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1Department of Information Engineering, University of Padua, Padua, Italy; and 2Department of Internal Medicine, Division of Endocrinology, Diabetes, Metabolism and Nutrition, Mayo Clinic and Foundation, Rochester, Minnesota
Submitted 21 September 2005 ; accepted in final form 17 May 2006
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ABSTRACT |
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nonsteady state; turnover; meal; kinetics; compartmental models
To circumvent these problems, a triple-tracer method (2) was proposed. This method used, in addition to the oral tracer (e.g., [1-13C]glucose), two intravenous tracers (e.g., [6-3H]glucose and [6,6-2H2]glucose) infused in patterns that minimize the change in their plasma ratio to oral tracer and endogenous glucose, respectively, thus minimizing non-steady-state errors and rendering the calculation of turnover essentially model independent. As a result, very similar patterns of Ra meal, EGP, and Rd were estimated using three different models: a steady-state formula, a single-compartment model (1-CM) (11, 12), and a two-compartment (9) model (2-CM). In contrast, when the three models were adopted to interpret data using only two of the three tracers, as is done with the dual-tracer method, Ra meal, EGP, and Rd were highly dependent on the model chosen and differed substantially among models. However, in these experiments, all of the intravenous tracer infusion rates were varied in time. This resulted in a more pronounced change in the tracer-to-tracee ratios than would normally have been observed with the conventional dual-tracer method, where the intravenous tracer infusion rate is kept constant. Therefore, although those studies provided both the theoretical and experimental rationales for the use of the triple-tracer method, they were unable to quantify the magnitude of the errors that occur with the conventional dual-tracer method and the extent to which these errors impact the estimation of individual components of postprandial glucose metabolism, i.e., Ra meal, EGP, and Rd.
The present studies, therefore, were undertaken to compare estimates of Ra meal, EGP, and Rd simultaneously measured in the same individual using the triple- and conventional dual-tracer methods. We did so to quantify the effect of non-steady-state errors and of model assumptions on calculation of postprandial fluxes. Subjects were studied on two separate days. The conventional dual-tracer protocol was used on both occasions. In addition, on one occasion a third tracer was infused in a pattern that mimicked the anticipated Ra of the meal, whereas on the other occasion the third tracer was infused in a pattern that mimicked the anticipated Ra of EGP, thereby enabling essentially model-independent measurements of these fluxes. Results obtained with the conventional dual-tracer method were compared with reference profiles obtained with the triple-tracer method to determine whether the magnitude of the errors observed with the dual-tracer method warrants the added complexity and cost of the triple-tracer method.
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METHODS |
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TOPABSTRACTMETHODSRESULTSDISCUSSIONGRANTSREFERENCES |
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Net insulin action and the effects of insulin on glucose disposal assessed by the oral glucose minimal models (4, 5) varied from 4.9 to 29.1 10–4 dl·kg–1·min–1 per µU/ml and 1.5 to 17 10–4 dl·kg–1·min–1 per µU/ml, respectively, indicating that subjects with a wide range of insulin sensitivity were studied.
Experimental design All studies were conducted at the Mayo Clinic General Research Center.
Mixed meals (10 kcal/kg, 45% carbohydrate, 15% protein, 40% fat) consisted of scrambled eggs, Canadian bacon, 100 ml of water, and Jell-O containing [1-13C]glucose (Cambridge Isotope Laboratories, Andover, MA), which were consumed within 15 min (7). The beaker containing the Jell-O was rinsed twice with 20 ml of water, and the rinse solution was consumed. To prepare the Jell-O, 1.2 g/kg body wt dextrose was dissolved in 200 ml of water by gentle heating. After being cooled to room temperature, sufficient [1-13C]glucose was added to achieve an enrichment of 
4%. Following thorough mixing, an aliquot was removed for analysis of [1-13C]glucose enrichment by GC-MS. The dextrose solution containing the [1-13C]glucose then was gently warmed, and 5 g of sugar-free gelatin (Knox unflavored gelatin; Nabisco, East Hanover, NJ) and 1 g of sugar-free orange flavored Kool-Aid (Kraft General Foods, White Plains, NY) were added. The mixture was allowed to solidify overnight in a refrigerator.
