## Abstract

In the present study, we have investigated the use of 1-[^{13}C]glucose and GC/combustion/isotope-ratio MS as an alternative to 6,6-[^{2}H_{2}]glucose and GC/MS in the determination of parameters of glucose metabolism using the IVGTT (intravenous glucose tolerance test) interpreted by labelled (hot) minimal models. The study has been done in four populations, normoglycaemics (subdivided into lean and obese individuals), subjects with impaired glucose tolerance and those with diabetes mellitus. Although the use of carbon label may in some circumstances be compromised by substrate recycling, our hypothesis was that this would not be an issue under the condition of suppression of hepatic glucose production during the short timescale of an IVGTT. In all four groups, we found that the methodology employing the carbon label gave equivalent results to those obtained using the conventional deuterated material, but the sensitivity of the measurement technique in the new approach was sufficient to allow an approx. 15-fold reduction in the quantity of isotope administered. In addition to the clear cost advantages, this represents a significant scientific advance in that true tracer status is more nearly attained in these measurements with near-physiological tracee loads.

- diabetes
- glucose effectiveness
- insulin sensitivity
- intravenous glucose tolerance test (IVGTT)
- minimal model
- stable isotope

## INTRODUCTION

Interpretation of the IVGTT (intravenous glucose tolerance test) by the minimal model of glucose kinetics is widely used in the determination of *S*_{I} (insulin sensitivity) [1]. The methodology, in its most sophisticated form, separates endogenous glucose production from disposal processes [2–4] by modelling glucose kinetics [5–7] after an intravenous bolus dose of isotope-labelled glucose. Stable isotopes are now the tracers of choice, customarily 6,6-[^{2}H_{2}]glucose measured in derivatized form by GC/MS [8]. Relatively large isotope concentrations are required, typically approx. 13% of the glucose dose (approx. 20 g in adult humans [9]), and so approx. 2.5 g of labelled material is needed for each measurement.

Previously, we published data [10,11] that indicated that GC/C/IRMS (GC/combustion/isotope-ratio MS) [12], which is two orders of magnitude more precise than GC/MS for isotope work [13], could be used, requiring only 120 mg of 1-[^{13}C]glucose for reliable estimates of minimal model parameters. However, validation over a wide range of insulin sensitivities is needed since, although the deuterium label at the 6-position of the glucose molecule is either directly incorporated into glycogen or lost in glycolysis [14] (this has been used to determine the relative contributions of these processes to glucose disposal [15]), skeletal carbon is retained during the course of glycolysis and is available for gluconeogenesis (Cori cycle). Thus label recycling in the course of an IVGTT could perturb parameter estimates. There have been numerous studies of the rates of gluconeogenesis (see [16] and cited references therein), but most of have been performed in the fasted state when hepatic glucose production (and hence gluconeogenesis) is at a maximum. During IVGTT, we anticipate that endogenous glucose release is inhibited by hyperglycaemia and that the effects of label recycling will be small.

Our previous work [10,11] has shown that, in subjects with normal glucose tolerance, ^{13}C-labelled glucose and GC/C/IRMS gave equivalent results to the ^{2}H label and GC/MS for *S*_{I}, but not for estimates of glucose self-clearance. The present study was designed to test further the comparison between the two methods by extending the range of glucose tolerance in the study population.

## METHODS

### Subjects

Permission was obtained from the Local Research Ethics Committee (LREC) to recruit to the study men in the age range 24–65 years either by advertisement or by direct approach to those registered on the Medical Research Council Human Nutrition Research database. Potential recruits were asked to complete a brief questionnaire, giving details of weight, height and a medical summary. Users of aspirin (in moderation), antihistamines and antihypertensive drugs were not excluded, but those on other medication likely to interfere with glucose metabolism were. Subjects with previously diagnosed diabetes, now controlled by diet and exercise, were immediately recruited to the DM (diabetic) group, but other subjects were invited to the Human Nutrition Research laboratories to partake in an OGTT (oral glucose tolerance test). Subjects gave written informed consent to partake in the study.

