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))
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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)
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