Subjects ingested the mixed meal labeled with [1-13C]glucose tracer on both occasions at time 0 (Fig. 1). On each occasion, a continuous infusion of [6,6-2H2]glucose (11.84 mg/kg bolus, 0.1184 mg/kg continuous infusion; Cambridge Isotope Laboratories, Andover, MA) was started 180 min before the meal and continued for 360 min. On one occasion, [6-3H]glucose (PerkinElmer Life Sciences, Boston, MA) was infused in a manner designed to mimic the anticipated pattern of appearance of the [1-13C]glucose contained in the meal, whereas on the other occasion [6-3H]glucose was infused in a manner anticipated to mimic the pattern of change of EGP, as suggested by previous studies (2). Blood was sampled from the arterialized venous site at –30, –20, –10, 0, 5, 10, 15, 20, 30, 40, 50, 60, 75, 90, 120, 150, 180, 210, 240, 260, 280, 300, and 360 min.
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Calculation. Ra meal, EGP, and Rd were calculated, using either the triple- or dual-tracer methods, with two different models of glucose kinetics: a 1-CM and a 2-CM (2). Briefly, the 1-CM assumes that the unknown and time-varying Ra and Rd take place in the accessible compartment, which has a volume equal to a fraction of the total distribution volume. 2-CM assumes time-varying Ra and Rd from the accessible compartment and constant-rate parameters between the accessible and the remote compartments. Below, we present the general formulas, which were particularized for the triple- and dual-tracer methods.
General formulas.
Both the 1-CM and 2-CM allowed the estimation of the (unknown) Ra in plasma of the tracee from the known rate of infusion of the tracer and measurements of tracer and tracee concentration in plasma (see Appendix A in Ref. 2 for details). According to the 1-CM,
 | (1) |
 | (2) |
As detailed in the following paragraph, the triple- and dual-tracer methods use Eqs. 1 and 2 to calculate Ra meal and EGP by adopting as tracer and tracee different glucose variables, namely natural glucose (Gnat, µmol/ml), i.e., glucose at natural composition coming from ingested glucose and from EGP; endogenous glucose (Gend, µmol/ml) derived from EGP only; ingested tracer (G13C µmol/ml); and infused tracers (G2H, µmol/ml and G3H, dpm/ml). The concentrations of these variables were derived from their measurements by using the procedure outlined in (2).
Triple-tracer Ra meal and EGP.
On day A, [6-3H]glucose was infused to mimic the Ra of [1-13C]glucose contained in the meal (referred to as Ra 13C; Fig. 1, bottom left). Ra 13C was calculated by the 1-CM (Eq. 1) or 2-CM (Eq. 2), assuming [6-3H]glucose as tracer and [1-13C]glucose as tracee. Ra meal was then calculated by multiplying Ra 13C by the ratio of total glucose to [1-13C]glucose in the meal, expressed as a function of the ratio between [1-13C]glucose and natural glucose measured in the meal (TTRmeal).
 | (3) |
 | (4) |
 | (5) |
Dual-tracer Ra meal and EGP. Because [6,6-2H2]glucose tracer is infused at a constant rate on both days A and B (Fig. 1, middle), dual-tracer calculations were performed twice. Ra 13C was calculated using the 1-CM (Eq. 1) or 2-CM (Eq. 2) with [6,6-2H2]glucose as tracer and [1-13C]glucose as tracee. Ra meal and Qmeal were calculated for the triple-tracer method using Eqs. 3 and 4, respectively. To calculate EGP, the total Ra of natural glucose was first calculated by the 1-CM or 2-CM (Eq. 1), with [6,6-2H2]glucose as tracer and natural glucose as tracee, and then Ra meal was subtracted from it. EGPS was calculated using Eq. 5.
Glucose Rd.
Once Ra meal and EGP were available, with either the triple- or the dual-tracer method, the postprandial profile of glucose disappearance was calculated with the 1-CM and 2-CM, respectively.
 | (6) |
 | (7) |
 | (8) |
Data analysis. All data are expressed as means ± SE. Postprandial fluxes are expressed as micromoles per kilogram per minute of lean body mass. Values obtained from –30 to 0 min (i.e., prior to the meal) were considered as basal.
The time derivatives of the tracer-to-tracee ratios and areas under curves have been calculated as in Ref. 2.
Wilcoxon's signed rank test was used to determine the statistical significance of differences. A P value <0.05 was considered to be statistically significant.
