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8.1 All water is not created equal
8.2 Observed baseline changes
8.3 Model of isotopic abundance of body water
8.4 Use of doubly-labelled water under conditions of changing baseline
8.5 References
Contributor: Dale Schoeller
Both deuterium and 18O are naturally occurring isotopes that are present in the body's organic compounds prior to the administration of doubly-labelled water. As such, tracer studies depend not on measurement of isotope concentration, but rather on concentration in excess of natural abundance or background isotope concentration. This would present little problem if the natural abundances were constant or if the isotopic tracers were dosed far in excess of natural abundance. Unfortunately, there are variations in isotopic natural abundances and these variations are not insignificant at economic doses of doubly-labelled water. The problem is most significant for 18O because of its high cost.
The nominal natural abundances of 2H and 18O are 155 and 2000 ppm respectively, but range from 80 to 200 ppm for 2H and 1900 to 2100 ppm for 18O. This may appear to be a small variation, but typical doses of doubly-labelled water only produce excess isotope abundances of 100 and 200 ppm for 2H and 18O respectively.
Adapted from Dansgaard 1
As discussed in Chapter 3, natural variations in isotopic abundance are easier to discuss in 'per mil' units relative to an international standard. Per mil units (‰) are defined as the difference in the ratio of the heavy to light isotope relative to the ratio in the standard, times 1000, or alternatively as 10 times the percent change:
Where R is the ratio of the heavy to light isotope, u is the unknown or sample, and std is the international standard. The commonly used standard for 2H and 18O in water is Standard Mean Ocean Water (SMOW). A relative abundance of 0 ‰ is identical with SMOW, a negative relative abundance indicates less heavy isotope than SMOW, and a positive relative abundance indicates more heavy isotope than SMOW. Recast in per mil units, the natural range of deuterium abundances is 450 to +50 ‰; and that of 18O is -60 to +50 ‰; (Figure 8.1).
These natural variations result from the accumulation of isotope effect as these elements are cycled through the hydro and biospheres. Of these natural variations, those of water have the greatest influence on the doubly-labelled water method. This is because water is the major source of hydrogen and oxygen that flows into body water and it has the major influence on the isotopic abundances of 2H and 18O in body water. Water is ingested either as a beverage or as moisture in food and is largely from fresh water derived from precipitation. The processes controlling the isotopic abundances of 2H and 18O in fresh water have been extensively described in hydrology literature 1. In brief, most meteoric water is largely derived from the oceans by evaporation. This evaporative process is governed by a kinetic isotopic process that depletes both 2H and 18O relative to SMOW. There is 3 ‰; change in the per mil enrichment of 2H for each 1 ‰; change in 18O enrichment under these conditions. This corresponds to a 0.25 ppm change for 2H for each 1 ppm change for 18O.
As the water vapour travels inland and away from the equator, the air cools, reaches the point of supersaturation and rain or snow falls. Again this process is subject to isotope fractionation. Under most conditions however, this fractionation is governed by an equilibrium process in which the precipitation is more enriched than the remaining water vapour. Thus, as this water vapour continues to travel inland, it becomes more and more depleted and the precipitation becomes more and more depleted. Thus, on the simplest level, rain near the equator has an isotopic abundance near that of SHOW, while that near the poles is highly depleted. Because this process is governed by equilibrium isotope fractionation, the 2H abundance changes 8 ‰ for each 1 ‰ change in 18O abundance. Meteoric water, when plotted in per mil units with 2H on the y axis and 18O on the x axis therefore falls on a line with a slope of 8 (Figure 8.1) 1. This corresponds to a slope of 0.6 when the data is plotted in ppm.
As this water falls through the atmosphere and when it collects on the surface of the earth, it is again subject to evaporation. This evaporative process is again subject to a kinetic isotope effect which carries off the lighter isotopes leaving progressively heavier water behind. This process is most noticeable in areas subject to long dry periods, the extreme examples of which are semi-arid areas. Changes in 18O of up to 20 ‰; have been noted ².
