# Chapter 13: Use of the doubly-labelled water method under difficult circumstances

Contributors:

Susan Roberts
Carla Fjeld
Klaas Westerterp
Michael Goran

## 13.1 General considerations

The single most important factor in determining the potential for error in doubly-labelled water measurements is the difference between the rates of 2H and 18O disappearance. In subjects such as healthy adults, the difference between the two disappearance rates is relatively large. However, in certain groups of subjects who have either very high rates of water intake and/or low metabolic rates in relation to body size, the difference between the two disappearance rates can be reduced substantially. In these cases, there is a much greater potential for error generated by various aspects of the method, in particular the precision of measurements of rate constants and intercepts, and factors such as the mathematical correction for isotopic fractionation.

The magnification of error associated with a low kO/kD ratio is illustrated in Figures 13.1 and 13.2, which show the error associated with measurement of the two dilution spaces (NO and ND) and the correction for isotopic fractionation, for kO/kD ratios ranging from 1.5 (the upper limit of values for adult athletes) to 1.1 (the lower limit of the range for infants). It can be seen that the kO/kD ratio has a major influence on the potential for error. For example, incorrect measurement (or assumption) of a ratio of ND/NO of 1.03 for an individual with a value of 1.06 will result in a difference in the calculated CO2 production rate of 6% when kO/kD is 1.5 compared to 43% when kO/kD is 1.1 (Figure 13.1).

Figure 13.1. Interaction between the kO/kD ratio and deviation of the true ND/NO ratio from an assumed value of 1.03

Labels on the 3 lines indicate the kO/kD ratio.

Figure 13.2. Effect of an error in the fractionation assumption on the final estimate of rCO2

The two panels illustrate the effect of error around initial assumptions of 0.5 (i.e. Lifson's value) and 0.2 (closer to the value anticipated in children).

Labels on the 4 lines indicate the kO/kD ratio.

Figure 13.3. Effect of weaning on the accuracy of doubly-labelled water at different dosing levels

Labels on the 3 lines are g H218O/2H2O per kg TBW.

Similarly, concerning the correction for isotopic fractionation (Figure 13.2), the maximum potential error associated with assuming that isotopic fractionation occurs in 50% of water output would affect the calculated CO2 production rate by 3% when kO/kD is 1.5 compared to 45% when kO/kD is 1.1. However, in this case, it is important to note that although the potential for error is great when kO/kD is low, the actual error generated is much less than this. This is because the probable range of water loss subject to isotopic fractionation is reduced when total water turnover is high (the usual cause of a low kO/kD ratio) 1. For example, when expressing fractionated water output as a percentage of total water output (x), the probable range for adults is 20-50% (giving a maximum error when using the mid-point of approximately 3%), whereas the range 10-20% is more usual in infants (giving a maximum error when using the mid-point of approximately 6%).

In subjects in whom there are no stepwise changes in water intake or carbon dioxide production during the doubly-labelled water study, compensation for a low kO/kD ratio can be achieved by increasing the number of data points used to determine outflow rates. A corollary of this statement is that the measurement of CO2 production rate in a subject with a low kO/kD ratio will be substantially less precise than a comparable measurement in a subject with a high kO/kD ratio unless more data points are used to determine the outflow rates of the isotopes. An additional means by which the precision of doubly-labelled water measurements can be enhanced during the study of difficult subjects with a low kO/kD ratio is to increase the doses of the isotopes given at the start of the study, while at the same time ensuring that the ratio of isotopes given is appropriate for the study population (see Chapter 11).

## 13.2 Use of the doubly-labelled water method in infants

There are several considerations that need to be addressed when using the doubly-labelled water method in infants:

1) In particular, infants have high rates of water intake in relation to body size and carbon dioxide production, leading to the increased potential for error discussed above. Mean values for kO/kD in premature infants are 1.13, with individual values being as low as 1.10 ², while in older infants a mean of 1.20 has been reported ³. Thus, the potential for error is approximately 4-fold greater in infants than in adults.

