## Abstract

Among the many tracer methods to indirectly estimate gluconeogenesis in humans, the [U-^{13}C_{6}]glucose method as proposed by Tayek and Katz (*Am J Physiol Endocrinol Metab *270: E709–E717, 1996; *Am J Physiol Endocrinol Metab*272: E476–E484, 1997) has the advantage of being able to simultaneously estimate hepatic glucose output and fractional gluconeogenesis. However, Landau et al. (Landau BR, J Wahren, K Ekberg, SF Previs, D Yang, and H Brunengraber. *Am J Physiol Endocrinol Metab *274: E954–E961, 1998) have shown that this method underestimates the rate of gluconeogenesis. The underestimation has been attributed to tracer dilution by other three-carbon substrates and the lack of isotopic steady state. Using a computer simulation of [U-^{13}C_{6}]glucose infusion, we demonstrate that the lack of isotope equilibrium in both the lactate and glucose compartments contributes substantially to the underestimation of gluconeogenesis. [U-^{13}C_{6}]glucose experiments were performed with the addition of a primed constant infusion of [U-^{13}C_{3}]lactate and the delay in M3 glucose equilibrium estimated from the isotopic steady-state value determined by modeling M3 glucose to a single-exponential fit. We found that, even with the addition of [U-^{13}C_{3}]lactate infusion, the M3 glucose enrichment of the last timed sample was ∼20% less than the isotopic steady-state value. Thus the lack of isotopic equilibrium of the glucose compartment potentially accounts for 20% of the underestimation of gluconeogenesis. The underestimation of gluconeogenesis using [U-^{13}C_{6}]glucose without the additional infusion of [U-^{13}C_{3}]lactate in previous publications is expected to be even greater because of the lack of isotope equilibrium in both the lactate and glucose compartments. These findings are consistent with the results from our computer simulation.

- mathematical modeling
- mass isotopomer distribution analysis, stable isotopes

the recognition that [u-^{13}
c_{6}]glucose has the property of being both a “nonrecyclable” and a “recyclable” tracer (9) has led Tayek and Katz (15, 16) to propose a method of estimating gluconeogenesis by the use of [U-^{13}C_{6}]glucose. During an infusion of [U-^{13}C_{6}]glucose (glucose labeled in all six positions, M6 glucose), glycolysis leads to the production of lactate labeled in all three carbon positions (m3 lactate). When^{13}C carbon atoms are recycled in gluconeogenesis, glucose molecules with 1, 2, or 3 ^{13}C substitutions (M1, M2, and M3 glucose) are produced. The appearance of mass isotopomers M1, M2, and M3 of glucose provides a measure of the rate of gluconeogenesis. Because the chance of two labeled triose phosphates combining to form glucose is negligible, M6 glucose behaves as a nonrecyclable tracer, and the steady-state enrichment of M6 glucose in plasma allows the determination of the hepatic glucose production rate. Thus the [U-^{13}C_{6}]glucose method has the advantage of being able to estimate simultaneously hepatic glucose output and fractional gluconeogenesis from the analysis of mass isotopomers in glucose. However, Landau et al. (7) have shown that, when [U-^{13}C_{6}]glucose is administered as a primed constant infusion, this method grossly underestimates the rate of gluconeogenesis. This underestimation could be attributed to dilution by other unlabeled gluconeogenic substrates and/or the lack of label steady state in m3 lactate and M3 glucose by the end of the study period. In the absence of experimental data, the magnitude of underestimation of gluconeogenesis by the [U-^{13}C_{6}]glucose method attributable to each of these sources of error remains controversial (2, 5, 11,12).

Because the ^{13}C label from M6 glucose is recycled through an intermediate compartment, namely lactate, before gluconeogenesis, the precursor-product relationship of labeled substrate from M6 glucose to newly synthesized glucose is complex. A basic principle of precursor-product relationship dictates that the isotope in each precursor pool must be in isotopic steady state before the subsequent pool can reach its plateau enrichment. Therefore, the time to reach isotopic steady state for M3 glucose (new glucose) can be significantly delayed, depending on the time to reach isotopic steady state of its precursors, namely m3 lactate and M6 glucose. Potentially, the lack of isotope equilibrium may contribute significantly to the underestimation of gluconeogenesis.

