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6.5.1 Assumed constant percentage of water output
In work with amphibians and other small animals, Nagy proposed that no fractionation correction be made. Evidence to date indicates that this assumption cannot be made for human applications of the doubly-labelled water method as breath and transcutaneous water vapour have been definitively shown to be isotopically fractionated.
In the original equation developed by Lifson ³, it was proposed that the rate of fractionated water loss be assumed to be 50% of water output. Human studies, however, have demonstrated that this is an overestimate for most populations. In a single adult, Klein et al 11 estimated maximal fractionated water loss to be 25% of water turnover, which would have introduced a 6% error in the calculated carbon dioxide production rate if the assumption of 50% had been made. Roberts et al 12 estimated the fractionated water loss to be 16% in premature neonates, which would have introduced a 15% error in the calculated carbon dioxide production if the assumption of 50% had been made. Thus, the 50% assumption is not universally applicable in human studies. Indeed, any assumed constant fraction of water loss can easily lead to modest (±5%) systematic errors in CO2 production when applied to all populations.
6.5.2 Individual estimates of fractionated water loss
From a physiological viewpoint, it is unlikely that any single constant percentage of water output can be assumed to be subject to isotopic fractionation. This is because fractionated water output does not change as a function of water turnover, but rather varies as a function of other physiologic variables. Specifically, only transcutaneous water vapour and breath water are subject to isotope fractionation. Classic studies of transcutaneous water loss indicate that non-sweat water loss is relatively constant in adults for most skin surfaces 13. The apparent exceptions are the palms of the hands and the forehead, but the larger water loss rates reflect sweating from glands that are constantly active 13. As such these excess water losses are probably not isotopically fractionated. Transcutaneous water loss per unit of skin surface is nearly the same for infants and adults 14, except for premature infants during the first few weeks of postnatal life in whom transcutaneous water loss is 2 to 8 fold greater due to the immaturity of the skin 14. Breath water loss is also not dependent on water turnover, but is probably related to the ventilation volume as significant quantities of water vapour exit during the expiratory phase of breathing.
Within this framework, two approaches to estimating fractionated water loss have been used as indicated in Section 6.3. Schoeller and co-workers 15 have estimated water loss from body surface area and ventilatory volume and expressed these both as functions of CO2 production. Coward 16 has also estimated breath water loss as a function of CO2 production, but suggests a constant value for transcutaneous water loss.
In the approach used by Schoeller et al 15, it is assumed that expired CO2 averages 3.5% of the 24 hour ventilatory volume and that expired air is 95% saturated with water vapour at 36°C 17. The latter two figures are taken from direct measurements in infants (and are slightly smaller than previously published assumptions of Schoeller et al 15). Assuming atmospheric pressure, the rate of respiratory water loss is therefore: rCO2 (1/0.035) x (44.5/760) x 0.95 = 1.59 rCO2. Transcutaneous water vapour loss is estimated from body surface area (m²) using the mean rate of non-sweating vapour loss of 0.14 g/min per m² 13, which is also slightly smaller than previous estimates used by Schoeller et al 15. Finally it is assumed that clothing reduces the rate of loss to 0.07 g/min per m² for the areas covered by clothing, which is estimated as 85% of the body in adults and 25% of the body surface area in infants in Western cultures. The reduction is assumed because of studies that have shown a reduction in non-sweat water losses when barriers are placed between the skin and the source of air flow 18.
In an adult, the calculated daily transcutaneous loss is therefore [0.85(0.7) + 0.15(0.14)] x 1440 = 116 g/d per m², or 6.4 mole/d per m². For a typical adult this averages 30% of the respiratory loss, so the two terms are combined for convenience to yield a total fractionated water loss of rH2Of = 2.1 rCO2.
For an infant the transcutaneous water loss is closer to 65% of respiratory losses because of the larger ratio of surface area to CO2 production, so the two terms are combined to yield a total fractionated water loss of rH2Of = 2.6 rCO2. For comparisons with other values, these correspond to about 30% and 13% of total water turnover for typical adults and infants living in temperate climates.
Coward 16 does not combine the terms for respiratory water loss and transcutaneous water loss, but does make individual fractionation corrections. He mesured the two components of water vapour loss in adults and observed that breath water vapour was only 55% of the saturation value and thus suggest a value of 1.1rCO2 (moles) for breath water loss. Measurements of transcutaneous water loss showed a high level of variability and did not detect any significant relationship to body surface area in adults. Therefore a constant value of 500 g/day was used.
