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7.3 The effect of sequestration on the performance of DLW

In order to illustrate the method of calculation of the effects of isotope sequestration it is helpful to use a completely defined system where all the relevant parameters have been experimentally determined. This is only possible in animal models where the end products can be extracted and their isotopic composition determined. The necessary analyses have been performed on the obese Zucker rat for fat and protein. This animal will serve as a useful example since its high rate of lipogenesis relative to body size should exacerbate the effect of sequestration on the performance of the DLW technique.

7.3.1 Calculation for an animal model

In order to clarify the calculation the usual units for r_H2O and r_CO2 and synthesis rates of grams and litres have been converted to moles. All the relevant raw data was obtained in rapidly growing immature obese Zucker rats (25 days old). The rate of ²H flux in such animals is around 1.906 moles/day, and since we are assuming no fractionated water loss the value of 1.906 moles/day will be taken as equal to r_H2O. r_CO2 measured by indirect calorimetry is approximately 0.2245 moles/day ¹⁸. Because each CO₂ molecule contains two oxygen atoms the H₂¹⁸O flux which occurs as a consequence of r_CO2 will be 0.4489 moles/day. Whole-body lipogenesis measured by incorporation of tritium from ³H₂O was 0.002731 moles/day ⁶. If deuterium is the hydrogen label then this will result in 53% of the hydrogens in newly synthesised fat being derived from water. Following the logic of Section 7.2.1 we estimate that 0.04582 moles/day of ²H will be incorporated. Since each molecule of water contains two atoms of hydrogen the extra water flux resulting from sequestration will be 0.02291 moles/day.

Protein synthesis was measured in rats of the same age and weight using the flooding-dose phenylalanine technique ¹⁹. The rate of whole-body protein synthesis was 1.914 g/day. Using the composition of the average human protein we calculate that the rate of amino acid incorporation into protein was 0.001575 moles/day. Using an average figure of 0.5 water hydrogen atoms sequestered per amino acid we can calculate the atoms of water hydrogen incorporated to be 0.000788 moles/day. Again, since each molecule of water contains two atoms then the extra water flux resulting from sequestration will be half this figure: 0.000394 moles/day.

When calculating the consequences of sequestration on the DLW technique it is very important to distinguish between the effect on r_H2O and r_CO2. This concept is readily illustrated in Figure 7.1 for the obese rat calculation where the components of flux are represented graphically. It is apparent from the figure that the absolute amount by which r_H2O is over-estimated is the same as that by which r_CO2 is under-estimated. Therefore, because r_CO2 is less than r_H2O the percentage error on r_CO2 is greater. It is in fact greater by the molar ratio of r_H2O/(2.r_CO2). We can use this to calculate the error on r_CO2 as:

This ratio (or its analog which is often expressed in terms of the rate constants k_D/k_O) has already been shown to be important in many aspects of the heavy water technique (see Chapters 5 & 6). However, in this case the ratio is not of primary importance since the error on r_CO2 can be predicted simply from the rate of sequestration and the true r_CO2. It serves only as an alternative method of calculation. Thus, fat synthesis in these animals will cause r_H2O to be over-estimated by 0.019016 moles/day and the percentage effect on r_H2O is +1.20%.

The effect of protein synthesis may be calculated in the same way and is +0.02%.

Using the molar ratio (r_H2O/2.r_CO2) of 4.25 and the above equation we can calculate the effect on r_CO2 of sequestration resulting from fat synthesis as -5.10% and that resulting from protein synthesis as -0.09%.

7.3.2 Calculation of the effect in human subjects

Unfortunately the process of sequestration in humans is very difficult to quantify because it is almost impossible to distinguish between ²H lost from the water pool as water and that lost by incorporation into stable carbon-hydrogen bonds. In order to do this it would be necessary either to sample the fat and protein of the body in order to measure isotope incorporation, as in the obese rat, or to compare the true water flux, determined by meticulous water balance studies, with isotopic estimates of water flux: the difference being that component which had entered non-labile positions in the body. The former is not possible in human subjects and the latter would be futile since the errors on the measurements would greatly exceed the likely magnitude of sequestration. Since it is not feasible to directly measure the process of incorporation, indirect methods must be found.

