Method Fundamentals

Stable Isotopes as Tracers

Although radioactive tracers are familiar tools, the use of tracer elements and compounds to measure metabolic processes was developed first with stable isotopes in the late 1930s by Schoenheimer and Rittenberg soon after 2H and 15N (both stable isotopes) became available. Unlike radioactive isotopes, which are largely man-made, unstable, and decay to other elements, stable isotopes do not decay and are ubiquitous. Virtually all elements exist in nature in at least two stable isotopic forms with the same numbers of electrons and protons but with differing numbers of neutrons in the nucleus. The level of a specific isotopic form in nature is called its natural abundance. For tracer experiments, an element or a simple compound containing it, enriched with one of the isotopes, is prepared by mass-dependent separation on an industrial scale. This is then incorporated into the substrate of interest for biological experiments. In the current context, 2H2O (deuterium oxide, heavy water) is readily available from the electrolysis of water. Water enriched with 18O is prepared directly by fractional distillation or from nitric oxide after its cryogenic distillation.

No radioactivity is involved in the use of stable isotopes in human experiments; thus, the only effects that have to be considered in relation to risk to the subject are related to the physical properties of the isotopic labeled compound. There is inevitably some degree of isotopic discrimination in physical and enzymatic processes, but because stable isotopes are normally present in all biological material at natural abundance levels, the relevant consideration is only by how much and for how long amounts are changed in experimental procedures. Because highly precise measurement techniques are used, it is necessary only to increase isotopic enrichments in body water from natural abundance by very small amounts. In a typical experiment, 2H enrichment might be increased from 150 to 300 parts per million (ppm) and 18O from 2000 to 2400 ppm, and a return to natural abundance levels will occur with a biological half-life of 5-7 days. There is no evidence that amounts many times larger than these have any harmful effects.

Measuring Isotopic Enrichment

Mass spectrometry is a generic name for a family of methodologies in which compounds are ionised and separated on the basis of mass:charge ratio. The method of choice for the measurement of isotopic enrichment with sufficient precision for DLW experiments is isotope ratio mass spectrometry. This technique is applicable only to relatively simple molecules. It separates ions such as [2H—1H]+ and [1H—1H]+ (mass 3 and 2) or [12C16O18O]+ and [12C16O16O]+ (mass 46 and 44) and measures isotopic ratios (R) relative to an international standard, such as Vienna Standard Mean Ocean Water (V-SMOW; Table 1). For the DLW method, therefore, the isotopic enrichment in water from biological samples has to be measured as hydrogen or carbon dioxide. For hydrogen isotope analysis, a variety of methods have been used for the conversion including reduction by reaction with hot uranium or zinc, but these methods are difficult to automate. Currently favoured methods are the exchange of hydrogen in the water sample with gaseous hydrogen by equilibration in the presence of a platinum catalyst or reduction with hot chromium. Both of these techniques are automated in commercially available equipment. For oxygen isotopes, samples are usually equilibrated

Table 1 Typical isotopic ratios and equivalent enrichments measured in DLW experimentsa

Sample

2H

2H

18O

18O

isotope

enrichment

sotope

enr chment

ratio

(%%

rat o

(% )

(ppm)

(ppm)

V-SMOW

155.76

0

2005.2

0

Background

152.28

-22.34

1995.74

-4.72

Postdose

342.67

1200

2305.98

150

aEnrichment = 103 (RRsample - 1Y

V-SMOW, Vienna Standard Mean Ocean Water.

aEnrichment = 103 (RRsample - 1Y

V-SMOW, Vienna Standard Mean Ocean Water.

with carbon dioxide with exchange of oxygen between the water and carbon dioxide. This procedure is also automated.

Single Pool Kinetics

Considering only hydrogen, Figure 1 represents a subject, in water balance, with a total body water of N mol with water (tracee) input and output rates of F mol/day containing 2H at a naturally abundant molar concentration, Cb. A fractional output or rate constant is defined as K = F/N.

If a small quantity (D mol) of water labeled with 2H tracer is added to the pool, it will be removed from it according to the monoexponential relationship qt - qb = De

-Kt where D is the amount of tracer given, qt is the total amount (mol) in the body pool at time t (days), and qb is the amount always present due to inflow at natural abundance. K is a fractional rate constant, sometimes defined in terms of the biological half-life T1/2. This can be calculated as T1/2 = ln2/K = 0.693/K.

Since input and output rates are the same and the amount of tracer added is small relative to the pool size, we can write qt - qb

Kt where C0 — Cb is the increment in isotopic concentration resulting from the administration of the dose, and N can be calculated as N = D/(C0 — Cb).

The foregoing equations have been written in terms of isotopic concentration (e.g., C = 2H/(2H + 1H)), but mass spectrometry measurements are in terms of ratio (e.g., R = 2H/1H) and in practice, for DLW calculations R or enrichment relative to a standard is invariably substituted for C with no effect on results at the low levels of enrichment applied in this methodology.