6.5.3 Measured water vapour loss
As an alternative to estimating fractionated water vapour loss several investigations have either measured insensible water loss or calculated it by difference from water balance studies. Before applying these methods, however, it should be remembered that insensible water loss does not necessarily equal fractionated water loss. Specifically, sweat losses are not subject to isotopic fractionation and will be erroneously totalled with fractionated water loss if insensible water loss is measured by weight change or water balance under conditions where sweating occurs. Note, that even under cool conditions, sweat is produced on the palms and forehead 13. Conversely, measured insensible water loss may underestimate fractionated water loss under humid conditions. Atmospheric water vapour does enter the body both through the lungs and the skin 19. Thus, there will be a unidirectional influx of unlabelled water that will reduce the net insensible water loss, while not altering the unidirectional loss of isotopically fractionated water loss. For example, if a person inhales 1 litre of air saturated with water vapour at 20°C (19 mg/l) this water will be absorbed and replaced with labelled body water, which will be exhaled at 36°C and 95% saturation 17 (45 mg/l). The net insensible water loss will be 45 - 19 = 26 mg, but the unidirectional water loss will be 45 mg. Water loss estimated from weight loss is thus a 40% underestimate of the true value, but even this would only introduce an error in carbon dioxide production of about 2% (Figure 6.2). If sweating occurs, then the error will be reversed because sweat losses increase the weight loss and hence the estimation of insensible water loss, but sweat is not subject to isotopic fractionation 8.
Recently, Vasquez-Velasquez has measured water vapour loss in infants living in The Gambia, West Africa and Cambridge, UK (PhD Thesis, University of Cambridge). Total water turnover was measured by deuterium elimination and insensible water loss was measured by the increase in water content of air passing over the infant while it was sleeping in an open circuit indirect calorimeter. Results are shown in Figure 6.3. Using a regression model, it was estimated that insensible water vapour loss was: 4.8 wt (kg) + 96 (g/d). For the infants living in the UK this was always 13% of total water turnover. For the Gambian infants however, insensible water loss was about 17% of water turnover at 2 kg body weight and 8% at 16 kg body weight due to the different water turnover rates. It should be noted, however, that these are net insensible water losses. The true insensible water loss will be higher as it is partially obscured by insensible water input from the ambient humidity. Assuming 40% relative humidity at 25°C, the underestimate would be about 35% at 2 kg body weight and 25% at 16 kg body weight.
6.5.4 Triply-labelled water
An objective method for measuring the rate of fractionated water loss has been proposed by Haggarty et al 10. This is the triply-labelled water (TLW) technique. With this method 3H2O, 2H2O and H218O are co-administered. The tritiated water is added to the usual loading dose because the fractionation factors between water and water vapour differ for deuterium and tritium. Thus, a small but measurable difference in the deuterium and tritium elimination curves will be introduced as the percentage of water lost via fractionated routes increases.
Data from Vasquez-Velasquez.
Equations 1 and 2 are not specific to deuterium and oxygen-18 but apply equally well to other isotopic species in water such as tritium or oxygen-17. Therefore after substitution of the appropriate tritium and oxygen-17 factors in these equations water flux and CO2 production could be derived from tritium and oxygen-17 flux rates. Considering only the case of heavy hydrogen; if the true evaporative loss (x) and fractionation factors are known the corrected deuterium flux must equal the corrected tritium flux. Conversely, if the fractionation factors are known and the flux rates are determined experimentally, x can be solved using the following relationship:
The obvious advantage of this method is that it provides an individual estimate of fractionated water loss and thus could minimise the error in calculated CO2 production. The difference between the deuterium and tritium fractionation factors must be known with a relative accuracy of 25% if the triply-labelled water method is to offer much advantage over the other techniques. However, as discussed in Section 6.2.1 the relative contribution of kinetic and equilibrium isotope effects has little effect on the DLW method if the total amount of fractionated water loss is known. The same is true of the TLW method and the maximum error on the calculation of CO2 production resulting from uncertainty about the predominant type of fractionation is only ±0.3% 10. There are values for tritium and deuterium fractionation factors in the literature, but further work needs to be done to improve the confidence in TLW. Schoeller et al 15 have pointed out the difficulties of measuring fractionation factors in vivo but for the purposes of TLW it is only necessary to determine fractionation in a mixture of tritiated and deuterated water in vitro; this is currently the subject of experimental investigation.
The TLW method has the obvious
disadvantage of using a radio-active isotope and will therefore be impossible to use in
many circumstances. However, even if it does not provide much improvement in individual
estimates of fractionated water loss, it will provide some valuable group estimates that
should all but eliminate the already small potential errors in the fractionation
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