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RESULTS |
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12,000 down to 6,000 dpm/µmol over the 6 h of study (Fig. 3, top left). On the other hand, on day B, the intravenous infusion [6-3H]glucose was varied so that it mimicked the anticipated pattern of change of EGP, resulting in a slow increase of the ratio of [6-3H]glucose to endogenous glucose from 400 to 600 dpm/µmol (Fig. 3, bottom left). In contrast, because [6,6-2H2]glucose was infused intravenously at a constant rate, the ratio of [6,6-2H2]glucose to [1-13C]glucose (used to calculate meal appearance with the dual method) and the ratio of [6,6-2H2]glucose to unlabeled glucose (used to calculate total glucose appearance with the dual method) rapidly and markedly fell after meal ingestion (Fig. 3, right).
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Glucose disposal. The postprandial pattern of Rd also differed when calculated with the dual- and triple-tracer methods. Compared with the triple-tracer method, Rd was underestimated with the dual-tracer method, regardless of whether the data were analyzed using the 1-CM or 2-CM (Fig. 4, bottom). In particular, the postprandial peak in Rd was underestimated with the dual-tracer method with both the 1-CM (day A: 52.4 ± 4.5; day B: 55.3 ± 4.2 vs. 76.3 ± 8.2%, P = 0.0117) and 2-CM (day A: 64.7 ± 6.3 vs. 79.4 ± 8.9%, P = 0.0357; day B: 66.8 ± 5.0 vs. 79.4 ± 8.9%, P = 0.0499). In addition, the postprandial area of Rd above basal normalized to the area under basal Rd(Rd I) was underestimated with both the 1-CM (day A: 109 ± 7; day B: 110 ± 7 vs. 148 ± 19%, P = 0.0117 ) and 2-CM (128 ± 9 and 124 ± 8 vs. 158 ± 20%, P = 0.0173).
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DISCUSSION |
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TOPABSTRACTMETHODSRESULTSDISCUSSIONGRANTSREFERENCES |
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The conventional dual-tracer method uses two tracers, one ingested and the other intravenously infused at a constant rate, to estimate Ra meal, total glucose appearance (the difference equaling EGP), and Rd by using either the 1-CM or 2-CM. The estimated Ra meal and EGP are dependent on both the structure and parameter values of the model used to derive them. The 1-CM has been used with a wide range of values for the distribution volume, ranging from 130 to 230 ml/kg (6). The 2-CM assumes a time-varying loss from the accessible pool and constant exchange parameters between the accessible and peripheral pools, likely providing a more realistic representation of glucose kinetics. The problem is that there has been no "gold" standard to determine which method yields the most accurate estimate of postprandial glucose turnover. Livesey et al. (6) reported that a 1-CM with a distribution volume equal to 230 ml/kg provides Ra meal and EGP profiles similar to those derived from a 2-CM. However, as shown in the present studies, this is not a proof of model validity, since both the 1-CM and 2-CM are affected by non-steady-state errors.
The triple-tracer method was proposed in an effort to minimize these errors; it requires a more complex experimental setting since it uses three tracers, one ingested and two intravenously infused at variable rates, but provides an almost model-independent assessment of Ra meal and EGP, i.e., not dependent on the model to derive them, either 1-CM and 2-CM, or on the value of parameters used in the models.
In the present study, eight subjects, characterized by a wide range of insulin sensitivity, were studied with a 2-day protocol designed to perform simultaneously dual- and triple-tracer studies. The conventional dual-tracer method (i.e., constant intravenous tracer infusion) was accompanied by the use of a third tracer infused to optimize estimation of either Ra meal (day A) or EGP (day B). As is evident in Fig. 3, the plasma ratio of [6-3H]glucose to [1-13C]glucose on day A and to endogenous glucose on day B were not perfectly constant. Obtaining perfectly constant TTRs is impossible, because this would require exact knowledge of the time course of Ra meal and EGP. In practice, only an approximate knowledge is necessary (2) to adjust the tracer infusion rates in a manner that substantially reduces the variation in TTRs, thereby markedly reducing the error introduced by the nonsteady state. Data were analyzed by using the 1-CM and 2-CM with parameters fixed to population values. The impact of model structure and nonindividual parameter values on estimated fluxes is minimized by the triple-tracer method (2), which can thus be used as a reference against which the ability of the dual-tracer method to provide estimates of postprandial fluxes can be evaluated. As expected, the dual-tracer method resulted in marked non-steady-state conditions, with very pronounced initial TTR declines, which rendered Ra meal and EGP estimation model dependent. Ra meal (Fig. 4, top) was markedly lower with 1-CM compared with 2-CM, and EGP showed a paradoxical pattern with both models (Fig. 4, middle), i.e., an initial increase above basal, more pronounced with the 1-CM, and a rapid decline to even negative values, more pronounced with the 2-CM.
