Use of a novel triple-tracer approach to assess postprandial
glucose metabolism
Rita
Basu1,
Barbara
Di Camillo2,
Gianna
Toffolo2,
Ananda
Basu1,
Pankaj
Shah1,
Adrian
Vella1,
Robert
Rizza1, and
Claudio
Cobelli2
1 Division of Endocrinology, Diabetes, Metabolism,
and Nutrition, Department of Internal Medicine, Mayo Clinic and
Foundation, Rochester, Minnesota 55905; and 2 Department
of Electronics and Informatics, University of Padua, Padua 35131, Italy
 |
ABSTRACT |
Numerous studies
have used the dual-tracer method to assess postprandial glucose
metabolism. The present experiments were undertaken to determine
whether the marked tracer nonsteady state that occurs with the
dual-tracer approach after food ingestion introduces error when it is
used to simultaneously measure both meal glucose appearance
(Ra meal) and endogenous glucose production (EGP). To do
so, a novel triple-tracer approach was designed: 12 subjects ingested a
mixed meal containing [1-13C]glucose while
[6-3H]glucose and
[6,6-2H2]glucose were infused intravenously
in patterns that minimized the change in the plasma ratios of
[6-3H]glucose to [1-13C]glucose and of
[6,6-2H2]glucose to endogenous glucose,
respectively. Ra meal and EGP measured with this approach
were essentially model independent, since non-steady-state error was
minimized by the protocol. Initial splanchnic glucose extraction (ISE)
was 12.9% ± 3.4%, and suppression of EGP (EGPS) was 40.3% ± 4.1%.
In contrast, when calculated with the dual-tracer one-compartment
model, ISE was higher (P < 0.05) and EGPS was lower
(P < 0.005) than observed with the triple-tracer approach. These errors could only be prevented by using time-varying volumes different for Ra meal and EGP. Analysis of the dual-tracer data with a two-compartment model reduced but did not
totally avoid the problems associated with marked postprandial changes
in the tracer-to-tracee ratios. We conclude that results from previous
studies that have used the dual-tracer one-compartment model to measure
postprandial carbohydrate metabolism need to be reevaluated and that
the triple-tracer technique may provide a useful approach for doing so.
glucose kinetics; initial splanchnic glucose uptake; nonsteady
state
 |
INTRODUCTION |
AFTER AN OVERNIGHT
FAST, the amount of glucose entering the systemic circulation
[i.e., endogenous glucose production (EGP)] approximates the amount
of glucose leaving the circulation [i.e., glucose disappearance
(Rd)]. Under these circumstances, EGP is primarily derived
from the liver, with a small contribution coming from the kidney
(6, 9, 10, 27). The situation becomes more complex after
food ingestion when glucose entering the systemic circulation can
originate from both the gut and EGP (9). An alteration in
either of these processes can substantially influence glucose tolerance.
In a pioneering series of experiments, Steele et al. (25)
introduced a dual-isotope method that enabled simultaneous in vivo
measurement of both the systemic rate of appearance of the ingested
glucose (Ra meal) and postprandial EGP. This approach utilizes two glucose tracers: one ingested and one infused
intravenously. The intravenously infused tracer measures the rates of
appearance (Ra) of the ingested tracer and of total glucose
(i.e., labeled and unlabeled). Appearance of the ingested glucose is
calculated by multiplying the Ra of the ingested tracer by
the specific activity (or tracer-to-tracee ratio if a nonradioactive
tracer is used) of the meal. Initial splanchnic glucose uptake is
calculated by subtracting the portion of the ingested glucose that
reaches the systemic circulation from the total amount of glucose
ingested. EGP is calculated by subtracting the Ra of the
ingested glucose from the total glucose appearance. Glucose
Rd is calculated by subtracting the change in glucose mass
from the total rate of glucose appearance.
This experimental approach has been used by a large number of
investigators to study postprandial glucose metabolism in several species, including rats, dogs, and humans (3, 11, 12, 14-19, 25, 29). Unfortunately, results have not always been consistent. As recently reviewed by Livesey et al. (16), estimates of
initial splanchnic glucose uptake have ranged from
4 to 35%
(3, 11, 12, 14-19, 29). The pattern of EGP also has
varied. Carbohydrate ingestion has been reported to result in either
rapid and near-complete suppression of EGP (EGPS; see Refs.
3 and 11), slow but partial EGPS (15, 16,
18), or an apparent initial paradoxical increase followed by a
subsequent fall in EGP (12, 14, 29). Although it is
possible that these differences are the result of biological variation,
it is more likely they are because (at least in part) of inadequacies
in the model used to calculated turnover during the marked nonsteady
state that occurs after carbohydrate ingestion.
Steele recognized that a single-compartment model (1CM) was
inadequate during nonsteady state (26). He therefore
proposed a constant commonly referred to as the pool fraction [the
so-called pool value (p) value] to try to account for incomplete
mixing within the single compartment. Over the ensuing years, the
proper value for p has remained a matter of debate (1, 16,
20). Even more problematic, experiments have shown that, under
non-steady-state conditions, the "correct" value for p varies with
time (1, 5, 16). In any case, because a 1CM is assumed,
the concentration gradients that are present throughout the glucose
system are ignored. These gradients result in errors that could be
particularly insidious when their magnitude differs between subjects
(e.g., diabetic vs. nondiabetic) or when the size of the gradient is
influenced by the conditions being studied (e.g., ingestion of a large
vs. a small meal). Two-compartment models (2CM) that allow
tracer-to-tracee gradients throughout the body have been proposed in an
effort to overcome this problem (17, 21). Recently,
Livesey et al. (16) compared the performance of a 2CM with
that of a 1CM with pV (where V is the volume of distribution) = 230 ml/kg (i.e., p = 1.0) and found a good agreement in the
average profiles of Ra meal and EGP calculated with the
two methods. However, the authors did not have a model-independent
measure of Ra and EGP, and this average agreement cannot be
considered a proof of validity because both 1CM and 2CM are well known
to be affected by non-steady-state errors. These errors can be avoided
if the tracer-to-tracee ratio can be maintained constant throughout the experiment. A variant of this approach, commonly referred to as the hot
"ginf" method, has been used to accurately measure glucose turnover
during a glucose clamp (5, 13). This is done by ensuring
that the specific activity (or tracer-to-tracee ratio) of the infused
glucose is the same as that present in plasma and by concurrently
adjusting the tracer infusion rate in a manner that mimics the
anticipated pattern of change of EGP. Taylor et al. (28)
proposed a similar approach to measure EGP after carbohydrate ingestion. Those experiments used a modification of the conventional dual-tracer approach in which the rate of infusion of intravenous tracer was adjusted to mimic the anticipated pattern of change of EGP.
This approach minimized the change in the tracer-to-tracee ratio of
endogenous glucose (i.e., the proportion of plasma glucose derived from
endogenous sources), thereby permitting more accurate measurement of
EGP. However, marked changes in meal and total glucose plasma
tracer-to-tracee ratios still occurred, thereby precluding accurate
measurement of meal appearance, total glucose appearance, and glucose
Rd.
In an effort to circumvent these problems, the present experiments
sought to determine whether a novel triple-tracer approach could be
used to minimize changes in both meal and endogenous plasma
tracer-to-tracee ratios, thereby permitting simultaneous measurement of
meal appearance and EGP. Changes in the plasma ratios of the
intravenous and ingested tracers were minimized by intravenously
infusing [6-3H]glucose in a manner anticipated to mimic
the systemic Ra of the [1-13C]glucose
contained in a mixed meal. At the same time, changes in the ratio
between [6,6-2H2]glucose tracer and
endogenous glucose were minimized by infusing [6,6-2H2]glucose in a pattern that mimicked
the anticipated pattern of change of EGP. Results were then compared
with those observed using the dual-tracer approach in which the
intravenously infused was used to trace the Ra of both the
ingested [1-13C]glucose and total unlabeled glucose, with
EGP being calculated as the difference between the two rates.
The dual-tracer data were analyzed using both 1- and 2CM to determine
whether increasing the complexity of the model decreases the impact of
the non-steady-state conditions. The accuracy of the dual-tracer method
was evaluated both when the [6,6-2H2]glucose
infusion rate was varied (accentuating the change in the
tracer-to-tracee ratio and therefore creating a "worst-case" scenario) and when the [6,6-2H2]glucose
infusion rate was simulated to remain constant (mimicking the
conditions generally present with the "conventional" dual-tracer approach).