Principles of the Method

When Lifson first began his physiological experiments with newly available 18O in the mid-1950s, it was already well-known that oral dosing with

Figure 1 A simple one-compartment model of water turnover.

2H2O and its dilution in body water was a way of measuring body water mass and turnover. Lifson showed that the oxygen in carbon dioxide, the waste product of energy metabolism, was in equilibrium in the body with body water:

H2O + CO2 H2CO3

He realized, therefore, that the greater apparent turnover of body water measured with H218O in comparison to turnover measured with 2 H 2O (Figure 2) was a consequence of carbon dioxide production, as shown in Figure 3. Thus, there was potential for a method that would permit the measurement of total CO2 output and hence energy expenditure over long periods merely by isotopic analysis of samples of body fluids. Initially, the method was applied only to small animals because

6 8 Days

Figure 2 Exponential loss of 2H and 18O from body water. The insert shows the data on a log scale.

6 8 Days

Figure 2 Exponential loss of 2H and 18O from body water. The insert shows the data on a log scale.

2H2O

C18O2

Figure 3 The fate of an oral bolus dose of 2H and 18O given as water (DLW).

C18O2

Figure 1 A simple one-compartment model of water turnover.

Figure 3 The fate of an oral bolus dose of 2H and 18O given as water (DLW).

2H2O

the 18O isotope was (and still is) expensive and instrumental limitations meant that relatively large doses had to be given to achieve adequate measurement precision. However, in the 1980s human studies, which are the focus of this article, became possible and in 1998 a basic unified methodological approach was established as a result of a meeting of the experts in the field (International Dietary Energy Consultancy Group). The publication derived from this meeting remains a valuable tool.

The following are the underlying assumptions of the method:

1. Body water is a single compartment that the isotopes label and from which they are lost.

2. 2H is lost only as water.

3. 18O is lost as water and carbon dioxide.

4. Total body water and output rates of water and carbon dioxide are constant.

5. Water and carbon dioxide loss occurs with the same enrichment as that coexisting in body water.

6. Background isotope intakes are constant.

Taking these in turn, assumption 1 is not correct. Evidence from many studies shows that the single compartments labelled by the isotopes are not the same size; 2H space is approximately 3% larger than 18O space. However, there is no evidence that isotope sequestration is a significant factor in human studies (assumptions 2 and 3). Water and carbon dioxide production rates are unlikely to be constant during a measurement period (assumption 4), but provided variations are random and not unidirectional during the measurement period, justifying the use of mean values for a period in any case, the method will not produce biased results.

Allowing assumptions 1-4, simple equations can be formulated (values of F and N are in mol and K in days-1). FHiO is measured as

FH2O = KDND

and the water plus carbon dioxide output (expressed in mol water equivalents) is

Fh2o + co2 = kono Carbon dioxide production is then

KoNO - KdNd

The factor of 2 arises because 2 mol of water is equivalent to 1 mol of carbon dioxide.

These simple relationships are in practice modified to correct for isotopic fractionation that, contrary to assumption 5, does occur. Where evaporative water losses occur, relatively less 2H and

18O leave the body in water vapour compared with liquid water. Fractionation factors are defined as

18o/16o)

18O/16O

liqiud

18o/16o)

Thus, water vapour is isotopically depleted in 2H and 18O and carbon dioxide is relatively more enriched in 18O compared to liquid water.

If it is assumed that a constant proportion (x) of water losses is fractionated, carbon dioxide production rate becomes

This procedure is most frequently used for infants and young children, in whom values of x are assumed to be 0.15-0.20.

For adults, fractionated water losses (Ff) are often defined in terms of FCOz (Ff = 2.1FCOJ, in which case

KoNo - KdNd

Assumption 6 relates to the requirement that a predose sample should represent the effect of normal natural abundance isotope input. In most cases, background isotopic enrichment is likely to vary only randomly during a measurement period and so the issues are about the relationship between the background sample measured, the mean background and its random variation during the experimental period, the extent to which background variations in 2H and 18O are covariant, and the size of isotope doses and postdose enrichments in relation to these variations. In most experimental situations investigated with affordable isotopic doses, background variation contributes to the internal errors of the method and limits the extent to which better analytical precision improves results. In some circumstances (e.g., subjects moving from one place to another and use of large amounts of rehydration fluids in hospitalised patients), it is possible that a predose sample taken to represent isotopic background is not at all meaningful and the best advice may be to avoid these circumstances rather than try to correct for them.

Finally, FCo2 values have to be converted into values for energy expenditure based on a fixed relationship between these quantities that depends on metabolic fuels used, expressed as a respiratory quotient (RQ). We can write

Energy expenditure (kJ) = FCo2

346.7

124.3

where FCOi is mol. RQ is calculated from dietary information or assumed to have a particular population value, such as 0.85.