2) In addition, rapid growth during doubly-labelled water measurements is common in infants. Premature infants can increase in weight by as much as 14% during a doubly-labelled water study, compared to 4% or less in normally growing 3-month infants and in adults in moderately severe positive or negative energy balance (Table 7.2). The increase in the isotope dilution space occuring during growth needs to be taken into consideration to avoid an under-estimation of CO2 production rate (see Appendix 3).

3) When growth rate is extremely rapid, as in the case of premature infants, the necessary adjustment to the calculation of outflow rates and CO2 production involves use of study means for the isotope dilution spaces (rather than individual measurements for the dilution spaces that are made at the start of the determination) in the calculation of outflow rates. In their study of premature infants Roberts et al ² used weighted study means (assuming an exponential change in water during the study) for each dilution space in the calculation of FH2O and FH2O+CO2. The weighted means were calculated using the general equation:

N = (N1 - N2)/{ln(N1/N2)}

where N is the mean dilution space during the study, and N1 and N2 are the dilution space volumes at the beginning and end of the doubly-labelled water study. The dilution space at the end of the study was determined from body weight, assuming proportional increases in dilution spaces and weight during the measurement. This procedure gives results that are similar to those obtained using a simple average for the study period that is based on linear weight change. By contrast, use of the initial dilution spaces measured at the start of the study results in a significant underestimation of carbon dioxide production (by an average of 10% in the case of the infants studied by Roberts et al ²).

4) When growth rates are not extremely rapid, as in the case of older infants, and in adults undergoing moderately severe positive or negative energy balance, the correction for weight change during the measurement makes only a very small difference to the calculated CO2 production rate. The correction described above for premature infants may be used.

5) The final theoretical factor that needs to be taken into consideration in doubly-labelled water studies in infants is the possibility that isotopic backgrounds may change significantly during the measurement period. This is because infants undergo major dietary changes during the normal course of infancy, and the different diets that are used may have very different 2H and 18O contents, as described in Chapter 8. Changes in isotopic backgrounds in the body will accompany changes in isotopic intakes. If such changes occur during a doubly-labelled water measurement, they can have a significant effect on the accuracy of the determination of CO2 production, the magnitude of which will be determined by the isotope dose intake and the duration of the doubly-labelled water study 4. For a study period of 7 days (equivalent to 3 half-lives for 2H disappearance), complete weaning from breast milk to infant formula during a doubly-labelled water study can result in an under-estimation of CO2 production rate ranging from 18% if a relatively low isotope dose is given (0.24 g/kg H218O and 0.08 g/kg 2H2O), to 6% if a high isotope dose is given (0.72 g/kg H218O and 0.24 g/kg 2H2O). (Figure 13.3). The implication of these calculations is that doubly-labelled water studies should be avoided during rapid weaning. If this is not possible, use of a large isotope dose will reduce the potential for error. In addition, control subjects who receive no isotope can be studied to quantify changes in backgrounds, which can then be used to correct the raw isotope data.

6) The ratio of 180 to 2H in dose water influences the accuracy of energy expenditure data. The optimal dose ratio for infants and young children exceeds the optimal ratio for most older people since rates of CO2 production per kg body weight are greater in the younger population. Schoeller 5 has discussed this issue in detail.

Some practical concerns include:

7) Discrepancies between weighed and administered doses can occur because of spitting or drooling during dose administration, or because of post-dose regurgitation. The effects of losses can be reduced by using doses with low percent enrichments. Doses may be administered by trickling the dose deep into the back of the mouth by pointing the syringe directly toward the uvula and repeatedly squirting small quantities which can be swallowed easily. In some infants, this is easier if they are crying. Swallowing can be encouraged by quickly blowing into the infant's face. Alternatively, a small diameter polythene tube can be attached to the syringe and placed in the back of the throat. This procedure may cause some infants to gag. A simple and worthwhile step is to test both dosing procedures using unlabelled water in each infant prior to the study. To quantify losses, a pre-weighed tissue can be sealed in a plastic bag, used to absorb drops lost by spitting, and reweighed to adjust the weight of dose administered.