In addition to natural variations,
human intervention can also introduce isotopic differences in source water. The most
obvious example is heating to either distill or boil water. Under most circumstances, this
will lead to a kinetic isotopic effect. If the water is partially distilled, then the
recaptured water vapour will be lighter than the mother liquor. Solutions for parenteral
administration are good examples of this phenomenon (Figure 8.2). The change in deuterium
enrichment will be about 3 ‰ for each 1 ‰; change in the 18O
enrichment, which will displace the solution to the right of the meteoric water line.
Conversely, boiled water will be heavier than the starting water as the lighter isotopes
are lost as water vapour. The degree of fractionation will be dependent on the percent of
water lost during boiling.
Several doubly-labelled water studies have been performed under conditions that result in changes in the baseline isotopic enrichment. DeLany et al ³ were investigating energy expenditure in soldiers during an exercise in which the soldiers moved from their base camp to a field camp in a low mountain range. Urines were collected periodically during the one month exercise and a significant decrease in the isotopic enrichment was noted (Figure 8.3). The changes in 2H and 18O isotopic abundances were 17 and 2 ‰ for 2H and 18O respectively. This is very close to the ratio of 8 to 1 expected for changes in drinking water in which both water sources lie on the meteoric water line.
Comparable changes in isotopic backgrounds would be observed in the case of the subject moving to another country or hemisphere during the DLW measurement, as calculated by Klein et al 4.
Seasonal variations have also been noted in two recent studies. Riumallo et al 5, performed a series of repeated doubly-labelled water studies in subjects living in Santiago, Chile. Baseline samples were collected at 12 week intervals when all measurable excess doubly-labelled water should have been washed out of the subjects. Deuterium abundances, however, increased from -81 to -59 ‰; (vs SMOW) and 18O abundances increased from -9.4 to -8.7 ‰; These changes do not illustrate the typical 8 to 1 ratio, and thus may not be due solely to a seasonal change in drinking water. Unfortunately, drinking water samples were not collected and thus isotopic analyses could not be performed. In a more complete baseline study, Coward et al (unpublished), analysed baseline samples collected throughout the year from subjects living in The Gambia, Africa. These samples showed a marked seasonal variation between the wet and dry seasons (Figure 8.4). The large variations are not atypical for locales which alternate between a very wet and very dry climate. The isotopic enrichment observed in the dry season is probably caused by the partial evaporation of surface water which leaves the water progressively heavier as the dry season progresses. Both of these observations contrast the nearly constant isotopic abundances observed in individuals living in Chicago 6. Drinking water in Chicago comes from either Lake Michigan or deep wells which are both large bodies of water that show little seasonal variation due to their large size relative to annual input from precipitation.
The third example of baseline change was reported by Schoeller et al 7 in patients placed on total parenteral nutrition. The water in the parenteral fluids was isotopically unusual because it was obtained by distillation. The 18O abundance was fortuitously similar to Chicago drinking water so there was little change in the 18O abundance, but there was a large shift in the 2H abundance (Figure 8.5). Because this was a simple step change in isotopic abundance, the isotopic abundance of body water demonstrated a classic mono-exponential change as the body equilibrated to the new isotopic input.
On the basis of a cross-sectional study, Roberts et al 10 reported significantly different isotopic backgrounds between breast-fed and formula-fed infants. In addition, as with the studies described above, the ratio of 2H to 18O abundance changes in the groups was substantially less than 8:1. The authors calculated the effects of an infant undergoing weaning during a DLW measurement from breast milk to formula. The magnitude of error varied greatly with study duration and isotope dose intake, ranging from 1-20%. It should be noted that this represents an extreme scenario in which it would be imprudent to use DLW.
Adapted from Schoeller et al 7
As indicated above, the isotopic abundance of body water and hence the baseline isotopic abundances for use with doubly-labelled water are highly influenced by the isotopic abundances of preformed water in food and beverages. The abundance, however, is not equal to that of preformed water, but rather tends to be enriched in both isotopes relative to preformed water (Figure 8.6). This reflects the effects of isotope fractionation during evaporative water loss caused by processing.