The relative importance of various factors contributing to the problems of accurately measuring gluconeogenesis is difficult to evaluate in clinical studies. It is costly and impractical to perform a large number of experiments using different infusion protocols to demonstrate the effects of many variables on isotope equilibrium (M6 glucose, m3 lactate, and M3 glucose). To obviate these difficulties, we have designed a computer model to simulate glucose and lactate tracer kinetics to examine the effects of tracer infusion on isotopic equilibrium of m3 lactate and M3 glucose and to test the effects of different assumptions of tricarboxylic acid (TCA) cycle dilution on the calculation of gluconeogenesis. Clinical experiments were performed using the same assumptions of tracer dilution from previous indirect methods to measure gluconeogenesis, and the plateau value was estimated using curve fitting with SAAM. The delay in isotopic equilibrium of the precursor pools (namely m3 lactate and M6 glucose) was minimized using a primed constant infusion ofl-[U-^{13}C_{3}]lactate andd-[U-^{13}C_{6}]glucose. The expected steady-state enrichment of M3 glucose was determined from the asymptote of the appearance curve fitted to a single exponential model using SAAM. With the assumption that our model holds for M3 glucose appearance, any underestimation due to lack of isotopic equilibrium of the newly produced labeled glucose can be determined from the difference between the asymptote and the observed value of M3 glucose.

## METHODS

### Computer Simulation of Glucose and Lactate Tracer Kinetics

#### The model.

The system through which [U-^{13}C_{6}]glucose carbon is recycled is inherently complex. As indicated in the model of Landau et al. (7) for the mass isotopomer distribution in glucose and lactate, there are three basic substrate pools, each of which has its own pool size and substrate turnover rate. A very large number of experiments are necessary to evaluate the effect of each model parameter on tracer kinetics. For this reason, we have chosen to use computer simulation to examine these effects on tracer kinetics. Computer simulation allows us to examine the individual effect by changing model parameters one at a time. We have modified the model of Landau et al., which simulates the mass isotopomer distribution in glucose and lactate at steady state during a [U-^{13}C_{6}]glucose infusion to allow the generation of time-dependent tracer kinetics (Fig.1). This is accomplished by *1*) defining small steps of hepatic glucose output indicated by gluconeogenesis (D) and glycogenolysis (E), *2*) manipulating the substrate turnover rate by changing either the glucose or lactate pool size, and *3*) modeling of loss of lactate carbon via the TCA cycle. Fractional gluconeogenesis is simulated by the ratio D/(D + E) and lactate dilution by the ratio A/(A + B). The model can simulate different combinations of primed and unprimed infusion of glucose and lactate by setting the [U-^{13}C_{6}]glucose priming dose (GP), [U-^{13}C_{6}]glucose infusion rate (GI), [U-^{13}C_{3}]lactate priming dose (LP), and [U-^{13}C_{3}]lactate infusion rate (LI). As an example, a set of parameters for the simulation of a primed constant infusion of [U-^{13}C_{6}]glucose is shown in Table1. The parameters are set to simulate the conditions of a typical [U-^{13}C_{6}]glucose infusion. The [U-^{13}C_{6}]glucose infusion rate is set to 5% of the glucose production rate. The turnover rate and the pool size of glucose and lactate are comparable. The gluconeogenesis rate is set to 50%.