### OGTT

The OGTT was performed according to World Health Organization protocols [17], which classifies subjects as DM, IGT (impaired glucose tolerance) or normal. In the present study, the latter group was stratified by BMI (body mass index) into NGT-L (normal glucose tolerant and lean; BMI <25 k/gm^{2}) and NGT-O (normal glucose tolerant and obese; BMI ≥30 k/gm^{2}) subjects.

### IVGTT

Subjects were studied on two occasions, separated by at least 2 weeks. The dosing and study day protocol has been fully described previously [11]. The isotopic composition of derivatized plasma glucose [18] was determined by GC/MS for the ^{2}H-labelled species and GC/C/IRMS for the ^{13}C-labelled material. Details of these and other relevant analytical procedures are given elsewhere [11].

### Modelling

Modelling was performed using a spreadsheet (Excel 2000, version 9.0.2720; Microsoft) with fitting of model parameters to experimental data achieved by non-linear optimization of the sum of the squared residuals between observed and calculated data using the built-in SOLVER function.

For 1CMM (one-compartment minimal model), the equations from the study by Yang et al. [19] were integrated to give functions for plasma glucose and insulin concentrations that could be calculated by numerical methods. Four adjustable parameters were used in fitting: the quantity of glucose (mol) in the accessible pool [determined using the equation: *G*_{b}=*V*_{G}*C*_{Gb}, where *V*_{G} is the apparent volume (litres) of the accessible pool, and *C*_{Gb} (mol/l) is the basal glucose concentration], *S*_{G} (glucose effectiveness; h^{−1}), *S*_{I} (pmol·l^{−1}·h^{−1}), and a parameter describing the rate of clearance of insulin from the remote pool, *p* (h^{−1}). End-test levels of total glucose and insulin were taken to represent basal values (that of labelled glucose is 0 by definition), and all time points after 8 min post-dose were allocated the same statistical weighting; earlier time points were zero-weighted. 1CMM can be evaluated from non-isotopic (unlabelled; cold) data only or from a combination of isotope and non-isotope data, in this case yielding three different sets of parameters which will be denoted by, for example, *S*_{I}^{1}, *S*_{I}^{1}**(H)* and *S*_{I}^{1}*(*C*) for the unlabelled, ^{2}H and ^{13}C data respectively.

The results were also interpreted on the basis of 2CMM (two-compartment minimal model) [5–7], where analysis was performed using Euler's method to solve the differential equations iteratively. The kinetic parameters found by the fitting process were combined to give parameters equivalent to those found by 1CMM, i.e. *G*_{1b}^{2}*, *S*_{G}^{2}*, *S*_{I}^{2}* and *p*^{2}*.

### Statistics

All statistics were calculated either from first principles or by the functions supplied in Excel. Values are means±S.E.M., unless otherwise stated. Designation of dependent and independent variables in linear regression was avoided by using Deming's method [20]. All regression coefficients are calculated using Pearson's product-moment method, which implies normal distribution of variables. Normality was achieved for *S*_{G} and *S*_{I} by log- and square-root transformation respectively [21].

The presence of differences between data obtained within subject groups was detected by repeated-measures ANOVA, and the differences isolated by the (two-tailed) Bonferroni *t* test. Specific comparisons were made using the standard two-tailed paired Student *t* test. Statistical significance was taken as 5%.

For ease of interpretation, repeatability was calculated using untransformed data where possible. The S.D.s of the repeated measurements were tested for independence of their mean value by non-parametric correlation using Spearman's method [22]. If significant relationships were observed, then the data were log-transformed (in this instance, log-transformation of *S*_{I} was preferred to the square-root for ease of interpretation). Repeatability was then calculated from the within-subject S.D. in each case. For untransformed data, repeatability indicates a range symmetric about the mean, whereas transformed data gives limits obtained by scaling the mean value [23].

