Breathing into Body Water

Companion to Inhale, Exhale on Science in the Queue. A steady-state oxygen mass balance that follows the O₂ an animal takes up, the CO₂ it breathes out and the vapor it exchanges into body water, in δ′¹⁸O and Δ′¹⁷O together.

MODEL orange controls set the physiology and the constants. VIEW blue controls only change the plotting window, in the drawer under each chart.

Where each breathing term moves body water

O₂ share of oxygen inputs f = 1/(W + RQ), CO₂ share of oxygen outputs v = f·RQ, all fluxes per O atom of O₂ taken upmass balance

O₂ taken up, δ¹⁸O = b − z(1 − X), with ¹⁷O set by the slope of the residual O₂, θ_resEpstein & Zeiri 1988, Kohn 1996 Eq. 2

CO₂ leaves at α¹⁸ = 1 + (17604/T − 17.93)/1000 relative to body water, α¹⁷ = (α¹⁸)^θBrenninkmeijer et al. 1983

R_{body water} = (sum of inputs)/(sum of outputs), solved for ¹⁸O/¹⁶O and ¹⁷O/¹⁶O separately, nothing linearizedsteady state

MODEL Parameters animal f, O₂ share of inputs fuel, RQ body temperature °C O₂ extraction X Epstein z ‰ θ residual O₂ θ CO₂–water

air O₂ mixed in, nothing fractionated uptake fractionation CO₂ leaves in equilibrium breath vapor body water same animal at θ 0.5229 and 0.529 the other archetypes VIEW

VIEW Plot window, view only, does not change the model

body water, δ′¹⁸O and Δ′¹⁷O

offset from drinking water

O₂ share of inputs f, CO₂ share of outputs v

O₂ taken up, δ′¹⁸O and Δ′¹⁷O

CO₂ term, slope of the shift and share of the O₂ imprint it returns

respired CO₂, δ′¹⁸O and Δ′¹⁷O

water budget

Archetype parameters and their sources

animal	water influx	RQ	breathing state, share of O₂	X	whole-breath extraction	T_b (°C)	exhaled air (°C)	ambient air
Kangaroo rat	WEI 0.07 mL/kJ, assumed	0.95	tidal, 1.0	0.29	0.20	37	27	25 °C, 50%
Human, resting	WEI 0.30 mL/kJ, assumed	0.85	tidal, 1.0	0.277	0.164	37	34	25 °C, 50%
Songbird	WEI 0.18 mL/kJ, within Nagy’s bird means	0.85	flow-through, 1.0	0.33	0.245	41	28.8	25 °C, 50%
Desert lizard	WEI 0.171 mL/kJ, Nagy’s desert reptile mean	0.75	intermittent, 1.0	0.40, assumed	0.245	33, assumed	31.5	25 °C, 50%
Dolphin	2.25 per O atom of O₂, fish prey water	0.75	resting breaths, 0.4 recovery breaths, 0.6 (assumed)	0.275 0.455	0.24 0.40	37	31	25 °C, 50%
Ground squirrel, hibernating	metabolic water + inhaled vapor + 0.15, assumed	0.703, fat	arousals, 0.825 torpor, 0.175	0.29 0.60, assumed	0.195 0.48	37 6.75	10.5 6.75	5 °C, 95% burrow

Published sources behind the parameters, alveolar and whole-breath extraction in mammals (Beaver et al. 1981; Stahl 1967; Chappell and Roverud 1990), parabronchial and whole-breath extraction in birds (Johansen and Bech 1983; Johannesen and Nicol 1990; Bech et al. 1985; Chappell and Bucher 1987), exhaled-air temperature (Schmidt-Nielsen et al. 1970; Cole 1954; Tieleman et al. 1999), intermittent breathing in reptiles (Glass et al. 1978; Bennett and Hicks 2001), water economy indices (Nagy 2004), end-expired O₂ in dolphins (Fahlman et al. 2018, 2019), and hibernation energetics and torpor (Karpovich et al. 2009; Geiser 2004; Webb and Milsom 2017). RQ follows fuel stoichiometry, 1.00 for carbohydrate, 0.85 mixed, about 0.74 for protein to uric acid and 0.703 for fat. Values marked assumed are constructed. Water influx is per O atom of O₂ taken up, from the water economy index (WEI) through the energy released per mole of O₂.

Published inputs, air O₂ at δ¹⁸O 23.881‰ and Δ′¹⁷O −0.440‰, the uptake relation of Epstein and Zeiri (1988) in the mass-balance form of Kohn (1996), the residual-O₂ slope 0.518 for human breath (Luz and Barkan 2005), which my breath holds bracket, the CO₂–water fractionation of Brenninkmeijer et al. (1983), and liquid–vapor fractionation with θ 0.529. Measured, z of 10.4‰ from my breath holds. Constructed, the six archetypes, with the assumed values marked in the parameter table above, all oxygen other than O₂ fixed at δ′¹⁸O −5‰ and Δ′¹⁷O +0.015‰ for every animal so that only breathing differs, and every number the model returns. The path switches the terms on one at a time, so its last point is the exact body water. Moving f rescales the water influx, and RQ and body temperature then act at that water economy.

The size of the signal is set by f

Body water offset from drinking water as the O₂ share of oxygen inputs changes, for the animal and settings above. Gray dots are the six archetypes at their own settings. Gill breathers sit at f near 2 × 10⁻⁴, where water crossing the gills swamps every other flux.

this animal, θ CO₂–water as set this animal at θ 0.5229 this animal at θ 0.529 archetypes gill breathers

Δ′¹⁷O offset per unit f, this animal

δ′¹⁸O offset per unit f, this animal

largest f this water budget allows

Constructed. f is the O₂ share of all oxygen entering the body, set by the water economy index and the fuel, not by metabolic rate itself. Beyond the largest f, the water lost in breath would exceed the water coming in. Gill breathers follow from dogfish gill water exchange (Giacomin et al. 2017).