We present data indicating that the dual-tracer approach analyzed with
a 1CM and a fixed value for pV is unable to accurately measure meal
appearance, EGP, and glucose Rd after food ingestion. The
dual-tracer approach analyzed with a 2CM reduces but does not totally
avoid the problems inherent in 1CM. The triple-tracer approach, by
minimizing change in the plasma tracer-to-tracee ratios, is essentially
model independent and therefore enables more accurate measurement of
factors involved in the regulation of postprandial glucose tolerance.
 |
METHODS |
Subjects
After approval from the Mayo Institutional Review Board, 12 healthy subjects (6 women and 6 men, mean age 25 ± 1 yr, height 172 ± 2 cm, weight 77 ± 4 kg, body mass index 25.7 ± 0.8 kg/m2, lean body mass 51 ± 3 kg) gave informed
written consent to participate in the study. All subjects were in good
health and did not participate in regular vigorous physical activity.
Experimental Design
All studies were conducted at the Mayo General Clinic Research
Center (GCRC). Subjects consumed a weight maintenance diet (55%
carbohydrate, 15% protein, and 30% fat) provided by the GCRC kitchen
for 3 days preceding the study. All subjects were admitted at 1600 on
the afternoon before study and were given a standard 10 kcal/kg meal
that was consumed between 1700 and 1730. No additional food was eaten
until the next morning. At ~0600 on the morning of study, an 18-gauge
cannula was inserted in a retrograde fashion in a dorsal hand vein. The
hand was then placed in a heated Plexiglas box (~55°C) to obtain
arterialized venous blood samples. Another 18-gauge cannula was
inserted in the opposite forearm for tracer infusion. A
primed-continuous infusion of
[6,6-2H2]glucose (11.84 mg/kg prime; 0.1184 mg · kg
1 · min
1
continuous; MassTrace, Woburn, MA) was started at 0700 and continued until the end of the study at 1600.
At 0900 (time 0), a mixed meal (10 kcal/kg, 45%
carbohydrate, 15% protein, and 40% fat) consisting of three scrambled
eggs, Canadian bacon, 100 ml water, and Jell-O containing
[1-13C]glucose was consumed within 15 min. The beaker
containing the Jell-O was rinsed two times with 20 ml water, and the
rinse solution was consumed. To prepare the Jell-O, 1.2 g/kg body wt
dextrose was dissolved in 200 ml water by gentle heating. After cooling to room temperature, sufficient [1-13C]glucose was added
to achieve an enrichment of ~4%. After thorough mixing, an aliquot
was removed for analysis of [1-13C]glucose enrichment by
gas chromatography-mass spectrometry (GC/MS). The dextrose solution
containing the [1-13C]glucose then was warmed gently, and
5 g sugar-free gelatin (Knox unflavored gelatin; Nabisco, East
Hanover, NJ) and 1 g sugar-free orange-flavored Kool-Aid (Kraft
General Foods, White Plains, NY) were added. The mixture was allowed to
solidify overnight in the refrigerator.
An infusion of [6-3H]glucose was started at time
0 (i.e., with the first bite), and the rate varied to mimic the
anticipated Ra of the [1-13C]glucose
contained within in the meal (Fig. 1). At
the same time, the rate of infusion of [6,6-
2H2]glucose was altered so as to approximate
the anticipated pattern of fall in EGP. 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, 360, and 420 min.

View larger version (10K):
[in this window]
[in a new window]
|
Fig. 1.
Study design. A mixed meal containing
[1-13C]glucose was ingested at time 0 (top). A primed-continuous infusion of [6,6
2H2]glucose was started at time 120
min and then varied from time 0 onward to mimic the
anticipated pattern of change of endogenous glucose production (EGP;
middle). An intravenous infusion of
[6-3H]glucose was started at time 0, and the
rate varied to mimic the anticipated pattern of appearance of the
ingested glucose (bottom).
|
|
Analytical Techniques
Plasma samples were placed on ice, centrifuged at 4°C,
separated, and stored at
20°C until assay. Plasma glucose
concentration was measured using a glucose oxidase method (YSI, Yellow
Springs, OH). Plasma insulin concentration was measured using a
chemiluminescence assay with reagents obtained from Beckman Coulter
(Access Assay; Beckman Coulter, Chaska, MN). Body composition was
measured using dual-energy X-ray absorptiometry (DPX scanner; Lunar,
Madison, WI). Plasma [6-3H]glucose specific activity was
measured by liquid scintillation counting, as previously described
(23). Plasma enrichment of [1-13C]glucose
and [6,6-2H2]glucose was measured using GC/MS
(Thermoquest, San Jose, CA) to simultaneously monitor the C-1 and C-2
and C-3 to C-6 fragments, as described by Beylot et al.
(4). Pilot experiments in five subjects established that,
under the conditions of the present experiment, enrichment of
13C resulting from carbon cycling is below the limit of
detection with this technique.
Calculations
To arrive at the formulas for calculating the fluxes, we first
derive the tracer and tracee glucose concentrations in plasma from the measurements.
Glossary
To do so, we used the following definitions
Tracee |
glucose at natural composition, coming from ingested glucose and EGP
|
TracerI |
[1-13C]glucose above natural
|
TracerII |
[6,6-2H2]glucose tracer, consisting primarily
of [6,6-2H2]glucose (tracer purity is 92%),
a minor amount of
[6,6-2H1-1H1]glucose,
and a negligible amount of [6,6-1H2]glucose
|
TracerIII |
[6-3H]glucose tracer
|
Gnat |
concentration of tracee in plasma (µmol/ml)
|
G13C |
concentration of tracerI in plasma (µmol/ml)
|
G2H |
concentration of tracerII in plasma (µmol/ml)
|
G3H |
concentration of tracerIII in plasma (dpm/ml)
|
F2H |
rate of intravenous infusion of tracerII (µmol/min)
|
F3H |
rate of intravenous infusion of tracerIII (dpm/min)
|
G |
plasma glucose concentration measured in the arterialized hand vein
samples (µmol/ml)
|
MR13C |
ratio of [1-13C]glucose to [1-12C]glucose
in plasma
|
MR13C,meal |
MR13C measured in the meal
|
MR2H |
ratio of [6,6-2H2]glucose to
[6,6-1H2]glucose in plasma
|
Measurements and tracer and tracee glucose concentrations.
MR13C is measured in the C-1 and C-2 fragments.
TracerI contributes to [1-13C]glucose only;
tracerII and tracee, having the carbon atom at natural
composition, contribute to [1-12C]glucose with 1/(1 + MR13C,nat) equal to 98.9% of their mass and
to [1-13C]glucose with the remaining
MR13C,nat/(1 + MR13C,nat) equal to 1.1%
|
(1)
|
where MR13C,net represents the ratio
between 13C and 12C in natural glucose, equal
to 0.011. Thus MR13C above natural, which is
determined from the mass-to-charge ratio (m/z) of
161 to 160 corrected for natural abundance of all atoms, is related to
tracerI, tracerII, and tracee by the following
formula
|
(2)
|
Similarly, MR13C,meal is proportional to
the ratio between tracerI and natural glucose in the meal
(ttrmeal)
|
(3)
|
MR2H is measured in the C-3 to C-6
fragment and is determined from the m/z
321-319 by correcting for natural abundance of all atoms. It
quantifies 92% of tracerII divided by tracee plus
tracerI
|
(4)
|
Total plasma glucose concentration (G) measures the sum of the
concentration of tracee, tracerI, and tracerII
in plasma
|
(5)
|
From Eqs. 2, 4, and 5,
G13C, G2H, and
Gnat can be quantified from the measurements
|
(6)
|
|
(7)
|
|
(8)
|
The concentration of plasma glucose derived from EGP,
(Gend) can be calculated by subtracting the contribution of
ingested natural glucose (which is proportional to
G13C as measured by ttrmeal) from
the total plasma glucose concentration (i.e., Gnat)
|
(9)
|
Calculation of postprandial rates of EGP, appearance of
meal-derived glucose, and glucose Rd.