## RESULTS

Ideally, equal numbers of subjects might have been recruited to each of the four groups but, with the local prevalence of undiagnosed IGT (4% of adults in nearby London [24]), it was accepted that fewer subjects would be recruited to this group than to the other three (Table 1). Two subjects newly diagnosed with diabetes during the screening process decided to continue to participate, and were allocated to the DM group.

### Direct comparison of tracer behaviour

The primary measure of the equivalence of the behaviour of the two tracers was the direct comparison of the plasma tracer concentrations [11]. For all 40 IVGTTs performed, the correlation between the mole fractions of the two tracers was extremely high with *r* in the range 0.976–0.993.

For each of the four groups, the mean value of the regression slope was not significantly different from the molar ratio of the labelled species in the dose, 0.06895 (*P*>0.3; Table 2). However, the results for the intercepts of the regressions were not so clear-cut. Significant deviation from zero was indicated (*P*<0.05) in three of the four subject groups. Only the IGT group, which comprises a very small number of subjects, tested null.

### Results from the minimal models

Five minimal models could be used to interpret each IVGTT (unlabelled, ^{2}H-1CMM, ^{13}C-1CMM, ^{2}H-2CMM and ^{13}C-2CMM), each giving estimates of *S*_{I}, *S*_{G} and *G*_{b} (Table 3). The unlabelled 1CMM gave negative or unlikely values for either *S*_{G}^{1} or *G*_{I}^{1} in three cases, and the labelled (hot) 1CMM failed similarly in two cases. In contrast, 2CMM was always successful. The incidence of obtaining unacceptable solutions from 1CMM has been reported to be in the range 4–61% [25] and dependent upon specific methods of implementation.

*S*_{I}

If all the subjects were treated as belonging to a single group, ANOVA indicated that the five measures of *S*_{I} [*S*_{I}^{1}, *S*_{I}^{1}*(*C*), *S*_{I}^{1}*(*H*), *S*_{I}^{2}*(*C*) and *S*_{I}^{2}*(*H*)] were equivalent, with the exception of those from the unlabelled minimal model (*S*_{I}^{1}), which underestimated *S*_{I} when compared with either of the two-compartment indices [*S*_{I}^{2}*(*C*) and *S*_{I}^{2}*(*H*); *P*<0.01 in both cases]. There was also a significant difference (*P*<0.001) between *S*_{I}^{1}*(*C*), and *S*_{I}^{2}*(*H*). A more detailed analysis showed that the unlabelled model gave significantly lower (*P*<0.005 in all cases) estimates for *S*_{I} than any of the four labelled models in the DM group only, and *S*_{I}^{2}*(*H*) differed significantly (*P*<0.001) from the values obtained from all of three 1CMMs in the NGT-L group. Otherwise no significant differences were observed.

The high degree of correlation between tracers is shown in Figure 1 within 1CMM (Figure 1, upper panel) and 2CMM (Figure 1, lower panel), and these findings are summarized in Table 4. Respectively, linear regression gave the relationships:
No significant difference was observed between *S*_{I}^{1}*(*C*) and *S*_{I}^{1}*(*H*) for any of the groups or when tested for the combined population. However, *S*_{I}^{2}*(*C*) was slightly lower than *S*_{I}^{2}*(*H*) both in the NGT-L and NGT-O groups (*P*<0.05), and when the overall comparison was made (*P*<0.005). A Bland and Altman analysis of the two compartment data is shown in Figure 2.

For repeated measures of *S*_{I}, means and S.D. were generally correlated; accordingly, log-transformation had to be carried out in order to assess repeatability. The mean values and their limits of repeatability are given in Table 5. The high degree of repeatability of *S*_{I}^{2}*(*C*) is shown further in Figure 3.

*S*_{G}

Comparison of *S*_{G} estimates from the five models was not consistent within the four groups. Table 6 shows which comparisons gave significant differences by *post*-*hoc* Bonferroni comparisons following ANOVA. As anticipated, the unlabelled 1CMM gave estimates very different from those from the tracer methodologies, but additionally it was found that the labelled 1CMM fitted differently for the two tracers for subjects in the DM group. This was in contrast with 2CMM, where the results were independent of label in all groups.

