Closed respirometry

for oxygen consumption simulation, see simulate_O2.

for open-flow respirometry, see Open respirometry.

Closed respirometry

Measure O2

Analyzing an oxygen trace from a closed respirometry system involves calculating the rate of oxygen consumption $\dot{V}O_{2}$ by tracking the decline of $O_{2}$ over time, while strictly correcting for the dilution effects caused by replacing sampled air.

1. Understanding the Core Metrics & Variables

Before running calculations, isolate and define the following variables from your experimental setup:

Total gas volume of the chamber minus the volume (mass) of the mouse.
Fractional concentration of oxygen in the replacement gas (eg, room air $\approx 0.2095$ , or pure $O_{2}$ .
Fractional concentration of oxygen measured in the chamber at time $t$ .
The volume of air pulled out at each interval.
$\Delta t$ :

2. Step-by-Step Data Analysis Outline

Scan the raw trace for sudden spikes or drops caused by mouse movement, leaks during sampling, or pressure fluctuations. Smooth or omit these artifacts.

Equilibration Phase: Discard the first 10–15 minutes of the trace. The mouse needs time to settle, and the chamber air needs to mix properly after sealing.

For any given interval between $t_{1}$ and $t_{2}$ before< the next sample/replacement happens:

Identify the change in fractional oxygen: $\Delta FO_2 = F_{t1}O_2 - F_{t2}O_2$
Calculate raw consumption: $VO_2 = V_{system} \times \Delta FO_2$

Because you are pulling out a sample $V_{sample}$ and replacing it with room air $F_{I}O_{2}$ , you are artificially injecting oxygen back into a depleted system.

The Math: The true oxygen consumption $\dot{V}O_2$ for the interval must account for the oxygen added during replacement.
Formula for Step-Corrected Concentration:
(1) $\begin{equation*} F_{corrected}=\frac{(V_{system}-V_{sample})\cdot F_{t1}O_{2}+(V_{sample}\cdot F_{I}O_{2})}{V_{system}} \end{equation*}$
Subtract your actual measured value from this theoretical corrected value to find the real volume consumed during that interval.

Step 4: Standardize to STP (Standard Temperature and Pressure)

Respirometry data must be standardized to compare across studies.

Multiply your volumes by the STPD correction factor:
(2) $\begin{equation*} V_{STPD}=V_{measured}\times \left(\frac{P_{baro}-P_{H_{2}O}}{760}\right)\times \left(\frac{273.15}{273.15+T_{chamber}}\right) \end{equation*}$

(Where $P_{baro}$ is barometric pressure, $P_{H_{2}O}$ is water vapor pressure if gas isn’t dried, and $T_{chamber}$ is chamber temperature in °C).

Step 5: Normalize to Animal Mass

Divide the final $\dot{V}O_{2}$ (usually in mL/hour) by the mouse’s body mass (in grams or kg) to get the mass-specific metabolic rate (eg, $mL \cdot g^{-1} \cdot h^{-1}$ .
Note: If comparing vastly different body sizes, consider using metabolic body size $\text{mass}^{0.75}$ instead of direct scaling.

3. Data Interpretation & Visualizations

Resting vs. Active Metabolic Rate (RMR vs. AMR): Plot $\dot{V}O_2$ against time. The lowest sustained plateaus represent the resting metabolic rate, while peaks correlate with periods of physical activity inside the chamber.
Total Energy Expenditure (TEE): Integrate the area under the entire $\dot{V}O_2$ curve over the course of the experiment.

Measure O2, Scrub CO2 and Water

When you scrub carbon dioxide ( $CO_{2}$ ) and water vapor ( $H_{2}O$ ) out of the system before the air reaches the analyzer, it simplifies the math.

By removing these gases, you eliminate volume fluctuations caused by the mouse’s respiration (since 1 mole of $O_{2}$ consumed does not always equal exactly 1 mole of $CO_{2}$ produced, depending on the fuel source).

Here is how scrubbing changes your approach and how to update the analysis pipeline:

1. Physical Setup Check

The Chain: Ensure the air stream passes through the water scrubber first, then the $CO_{2}$ scrubber, before hitting the analyzer sensor.
Chemicals Used:>Water: Typically Drierite or in combination with anhydrous magnesium perchlorate.
$CO_{2}$ : Typically Soda Lime, Ascarite, or Carbosorb.

2. How the math changes

Because the air entering your analyzer is completely dry and free of $CO_{2}$ , you are measuring the fractional concentration of oxygen in a dry, $CO_{2}$ -free gas mixture $F_{d}O_{2}$ .

Updated STP Correction (No Water Vapor)

You no longer need to calculate or subtract water vapor pressure $P_{H_{2}O}$ from your barometric pressure reading. Your STPD calculation drops that term entirely:

(3) $\begin{equation*} V_{\text{STPD}} = V_{\text{measured}} \times \left( \frac{P_{\text{baro}}}{760} \right) \times \left( \frac{273.15}{273.15 + T_{\text{chamber}}} \right) \end{equation*}$

The “With Replacement” Math Adjustment

Since you are pulling a sample out and replacing it with room air, your replacement gas contains $CO_{2}$ and moisture, but your chamber air is continuously being scrubbed (or the sample is scrubbed right before analysis).

If the scrubbing happens inside the loop/chamber:

The effective $V_{system}$ shrinks slightly because the physical volume of the chemicals must be subtracted from the total volume.
The replacement fractional concentration $F_{I}O_{2}$ must match how the analyzer sees room air. Pull a sample of the replacement room air through the scrubbers to establish your true baseline $F_{I}O_{2}$ (eg, 0.2095).

3. Updated Step-by-Step Data Protocol

Zero and Span the Analyzer: Run filtered outside ambient air through your scrubber train into the analyzer to lock down your baseline $F_{I}O_{2}$ .
Log Dilution Events: Timestamp every interval draw. Because you are replacing volume with air that has not yet been scrubbed inside the chamber, expect a temporary, predictable artificial spike in $O_{2}$ values immediately following a replacement event.
Use the “Dry” Haldane Transformation (if continuous): If you are calculating consumption over intervals where volume is steady between draws, the simplified equation for volume change is:
(4) $\begin{equation*} {V}O_{2}=V_{system}\times \frac{F_{t1}O_{2}-F_{t2}O_{2}}{1-F_{t2}O_{2}} \end{equation*}$

(The denominator $1 - F_{t2}O_2$ mathematically corrects for the volume reduction caused by scrubbing out the metabolic $CO_{2}$ and water).

R code