Postprandial rates of EGP, appearance of meal-derived glucose, and
glucose Rd were calculated using either the triple-tracer or dual-tracer methods.
Triple-tracer method
Rates of turnover are calculated using three separate models.
Each uses three tracers. In each, [6-3H]glucose traces
the systemic Ra of the [1-13C]glucose
contained in the meal (referred to as Ra 13C), whereas [6,6-2H2]glucose traces the
Ra of endogenously produced glucose. The ratio of the
plasma concentration of [6-3H]glucose to
[1-13C]glucose (i.e., the
G3H-to-G13C ratio) is
used to calculate Ra 13C, and the ratio of the plasma
concentration of [6,6-2H2]glucose to the
plasma concentration of endogenous glucose (i.e., the
G2H-to-Gend ratio) is used to
calculate EGP.
Triple-tracer method calculated with a tracer-to-tracee
"clamp" formula.
Assuming a "perfect" clamp of the plasma tracer-to-tracee ratio
(i.e., variations of
G3H-to-G13C ratio are
negligible), Ra 13C equals the infusion rate
of the tracer (i.e., [6-3H]glucose) divided by the plasma
tracer-to-tracee ratio (i.e., G3H-to-G13C ratio)
|
(10)
|
The systemic Ra of ingested glucose
(Ra meal) is calculated by multiplying
Ra 13C by the meal enrichment [i.e., the ratio of
total glucose (tracee + tracerI) to
tracerI in the meal]
|
(11)
|
Initial splanchnic glucose extraction (ISE) is then calculated
as
|
(12)
|
where D is the total amount of glucose ingested, and the amount
of the ingested glucose that reaches the systemic circulation is equal
to the area under the curve of Ra meal over the 7 h
of study; t is time.
EGP is calculated by dividing the infusion rate of
F2H by the plasma ratio
G2H to Gend
|
(13)
|
Suppression of EGP (EGPS) is calculated by normalizing the area
below basal to the basal area
|
(14)
|
where EGPb is the basal rate of EGP. Although the
estimation of Ra meal and EGP is model independent, that
of the rate of glucose Rd requires the assumption of a
model. We have calculated Rd by assuming a 1CM (see
Eq. 19 below).
Triple-tracer method calculated with a 1CM.
This model is based on a single-compartment description of the system
and was introduced in Ref. 22. As detailed in
APPENDIX A, an expression for Ra 13C is
derived by first expressing the disappearance rate parameter
k01 from the mass balance equation of
[6-3H]glucose tracer
|
(15)
|
where V is the glucose volume of distribution and p is the pool
fraction, and then by using Eq. 15 in the mass balance
equation of [1-13C]glucose tracer
|
(16)
|
By applying the same rationale to
[6,6-2H2]glucose and endogenous glucose,
expressions of the disappearance rate parameter of
[6,6-2H2]glucose tracer
k01,2H (min
1) and EGP
are derived
|
(17)
|
|
(18)
|
Ra meal, ISE, and EGPS are calculated using
Eqs. 11, 12, and 14. Rd
(µmol/min) is calculated as
|
(19)
|
V was initially assumed to equal 200 ml/kg body wt and p
to equal 0.65 (pV = 130 ml/kg). Values for pV were then
subsequently varied from 130 to 160 (which represents a total glucose
distribution volume of 250 ml/kg, according to Ref. 7
multiplied by a p equal to 0.65) to 230 (as proposed in Ref.
16) ml/kg to examine the dependence of dual- and
triple-tracer approaches on the assumed glucose V.
Triple-tracer method calculated with a 2CM.
This model (22) assumes a two-compartment description of
the system with a time-varying Rd of glucose from the
accessible compartment (k01) and constant rate
parameters between the accessible and the peripheral compartments
(k21, k12). As derived in
APPENDIX A, expressions for the disappearance rate
parameter k01 of the [6-3H]glucose
tracer and Ra 13C are
|
(20)
|
|
(21)
|
where V1 is glucose volume of distribution of the
accessible pool (assumed to equal 130 ml/kg),
k21 and k12 are constant rate parameters between the peripheral and the accessible compartment (assumed equal to 0.05 and 0.07 min
1, respectively), and
Q2,13C and Q2,3H are
the amounts of [1-13C]glucose and
[6-3H]glucose tracer present in the peripheral
compartment (determined by integrating model equations as detailed in
APPENDIX A).
Similarly, EGP and the time-varying disappearance rate parameter
k01 of
[6,6-2H2]glucose tracer are expressed as
|
(22)
|
|
(23)
|
where Q2,2H and Q2,end are
the amounts of [6,6-2H2]glucose tracer and
endogenous glucose in the peripheral compartment determined by
integrating model equations.
Ra meal, ISE, and EGP are calculated as indicated before
by using Eqs. 11, 12, and 14
Rd can be expressed as
|
(24)
|
where Q2 is the amount of glucose in the peripheral
compartment to be evaluated by integrating model equations.
Worst-Case Dual-tracer Method
In the present experiment, the infusion rate of
[6,6-2H2]glucose was varied in a pattern that
approximated the anticipated pattern of change of EGP. Although this
minimized the change in the ratio of
[6,6-2H2]glucose to endogenous glucose
concentration (used to calculate EGP with the triple-tracer method), it
accentuated the change in the ratio of the plasma
[6,6-2H2]glucose to total glucose (used to
calculate total glucose appearance with the dual-tracer method) and the
ratio of plasma [6,6-2H2]glucose to
[1-13C]glucose (used to calculate meal appearance with
the dual-tracer method). This analysis therefore is referred to as the
worst-case dual-tracer method. Ra 13C was
calculated using the 1CM equation similar to Eq. 16, with
F2H and G2H in place of
F3H and G3H,
respectively. Ra meal and ISE were calculated as for the
triple-tracer method by using Eqs. 11 and 12,
respectively. The total Ra for glucose was calculated by
applying an equation similar to Eq. 18, with G in place of
Gend. EGP was calculated by subtracting both
Ra meal and the infusion rate of
[6,6-2H2]glucose from Ra. EGPS
was calculated using Eq. 14.
The 2CM also was used to calculate turnover.
Ra 13C was calculated by applying the 2CM
equation similar to Eq. 21, with F2H
and G2H in place of F3H
and G3H, respectively. Ra meal and
ISE were calculated as for the triple-tracer method, by using Eqs. 11 and 12, respectively. Ra was
calculated by applying the 2CM equation similar to Eq. 23,
with G in place of Gend. EGP was then calculated by
subtracting Ra meal and the infusion rate of
[6,6-2H2]glucose from total Ra.
EGPS was calculated using Eq. 14.
In contrast to the triple-tracer approach, the marked variation in the
ratios of G2H to G13C
and G2H to G that occur with the dual-tracer
approach precluded the use of the clamp formula (CF) to calculate turnover.
Data Analysis
All data are expressed as the means ± SE. Rates of glucose
turnover are expressed as micromole per kilogram lean body mass. Values
obtained from
30 to 0 min (i.e., before the meal) were considered as basal.
The time derivatives of the tracer-to-tracee ratios appearing in both
1CM and 2CM (Eqs. 15-24) have been calculated by using
a new algorithm based on a stochastic regularization method (Ref. 8). Traditional methods evaluate time derivatives using a
two-step process, i.e., the data are first smoothed followed by
numerical estimation of the time derivatives. The new algorithm, by
simultaneously performing both data regularization the time-derivative
calculations, provides an estimate of the time derivatives on a
uniform, arbitrarily fine grid. However, because the tracer infusions
used in the present experiments were changed in a stepwise manner at
times that coincided with some of the sampling times, the derivative
estimation at these times can be problematic, since tracer
concentrations, and thus tracer-to-tracee ratios, can have a
discontinuous time derivative. To avoid this problem, 1CM and 2CM
calculations were performed at midpoints between sampling times.
To avoid oversmoothing during the initial few minutes after meal
ingestion, the initial
G3H-to-G13C ratio, at
time 10 min, was not used to calculate Ra meal
in the triple-tracer analyses. This time point was excluded either
because measurements were not available [G13C
and G3H were below the limit of detection in 3 and 6 subjects, respectively] or because the ratio was very high and
of uncertain reliability, as indicated by an error propagation analysis, in the remaining subjects. Based on the same rationale, G2H-to-G13C ratios at
time 10 and 15 min were not used in the calculation of Ra meal in the dual-tracer analyses.