A more comprehensive investigation of the differences in tracer behaviour is provided by direct comparisons of *S*_{G}^{1}*(*C*) with *S*_{G}^{1}*(*H*) and of *S*_{G}^{2}*(*C*) with *S*_{G}^{2}*(*H*). For 1CMM, the correlation obtained (*r*=0.30, *P*=0.07) did not demonstrate a relationship between the estimates obtained from the two labels (*P*=0.07), but for 2CMM the relationship is highly significant (*r*=0.75, *P*<10^{−4}). Analysis by linear regression gave *ln*[*S*_{G}^{2}*(*C*)]=(0.94±0.09)*ln*[*S*_{G}^{2}*(*H*)]−(0.09±0.04), the intercept not being different from zero and the slope not different from unity. Furthermore, a Bland and Altman [26] analysis of *ln*[*S*_{G}^{2}*(*C*)] and *ln*[*S*_{G}^{2}*(*H*)] showed no linear trend (|*r*|<0.5, *P*>0.15 for all intra-group analyses; *r*=−0.08, *P*=0.6 overall) clearly indicating that the two measures of *S*_{G}^{2}* were equivalent.

Comparison of 1CMM with 2CMM using the same tracer indicated that *ln*[*S*_{G}^{1}*(*C*)] and *ln*[*S*_{G}^{2}*(*C*)] were not quite significantly correlated (*r*=0.30, *P*=0.06), and the values obtained from the two models were significantly different as determined using a paired Student *t* test (*P*<0.001). From an analysis of *ln*[*S*_{G}^{2}*(*C*)]−*ln*[*S*_{G}^{1}*(*C*)], it was concluded that 1CMM underestimated *S*_{G}(*C*) by 11±3% compared with 2CMM. A similar result was obtained for *ln*[*S*_{G}^{1}*(*H*)] and *ln*[*S*_{G}^{2}*(*H*)], except that, in this case, the correlation observed between the data from the two models was even weaker (*r*=0.25, *P*=0.12).

Within-subject variation was calculated from untransformed data as 1.39 h^{−1} for *S*_{G}^{1}, representing 121% of the overall mean value, compared with *S*_{G}^{1}*(*H*) (0.21 h^{−1}; 76%), *S*_{G}^{1}*(*C*) (0.15 h^{−1}; 44%), *S*_{G}^{2}*(*H*) (0.28 h^{−1}; 62%) and *S*_{G}^{2}*(*C*) (0.26 h^{−1}; 68%). Although no significant differences were detected in between-visit results in any model, significant correlation between the results at two visits was achieved only in the case of the labelled 2CCM models [*S*_{G}^{2}*(*H*) and *S*_{G}^{2}*(*C*); *r*=0.6, *P*<0.005 in both cases].

*S*_{G} at zero insulin concentration

Some of the ambiguities found in inter-group comparisons of *S*_{G} can be removed by subtraction of the contribution of basal insulin. When this was done, it was found that the parameter [*S*_{G}^{1}(*I*=0)] derived from the unlabelled model was not consistent with any of those derived from the labelled data. However, no differences were detected between the parameters when they were derived from any of the labelled models and methods.

For 1CMM, the estimates of *S*_{G}^{1}*(*I*=0) from the two tracers were correlated (*r*=0.42, *P*<0.02), which was in contrast with the behaviour of basal *S*_{G} (*S*_{G}^{1}*); *S*_{G}^{1}*(*I*=0) and *S*_{G}^{2}*(*I*=0) were uncorrelated for either tracer (*P*>0.15 in both cases).

*G*_{b}

There was general concordance between the three 1CMMs and also between the two 2CMMs (Table 3c). The only exception was for the DM group, where *G*_{b}^{1}**(C)* and *G*_{b}^{1}**(H)* were significantly higher than *G*_{b}^{1}. 2CMM gave estimated pool sizes that were independent of the label used and were always different from any of the 1CMM estimates.