7.3.2.i Experimental evidence for sequestration in humans

Isotopic hydrogen from water is incorporated into tissue but this is not simply a uni-directional process, it occurs as a result of the constant turnover of the constituents of the body, and we can therefore predict that ²H will be re-released into the body water pool when labelled material is catabolised. This simple model of sequestration and release of water hydrogen is illustrated in Figure 7.2a. The body tissue is shown as a single pool and the single arrow in and out implies one rate of turnover. However, this is a simplification since we would expect the body tissue pool to be heterogeneous consisting, for example, of protein, fat and carbohydrate, and even of sub-pools turning over at different rates. Whatever the precise nature of this pool it should be possible to quantify the rate of incorporation from the amount re-released. However, in order to observe this recycling we have to sample the body water for much longer than the 14-21 days normally used in a human DLW study. Such extended monitoring of H isotopes in the body water has been carried out for workers in the nuclear industry who have been accidentally contaminated with high activity tritiated water. The subjects were monitored for periods of up to one year to assess the radiological risk associated with persisting isotope in the body. The data obtained from such subjects uncovers a number of points which we do not see during the relatively short time course of a DLW experiment, points which help to elucidate the process of sequestration. These studies show that isotope decay is more complex than our simple models suggest. They yield double exponentials ^20-22, triple exponentials ²³ and exponentials in combination with sines and damped sines ²⁴. The latter two models imply that the sequestered hydrogen resides in a heterogeneous pool with more than one rate constant. Whatever the number of pools, these secondary components to the curve only become apparent at around 100 days after dosing (see Figure 7.2b) but the effect of this slowly turning over compartment (half-life approximately 34 days), although masked, is present throughout the labelling period. Figure 7.2b was drawn from experimental data presented by Snyder et al ²² for an adult (41 years) weight-stable male after contamination by tritiated water. Apart from the appearance of the second exponential at 100 days there is some evidence of a sine wave at 200-260 days. These secondary components represent labelled hydrogen which has been incorporated from water into stable carbon-hydrogen bonds during reductive biosynthesis. Because the compounds are constantly turning over then this hydrogen is released back into the body water during catabolism thereby superimposing the kinetics of a secondary pool on the primary process of single exponential decay which we normally see in DLW studies.

The theoretical premise that sequestration should occur in humans is therefore borne out by this complicated description of hydrogen isotope decay but the question remains as to the likely effect of such a process on the DLW technique? Snyder et al ²² calculate that approximately 1.7% of the ³H flux passed through the slowly turning over secondary pool, or pools, which represent the carbon-bound hydrogen in body tissue. This would cause a direct overestimate of r_H2O of 1.7% and an even greater underestimate of r_CO2. The actual effect can be calculated from knowledge of the error on r_H2O and the molar ratio of r_H2O/(2r_CO2) as described in Section 7.3.1. A typical ratio of r_H2O/(2r_CO2) in human subjects is 3.64 25 which results in an error on r_CO2 of -5.59%. Also, this effect was estimated using ³H as the hydrogen isotope and, because of mass effects, the error on r_CO2 would be increased to -6.74% with ²H (see Section 7.2.1).

This calculation was based on the assumption that the total H isotope ingested by the subject was in the form of water at zero time. We can however see that 3 days before contamination, the subject already had significant levels of ³H in the body water. This will have the effect of over-estimating the proportion of ³H flux which passes through the secondary pool since some of the re-released isotope will have been incorporated at an earlier time and will not be derived from the estimated dose at the beginning of the decay curve. Therefore, studies on such subjects serve only to illustrate qualitatively that sequestration of water hydrogen does occur, that it can be experimentally detected and that we can obtain information on the half life of the sequestered hydrogen. Quantitative conclusions cannot be drawn from this example.

7.3.2.iii Calculation of sequestration from rates of deposition

Another method of estimating the effect of sequestration on the DLW technique would be to assume that any fat and protein deposited is synthesised de novo, and to calculate the effect of tissue deposition from knowledge of the stoichiometry of ²H incorporation into fat and protein 4,26, The results of such hypothetical calculations, using data on changes in body composition during extreme weight gain in adults ²⁷, are shown in Table 7.2. As in the obese rat by far the greatest effect arises from the synthesis of fat (5% underestimate of r_CO2). This is quantitatively more important than protein synthesis not only because more fat is deposited but also because fat incorporates 144 times more water H than an equal weight of protein.

Table 7.2. The effect of weight gain on the DLW technique (using ²H₂¹⁸O)

^a From Norgan and Durnin ²⁷.

^b Calculated assuming values for an adult male of: body water 44 l; r_H2O = 3.3 l/day; r_CO2 = 560 l/day; and molar ratio r_H2O/(2.r_CO2) = 3.64 (Schoeller et al ²⁵).