Areas under curves appearing in Eqs. 12 and 14
were calculated using the trapezoidal rule. Area under the
Ra meal curve was calculated by assuming that the systemic
Ra of ingested glucose was zero until plasma
G13C first became detectable. Triple-tracer Rd and dual-tracer EGP (both of which require knowledge of
Ra meal) were calculated starting from the time when
Ra meal was first reliably detected.
The Wilcoxon's signed-rank test was used to determine the statistical
significance of differences. A P value of <0.05 was considered to be statistically significant.
 |
RESULTS |
Plasma Glucose, Glucose Tracer, and Insulin Measurements
Plasma glucose concentrations averaged 4.8 ± 0.1 mmol/l
before meal ingestion and peaked 40 min after meal ingestion at
8.9 ± 0.4 mmol/l (Fig. 2). Glucose
concentrations returned to values that no longer differed from basal by
~180 min. Insulin concentration averaged 21 ± 3 pmol/l before
meal ingestion and peaked ~30 min after meal ingestion at 494 ± 77 pmol/l. As with glucose, insulin concentrations returned to basal
values by ~180 min.

View larger version (9K):
[in this window]
[in a new window]
|
Fig. 2.
Mean glucose and insulin concentrations, the plasma ratio
of [1-13C]glucose to [1-12C]glucose (above
natural), the plasma ratio of
[6,6-2H2]glucose to
[6,6-1H2]glucose, and the
[6-3H]glucose concentration measured in plasma during the
time course of the experiment. See Glossary for
definitions.
|
|
MR13C in plasma averaged a maximum value of
3.45 ± 0.3% above basal ~120 min after meal ingestion and then
declined to 1.38 ± 0.14% above basal at the end of the
experiment. MR2H in plasma averaged 4.20 ± 0.16% before meal ingestion, it declined to a minimum value of
0.68 ± 0.05% at ~150 min after meal ingestion, and then
increased to 2.92 ± 0.15% at the end of the experiment. [6-3H]glucose tracer concentration peaked at 2,232 ± 142 dpm/ml at ~50 min after meal ingestion and then decreased to
1,115 ± 102 dpm/ml on the average.
Plasma Glucose Tracer-to-Tracee Ratios
The triple-tracer approach uses
[6,6-2H2]glucose to trace the Ra
of endogenously produced glucose and [6-3H]glucose to
trace the Ra of the ingested glucose. To do so, the intravenous infusion rate of [6,6-2H2]glucose
tracer was varied to mimic the anticipated pattern of change of EGP,
whereas the intravenous infusion rate of [6-3H]glucose
was varied to mimic the anticipated Ra of the ingested [1-13C]glucose. Figure 3,
left, shows that this approach minimized the postprandial
change in the plasma ratio of
[6,6-2H2]glucose tracer to endogenous
glucose. On the other hand, as shown in Fig. 3, bottom left,
there was a decrease (~2-fold) in the plasma ratio of
[6-3H]glucose to [1-13C]glucose during the
first 15-40 min after meal ingestion, with modest changes
thereafter.

View larger version (20K):
[in this window]
[in a new window]
|
Fig. 3.
Plasma tracer-to-tracee ratios used with the
triple-tracer technique (left) and the "worst"-case
dual-tracer technique (right).
|
|
More pronounced variations were obtained when the
[6,6-2H2]glucose was used to trace the
Ra of both unlabeled glucose and
[1-13C]glucose. The rate of infusion of
[6,6-2H2]glucose was varied as part of the
triple-tracer protocol. Because this created even more marked changes
in the tracer to tracee ratios, it is referred to as a worst-case
scenario for the dual-tracer approach. As is evident from Fig.
3, right, this resulted in an ~10-fold variation in the
plasma [6,6-2H2]glucose tracer to the
ingested [1-13C]glucose ratio (Fig. 3, bottom
right) and an ~6-fold variation in the ratio of
[6,6-2H2]glucose tracer to total glucose
concentration (Fig. 3, top right).
Glucose Fluxes Calculated Using the Triple-Tracer Method
The systemic Ra of the ingested glucose calculated
with 1CM and 2CM and the triple-tracer approach were almost
superimposable. Calculation with CF (which assumes complete
tracer/tracee steady state) provided a similar pattern; however, rates
were slightly lower than with either the 1CM or 2CM until ~70 min and
slightly higher thereafter (Fig.
4A). ISE did not differ when
calculated with 1CM, 2CM, or CF (12.9 ± 3.4 vs. 13.7 ± 3.6 vs. 12.2 ± 3.5%), and the individual values were strongly
correlated (CF vs. 1CM: r = 0.94, P < 0.0001; CF vs. 2CM: r = 0.84, P < 0.0005; 1CM vs. 2CM: r = 0.97, P < 0.0001).

View larger version (18K):
[in this window]
[in a new window]
|
Fig. 4.
Systemic rate of appearance of meal-derived glucose
(A), EGP (B), and glucose disappearance
(C) calculated with the triple-tracer approach using the
clamp formula (CF) and one (1CM)- and two (2CM)-compartment models.
|
|
The pattern of change of postprandial EGP was influenced by the choice
of the formula used for its calculation (Fig. 4B). All three
formulas showed a similar rate of suppression. However, the rise toward
basal rates was faster with 2CM than 1CM, which in turn was faster than
that observed with CF. The pattern tended to reverse at ~225 min when
the rise was faster with CF than the other two formulas. However,
although the patterns differed slightly, the degree of suppression was
similar with 1CM, 2CM, and CF (40.3 ± 4.1 vs. 38.6 ± 4.4 vs. 37.8 ± 4.1%). In addition, the individual values were
strongly correlated as follows: r = 0.99, P < 0.0001 for 1CM vs. 2CM; r = 0.99, P < 0.0001 for CF vs. 1CM; and r = 0.97, P < 0.0001 for CF vs. 2CM.
Calculation of turnover using the 1CM, 2CM, and CF indicated a similar
pattern of change of glucose Rd after meal ingestion (Fig.
4C). However, 2CM suggested a slightly less rapid rise and slightly less rapid fall in glucose Rd than did 1CM and CF.
The postprandial increment in glucose Rd, measured as the
area above basal, did not differ for 1CM, 2CM, and CF (5.6 ± 0.4 vs. 5.6 ± 0.3 vs. 5.9 ± 0.4 mmol · kg
1 · 7 h
1), with values for each individual being strongly
correlated (r = 0.98, P < 0.0001 for
1CM vs. 2CM; r = 0.97, P < 0.0001 for
CF vs. 1CM; and r = 0.91, P < 0.0001 for CF vs. 2CM).
Glucose Fluxes Calculated Using the Worst-Case Dual-Tracer Method
As is evident from Fig. 3, ingestion of a carbohydrate-containing
meal and variation of the [6,6-2H2]glucose
infusion rate resulted in a rapid fall in both the plasma
[6,6-2H2]glucose-to-[1-13C]glucose
ratio and the [6,6-2H2]glucose-to-total
plasma glucose ratio. Because of wide variation in the
G2H-to-G13C ratio (see
Fig. 3, bottom right), rates of meal appearance could not be
calculated reliably with either model until at least 25 min after meal ingestion.
With the 1CM, appearance of ingested glucose measured with the
dual-tracer approach peaked later (34 ± 2 vs. 23 ± 1 min;
P < 0.005) and at a lower rate (52.0 ± 5.4 vs.
84.3 ± 4.2 µmol · kg
1 · min
1;
P < 0.005) than did that measured with the
triple-tracer approach (Fig. 5A,
top). Appearance of ingested
glucose measured with the dual-tracer approach and 2CM peaked slightly
later (37 ± 3 vs. 26 ± 2 min; P < 0.01)
than did that measured with the triple-tracer approach and 2CM, but the
rate was not significantly different (81.2 ± 6.6 vs. 85.8 ± 4.3 µmol · kg
1 · min
1;
Fig. 5B, top). The dual-tracer approach and 1CM
indicated that less (P < 0.005) meal-derived glucose
entered the systemic circulation during the 7 h of study than did
the triple-tracer approaches (6.3 ± 0.5 vs. 8.1 ± 0.5 mmol · kg
1 · 7 h
1). ISE calculated with the dual-tracer approach and 1CM
was thus higher (P < 0.005) than that calculated with
the triple-tracer approach (32.9 ± 4.4 vs. 12.9 ± 3.4%).