#### Effect of tracer priming on tracer kinetics.

The tracer appearance curves of M6 and M3 glucose may follow a single-exponential equation or multiexponential equation, depending on the site of infusion and priming in a multicompartment system. To illustrate the effects of priming doses of [U-^{13}C_{6}]glucose and/or [U-^{13}C_{3}]lactate on the tracer kinetics of M6 and M3 of glucose and m3 of lactate, we focused on the simplified condition that m3 of lactate can be converted only to m3 phospho*enol*pyruvate (PEP). The simulations were performed with no prime (Fig. 2
*A*), [U-^{13}C_{6}]glucose prime only (Fig.2
*B*), and [U-^{13}C_{6}]glucose and [U-^{13}C_{3}]lactate prime (Fig. 2
*C*). The SAAM curve-fitting program is used to test whether the M6 glucose (M6), m3 lactate (m3), and M3 glucose (M3) tracer appearance from the simulation fits that of a single exponential or multiexponential equation. Each appearance curve is initially modeled with the single-exponential *Eq. 1
*
Equation 1where ya(*t*) is the calculated enrichment for a given time (*t*) and ya(0) = 0 and A_{0} = A_{1}. A_{0} is the calculated plateau enrichment and *a*
_{1} is the flux (decay) constant.

When it is not possible to achieve a good fit with *Eq. 1
*, attempts to curve the fit with the two-exponential *Eq. 2
* and the three-exponential *Eq. 3
* are made until a good fit is arrived at according to the Akaike Information Criterion (AIC) criteria.
Equation 2
Equation 3
where ya(*t*) is the calculated enrichment for a given time (*t*) and ya(0) = 0 and A_{0} = A_{1} + A_{2} for*Eq. 2
* or A_{0} = A_{1}+ A_{2} + A_{3} for *Eq. 3
*. The flux (decay) constants of the respective compartments are*a*
_{1}, *a*
_{2}, and*a*
_{3}.

#### Effect of tracer conversion.

The effect of the loss of ^{13}C during the conversion of lactate to PEP is simulated by setting the conversion of m3 lactate to m3, m2, and m1 PEP with a ratio of 0.3:0.3:0.4, assuming no loss of labeled molecules. That is, 100% of m3 lactate is converted to labeled PEP, with the distribution of mass isotopomers in PEP being 0.3:0.3:0.4, and there is no further loss of m2 and m1 lactate. The choice of m3, m2, and m1 and their ratio is arbitrary. Under the assumption of “no loss of labeled molecules,” the simulation is applicable to the most general case such that m3, m2, and m1 may as well be mα, mβ, and mγ and their ratio*x*:*y*:*z*, as long as mα, mβ, and mγ cannot become m0 through the TCA cycle.^{1}

### Clinical Studies: Subjects and Methods

#### Protocols.

To demonstrate the lack of isotope equilibrium, gluconeogenesis was studied in four healthy volunteers in the General Clinical Research Center (GCRC) at Harbor-UCLA Medical Center by use of a primed constant infusion of glucose and lactate. The project was approved by the Institutional Review Board. Subjects consisted of two women and two men. Table 2 shows the subject characteristics for each subject. All subjects were instructed to maintain a diet with ≥200 g of carbohydrates per day for the 3 days preceding the study. Subjects were also instructed not to eat or drink anything after midnight the night before the study. Subjects arrived at the GCRC ∼8:00 AM on the day of the study. All studies were initiated between 9:00 and 10:00 AM after an overnight fast (≥9 h) and after informed consent was obtained. Subjects had cannulation of a deep vein in each arm, one for blood sampling and the other for infusion of tracers. After baseline blood samples were obtained, a priming dose of [U-^{13}C_{6}]glucose (0.5 g) and of [U-^{13}C_{3}]lactate (0.25 g) was infused over the first 15 min. The priming doses were followed by a constant infusion of labeled glucose (0.5 g/h) and labeled lactate (0.25 g/h) over the remainder of the 3-h study. Blood sampling was performed at 20-min intervals. Samples were placed on ice immediately and processed to obtain the plasma fractions, which were stored at −20°C until gas chromatography-mass spectrometry (GC-MS) analyses. Two subjects returned for a second study. The second study was identical to the first study, except that the rate of labeled lactate infusion was increased (0.5 g prime and 0.5 g/h) and both the labeled glucose and labeled lactate infusions were extended to 4 h. The high-dose lactate infusion study was performed to determine whether we could further improve estimations of M3 glucose plateau enrichment.

