This example shows how to derive the equation for converting flow rate and the animal-induced change in oxygen concentration into the rate of oxygen consumption (VO_{2}, ml/min). Please assume that the V symbols represent rates (and therefore should have a dot over the V, if I knew how to do that in html).

The arrangement of the respirometry system is the **LabAnalyst 'Mode 1'** configuration, with the flowmeter upstream from the animal chamber and both CO_{2} and water vapor absorbed before O_{2} concentration is measured:

Obviously VO_{2} is simply the difference between the amount of O_{2} entering the metabolism chamber and the amount of O_{2} leaving the chamber (all in ml/min):
(1) VO_{2} = O_{2in} - O_{2out}
More specifically:

O_{2in} = FLOW_{in} * F_{i}O_{2} and O_{2out} = FLOW_{out} * FeO_{2}

Where FLOW_{in} is the incurrent air flow into the chamber (ml/min), F_{i}O_{2} is the concentration of O_{2} in incurrent air (usually .2095), FLOW_{out} = the excurrent air flow out of the chamber (ml/min), and F_{e}O_{2} is the O_{2} concentration in excurrent air.
In the **Mode 1** arrangement, FLOW_{in} is measured, but FLOW_{out} is not. But we can calculate FLOW_{out} as:

FLOW_{out} = FLOW_{in} + VCO_{2} + VH_{2}O - VO_{2}

Where VCO_{2} is CO_{2} production by the animal and VH_{2}O is water loss from the animal (both in ml/min). Since the **Mode 1** arrangement uses scrubbers to remove both water and CO_{2} from excurrent air:

FLOW_{out} = FLOW_{in} - VO_{2}

Accordingly, we can re-write equation (1) as:

(2) VO_{2} = FLOW_{in} * F_{i}O_{2} - (FLOW_{in} - VO_{2}) * F_{e}O_{2}

rearranging:

(3) VO_{2} = FLOW_{in} * F_{i}O_{2} - FLOW_{in} * F_{e}O_{2} + VO_{2} * F_{e}O_{2}

and:

(4) VO_{2} = FLOW_{in} * (F_{i}O_{2} - FeO2) + VO_{2} * F_{e}O_{2}

rearranging again:

(5) VO_{2} - (VO_{2} * F_{e}O_{2}) = FLOW_{in} * (F_{i}O_{2} - F_{e}O_{2})
(6) VO_{2} * (1 - FeO2) = FLOW_{in} * (F_{i}O_{2} - F_{e}O_{2})

and finally:

(7) VO_{2} = FLOW_{in} * (F_{i}O_{2} - F_{e}O_{2}) / (1 - F_{e}O_{2})

Reminder: all of the V symbols should have a dot over the letter V, indicating a **rate** instead of a volume.