8) The potential for regurgitation after feedings and requirements for more frequent feedings in comparison to protocols used in studies of older people necessitate special procedures in studies of infants and young children during the 3 to 5 hour interim between dosing and isotopic equilibration. Most adult studies using isotope dilution to measure total body water have withheld food and water from the subjects during the interim between dosing and completion of the urine sample protocol. Isotope losses due to post-dose regurgitation may be reduced by delaying the post-dose feeding until isotopic equilibration has been achieved. However, since this interval may exceed the recommended period of fasting for infants, a feeding is usually offered at 0.5 to 1 hour post-dose. Since this additional water must equilibrate with the dose and body water, it effectively extends the equilibration period. Isotopic equilibration between diet water, body water and dose water should be evidenced by the finding of no biologically significant difference between isotopic enrichment in the urine used to calculate total body water volume (ie 3 to 5 hours post-dose) and the urine sample which preceded it. A reasonable cut-off for the difference is 2 to 4%, depending on the application of the data. Although diet volume is small (<5%) in comparison to total body water, some investigators subtract the volume ingested from the dilution space to calculate total body water volume. A related problem may be that the exact amount of dietary intake is unknown, particularly when infants are breastfed - mothers may elect to suckle their infants during the equilibration period. The investigator needs to be aware in advance of the dosing if an infant is being breastfed, and should attempt to weigh the infant before and after the feeding to estimate the volume ingested.

9) In clinical studies of infants, doses may be administered by oral or nasal gavage. This procedure requires a wash or "chaser" to rinse isotope from the tubing and has the disadvantage that some tracer may adhere to the sides of the tube as it is withdrawn from the infant.

## 13.3 Application of the doubly-labelled water method at high activity levels

The doubly-labelled water method is ideal for measuring the energy cost of heavy work since it dose not interfere with the performance of the subject. However, when planning observations at high activity levels there are some extra precautions and assumptions to be made compared with observations in the "normal" sedentary adult.

1) Length of the observation period

For maximal precision, the observation period should be one to three biological half-lives of the isotopes 5. During heavy sustained exercise the half-lives of 18O and 2H decrease to 2-4 days, about one third of the values in the "normal" adult 6. Consequently, depending on the expected activity level, the observation period should be shortened. As a rule of thumb, daily energy expenditure is 1.5 times basal metabolic rate for sedentary people and 4-5 times basal metabolic rate at maximum performance. The length of the observation period should be adjusted accordingly.

2) Isotope fractionation corrections

At high activity levels the rate of water loss via fractionating gaseous routes increases as does the rate of carbon dioxide production. Breath water vapour is proportional to the ventilation volume. Transcutaneous water loss increases proportionally more than carbon dioxide production 7 but here the major part is unfractionated sweat. These effects therefore have a tendency to cancel, and there may be no need to apply different fractionation corrections at high and low activity levels. However, each situation should be critically assessed with the aid of information provided in Chapter 6.

3) The energy equivalent of CO2

At high activity levels people tend to have a different diet from the general population. Therefore it is preferable to measure dietary intake simultaneously with carbon dioxide production when the latter data have to be converted to energy expenditure. In The Netherlands the FQ for the average subject is close to 0.85 while for instance endurance athletes have FQ values generally higher than 0.90 8 due to a higher carbohydrate intake. Calculating the RQ, one has to know the FQ and the change in body composition over the observation interval. The latter is not really feasible over intervals with the length of a DLW run so the best that can be done is to measure body mass and body water volume at the start and end of the observation period and translate any changes in the energy equivalent of CO2.

4) Potential accuracy

The potential error in the calculated rate of carbon dioxide production decreases with increasing activity level. Subjects at a high activity level have a relatively higher rCO2 than rH2O compared with sedentary subjects, as derived from the ratio between ko and kd (Table 13.1).