#### Materials.

d-[U-^{13}C_{6}]glucose (99% enriched) and l-[U-^{13}C_{3}]lactate (99% enriched) were purchased from Isotec (Miamisburg, OH). The isotopes were dissolved in isotonic saline and tested to be sterile and pyrogen free by the research pharmacist of the Harbor-UCLA Research and Education Institute.

#### Laboratory analyses.

Plasma glucose, insulin, and lactate were measured in all samples from an individual study in duplicate in the same assay. Plasma glucose was measured using the hexokinase method with an Abbott autoanalyzer (1). Plasma insulin was measured by sensitive radioimmunoassay (18). Plasma lactate was collected in perchloric acid and measured using a fluorescence polarization immunoassay.

#### Sample preparation and GC-MS analyses.

Plasma samples (200 μl) were deproteinized with 6% perchloric acid. The supernatant was neutralized and then passed through a set of tandem columns of Dowex 50 and Dowex 1 to isolate glucose and lactate. These fractions were dried by blowing air and were used for subsequent GC-MS analyses. Mass spectral data were obtained on the HP5973 mass spectrometer connected to an HP6890 gas chromatograph. GC conditions: inlet 230°C, transfer line 280°C, MS source 230°C, and MS Quad 150°C. An HP-5 capillary column (30 m length, 250 μm diameter, and 0.25 μm film thickness) was used for glucose and lactate analysis. Glucose was converted to its aldonitrile pentaacetate derivative for GC-MS analysis according to a modification of the method of Szafranek et al. (14). Ions around mass-to-charge ratio (*m*/*z*) 328 were monitored under positive chemical ionization condition to give the isotopomeric distribution of glucose. Lactic acid was converted to its*n*-propylamide-heptafluorobutyric ester for GC-MS analysis according to the method of Tserng et al. (17). The mass spectrum of *n*-propylamide heptafluorobutyrate of lactate has two major ion clusters around *m*/*z* 328 and 241, representing fragments containing C1-C3 and C2-C3 of lactate. The molecular ion *m*/*z* 328 was used in the quantitative analysis of lactate and mass isotopomer determination. Mass isotopomer distribution was determined from spectral data by use of a matrix method, which corrects for the natural abundance of^{13}C (3).

### Calculations

#### Gluconeogenesis.

Because we infused [U-^{13}C_{3}]lactate together with [U-^{13}C_{6}]glucose, the calculation followed the traditional approach of determining gluconeogenesis from labeled lactate infusion. Total glucose production (R_{a}) was first calculated using *Eq. 4
*
Equation 4where R_{a} is total glucose production rate and RM6 is the rate of infusion of [U-^{13}C_{6}]glucose in milligrams per kilogram per minute and M6 is the M6 glucose enrichment at steady state.

The appearance of new glucose (RM3 + RM2 + RM1), represented by appearance of M3, M2, and M1 glucose, was then calculated using*Eq. 5
*
Equation 5where (RM3 + RM2 + RM1) is the rate of appearance of new glucose and (M3 + M2 + M1) is enrichment of the respective glucose mass isotopomers at steady state.

When (m3 + m2 + m1) lactate was converted to (M3 + M2 + M1) glucose, new glucose production (R_{aNEW}) from lactate was determined by dividing the (M3 + M2 + M1) enrichment in glucose by 2 times the (m3 + m2 + m1) enrichment in lactate (*Eq. 6
*)
Equation 6The factor 2 is the stoichiometric relationship between glucose and lactate.^{2}

The gluconeogenic fraction is given by
Equation 7
*Equation 7
* is essentially the same as the one used by Landau et al. (7).