The isotopic abundance of body water is actually a balance between the isotopic abundances of all the hydrogen and oxygen entering the pool and the isotope effects that tend to carry the lighter isotopes out of the body. Under these conditions, the isotopes reach a steady state at enrichments greater than the input material at the time when average isotopic abundances of all material entering the water pool equal those of all material leaving the pool. The inputs to body water include preformed water, metabolic water, molecular oxygen, and traces of water vapour; while the outputs include liquid water, fractionated water vapour, small amounts of solid waste carbon dioxide (Figure 8.7). The steady state equations for the isotopic abundances are therefore 18O:
rH2ORH2O + rFORFO + 2rO2f4RO2 = rH2OLRBW + rH2OFf2RBW + 2rCO2f3RBW
Meteoric water lines for the Northern (---) and Southern (---) Hemispheres are drawn for reference. Regression lines and individual data points from top to bottom are for Chicago, USA (open boxes); Lausanne, Switzerland (open triangles) and Lima, Peru (open circles). Adapted from Schoeller et al 8.
Isotopic abundances are expressed as the ratio (R) of heavy-to-light isotope; isotope fractionation relative to body water is symbolised by f1, for 2H in water vapour, f2 for 18O in water vapour, f3 for 18O in CO2 and f4 for O2. Rates (r) are expressed in moles/d. Subscripts indicate the following: local water source (W), O2 from food (FO), hydrogen from food (FH), molecular O2, CO2, body water (BW), liquid water loss (H2OL) and fractionated water vapour loss (H2OF). Adapted from Schoeller et al 8.
and 2H:
rH2ORH2O + rFHRFH/2 = rH2OLRBW + rH2Off1RBW
where the symbols are defined in
Figure 8.7. This is similar to the model published previously by Schoeller et al 8
except that it includes a fractionation factor for the uptake of molecular oxygen.
A change in the baseline isotopic abundance of body water can introduce a significant error into a doubly-labelled water study. Figure 8.8 illustrates the problem in which a change in the baseline results in an erroneously low calculated turnover rate resulting from an undetected increase in the isotopic baseline during the washout period. The central problem is that the change in the baseline cannot be detected in an individual after administration of the isotope unless the washout period is extended for about 10 elimination half-lives such that all the excess isotope is eliminated. This obviously requires a long time and is rather impractical.
Because a major cause of a baseline change is the change in the abundances of water coming into the body water pool, one of the simplest methods of reducing potential errors is to ensure that the subjects are fully equilibrated on the water source to be used in a study. This is not typically a problem when the subjects remain in the same locality and maintain a relatively constant diet 6. If there is a dietary change, however, such as with the implementation of total parenteral nutrition, then the investigator can sometimes afford to wait for a new baseline to be established before administering doubly-labelled water and in this way avoid any error due to the changing baseline. If the change in the isotopic abundances of the input is not too large for example <2 ‰ or 3 ‰ for 2H or 18O, respectively, then this only requires 2 to 3 biological half-lives of water turnover. This approach was used by Schoeller et al 7 in a validation of doubly-labelled water in patients receiving total parenteral nutrition.
The true enrichment X will be erroneously estimated as Y. Adapted from Jones et al 9.
If the delay for re-equilibration is impractical, then other approaches can be used. The first is to include a placebo group as part of the doubly-labelled water study. These subjects are treated the same as the treatment group, except that they do not receive doubly-labelled water. Physiologic samples are collected from the placebo group in parallel to the treatment group. The baseline change is measured in the placebo group and used to correct the apparent enrichments in the treatment group. This method was used by DeLany et al ³ in soldiers during a field exercise.
The third approach is to model the anticipated baseline change from knowledge of the initial baseline and the change in isotopic abundances of the input water. This method is more complex than the placebo method, but is more flexible because it does not require the assumption that all subjects will behave identically to the change in the isotopic abundance of the input water. This approach has been used by Jones et al 9 in infants being weaned from total parenteral nutrition.