## DISCUSSION

### Comparison of tracer behaviour

Comparison of the disappearance of the two tracers from the blood agreed with our previous findings [10,11]. The very strong correlation observed between the tracer concentrations indicates equivalent behaviour, but is insufficient to prove that the labelled species may be used interchangeably; the slopes of the regressions (Table 2) are not significantly different from the molar ratios of the label used, but the small significant deviations of the intercepts from zero require further discussion.

Analysis of the residuals (Figure 4) indicates that, after administration of the dose, they are symmetrically distributed about zero. If label recycling were an issue then it would be more apparent at the end of the test, rather than at the beginning, and a bias in the residual distribution would develop as a function of time. Even though the IVGTTs were continued for longer than usual, no such bias was observed. Thus re-appearance of label in plasma is not the primary cause of the non-zero regression intercepts.

Prior to dose administration, however, the residuals behaved differently. At these times mean values were significantly different from zero, indicating that the basal isotope ratios adopted are inappropriate.

There is no *a priori* reason to assume that the natural abundance of glucose obtained from the pre-IVGTT plasma samples is the same as that obtained during and after the intravenous administration. In foods, a range of carbon abundance of 1.08–1.10% ^{13}C has been reported [27] and a substantial part of this variation could be apparent in plasma glucose. In addition, the source of the glucose used in dose preparation is unknown. For GC/MS measurement, the (*M*+2)/*M* isotopomer ratio would be expected to change by approx. 0.015% absolute (e.g. from 2.272 to 2.286% of the base peak) due to this natural variation, approximately the precision of the measurement itself. In contrast, GC/C/IRMS techniques are powerful enough to detect natural abundance variations, and the choice of basal abundance is more critical. In the context of the present experiments, simulation indicated that an underestimate of the basal isotope ratio of 10 p.p.m. would give rise to an intercept value of approx. +0.0007 mmol/l, indicating that the basal isotope levels most appropriate for these IVGTTs were generally approx. 30 p.p.m. higher than those measured in the fasted state.

The correct value to use for the basal abundance is always important in low-dose tracer studies. However, in the present study, we have shown that even at the low doses used in the GC/C/IRMS methodology a systematic error introduced does not affect the estimates of the parameters of glucose.

The influence of the IVGTT protocol is a possible confounding factor when comparing label behaviour. Augmentation of the endogenous insulin response improves the precision of the estimated model parameters [28]. One of the study groups we investigated in the present study were subjects with diabetes and tolbutamide administration was inappropriate; instead, an insulin injection was used [29] to mimic the insulin profile typically obtained from tolbutamide administration. This produces a second insulin peak concentration of approx. 1100 pmol/l [30]. This dose is less than that used by others [31]; concerns have been raised that at high peak insulin concentrations saturation of insulin transport occurs, leading to underestimation of *S*_{I} [32]. We also wished to restrict the hypoglycaemia inevitable in later stages of tests with larger insulin doses. This causes a marked overestimation of *S*_{G}^{1} and underestimation of *G*_{I}^{1} [33] as other hormonal responses (principally glucagonic) stimulate endogenous glucose production [34] and potential isotope recycling.

### Results from the minimal models

#### General comments

2CMM, in contrast with 1CMM, can be unambiguously fitted to IVGTT data only with some independent knowledge of the relationships between kinetic parameters [5]. Regardless of subject group, we applied the two internal constraints used in the most recent model [7], although they are unlikely to be universally applicable [7,35]. Appropriate values for each of our four subject categories are not known, but this study is concerned with investigating the equivalence of the behaviour of two different tracers and detection techniques. We have, however, included correction for urinary losses which are significant for DM subjects but not healthy individuals [15].

We have not directly compared the values for *S*_{I} with those obtained by other workers. Cross-study comparisons are unlikely to be fruitful as the numerical value obtained for *S*_{I} is very dependent on the insulin analysis employed [36]. However some comment may be useful.