#### Mathematical modeling of clinical studies.

To assess the impact of primed constant infusion of lactate and glucose, we applied the curve-fitting program on measured M3 glucose enrichment of each time point from the same subject. The multicompartmental model of Landau et al. (7) predicts that the appearance of M3 glucose follows that of a multiexponential equation. The appearance of M3 glucose can be fitted to a single exponential only when both glucose and lactate pools are primed with the respective tracers. The purpose of modeling the clinical data is to determine whether appearance of plasma M3 glucose enrichment fits a single exponential model. A fit would provide evidence that the tracer priming is adequate and that the in vivo system behaves like the model of Landau et al. Modeling of clinical data is used to determine whether the M3 glucose appearance curve could be predicted using a single exponential equation and, if so, what the M3 enrichment is at the true plateau (13). The Simulation Application for the Analysis of Models (SAAM) program for exponential fit provides the estimation of AIC as a measure of the goodness of fit. The ratio of the M3 glucose plateau enrichment observed at the end of the study to the calculated M3 glucose plateau enrichment gives the degree of underestimation of plateau enrichment. The observed gluconeogenic fraction can be corrected to give a better estimate of gluconeogenic fraction by use of this factor.

## RESULTS

### Computer Simulation of Glucose and Lactate Tracer Kinetics

#### Effect of tracer priming.

When there is no priming of [U-^{13}C_{6}]glucose and [U-^{13}C_{3}]lactate (Fig. 2
*A*), the enrichment of M6 glucose exhibits the characteristics of a single exponential curve having a half-life of ∼35 relative time units. The curves for m3 lactate and M3 glucose are better characterized by curves of two or three exponential terms, consistent with the tracer kinetics of a multicompartmental system. The results of SAAM analysis are shown in Table 3. In most clinical experiments, four half-lives for M6 glucose is conventionally used as the optimal time to reach equilibrium. It is obvious that, even if M6 glucose is at equilibrium, neither m3 lactate nor M3 glucose achieves steady state without priming (Fig. 2).

[U-^{13}C_{6}]glucose priming (Fig.2
*B*) converts the M6 glucose enrichment to a step function. The m3 lactate enrichment now fits a single-exponential curve, but M3 glucose enrichment requires two-exponential curves to achieve a fit (Table 3). It is only with both [U-^{13}C_{6}]glucose and [U-^{13}C_{3}]lactate priming (Fig. 2
*C*) that the enrichment in M3 glucose approaches that of a single-exponential curve (Table 3).

The effect of priming on estimation of fractional gluconeogenesis is shown in Fig. 3. In this simulation, the fractional gluconeogenesis is set at 50%, or 0.5. Without priming, fractional gluconeogenesis at four glucose half-lives is ∼0.3, or 60% of the true value. With [U-^{13}C_{6}]glucose and [U-^{13}C_{3}]lactate priming, the underestimation is progressively reduced. Fractional gluconeogenesis at four half-lives approaches 0.48, or 96% of the true value.

#### Effect of tracer conversion.

The effect of the loss of ^{13}C during the conversion of lactate to PEP was simulated by setting the conversion of m3 lactate to m3, m2, and m1 PEP with a ratio of 0.3:0.3:0.4, with the assumption of no loss of labeled molecules. The appearance curves of m3, m2, and m1 lactate are clearly different from one another. These differences are reflected in the isotopomer enrichment of M3, M2, and M1 glucose over time (Fig. 4
*A*). The curves for enrichment of M6 glucose, new glucose (M3 + M2 + M1), and labeled lactate (m3 + m2 + m1) (Fig. 4
*B*) resemble those shown in Fig. 2
*C*.

Fractional gluconeogenesis calculated using *Eq. 7
* for primed constant infusion of [U-^{13}C_{6}]glucose with [U-^{13}C_{3}]lactate priming is compared with primed constant infusion of [U-^{13}C_{3}]lactate and shown in Fig. 3. Even under the assumption of no loss of labeled molecules, the delay in the filling of the m2 and m1 lactate pool results in a less than 5% underestimation of fractional gluconeogenesis. When 50% of m1 and m2 lactate is allowed to become m0 PEP, the underestimation of gluconeogenesis is ∼15% because of the loss of labeled molecules (data not shown).