In two respects the example given in Table 7.2 is likely to give an exagerated assessment of error. Firstly it assumes a weight gain of 1 kg/week which is normally only achieved by deliberate over-feeding or during rehabilitation from illness. Secondly, it assumes that all of the fat gained was synthesised de novo which is known to be untrue on the high fat diets (3540%) typical of developed countries. When energy requirements are exceeded such diets provide an excess of fat which may be deposited directly, therefore the assumption of total de novo synthesis will over-estimate the effect on r_CO2. However, in underprivileged rural communities in most areas of the developing world the average diet contains only 5-20% of energy from fat and 70-85% from carbohydrate. This level is comparable with the very low fat diets fed to small animals and which result in high levels of lipogenesis. Therefore when assessing the likely magnitude of sequestration in DLW studies it is important to distinguish between groups on high and low fat diets. Set against this is the fact that developing country diets are usually marginal and the people consuming them are unlikely to be depositing much fat. A third limitation of the calculation would result in it being over-optimistic. This relates to the fact that it uses a figure for net synthesis based on deposition and takes no account of fat and protein turnover which could result in fat synthesis and therefore sequestration without any change in the amount of body fat. Such a situation did occur in the weight-stable subject studied by Snyder et al ²² (see Section 7.3.2.i).

It would be preferable to avoid these ambiguities by using rates of synthesis measured directly with tracer techniques, and such data have been obtained for protein synthesis in humans in many different physiological states. Using the calculations described above it can be shown that one of the highest rates of protein synthesis observed (286 g/day ²⁸) accounts for only 1 g/day of water flux leading to a maximum error on r_CO2 of 0.11% in normal adults. In infants r_H2O would be over-estimated by around 0.03% and r_CO2 under-estimated by 0.21%. These estimates will be further reduced if a proportion of the synthesised protein is broken down on the same day. The magnitude of degradation rates suggest that this could occur but we have no direct evidence.

Unfortunately, whole-body fatty acid turnover has not been measured in human subjects largely because there are no equivalent techniques to the ¹⁵N glycine and carbon labelled amino acid procedures, therefore we cannot draw quantitative conclusions as to the likely effect of fatty acid turnover in the body. Glycogen turnover has also proved difficult to measure but in this case we know that at least in adult weight-stable subjects, the effect on r_CO2 is less than 1%; if all the estimated 500 g of glycogen in the body turned over within a 14 day DLW study this would result in the sequestration of 100 g of water equivalents or 7.1 g/day, and for a typical molar ratio of r_H2O/2r_CO2 in an adult human of 3.64 this would translate into an error on r_CO2 of -0.8%.

7.3.2.iv Validation studies

Another way to estimate the effect of sequestration on the DLW technique would be to compare the values for r_CO2 derived isotopically with independent measurement of respiratory gas exchange for example. If a process such as sequestration were to have a measurable effect on the calculation of r_CO2 we might expect to find discrepancies between r_CO2 measured by independent methods and that measured isotopically A number of these validations have been carried out in adults (see Chapter 1, Table 1.2). In, all but one of these studies DLW over-estimated r_CO2; the average over all the studies was +2%. In two of the validation studies in infants DLW provided a 0-1% under-estimate of r_CO2 whilst the third study found that DLW under-estimated r_CO2 by 8.7%. Thus with the exception of this last study, DLW has been reported to yield values which, within the stated precision of the method, agree well with independent estimates of r_CO2 and if there is any bias it is toward over-estimation of r_CO2. Since sequestration would lead to an under-estimate of r_CO2 we might come to the conclusion that no sequestration had occured in these subjects or that the effect was negligible. Indeed these results would be very encouraging were it not for the fact that r_CO2 was calculated by each group in a different way. This highlights the problem of using such validation studies to assess the validity of individual assumptions such as 'there is no loss of isotope in products other than CO₂ and water' or that 'our estimates of fractionated water loss are correct'. In order to use this approach we have to be sure that, with the exception of the assumption to be tested, all the other factors which affect the calculation are known and that they are invariant. For example, Haggarty et al ²⁹ have attempted to estimate the effect of sequestration by comparing r_CO2 measured by DLW and by respiratory gas exchange in rapidly growing pigs. They found that r_CO2 measured by DLW was under-estimated by 4.8% during rapid growth. However, the calculation of r_CO2 from isotope flux rates is very sensitive to the estimate of fractionated water loss ^{4, 30} and the 4.8% under-estimate of r_CO2 could be completely removed by reducing the assumed value for fractionated water loss by 0.25. Since we would expect sequestration in human subjects to be lower than that found in rapidly growing pigs on a low fat diet then the errors on r_CO2 due to sequestration could easily be obscured by small errors in our estimate of fractionated water loss.

