1 or Mask Mode 3): VCO2 = STP * (FR * (FeCO2 - FiCO2) - FiCO2* VO2) / (1 - FiCO2)If the flowmeter is downstream and CO2 is scrubbed prior to flow measurement (Mode 3 or Mask Mode 2): VCO2 = STP * (FR * (FeCO2 - FiCO2) - FeCO2* VO2) / (1 + FeCO2) In 'calculate from % O2' mode: If the flowmeter is upstream from the chamber (Mode 1): VCO2 = STP * FR * ((FeCO2 - FiCO2) - FeCO2* (FiO2 - FeO2)) / (1 - FeCO2)If the flowmeter is downstream from the chamber and CO2 is not scrubbed prior to flow measurement (Mode 2 or Mask Mode 1 or Mask Mode 3): VCO2 = STP * FR * ((FeCO2 - FiCO2) + FiCO2* (FiO2 - FeO2)) / (1 + FiCO2)If the flowmeter is downstream and CO2 is scrubbed prior to flow measurement (Mode 3 or Mask Mode 2): VCO2 = STP * FR * ((FeCO2 - FiCO2) + FiCO2* (FiO2 - FeO2)) / (1 + FeCO2 - FiCO2)