### Clinical Studies

The plasma glucose, insulin, and lactate results are shown in Table 2. For the initial study, mean basal plasma glucose was 90.8 ± 7.2 mg/dl, mean basal plasma insulin was 9.4 ± 2.6 μU/ml, and mean basal plasma lactate concentration was 1.1 ± 0.4 mmol/l. At the end of the study, these values were unchanged.

#### Mass isotopomers of glucose and lactate.

With the [U-^{13}C_{3}]lactate infusion, we were able to achieve an M3 enrichment of ∼1% with a concurrent M6 enrichment of ∼5% at 180 min. The precision of M3 at levels below 0.5% was poor, and the coefficient of variation ranged from 10 to 50%. The lactate enrichment (m3 + m2 + m1, the sum of labeled molecules expressed as a fraction of the lactate molecules) curve is shown in Fig. 5. It is clear that, despite priming of the lactate pool, we did not achieve constant m3 lactate enrichment. However, the degree of priming was sufficient to permit a good fit of the M3 glucose appearance to that of a single exponential, as discussed in *SAAM model*.

#### Gluconeogenesis.

In Table 4, the results of total glucose production, gluconeogenesis, and the gluconeogenic fraction of total glucose production for each subject are shown. In the low-dose lactate study, the mean total fasting glucose output, R_{a}, was 1.94 ± 0.23 mg · kg^{−1} · min^{−1}. The gluconeogenic fraction, based on the measured plateau, was 31.07 ± 7.88%. In the two subjects with a second study, the total glucose output was 1.56 and 1.98 mg · kg^{−1} · min^{−1}. The fractional rates of gluconeogenesis based on measured plateau values were 38.83 and 31.68%.

#### SAAM model.

The SAAM models of M3 glucose plasma enrichment for each study are shown in Fig. 6. The SAAM exponential model for M3 glucose enrichment is shown by the dashed curve. For each subject, the measured plateau enrichment, the calculated plateau enrichment, and the correction factor are shown. The results of SAAM modeling are summarized in Table 5. Each subject had a good fit to a single-exponential model for M3 glucose enrichment with the use of SAAM according to the AIC criteria. The negative AIC indicates a good fit of the experimental data to the model in each study. The flux constant (a_{1}) and the calculated M3 glucose plateau enrichment (A_{0}) with their respective confidence intervals are also shown in Table 5.

#### Correction for underestimation of plateau.

The calculated M3 glucose plateau enrichments based on the SAAM model were used to determine the amount of underestimation of the measured “plateau” enrichment. The results are summarized in Table6. The measured plateau enrichment (*column 2*) ranged from 0.46 to 1.27%. The underestimation of the mathematically predicted value by the measured plateau is shown in *column 4*. The correction factor for the low-dose lactate infusion study ranged from 0.73 to 0.88. With the high-dose lactate infusion study, the underestimation appears to be less. The calculated plateau enrichment (*column 5*) ranged from 0.52 to 1.47%. The measured M3 glucose fraction was only 81.0 ± 7.9% of the corrected plateau value. Thus the corrected fractional gluconeogenesis was 39.1 ± 12.3%. In the two subjects with a second study, the measured M3 glucose enrichment was 86.1 and 109.3% of the calculated plateau by the end of the primed infusion. Thus the corrected rates of gluconeogenesis were 45.1 and 29.0%. In the six separate studies, the average gluconeogenic fraction was 38.4%, with a range of 24.8–54.7%. These values are not different from the observed gluconeogenic fraction in humans after a 14-h fast with the use of the deuterated water method (6).