A comparison of the dual-tracer fluxes with the triple-tracer reference fluxes (Fig. 4) confirmed previous findings (2). The dual-tracer and 1-CM performed poorly, with Ra meal peak significantly lower and delayed compared with the triple-tracer reference, resulting in a significantly lower estimation of the total amount of ingested glucose, and EGP initially overestimated (0- to 40-min period following glucose ingestion) with respect to the triple reference, resulting in a significant underestimation of EGP suppression. The 2-CM performed better than the 1-CM, particularly for Ra meal, which peaked at a similar value, even if it was somewhat delayed. The total amount of ingested glucose was still significantly underestimated compared with reference, although to a minor extent compared with the 1-CM. The dual-tracer method and the 2-CM still provided a paradoxical pattern of EGP, but with a correct estimate of the total suppression index, since initial overestimation of EGP (0- to 40-min period following glucose ingestion) was compensated by late underestimation (40–120 min).
Rd also can be calculated once Ra meal and EGP are known. Both dual and triple-tracer methods can provide an estimate of Rd from mass balance equation of the accessible compartment, i.e., from rate of change of glucose mass. Estimation of Rd is thus sensitive to the model structure and parameter values with both dual and triple-tracer approaches, but the triple tracer has the advantage of a more accurate measure of total glucose appearance (i.e., Ra meal + EGP) than does the conventional dual tracer. In the present studies, Rd peak and above-basal increase estimated with either the 1-CM or 2-CM were similar with the triple- but not with the dual-tracer method, thus confirming that dependence of Rd on model structure is less critical with the triple-tracer method. Assuming the triple tracer as a reference (Fig. 4), the dual-tracer approach using either the 1-CM or 2-CM significantly underestimated both Rd peak and its overall increase above basal.
These results indicate that, although triple-tracer flux estimates are almost model independent, those derived with the dual-tracer method are dependent on the model used to derive them. However, it is important to point out that all of these results were derived by fixing some model parameters to specific values. With the 1-CM, calculations required to fix the product of the total distribution volume (V) by an operational pool fraction (p). We used for pV a value equal to 130 ml/kg, but we have previously shown (2) that, although the value chosen for pV has a marked effect on fluxes calculated with the dual-tracer method, the triple-tracer calculations are essentially independent of the assumed volume of distribution. For instance, as pointed out by Livesey et al. (6), the Ra meal measured with the dual-tracer method increased as the volume assumed for pV was increased. However, no single pV value appeared to be adequate for deriving glucose fluxes with the dual-tracer method, since three different time-varying pV profiles would be required to derive Ra meal, EGP, and Rd equal to the reference values derived with the triple-tracer method. With the 2-CM, exchange rate parameters k12 and k21 and the volume of distribution of the accessible pool need to be fixed. Ideally, these parameters should be determined separately in each individual, but this would require an additional tracer experiment. Therefore, we fixed them to values derived from previous studies in normal subjects (9). As is evident from inspection of 2-CM equations, the influence of model parameters on estimated fluxes is more pronounced when the tracer-to-tracee ratio varies in time, as with the dual-tracer method. However, the extent to which use of individual vs. population rate parameters improves the performance of the 2-CM is difficult to predict.
In conclusion, our results show that changes in tracer-to-tracee ratios that occur with the conventional dual-tracer method preclude accurate estimation of postprandial fluxes Ra meal, EGP, and Rd. The use of the 2-CM with the dual-tracer approach reduces but does not completely avoid these errors. The dual-tracer method underestimates Ra meal and Rd and inaccurately assesses the degree and pattern of suppression of EGP. Of concern, the size of these errors differs depending on the degree of tracer-to-tracee nonsteady state, making comparison of fluxes in individuals with different degrees of glucose tolerance (e.g., diabetic vs. nondiabetic subjects) problematic. Although it is experimentally more complex, the triple-tracer method minimizes non-steady-state errors, thereby enabling more accurate assessment of postprandial fluxes Ra meal, EGP, and Rd. However, if the purpose of the experiment is to assess Ra meal alone or EGP alone, then only two tracers are required, i.e., the oral tracer plus a second intravenous tracer properly infused to optimize estimation of Ra meal in the former case and EGP in the latter.
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GRANTS |
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ACKNOWLEDGMENTS |
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FOOTNOTES |
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The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.
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REFERENCES |
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