In contrast, neither the total amount of meal-derived glucose that
entered the systemic circulation during the 7 h of study (7.9 ± 0.6 vs. 8.1 ± 0.5 mmol · kg
1 · 7 h
1) nor ISE (15.1 ± 5.3 vs. 13.7 ± 3.6%)
differed with dual-tracer 2CM and triple-tracer 2CM approaches.
However, the correlation of the individual values as determined in the
two cases was only modest (r = 0.64; P < 0.023).

View larger version (17K):
[in this window]
[in a new window]
|
Fig. 5.
Results obtained using the triple-tracer approach and the
worst-case dual-tracer approach. Rates of meal glucose appearance
(A and B, top) and EGP (A
and B, bottom) were calculated with the 1CM
(A) and 2CM (B).
|
|
The pattern of change of postprandial EGP also differed with the
dual-tracer approach and 1CM vs. triple-tracer approach and 1CM (Fig.
5A, bottom). EGP calculated with the dual-tracer
approach and 1CM was lower (P < 0.005) during the
first 25 min after mean ingestion than that calculated with the
triple-tracer approach. Both methods showed a comparable rise toward
basal from 70 min onward. Percent suppression below basal was lower
(P < 0.005) with the dual- than triple-tracer approach
(34.8 ± 4.5 vs. 40.3 ± 4.1%). In contrast, the pattern of
change of postprandial EGP was similar from 25 min onward (i.e., the
first time when EGP can be calculated with the dual-tracer approach)
with the dual-tracer 2CM and triple-tracer approaches (Fig.
5B, bottom); the postprandial nadir was the same
(69 ± 16 min), with a comparable subsequent rate of rise toward
basal. The degree of EGPS was also the same (42.9 ± 3.8 vs.
38.6 ± 4.4%), and the individual rates of suppression were well
correlated (r = 0.982, P < 0.0001).
Fractional Clearance of Tracer Calculated with the 1CM and 2CM
Infusion of a tracer allows calculation of the clearance rate of
the tracer from which Ra and Rd can be derived.
Two tracers were infused simultaneously with the triple-tracer approach
(i.e., [6,6-2H2]glucose and
[6-3H]glucose). This enabled the time course of the
fractional disappearance rate parameter k01 to
be determined for each tracer using Eqs. 15 and 17 for the 1CM approach and Eqs. 20 and 22 for the 2CM approach. When calculated with the 2CM
approach, the time course of k01 for
[6,6-2H2]glucose and
[6-3H]glucose was very similar, particularly from 35 min
onward (Fig. 6A). In contrast,
the time course of k01 for
[6,6-2H2]glucose and
[6-3H]glucose differed markedly when calculated with the
1CM approach (Fig. 6B), indicating a failure of this model
to accurately describe the postprandial tracer (and therefore tracee)
kinetics.

View larger version (14K):
[in this window]
[in a new window]
|
Fig. 6.
Fractional glucose clearance (k01)
derived for the [6-3H]glucose and
[6,6-2H2]glucose tracers using a 2CM
(A) or 1CM (B). C: time course of the
1CM volume pV that needs to be used to obtain the same pattern of
k01 for both tracers.
|
|
The V of the 1CM calculation was assumed to be constant and equal to
130 ml/kg. By equating Eqs. 15 and 17 and solving
for pV, one can determine the value of pV at each time point that is
required for the pattern of change of k01 to be
the same for both of the intravenously infused tracers. As shown in
Fig. 6C, the requisite value for pV varies over time,
ranging from 125 to 293 ml/kg, indicating the inability of the 1CM and
any fixed pV to accurately describe postprandial tracer (and therefore
tracee) kinetics.
Role of p and V in 1CM Calculations
Previous studies have used p values ranging from 0.65 to 1 and pV
values ranging from 130 to 230 ml/kg. Recently, Livesey et al.
(16) have suggested that the use of a V of 230 ml/kg (i.e., p = 1) enables accurate estimation of postprandial
turnover. We therefore determined the effect of varying pV from 130 to
160 to 230 ml/kg on meal appearance, EGP, and glucose Rd
calculated using the dual- and triple-tracer approaches. As is evident
in Fig. 7, meal appearance, EGP, and
glucose Rd calculated with the triple-tracer approach were
essentially independent of the value assumed for pV. In contrast, the
value assumed for pV had a marked effect on turnover calculated with
the worst-case dual-tracer approach. The apparent Ra of the
ingested glucose increased and glucose Rd decreased as pV
was increased from 130 to 160 to 230 ml/kg (Fig. 8, A and
C). Similarly, the apparent
pattern of EGPS was dependent on the value of pV (Fig. 8B),
with EGP appearing to paradoxically increase during the first 25 min
with respect to basal value when pV was assumed to equal 230 ml/kg.

View larger version (18K):
[in this window]
[in a new window]
|
Fig. 7.
Systemic rate of appearance of meal-derived glucose
(A), EGP (B), and glucose disappearance
(C) calculated with the 1 CM triple-tracer approach using a
pV value of 130, 160, or 230 ml/kg.
|
|

View larger version (20K):
[in this window]
[in a new window]
|
Fig. 8.
Systemic rate of appearance of meal-derived glucose
(A), EGP (B), and glucose disappearance
(C) calculated with the 1 CM worst-case dual-tracer approach
using a pV value of 130, 160, or 230 ml/kg.
|
|
Because no single pV appeared to be adequate when used with the 1CM
dual-tracer approach, we calculated the time-varying pV values required
to derive glucose fluxes equal to those obtained with triple-tracer
2CM. As is evident in Fig. 9, the
resultant pV values for meal appearance ranged from 166 to 314 ml/kg
(mean 204 ml/kg), for EGP from 60 to 135 ml/kg (mean 122 ml/kg), and for glucose Rd from 70 to 319 ml/kg (mean 196 ml/kg).

View larger version (17K):
[in this window]
[in a new window]
|
Fig. 9.
Values and time course of pV that needs to be used with
the 1CM dual-tracer approach to yield rates of meal glucose appearance,
EGP, and glucose disappearance equal to those obtained with the
triple-tracer approach.
|
|
 |
DISCUSSION |
The rate and pattern of change of plasma glucose concentration is
determined by the difference between the amount of glucose entering and
the amount of glucose leaving the systemic circulation. After
carbohydrate ingestion, glucose entering the circulation can either be
derived from the meal or produced by the liver (and perhaps the
kidney). The so-called dual-tracer approach has been used extensively
to study the regulation of these processes under a variety of
conditions (3, 11, 12, 14-19, 25, 29). Unfortunately,
accurate measurement of meal appearance and EGP after food ingestion is
difficult because both vary with time. This creates a non-steady-state
situation that necessitates the use of a model to describe the glucose
system. Data from the present study indicate that a 1CM and a fixed V
is not adequate when the tracer-to-tracee ratio exhibits large
variations as in the present study when only the
[6,6-2H2]glucose tracer is used to evaluate
both meal appearance and EGP (worst case dual tracer). Use of a 2CM
substantially improves estimates of these fluxes. However, this
approach is still limited, since the results depend on the reliability
of the assumed model. The triple-tracer approach, by minimizing
postprandial changes in meal and endogenous plasma tracee-to-tracer
ratios, is essentially model independent, thereby enabling reliable
assessment of meal appearance and EGP.