Although the placebo and calculated baseline change approaches have been used and seen to give valid results, the coefficient of variation of the doubly-labelled water method did increase 3, 10. The exact loss of precision is not known, but probably ranges between 2 and 10% depending on the magnitude of the baseline change and the dissimilarity of the subjects' responses.
The final, and possibly the most important method, for reducing the error associated with changing isotopic backgrounds on the calculated CO2 production rate is either to increase the isotope dose given, or to reduce the study duration within the recommended range of 1-3 half-lives for 2H disappearance. This is because it is the magnitude of isotopic abundances of body water remaining at the end of the study that determine the importance of isotopic background changes, and these are in turn determined by the isotope dose intake and study duration. An example of the effect of these factors was given by Roberts et al 10 in the study of isotopic backgrounds in infancy. They determined that for an infant undergoing complete weaning during a doubly-labelled water measurement, the error associated with the determination of CO2 production rate would be 6-18% for a study lasting 7 days (equivalent to 3 half-lives for 2H disappearance) when a moderate isotope dose was used compared to only 3-8% where a 5 day study was employed.
Another important factor that
influences the precision of the doubly-labelled water method in the face of changes in
baseline is the ratio of 2H to 18O in the loading dose. Because the
doubly-labelled water method depends on the difference in the elimination rates, error in
elimination rates can be tolerated if it is identical for both isotopes. Thus, if the
loading dose is adjusted such that the per mil enrichments of 2H and 18O
above initial baseline are in the same ratio as the baseline changes in abundance, then no
error will be introduced to the calculated CO2 production rates 6, 9.
Schoeller 6 has discussed the selection of optimal dosing ratios, and further
consideration is given in Appendix 5 which presents a simple formula for predicting the
required doses.
1. Dansgaard W (1964) Stable isotopes in precipitation. Telus; 16: 436-468.
2. Conrad G & Fonles J-Ch (1970) Hydrologie Isotopique du Sahara Nerd-Occidental. In Isotope Hydrology, IAEA, Vienna pp 405-419.
3. DeLany JP, Schoeller DA, Hoyt RW, Askew EW & Sharp MA. (1989) Field use of D218O to measure energy expenditure of soldiers at different energy intake. J Appl Physiol; (submitted)
4. Klein PD, James WPT, Wong WE, Irving CS, Murgatroyd PR, Cabrera M, Dallosso HM, Klein ER & Nichols BL (1984) Calorimetric validation of the doubly-labelled water method for determination of energy expenditure in man. Hum Nutr: Clin Nutr; 38C: 95-106.
5. Riumallo JA, Schoeller D, Barrera G. Gattas V & Uauy R (1989) Energy expenditure in underweight free-living adults: impact of energy supplementation as determined by doubly labelled water and indirect calorimetry. Am J Clin Nutr; 49: 239-246.
6. Schoeller DA (1983) Energy expenditure from doubly labelled water: some fundamental considerations in humans. Am J Clin Nutr; 38: 999-1005.
7. Schoeller DA, Kushner RF & Jones PJH (1986) Validation of doubly labelled water for energy expenditure during parenteral nutrition. Am J Clin Nutr; 44: 291-298.
8. Schoeller DA, Leitch CA & Brown C (1986) Doubly labelled water method: In vivo oxygen and hydrogen isotope fractionation. Am J Physiol; 251: R1137-R1143.
9. Jones PJH, Winthrop AL, Schoeller DA, Filler RM, Swyer PR, Smith J & Heim T. (1988) Evaluation of doubly-labelled water for measuring energy expenditure during changing nutrition. Am J Clin Nutr; 47: 799-804.
10. Roberts SB, Coward WA, Ewing G,
Savage J, Cole TJ & Lucas A (1988) Effect of weaning on accuracy of doubly-labelled
water method in infants. Am J Physiol; 254: R622-R627.