In conclusion, there are extra precautions and assumptions to be made when one uses the doubly-labelled water method at high activity levels. The single validation study performed at high activity indicates that the method has a similar precision at low- and high-activity levels 7.

## 13.4 Application of DLW under tropical conditions

There is an inevitable loss of precision when DLW is used under conditions where high ambient temperatures cause high rates of water turnover with a consequent reduction in the kO/kD ratio. In studies in The Gambia 9, 10 precision was about 3 times worse than similar measurements in temperate climates. There is little that can be done about this except to increase dose levels and pay extra attention to analytical precision.

## 13.5 Application of DLW in non-compliant subjects

One of the major advantages of DLW is limited level of compliance which is necessary. Young children represent one group in which compliance is low and yet in which the technique has been very successfully applied. Studies have also been performed in a group of highly non-compliant elderly, mental patients with good results 11.

## 13.6 Application of DLW in clinical situations

The major constraint of the method in most clinical circumstances is the need to study several half-lives. This means that rapidly changing clinical states cannot be successfully studied.

The method has been used in children treated for burn injury 12. Depending upon the type of treatment given fractionation amy be high due to high levels of water loss accross the burn. This generates the greatest methodological problem which must be assessed on an individual basis.

Table 13.1. kd/ko in subjects at low and high activity levels

 Activity level n TEE/BMR kd/ko low 5 1.4 ± 0.09 0.78 ± 0.02 high 8 2.6 ± 0.25 0.74 ± 0.03 very high 15 4.9 ± 0.57 0.74 ± 0.04

Values are means ± sd.

## 13.7 References

1. Coward WA (1988) The 2H218O meshed - principles and practice. Proc Nutr Soc; 47: 209-218.

2. Roberts SB, Coward WA, Schlingenseipen K-H, Norhia V & Lucas A (1986) Comparison of the doubly labelled water (2H218O) method with indirect calorimetry and a nutrient balance study for simultaneous determination of energy expenditure, water intake, and metabolisable energy intake in preterm infants. Am J Clin Nutr; 44: 315-322.

3. 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.

4. 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.

5. Schoeller DA (1983) Energy expenditure from doubly labelled water: some fundamental considerations in humans. Am J Clin Nutr; 38: 999-1005.

6. Westerterp KR, Saris WHM, van ES M & ten Hoor F (1986) Use of the doubly labelled water technique in humans during heavy sustained exercise. J Appl Physiol: 61: 2162-2167.

7. Westerterp KR, Brouns F. Saris WHM & ten Hoor F (1988) Comparison of doubly labelled water with respirometry at low- and high-activity levels. J Appl Physiol; 65: 53-56.

8. Erp-Baart AMJ van, Saris WHM, Binkhorst RA, Vos JA & Elvers JWH (1989) Nationwide survey on nutritional habits in elite athletes; part 1 energy, carbohydrate, protein and fat intake. Int J Sports Med.; 10 (suppl 1): 3-10.

9. Singh J. Prentice AM, Diaz E, Coward WA, Ashford J. Sawyer M & Whitehead RG (1989) Energy expenditure of Gambian women during peak agricultural activity measured by the doubly-labelled water method. Br J Nutr; 62: 315-329.

10. Diaz E, Goldberg GR, Taylor M, Savage JM, Sellen D, Coward WA & Prentice AM (1990) Effects of dietary supplementation on work performance in Gambian labourers. Am J Clin Nutr; in press.

11. Prentice AM, Leavesley K, Murgatroyd PR, Coward WA, Schorah CJ, Bladon PT & Hullin RP (1989) Is severe wasting in elderly mental patients caused by an excessive energy requirement? Age and Ageing; 18: 158-167.

12. Goran MI, Peters EJ, Herndon DN & Wolfe RR. Energy expenditure in burned children with the doubly-labelled water technique. Am J Physiol (submitted).