7.3.2.v Special groups

The validation studies described in the previous section, although spanning a large age range, were performed in what might be termed 'normal' subjects in that they were not in any unusual physiological state with the possible exception of the validation of Westerterp et al ³¹ where subjects underwent strenuous activity. When considering sequestration our concern is with physiological states which involve increased reductive biosynthesis or accelerated turnover of the body constituents, states which often occur simultaneously. Apart from the growth of infants and children the main states in which reductive biosynthesis occurs are during pregnancy and lactation.

Pregnancy

Protein synthesis will not materially affect the calculation of r_CO2 during pregnancy. With respect to fat synthesis Coward ⁴ has calculated the effect of a pregnant woman depositing 4 kg of fat in nine months (approximately 15 g/day). He suggested that the error introduced into the DLW technique (making the exagerated assumption that the deposited fat is entirely synthesised de novo) would be of the order of 1%. Using slightly different assumptions we have also found the error on r_H2O and r_CO2 to be small; +0.20% and -1.72% respectively. However, it has already been pointed out that this approach is flawed because the contribution of dietary fat to deposition is not known and because no account is taken of the continual turnover of the body fat (section 7.3.2.iii).

Lactation

Protein can be ignored since it has been shown above that a protein synthesis rate 100 times that of the protein exported in milk has little effect on r_CO2. Assumptions about the maximum likely amount of de novo fat synthesis during milk production can be drawn from the fatty acid composition of milk. On this basis Prentice & Prentice ³² have estimated that women on high and low fat diets synthesise approximately 12% and 36% of their milk fat respectively giving absolute daily synthesis rates of about 3.6 and 10.8 g/day. (The remainder is transfered directly from the diet.) From these values it can be calculated that exported fat in milk could cause r_CO2 to be under-estimated by 0.32 - 1.00% (Table 7.3). The export of lactose may result in a further error of about 1.11% giving a combined effect for sequestered ²H of about 1.4 - 2.1%.

7.3.3 The effect of sequestration on the assumption of steady state

So far we have only considered the effect of sequestration on the calculation of r_H2O and r_CO2 over the full duration of a DLW study but there is another possible consequence which would arise because of discontinuous sequestration and release of H isotope. Such a process would introduce variability into the deuterium decay data and consequently reduce the precision with which r_H2O and r_CO2 are calculated without necessarily causing the over-estimation of r_H2O and under-estimation of r_CO2 described previously. The main concern would be fluctuations in glycogen, the levels of which change markedly in response to carbohydrate supply and demand. Liver glycogen turns over very rapidly being reduced by an overnight fast to less than half its pre-fasting value. Depletion and repletion of muscle glycogen can also be very rapid during and after exercise. Rapid sequestration associated with the replenishment of muscle glycogen after exercise will introduce variability into deuterium decay by causing transient sequestration of ²H which may be re-released during subsequent bouts of exercise. For instance, deposition of 300g of muscle glycogen over a 12 hour period would cause a transient 3.7% over-estimate in r_H2O and a consequent 13.3% under-estimate in r_CO2.

Table 7.3. The effect on the DLW method of sequestration into the components of human milk ^a

^a Calculated using values for a lactating woman of: body water = 30 l; r_H2O = 3.0 l/day: r_CO2 = 370 l/day; and molar ratio r_H2O/(2r_CO2) = 5.05 (Prentice et al, unpublished data).

^b Calculated from Table 7.1.

^c Calculated from Table 7.1 (assuming stoichiometry of sequestration is the same as for glycogen).

7.3.4 Sequestration of oxygen

The above discussion has concentrated exclusively on the problems of ²H sequestration largely because the reduced state of the body constituents (H:O ratio for fat = 32, for protein = 5, and for carbohydrate = 2) means that ²H sequestration will have a much greater impact on the DLW method than ¹⁸O sequestration. However, it must be remembered that there are possible routes of ¹⁸O sequestration. These have not been quantified and cannot therefore be discussed in detail, but their effect will always be to offset some of the error on r_CO2 incurred due to ²H sequestration.

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