The triple-tracer approach used in the present studies sought to
minimize the change in the plasma ratios of [6-3H]glucose
to [1-13C]glucose and [6,6-
2H2]glucose to the endogenous glucose
concentration. To do so, the [6-3H]glucose had to be
infused intravenously in a manner that precisely matched the systemic
Ra of the ingested [1-13C]glucose. This
obviously is impossible, since the Ra of
[1-13C]glucose is influenced by multiple factors,
including the rate of gastric emptying, the rate of glucose absorption,
and the rate of hepatic glucose uptake. Although these processes almost
certainly vary from individual to individual, on the average, they were sufficiently consistent so that a [6-3H]glucose infusion
profile mimicking [1-13C]glucose appearance could be
devised following a few pilot experiments. However, the
[6-3H]glucose-to-[1-13C]glucose ratio still
varied among subjects during the first 10-15 min after meal
ingestion. This occurred for at least two reasons. First, neither
tracer was present before the meal was eaten, and thus the ratio
between [6-3H]- and [1-13C]glucose tracer
concentrations either started from zero or infinity, depending on
whether [1-13C]glucose appeared before or after
[6-3H]glucose.
The uncertainty during the first 10-15 min after meal ingestion
potentially could be avoided if both tracers were infused before meal
ingestion in a ratio approximating that anticipated to be present in
plasma after meal ingestion. However, this would further increase the
complexity of an already complicated protocol. Second, glucose
absorption likely is more variable immediately after eating than it is
once the stomach begins emptying nutrients at a relatively constant
rate in the duodenum. Therefore, it is more difficult to guess how much
[6-3H]glucose needs to be infused in the first few
minutes after food ingestion. On the other hand, as is evident in Fig.
3, the change in the ratio of [6-3H]glucose to
[1-13C]glucose over this interval was approximately
fivefold lower than the change in the plasma enrichment of
[6,6-2H2]glucose over the same interval. This
led to a lower error in measurement of meal appearance with the triple-
than the dual-tracer approach. Ideally, meal appearance should be
measured accurately immediately after the start of a meal. The present
data indicate that, even with the triple-tracer approach, meal
appearance only can be reliably estimated from ~15 min onward.
However, this is not a major limitation, since gastric emptying and
therefore meal appearance is likely to be minimal before this time.
Previous estimates of ISE obtained using the conventional dual-tracer
method have varied widely, ranging from 0 to 45% (3, 11, 12,
14-19, 29). Although differences in the type of subject studied, composition of food ingested, and metabolism of the tracers used may have contributed to this variability, inaccuracy introduced by
nonsteady state and the volume correction factor assumed for "p" in
Steele's 1CM likely has been a major factor (26). Use of
the triple-tracer approach indicates that ISE averaged ~13% in the
present experiments. Recent experiments by ourselves (2) and others (17) using the hepatic catheter technique
combined with a multiple-tracer approach indicate that splanchnic
clearance of enterally infused glucose ranges from ~15 to 25% in the
presence of prolonged steady-state hyperglycemia and hyperinsulinemia. However, it is currently unknown whether splanchnic clearance of
glucose in the presence of prolonged and sustained hyperglycemia and
hyperinsulinemia is the same as that which occurs after meal ingestion
when glucose and insulin concentrations are continuously changing. In
addition, it is not known whether the gut and liver (the main
contributors to splanchnic glucose uptake) clear the same amount of
glucose in the presence of additional enteral nutrients (i.e., fat and protein).
The triple-tracer approach uses the ratio between
[6,6-2H2]glucose and endogenous glucose to
calculate EGP. The endogenous glucose concentration is determined by
subtracting from plasma glucose concentration the contribution of the
ingested glucose, which is proportional to the concentration of the
meal tracer (e.g., [1-13C]glucose) in plasma. Accurate
measurement of EGP requires maintenance of the ratio of
[6,6-2H2]glucose to the endogenous glucose
concentration constant (5, 13, 28). This is more difficult
after meal ingestion than it is during a traditional hyperinsulinemic
euglycemic clamp, since the infusion rate of both tracer and exogenous
glucose is known in the latter but not in the former instance. As
previously discussed (28), this ratio can be kept
relatively constant by decreasing the infusion rate of the tracer (in
this case [6,6-2H2]glucose) in a manner
anticipated to mimic the pattern of change of EGP. Clearly, a priori
knowledge of the pattern of EGPS is required for this approach to
succeed. The pattern of suppression of glucose production likely will
be influenced by a variety of factors, including age, nutrition, and
the presence of a disease (e.g., diabetes mellitus). Therefore, if this
information is not already available in the literature, a few pilot
studies also may be required to optimize the tracer infusion profile.
Because the triple-tracer approach infused two tracers intravenously in
different patterns, it offered the opportunity to assess the validity
of 1CM and 2CM in the postprandial setting. In the absence of model
errors, the time course of the fractional disappearance rate parameter
k01 should be the same for the two tracers,
regardless of the format of tracer administration. As is evident from
Fig. 6, the time course of k01 was virtually
superimposable from 35 min onward when calculated with a 2CM. In
contrast, the time course of k01 for the two
tracers was markedly different when calculated with a 1CM and a fixed
glucose distribution volume. The k01 for the two
tracers only was equal when a time-varying p was used in the 1CM. This
unequivocally indicates the superiority of a 2CM compared with a 1CM in
the postprandial setting, regardless of the size of the glucose pool
assumed for the latter. On the other hand, the comparable rates of meal
appearance and EGP with the triple-tracer approach when calculated with
either a 1CM or 2CM (see Fig. 4) indicate that the advantage of the
latter is minimal when marked changes in the tracer-to-tracee ratio are avoided. Nevertheless, as shown in Fig. 3, it is difficult to maintain
either the meal or the endogenous glucose tracer-to-tracee ratio
absolutely constant. Therefore, although the error with 1CM likely will
be small when used in conjunction with the triple-tracer method, it
presumably will be even smaller when the 2CM is used to calculate
glucose turnover.
Although the triple-tracer approach is more accurate than the
dual-tracer approach, it also is more complex. A key question is
whether it is worth the added effort and cost. With the triple-tracer protocol, both intravenous infusions vary in time, thus preventing us
from reproducing the conventional dual-tracer approach. This created a
worst-case scenario for the dual-tracer approach, since the infusion
rate of the intravenous [6,6,-2H2]glucose
tracer was decreased, whereas it would have been kept constant with the
conventional dual-tracer approach. This resulted in more pronounced
changes in the relevant tracer-to-tracee ratios than would normally be
observed with the conventional dual-tracer approach. As is evident from
Fig. 5, the 1CM approach deteriorated when there were marked changes in
the tracer-to-tracee ratios. A 2CM performed much better than 1CM,
albeit the quality of its results remained inferior to those observed
when either 1CM or 2CM was used with the triple-tracer approach. For
instance, ISE calculated by the 2CM dual-tracer approach was similar to
that estimated with the triple-tracer approach (~15 vs. ~14%);
however, individual values were poorly correlated. In addition, EGP
could not be reliably calculated with the 2CM dual-tracer approach
until ~30 min after the start of the meal. Although these results
suggest vulnerability of both 1CM and 2CM dual-tracer approaches to
nonsteady state, further experiments are necessary to evaluate the
magnitude of the error that would occur when results obtained with the
conventional dual-tracer approach are compared with those obtained with
the triple-tracer approach. A simulation of the anticipated size of the
errors for the 1CM is given in APPENDIX B. The results, albeit obtained under ideal noise-free conditions, are in keeping with
the worst-case scenario.
The present experiment suffers from certain limitations. One limitation
is the lack of a gold standard to which the triple-tracer method can be
compared. The hepatic catheterization technique is an obvious
candidate. However, because tracers also are required for measurement
of meal appearance and splanchnic glucose production, the nonsteady
state that occurs after food ingestion is problematic for this method
as well (17). Only a single meal consisting of scrambled
eggs, bacon, and Jell-O was evaluated. Presumably changes in the plasma
tracer-to-tracee ratios would have been smaller if the meal had
contained less carbohydrate and/or if its composition resulted in
slower gastric emptying (e.g., presence of complex carbohydrates).
Conversely, the non-steady-state error presumably would have been
larger if the meal contained more carbohydrate and/or if glucose alone
had been ingested.
Although the triple-tracer approach minimizes error in measurement of
EGP and appearance of meal-derived glucose, problems with measurement
of glucose Rd persist. Glucose Rd is calculated by subtracting the change in glucose mass from the total rate of
glucose appearance. Because the triple-tracer approach minimizes error
resulting from tracer nonsteady state, it provides a more accurate
measure of total glucose appearance (equal to the sum of endogenous
glucose appearance and meal appearance) than does the conventional dual
approach. However, both methods calculate the change in glucose mass by
multiplying the change in plasma glucose concentration by the V of
glucose (i.e., pV in Steele's equations). Therefore, an error in the
value (generally assumed) of the volume will introduce error in the
calculation of glucose Rd.