Insertion of typical Western adult values (NO = 2000, Nd = 2066, KO = 0.12, and KD = 0.10) into the relevant equations and 'what if' experimentation will allow the reader to test the effect of making changes to the assumptions and values. Table 2 provides examples that show that serious errors or bias, for groups or individuals, are unlikely unless the applied population means for assumed values are grossly incorrect or the coefficient of variation (CV) is large.

Experimentation with the data, however, will also show that the magnitude of the difference between KONO and KDND is crucial. The method depends on precisely determining a relatively small difference between these two experimentally measured, larger values. This difference is approximately 20% in the example but can be much less when water turnover is high relative to carbon dioxide production (e.g., very young infants or subjects living in the tropics).

For the slopes (KO and KD) a minimum of two time points are required sufficiently far apart in time (two or three biological half-lives) to allow good precision on the slope determination with doses of sufficient magnitude to avoid detrimental effects of natural abundance variations and the limitations of analytical precision, especially at the end of the measurement period. In some protocols, more than two samples are measured, and this permits error calculations based on the goodness of fit of the data. Isotope distribution

Table 2 'What if' calculations for a typical subject (NO = 2000, Nd = 2066, KO = 0.12, Kd = 0.10)

Fractionated water losses defined in CO2 production relative terms of Fqq2 (Ff = 2.1 Fqq2) for mean and assumed CV = 10% -2 SD = 1.68 FCQ2 Mean = 2.1 Fcq2 +2 SD = 2.58 Fco2 Assumed RQ (typical mean ±2 SD)

to value for mean

1.010 1

0.981 Energy expenditure relative to value for mean 1.024 1

0.978

spaces are calculated from samples taken soon after dose administration (the 'plateau method') or by extrapolation of the disappearance curves to t = 0. Distribution spaces may be normalized to population-based estimates (ND and NO) of their relation to total body water (TBW):

Figure 4 illustrates some aspects of total imprecision and the origins of the variance for a typical subject defined in Table 3 when different dosing regimes are applied, with 18O enrichment being varied at a constant initial 2H:18O ratio of 8.

The following are general considerations:

1. Naturally occurring covariance in 2H and 18O enrichment in baseline samples can be used to mitigate errors resulting from physiological variation in these values if dose sizes are suitably tailored to the slope of the variation. Optimum doses in this respect are predicted by

optimal where (2H/18O)optimal is the ratio of immediate postdose - background enrichments (rel V-SMOW) for

cd 50 o

25 50 100 150 200 250 Initial 18O enrichment (%0 rel V-SMOW)

I | Background (natural abundance variation)

20 18 16

w CO

CV, coefficient of variation; RQ, respiratory quotient.

25 50 100 150 200 250 Initial 18O enrichment (%0 rel V-SMOW)

I | Background (natural abundance variation)

| Post dose (biological variation)

| | Post dose (analytical error)

j^jj Background (analytical error)

— Measurement CV

Figure 4 Origin of errors and their size in DLW experiments. The line and right axis show the total CV at different isotope doses in a typical subject defined in Table 3. The bars and left axis indicate the proportion of the total variance derived from each source of error.

Table 3 Typical estimates and measurement precision in a DLW experiment lasting 14 d

Parameter

Value

nO

2000 mol

nD

2066 mol

kO

0.12 day"1

kd

0.10 day"1

Proportional error in postdose 2H

0.01

samples originating from variations

in water turnover (SD)

Variance in postdose 18O accounted

90%

for by variance in 2H (excluding

analytical errors)

18O analytical error at baseline (SD)

0.15%

2H analytical error at baseline (SD)

1.5%

18O analytical error for enriched

0.5% of value + 0.15%

samples (SD)

2H analytical error for enriched

0.5% of value +1.5%

samples (SD)

18O background variation (SD)

0.15%

2H background variation (SD)

1.2%

Variance in background 2H

100%

accounted for by variance in 18O

(excluding analytical errors)

Slope of background 2H enrichment

8

on background 18O enrichment

2H and 18O, S is the slope of background 2H enrichment on background 18O enrichment, n is the experiment duration in terms of the number of biological half-lives for the 2H isotope, and p is Ko/Kd.

2. Much of the deviation of the 2H and 18O data from the model for the postdose samples is cov-ariant because it relates to inconstancy of water turnover. Errors thus tend to cancel, and this considerably reduces the potential impact of variance from this source.

3. Although the analytical errors applied in this case are not the lowest reported, they are probably typical and it can be seen that they always account for much of the variance.

4. Errors consequent on background uncertainty become very important when amounts of dose are reduced, but in practice, cost always limits the amount of 18O that can be given. For this example, adequate precision in the total energy expenditure(TEE) measurement is predicted for 18O doses producing initial enrichment in the range of 100-150% rel V-SMOW.

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