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Chapter 11: Practical recommendations and worked examples

11.1 Choice of two-point or multi-point technique
11.2 Procedure for calculating two-point data
11.3 Procedure for calculating multi-point data
11.4 Practical hints
11.5 References


Andrew Prentice
Andy Coward
Tim Cole
Dale Schoeller
Paul Haggarty

This section summarises the salient recommendations contained in the main body of the report and adds some practical advice for new users of the method.

11.1 Choice of two-point or multi-point technique

As discussed in Chapters 4, 5 and 9 the two generic methods of applying DLW, namely the two-point and multi-point versions, each have advantages and disadvantages. These are listed below:

11.1.1 Two-point


1) Requires much less sample collection, handling and mass spectrometric analysis.

2) Robust to large, step changes in water turnover and CO2 production during the measurement period (Section 9.2).

3) The protocol can often be arranged to permit sample collection under clinical conditions thus ensuring greater control.


1) Provides no information on possible deviations from the original Lifson model during the measurement.

2) Less robust to random error in isotope enrichments and therefore yields a less precise estimate than the multi-point version unless very high doses of isotope can be afforded.

3) Provides no individual estimate of precision.

4) May yield a large error if the factor of 1.03 used to calculate the single pool is significantly different from the real physiological difference in the two pool sizes.

11.1.2 Multi-point


1) Robust to random errors in isotopic enrichments and therefore provides a more precise estimate particularly at the low levels of enrichment usually employed in human studies (Section 9.3).

2) Inspection of residuals provides information on deviations from the Lifson model and permits exclusion of data from any measurement in which serious deviations occur.

3) Provides an individual estimate of precision for every answer by propagation of error analysis.

4) The extent of covariance of 2H and 18O residuals provides an assessment of analytical accuracy.

5) Avoids potential errors inherent in the assumption of a fixed 1.03 ratio between 2H and 18O pool sizes.


1) Involves considerably more work in sample collection, handling and analysis.

2) Less robust than the two-point method to step changes in water or carbon dioxide turnover. However, such changes can be detected from residual plots and the data can be recalculated using the two-point approach providing that a plateau sample has been collected.

In practice the major determinant of which method is used by different laboratories tends to be the type of mass spectrometer available. The multi-point method is impossibly time-consuming unless a fully automated instrument is used. Perhaps the major advantage of collecting data in the multi-point mode is that it can always be recalculated as two-point data (provided that the sampling regime contains time-points appropriate for the estimation of plateau enrichments). This gives maximum flexibility when it comes to the final analysis. If analytical time is at a special premium, if the investigator can accept a lower level of precision on individual estimates (as for example in large sample studies where the mean value is of interest), or when residual plots indicate significant deviation from the Lifson model it becomes appropriate to select the two-point method. Otherwise the multi-point method is marginally preferable. The most important conclusion, however, is that given reasonable data-sets the two methods give essentially the same answer (see Table 9.6) and neither need be considered inferior.

11.2 Procedure for calculating two-point data

11.2.1 Estimating N from plateaus

The equation for calculating N from enrichments (d) is given in Section 4.3. Most users follow Schoeller's recommendation of assuming a fixed ND/NO ratio of 1.03 (although Table 4.2 suggests that a marginally higher value of 1.035 might be slightly preferable). If only one space measurement is used the other should be calculated from it. If both are measured the values can be appropriately weighted.

11.2.2 Flux rates

Calculation of the elimination rate by the two point method is straightforward. Isotopic enrichments relative to baseline are calculated by taking the simple arithmetic difference. The elimination rate is then calculated as:

(lnd2 - lnd1)/(t2 - t1)

Except for very short times after the dose, time should be recorded to nearest hour of collection. Time for blood samples are equal to the collection time. Time for urine samples have generally been taken as the collection time, although urine is somewhat older than collection time because it is secreted into the bladder over the time between voidings. Pharmacologists generally use the midpoint of the interval between voidings as the time, however, unlike drugs, 18O and 2H labelled water does exchange slowly across the bladder rendering even this calculation inexact. Before becoming overly concerned, however, it should be remembered that an error of even two hours is only 1% of 7 days. In general, samples should be collected at the same time of the day (to within a few hours) because of diurnal variation in energy expenditure and water flux.

One obvious problem of the two point method is that two points always make a straight line. Thus, it is impossible to detect an analytical error or a sample mislabelling. Analytical errors can be detected by repeating the isotopic analysis on a separate day. Analytical errors and labelling errors can be detected by collecting a sample near the midpoint of the metabolic period (thus making it a 3-point method). The carbon dioxide production rate can then be calculated over half the metabolic period and the entire period. Unless subjects change their expenditure dramatically, these two values should agree within 2 standard deviations of the measurement error or about 8%. If not, an error has usually been made and samples should be reanalysed.

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