Finally, values derived from previous studies in normal subjects were
used as the exchange rate parameters k21 and
k12 in 2CM (22). Ideally, these
parameters should be determined separately in each individual. However,
this would require additional sampling for determination of tracer
concentrations (e.g., [6,6-2H2]glucose)
during the 2-3 h before meal ingestion. The extent to which use of
individual vs. population rate parameters improves the performance of
2CM is difficult to predict. It is likely that the improvement would be
greater for the 2CM dual- than triple-tracer model. Additional sampling
may be feasible in future triple-tracer protocols, since as few as four
samples, if placed optimally, are necessary to estimate the
two-compartment parameters in a given individual (7).
In summary, the present experiments provide evidence that the rapid and
marked changes in the plasma tracer-to-tracee ratios that occur after
food ingestion with the conventional dual-tracer method preclude
simultaneous measurement of meal appearance and EGP if a 1CM is used to
analyze the data. This problem can be minimized by the use of a
suitable 2CM and almost completely avoided by use of a triple-tracer
approach. Meal appearance measured with the triple-tracer approach is
greater and postprandial EGPS smoother than that derived using the
dual-tracer approach and a 1CM.
On the other hand, although more accurate, the triple-tracer method
also is more complex than the conventional dual-tracer method.
Therefore, the triple-tracer method may not be necessary for all
experiments. If the purpose of the experiment is to assess meal
appearance alone or EGP alone, then only two tracers are required. In
the first instance, if changes in the plasma tracer-to-tracee ratio are
to be minimized, the profile of the intravenously infused tracer needs
to be varied to mimic the anticipated Ra of the ingested glucose. In the second instance, the profile of the intravenously infused tracer needs to be varied to mimic the anticipated pattern of
change of EGP. In contrast, if the purpose of the experiment is to
simultaneously assess both meal appearance and EGP, then three tracers
are required. The present data also indicate that conclusions reached
using the dual-tracer approach in conjunction with the traditional 1CM
in ours as well as other investigator's previous studies needs to be
reevaluated and that the triple-tracer technique may provide a useful
approach for doing so.
 |
APPENDIX A |
1CM
The 1CM of glucose kinetics (22) assumes that
Ra and Rd of glucose and glucose tracers take
place in the accessible compartment, which has a volume equal to a
fraction p of the total glucose distribution volume V. The mass balance
equation of [6-3H]glucose is then
|
(A1)
|
where G3H is the concentration of
[6-3H]glucose tracer in plasma,
F3H is the rate of [6-3H]glucose
infusion, and Rd 3H is the rate of
[6-3H]glucose tracer disappearance in plasma.
Similarly, for the [1-13C]glucose tracer
|
(A2)
|
where G13C is the concentration of
[1-13C]glucose tracer in plasma,
Ra 13C and Rd 13C
are, respectively, the rate of [1-13C]glucose tracer
appearance and disappearance in plasma.
Isotopic indistinguishability allows one to link the disappearance rate
of the two tracers to their amount in the accessible compartment
|
(A3)
|
where k01 is the disappearance rate
parameter, which is assumed to vary during the experiment.
By using Eq. A3, Eqs. A1 and A2 can be
rewritten as
|
(A4)
|
|
(A5)
|
From the [6-3H]glucose mass balance equation
(Eq. A4), an expression for k01
(labeled hereafter as k01,3H) can be
derived
|
(A6)
|
By using Eq. A6 into Eq. A5, one obtains
the equation to calculate Ra 13C, since either
known (F3H, pV) or measured (G3H, G13C) variables
are needed
|
(A7)
|
2CM
The 2CM assumes exchange between the accessible and the remote
compartments and irreversible loss from the accessible compartment only.
Mass balance equations of [6-3H]- and
[1-13C]glucose tracers in the accessible compartment
are
|
(A8)
|
|
(A9)
|
where R01,3H and
R01,13C denote the irreversible flux of the two
tracers from the accessible compartment and
R12,3H, R21,3H, R12,13C, and R21,13C are
exchange fluxes.
Isotopic indistinguishability provides
|
(A10)
|
The model assumes that parameters k12 and
k21 remain constant and that
k01 varies during the experiment. By using
Eq. A10, Eqs. A8 and A9 can be
rewritten as
|
(A11)
|
|
(A12)
|
where Q2,13C and
Q2,3H are the amounts of
[1-13C]glucose and [6-3H]glucose tracer in
the peripheral compartment.
From the [6-3H]glucose mass balance equation (Eq. A11), an expression for k01 (labeled
hereafter as k01,3H) can be derived
|
(A13)
|
By using Eq. A13 into Eq. A12, the
following equation for Ra 13C is derived
|
(A14)
|
Equation A14 expresses
Ra 13C as a function of known
(F3H, V1,
k12) or measured (G3H,
G13C) variables but also of
Q2,13C and Q2,3H, which
are not measured. These last variables were evaluated by solving the
mass balance equations of the [6-3H]- and
[1-13C]glucose tracers in the peripheral compartment
|
(A15)
|
|
(A16)
|
The procedure outlined in Ref. 17 was followed,
which provides equations more suitable for implementation on a spreadsheet.
 |
APPENDIX B |
To simulate the conventional dual-tracer experiment, a
two-compartment model similar to that used to analyze
the experimental data (2CM) was adopted. Parameters
k12 and k21 were assumed
to be constant and equal to 0.07 and 0.05 min
1,
respectively, whereas parameter k01 was assumed
to vary in time, with a profile equal to the average profile that we
found in our 12 subjects with the triple-tracer method and 2CM by using
[6,6-2H2]glucose tracer (Fig. 6A).
A value of 130 ml/kg body wt was used for the V of the accessible compartment.
To simulate the cold (unlabeled) glucose concentration data,
model equations were integrated by assuming as initial condition the
basal glucose value and as model input the sum of the average Ra meal plus EGP profiles, estimated with the
triple-tracer approach and 2CM (Fig. 4). Similarly, to simulate
[1-13C]glucose concentration data, model equations were
integrated starting from initial conditions equal to zero and assuming
as model input a 5% fraction of average Ra meal. Finally, [6,6-2H2]glucose concentration data were
simulated by assuming a constant infusion of tracer (at a rate equal to
0.48 µmol · min
1 · kg
body wt
1) from 2 h before the meal administration up
to the end of the experiment.
The simulations are realistic (Fig.
10): plasma
[6,6-2H2]glucose tracer to the ingested
[1-13C]glucose ratio markedly (~7-fold) fell, reaching
a nadir ~90 min after meal ingestion. This ratio then slowly returned
toward basal values over the 4 h. The plasma ratio of
[6,6-2H2]glucose tracer to total glucose
concentration showed a similar pattern. It fell rapidly immediately
after meal ingestion (~3-fold), also reaching a nadir at ~90 min
followed by a slow increase thereafter (Fig. 3, top right).

View larger version (12K):
[in this window]
[in a new window]
|
Fig. 10.
Plasma tracer-to-tracee ratios during the simulated
dual-tracer protocol; the meal glucose appearance and EGP calculated
using the 1CM with a pV value of 130, 160, or 230 ml/kg against the
"true" rates; the time course of pV that needs to be used to yield
rates of meal glucose appearance and EGP that are equal to the true
rates.
|
|
On the basis of these data, Ra 13C was
calculated using the 1CM equation similar to Eq. 16, with
F2H and G2H in place of
F3H and G3H,
respectively. Ra meal and ISE were calculated as for the
triple-tracer method by using Eqs. 11 and 12,
respectively. To calculate EGP, Ra was first calculated
using an equation similar to Eq. 18, with G in place of
Gend. EGP is then calculated by subtracting Ra meal and the infusion rate of
[6,6-2H2]glucose from total Ra.
EGPS is calculated using Eq. 14. To determine the effect of
assuming different pV values in 1CM, calculations were performed with
pV = 130, 160, and 230 ml/kg. Estimates of both
Ra meal and EGP (Fig. 10) show systematic deviations with
respect to the true values, which are more consistent when a low pV
value, 130 or 160 ml/kg, is used in the calculations.