## DISCUSSION

Gluconeogenesis, defined as the conversion of nonglucose substrate to glucose, has been the subject of intensive research interest. Direct measurement of gluconeogenesis is possible but requires invasive catheterization to measure the balance of glucose and nonglucose substrates across the liver. Indirect methods to determine gluconeogenesis by use of tracers depend on the assumption of isotopic steady state and the models of tracer dilution before the final step of the combination of two triose phosphates.^{3} In the [U-^{13}C_{6}]glucose or [U-^{13}C_{3}]lactate method, possible sources of tracer dilution include dilution of lactate by other gluconeogenic substrates such as alanine and glutamate, dilution due to^{13}C exchange at the level of the TCA cycle, and dilution at the level of triose phosphate by glycerol. In the TCA cycle, the regeneration of oxaloacetate leads to significant exchange of^{13}C carbon with ^{12}C of acetyl-CoA leading to the formation of m0, m1, m2, and m3 of PEP. It is generally agreed that the fraction of labeled lactate becoming m0 PEP by isotope exchange is small when the relative flux of pyruvate carboxylase to that of the citric acid cycle is >2 (3, 9). When the amount of m0 PEP generated is small, essentially every labeled molecule is recycled as a labeled molecule. Under such conditions, Landau et al. (7) argued that the gluconeogenic fraction can be calculated using*Eq. 7
* and no correction for the TCA cycle dilution is required. We have shown in our simulation that this argument is valid. Other methods to correct for TCA cycle dilution with (M1 + M2 + M3)/M3 as a dilution factor are valid only if m3 lactate is very much larger than the sum of m1 and m2 lactate (i.e., m1 + m2 is much smaller than 1 or 2% of m3 lactate). When m1 and m2 constitute >10% of the labeled lactate, M1 and M2 glucose can be formed from m1 and m2 lactate and the correction factor consistently overcorrects for the dilution and overestimates fractional gluconeogenesis, as pointed out by Landau et al.

Because the dilution at the level of triose phosphate by glycerol and pyruvate by gluconeogenic amino acids does not result in change of the distribution of mass isotopomers, dilution at these levels cannot be addressed by the [U-^{13}C_{6}]glucose method. The contribution of carbon from glycerol in the postabsorptive state is believed to be small (∼3–5%) (8). It is difficult to estimate correctly the contribution of carbon from gluconeogenic amino acids because of extensive equilibration of isotope label and recycling of isotope. In our model, we assume that such processes contribute to the size of the lactate pool and that their effects can be minimized with [U-^{13}C_{3}]lactate priming.

Our simulation demonstrates that the distribution and the kinetics of the individual mass isotopomer are greatly affected by the compartment in which tracer is infused and the use of priming dose. Using the multicompartmental model of Landau et al. (7), we have shown by simulation that the appearance of M3 glucose follows that of a multiexponential equation (*Eq. 3
*) when no isotope priming is used. Thus M3 glucose does not reach isotopic steady state even when M6 has reached its steady state, resulting in gross underestimation of gluconeogenesis. However, M3 glucose follows that of a single exponential when the lactate pool is primed with m3 lactate. This is understandable from the perspective of *Eq. 3
*. When the priming dose is applied to a compartment, it is equivalent to setting the exponential term to its equilibrium value, which is zero. With successive priming of glucose and lactate, *Eq. 3 *is reduced to that of a single-exponential term.^{4} Our finding of the M3 glucose appearance curve to fit that of a single-exponential equation by SAAM analysis is consistent with the expected outcome of our simulation. Slow turnover compartments may exist that could alter the ultimate experimental M3 glucose plateau. The effect of fitting data to a single exponential when the model is actually a multiple-exponential (multicompartmental) structure is to underestimate the “true” plateau value. Longer infusion protocols are needed to determine whether the M3 appearance curve fits that of a single exponential out to experimental plateau, as predicted by our model. The advantage of using [U-^{13}C_{3}]lactate infusion can be visualized in the top curve of Fig. 3, where very little or no underestimation of fractional gluconeogenesis is achieved only when the addition of a primed constant infusion of [U-^{13}C_{3}]lactate is simulated. This approach needs further investigation.