*S*_{I}

Analysis of 1CMM indicates that *S*_{I} should be smaller when measured by tracer techniques than when using unlabelled glucose [2]. However, others have observed previously that *S*_{I}^{1}≤*S*_{I}^{1}*. Inspection of the published data shows that the difference was significant (as judged by paired Student's *t* test) using radiolabel in the dog [2], but, although the same trend has been observed in man, the differences have not proved significant for healthy subjects studied using radiolabel [4] or stable label [3], or in DM subjects studied with stable label [37]. Our observations are largely consistent with the human studies reported previously; however, the discrepancy between the unlabelled and labelled methodologies in DM subjects is new.

For 1CMM, the regression had unit slope and zero intercept. For 2CMM, the correlation was only marginally weaker, and still well in excess of 0.9, but the slope deviated slightly from unity. Analysis of the residuals for each of the two regressions showed normal distribution in both cases with no apparent outliers. Bland and Altman analysis indicated a discrepancy between *S*_{I}^{2}*(*C*) and *S*_{I}^{2}*(*H*) in the NGT groups only.

To understand the insensitivity of the ^{13}C methods to possible label recycling we investigated the sensitivity functions:
for three subjects who exhibited the highest, lowest and median values of *S*_{I}. The subject with the highest *S*_{I} was classed NGT-L; the other two were NGT-O. The calculation of σ_{i}^{1}* is straightforward, but care is required in the evaluation of σ_{i}^{2}*, because *S*_{I}^{2}* does not appear in the equations of 2CMM. The approach adopted was to allow two of the parameters, *k*_{12} and *k*_{21}, to vary so that *S*_{I}^{2}* changed, but *S*_{G}^{2}* remained constant. This was achieved by expressing the total derivatives of *S*_{G}^{2}* and *S*_{I}^{2}* as sums of their partial derivatives with respect to the rate constants to be varied.

The sensitivities are plotted as a function of the progress of the IVGTT in Figure 5, and should be compared with data reported previously [37]. For 1CMM, the magnitude of the sensitivity function increases over the first 2 h of the test and, in general, the plateau sensitivity increases in magnitude with the subject's *S*_{I}. The sensitivity profile for 2CMM is somewhat different and more allied to that seen in the unlabelled model [37]. 2CMM gives sensitivity functions numerically larger than 1CMM, leading to improved precision in the parameter estimates from this model.

For 2CMM, the plasma concentration of labelled glucose is most sensitive to *S*_{I}^{2}* in the initial period of the study up to approx. 2 h. However, it is precisely during this period of time that endogenous glucose production is largely inhibited both in normal and DM subjects [31]. Therefore, even if significant label recycling were to occur during the IVGTT, it would have little impact on *S*_{I}^{2}*.

*S*_{G}

It is well known that estimates of *S*_{G} from unlabelled models are much greater than those from labelled models, since the former represents both disposal and production, but the labelled parameter describes disposal only [4]. The poor correlation for 1CMM indicates an inadequate model. The validity of monocompartmental glucose distribution in 1CMM has been questioned on many occasions [38–43].

In conclusion, we have demonstrated that, recycling notwithstanding, 1-[^{13}C]glucose is a suitable tracer material for use in the labelled minimal model interpretation of an IVGTT in man. The determination of isotopic enrichment by GC/C/IRMS is sufficiently sensitive for the amount of label given to be substantially reduced from that customarily administered with ^{2}H_{2} material. This has clear cost advantages, but the significant scientific advance is towards an isotope technique that approaches true tracer status and measurements with physiologically normal tracee loads.

**Abbreviations:**
1CMM, one-compartment minimal model;
2CMM, two-compartment minimal model;
BMI, body mass index;
DM, diabetic;
Gb, quantity of glucose in the accessible pool;
GC/C/IRMS, GC/combustion/isotope-ratio MS;
IGT, impaired glucose tolerance;
IVGTT, intravenous glucose tolerance test;
NGT-L, normal glucose tolerant and lean;
NGT-O, normal glucose tolerant and obese;
OGTT, oral glucose tolerance test;
SG, glucose effectiveness;
SI, insulin sensitivity

- The Biochemical Society