Breath-Hold Oxygen

Companion to Inhale, Exhale on Science in the Queue. Triple oxygen isotopes of the O₂ left in the lungs after breath holds of 0 to 80 seconds, measured at the UNM Center for Stable Isotopes in September 2023, and what they say about the O₂ the lungs took up, and how my breath CO₂ tests the θ of CO₂–water equilibrium.

MODEL orange controls set the slope or relation drawn against the data. VIEW blue controls only change the plotting window.

The O₂ left behind moves away from air along one slope

Δ′¹⁷O = δ′¹⁷O − 0.528 δ′¹⁸O, with δ′ = 1000 ln(1 + δ/1000)notation
residual O₂ follows δ′¹⁷O = θ δ′¹⁸O + c, so Δ′¹⁷O falls by (0.528 − θ) for every per mil of δ′¹⁸Oweighted fit, intercept free
MODEL Slope θ drawn fit to set θ to
clean samples, ±1 SE 8 September, affected by argon air through a dirty sieve slope θ as set, through the fitted set reference slope 0.528
VIEW Plot window, view only, does not change the model
best-fit θ, set selected above
misfit at the θ drawn, χ² per degree of freedom
human breath, Luz and Barkan (2005)
0.518 ± 0.002, published
O₂ diffusion in air, kinetic theory
0.5127 constructed from masses
Data table, every sample

Measured, my September 2023 breath series. O₂ was extracted from exhaled breath on the vacuum line and analyzed for δ¹⁷O and δ¹⁸O. Values are means of n analysis cycles with ±1 standard error. The 8 September samples were affected by argon and one air sample passed through a dirty sieve, so both are shown for comparison and left out of the fits. The fit weights each sample by 1/SE² and widens the slope error by √χ² where that exceeds 1. Published, the human value of Luz and Barkan (2005). Constructed, the kinetic-theory slope for O₂ diffusing through air, from the exact isotopologue masses.

How much O₂ the lungs used, and what they took

fraction of the inhaled O₂ used, X = 1 − (O₂/N₂)breath/(O₂/N₂)airmeasured
exhaled O₂, δ¹⁸O = b + zX, linear in XEpstein & Zeiri 1988, Eq. 1
closed system, ln(Rbreath/Rair) = (α − 1) ln(1 − X)Rayleigh reading
O₂ taken up by mass balance, δ¹⁸O = b − z(1 − X), with b the inhaled airKohn 1996 Eq. 2
MODEL Uptake Epstein z ‰ closed-system α X for the readout
clean holds 30 s hold, affected by argon linear, δ¹⁸O shift = zX resting range z 9.2 to 13‰ closed system, α as set
O₂ taken up, mass balance (Kohn Eq. 2) inhaled air O₂ holds, by mass balance steady breathing, X 0.28 to 0.40
z of the 50, 70 and 80 s holds
closed-system α of the same holds
O₂ taken up at X, mass balance
O₂ taken up in the 50 to 80 s holds

Measured, O₂/N₂ of the exhaled gas for each hold time and the δ¹⁸O shift against air measured the same week (the argon-affected 30 s hold against the 8 September air), so the shifts do not depend on the offset between my air value and the published one. The O₂ taken up is the mass-balance complement of the exhaled O₂, computed separately for ¹⁷O and ¹⁸O. Published, the linear relation and the resting range of z for 14 healthy volunteers (Epstein and Zeiri 1988), and Kohn's (1996) Eq. 2. Constructed, the closed-system reading. The 5 s hold sits below both relations, one reason to measure O₂/N₂ on every aliquot in the next series.

My breath CO₂ against the model, across θ

body water from breath CO₂, Δ′¹⁷Obw = Δ′¹⁷OCO₂ − (θ − 0.528) × 1000 ln αCO₂–waterequilibrium at 37 °C
model body water for me, the steady-state mass balance for a resting human with drinking water set so its δ′¹⁸O matches the CO₂human archetype
MODEL Readout θ CO₂–water set θ to Δ′¹⁷O of all non-O₂ oxygen ‰
body water from my breath CO₂ ±1σ of the CO₂ model for me, non-O₂ Δ′¹⁷O as set model, non-O₂ Δ′¹⁷O −0.010 to +0.045‰ laboratory θ, 0.522 ± 0.002
VIEW Plot window, view only, does not change the model
θ where breath and model agree
same, with the CO₂ Δ′¹⁷O at ±1σ
breath against model
O₂ share f the model would need to agree at θ 0.529