The main question addressed by this study is whether delayed m3 lactate recycling contributes to underestimation in gluconeogenic fraction with the use of the primed constant infusion of [U-^{13}C_{6}]glucose. Without priming of the lactate compartment, [U-^{13}C_{6}]glucose carbon has to traverse two additional compartments before appearing as M3 glucose. The kinetic behavior of the M3 enrichment is best described by a multiexponential function. Thus the true plateau value can be missed if the rise in enrichment is slow toward the end of the infusion. We have shown that, when [U-^{13}C_{3}]lactate priming is used, the appearance of M3 glucose behaves like that of an exponential equation, as predicted by our simulation model. Furthermore, despite [U-^{13}C_{3}]lactate priming, M3 glucose enrichment did not reach plateau in the typical experimental time frame used by other investigators. If we assume that our model is correct, the modeling of the M3 glucose enrichment data using a curve-fitting program allows for the extrapolation of M3 enrichment to that of isotope steady state. We found that the plateau enrichment of the last time point was only 73–88% of the true plateau value as estimated using mathematical modeling with SAAM. Therefore, the lack of isotope equilibrium of the M3 glucose pool potentially contributed to 12–27% of the underestimation. The significance of the underestimation is also seen from the locations of the observed M3 being at the lower limits of the 95% confidence interval of the predicted values. In previous studies carried out without the primed constant infusion of lactate, this underestimation is expected to be even larger, because the m3 lactate compartment cannot reach its plateau value within the duration of the study. As demonstrated by simulation, without the additional infusion of labeled lactate, the underestimation of gluconeogenesis using the [U-^{13}C_{6}]glucose method is sufficiently large to account for the gross underestimation of gluconeogenesis in previous studies when the correct equations are applied.

## Acknowledgments

We are indebted to the nurses, dietary staff, and core laboratory technicians of the Clinical Study Center at Harbor-UCLA Medical Center for excellent assistance in the performance of these studies.

## Footnotes

These studies were supported in part by a grant from the National Institutes of Health (NIH)-National Center for Research Resources (M01 RR-00425–27S8 to C. S. Mao) and the American Diabetes Association (to W.-N. P. Lee) and by a grant to the General Clinical Research Center at Harbor-UCLA Medical Center (NIH MO1-RR-00425).

Address for reprint requests and other correspondence: C. S. Mao, Harbor-UCLA Medical Center, 1000 W. Carson St., Torrance, CA 90509–2910 (E-mail: Mao{at}GCRC.REI.edu).

↵1 Many methods of correction for tracer dilution through the TCA cycle are based on the assumption of a single precursor species of labeled lactate (see review in Ref. 11). The presence of significant amounts of m2 and m1 lactate essentially invalidates this assumption. At present, the assumption of “no loss of labeled molecules” is probably the best approximation of the tracer dilution through the TCA cycle.

↵2

*Equation 6*assumes that there is no loss of labeled molecules via the TCA cycle. It is identical to the equation for gluconeogenesis of Ref. 7. The factor 2 should be 2 × p × (1 − p), where m3 + m2 + m1 is the enrichment of labeled lactate and (1 − p) the unlabeled lactate. The use of 2 instead of 2 × p × (1 − p) is the source of the 2–5% underestimation; it can result in a larger underestimation when the enrichment of labeled lactate is higher (4).↵3 The precursor enrichment is independently estimated in the combinatorial isotopomer analysis (MIDA) of Neese et al. (10).

↵4

*Equation 3*has three exponential terms; ya(*t*) = A_{0}− A_{1}× exp(−*a*_{1}×*t*) − A_{2}× exp(−*a*_{2}×*t*) − A_{3}× exp(−*a*_{3}×*t*). At equilibrium, that is, when*t*for that term is very large, A_{1}× exp(−*a*_{1}×*t*) approaches zero. By successive priming, we are, in effect, increasing*t*and reducing the importance of each term successively. A constant term or a constant plus a single exponential can thus approximate*Eq.3*.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.10.1152/ajpendo.00210.2001

- Copyright © 2002 the American Physiological Society