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

Contributors:

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.

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**

__Advantages__

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

2) Robust to large, step changes in water turnover and CO

_{2}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.

__Disadvantages__

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**

__Advantages__

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

^{2}H and^{18}O residuals provides an assessment of analytical accuracy.5) Avoids potential errors inherent in the assumption of a fixed 1.03 ratio between

^{2}H and^{18}O pool sizes.

__Disadvantages__

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.

**11.2.1 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 N_{D}/N_{O} 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:

(lnd_{2} - lnd_{1})/(t_{2}
- t_{1})

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, ^{18}O
and ^{2}H 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.