In Fig. 10, the pV values required to derive glucose fluxes equal to
the true ones are also shown; only the use of a time-varying pV would
theoretically eliminate the errors in glucose flux estimates.
 |
ACKNOWLEDGEMENTS |
We thank R. Rood, B. Dicke, C. Etter, J. J. Feehan, B. Norby, M. Otte, T. Hammer, and L. Wahlstrom for technical assistance and
assistance in recruiting the subjects, M. Davis for assistance in the
preparation of the manuscript, and the staff of the Mayo General
Clinical Research Center for assistance in performing the studies. We
also thank other members of the program project team, including Drs. S. Nair, M. Jensen, and S. Khosla, for thoughtful suggestions.
 |
FOOTNOTES |
This study was supported by the U.S. Public Health Service
(AG-14383 and RR-00585), a Novo Norkisk research
infrastructure grant, the Ministero Universita Ricerca Scientifica
Tecnica (Murst), Italy, and the Mayo Foundation. Dr. R. Basu was
supported by an American Diabetes Association mentor-based fellowship.
Address for reprint requests and other correspondence:
R. A. Rizza, Mayo Foundation, 200 1st St. SW, Rm. 5-194
Joseph, Rochester, MN 55905.
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.00190.2001
Received 1 May 2001; accepted in final form 22 August 2002.
 |
REFERENCES |
1.
Allsop, JR,
Wolfe RR,
and
Burke JF.
The reliability of rates of glucose appearance in vivo calcuated from constant tracer infusions.
Biochemistry
172:
407-416,
1978.
2.
Basu, A,
Basu R,
Shah P,
Vella A,
Johnson CM,
Jensen M,
Nair KS,
Schwenk F,
and
Rizza R.
Type 2 diabetes impairs sphlanchnic uptake of glucose but does not alter intestinal glucose absorption during enteral glucose feeding: additional evidence for a defect in hepatic glucokinase activity.
Diabetes
50:
1351-1362,
2001[Abstract/Free Full Text].
3.
Benn, JJ,
Bozzard SJ,
Kelley D,
Mitrakou A,
Aoki T,
Sorensen J,
Gerich J,
and
Sonksen PH.
Persistent abnormalities of the metabolism of an oral glucose load in insulin-treated type I diabetics.
Metabolism
38:
1047-1055,
1989[ISI][Medline].
4.
Beylot, M,
Previs SF,
David F,
and
Brunengraber H.
Determination of the 13C-labelling pattern of glucose by gas chromatography-mass spectrometry.
Anal Biochem
212:
526-531,
1993[ISI][Medline].
5.
Butler, PC,
Caumo A,
Zerman A,
O'Brien PC,
Cobelli C,
and
Rizza RA.
Methods for assessment of the rate of onset and offset of insulin action during nonsteady state in humans.
Am J Physiol Endocrinol Metab
264:
E548-E569,
1993[Abstract/Free Full Text].
6.
Cersosimo, E,
Judd RL,
and
Miles JM.
Insulin regulation of renal glucose metabolism in conscious dogs.
J Clin Invest
93:
2584-2589,
1994[ISI][Medline].
7.
Cobelli, C,
Toffolo G,
and
Ferrannini E.
A model of glucose kinetics and their control by insulin, compartmental and noncompartmental approaches.
Math Biosci
72:
291-315,
1984[ISI].
8.
DeNicolao, G,
Sparacino G,
and
Cobelli C.
Nonparametric input estimation in physiological systems: problems, methods, case studies.
Automatica
33:
851-870,
1997[ISI].
9.
Dinneen, S,
Gerich J,
and
Rizza R.
Carbohydrate metabolism in non-insulin-dependent diabetes mellitus.
N Engl J Med
327:
707-713,
1992[ISI][Medline].
10.
Ekberg, K,
Landau BR,
Wajngot A,
Chandramouli V,
Efendic S,
Brunengraber H,
and
Wahren J.
Contributions by kidney and liver to glucose production in the postabsorptive state and after 60 h of fasting.
Diabetes
48:
292-298,
1999[Abstract/Free Full Text].
11.
Ferrannini, E,
Simonson DC,
Katz LD,
Reichard GJR,
Bevilacqua S,
Barrett EJ,
Olsson M,
and
DeFronzo RA.
The disposal of an oral glucose load in patients with non-insulin-dependent diabetes.
Metabolism
37:
79-85,
1988[ISI][Medline].
12.
Féry, F,
and
Balasse EO.
Glucose metabolism during the starved-to-fed transition in obese patients with NIDDM.
Diabetes
43:
1418-1425,
1994[Abstract].
13.
Finegood, DT,
Bergman RN,
and
Vranic M.
Modeling error and apparent isotope discrimination confound estimation of endogenous glucose production during euglycemic glucose clamps.
Diabetes
37:
1025-1034,
1988[Abstract].
14.
Firth, R,
Bell P,
Marsh M,
and
Rizza RA.
Effects of tolazamide and exogenous insulin on pattern of postprandial carbohydrate metabolism in patients with non-insulin-dependent diabetes melitus.
Diabetes
36:
1130-1138,
1987[Abstract].
15.
Firth, RG,
Bell PM,
Marsh HM,
Hansen I,
and
Rizza RA.
Postprandial hyperglycemia in patients with noninsulin-dependent diabetes mellitus.
J Clin Invest
77:
1525-1532,
1986[ISI][Medline].
16.
Livesey, JH,
Wilson PDG,
Dainty JR,
Brown JC,
Faulks RM,
Roe MA,
Newman TA,
Eagles J,
Mellon FA,
and
Greenwood RH.
Simultaneous time-varying systemic appearance of oral and hepatic glucose in adults monitored with stable isotopes.
Am J Physiol Endocrinol Metab
275:
E717-E728,
1998[Abstract/Free Full Text].
17.
Mari, A,
Wahren J,
DeFronzo R,
and
Ferrannini E.
Glucose absorption and production following oral glucose: comparison of compartmental and arteriovenous-difference methods.
Metabolism
43:
1419-1425,
1994[ISI][Medline].
18.
Mitrakou, A,
Kelley D,
Veneman T,
Jenssen T,
Pangburn T,
Reilly J,
and
Gerich J.
Contribution of abnormal muscle and liver glucose metabolism to postprandial hyperglycemia in NIDDM.
Diabetes
39:
1381-1390,
1990[Abstract].
19.
Pehling, G,
Tessari P,
Gerich JE,
Haymond MW,
Service FJ,
and
Rizza RA.
Abnormal meal carbohydrate disposition in insulin-dependent diabetes.
J Clin Invest
74:
985-991,
1984[ISI][Medline].
20.
Proietto, J,
Rohner-Jeanrenaud F,
Ionescu E,
Terrettaz J,
Sauter J-F,
and
Jeanrenaud B.
Non-steady-state measurement of glucose turnover in rats by using a one-compartment model.
Am J Physiol Endocrinol Metab
252:
E77-E84,
1987[Abstract/Free Full Text].
21.
Radziuk, J,
McDonald TJ,
Rubenstein D,
and
Dupre J.
Initial splanchnic extraction of ingested glucose in normal man.
Metabolism
27:
657-669,
1978[ISI][Medline].
22.
Radziuk, J,
Norwich KH,
and
Vranic M.
Experimental validation of measurements of glucose turnover in nonsteady state.
Am J Physiol Endocrinol Metab Gastrointest Physiol
234:
E84-E93,
1978[Abstract/Free Full Text].
23.
Rizza, RA,
Mandarino LJ,
and
Gerich JE.
Dose-response characteristics for effects of insulin on production and utilization of glucose in man.
Am J Physiol Endocrinol Metab
240:
E630-E639,
1981[Abstract/Free Full Text].
25.
Steele, R,
Bjerknes C,
Rathgeb I,
and
Altszuler N.
Glucose uptake and production during the oral glucose tolerance test.
Diabetes
17:
415-421,
1968[ISI][Medline].
26.
Steele, R,
Wall J,
DeBodo R,
and
Altszuler N.
Measurement of size and turnover rate of body glucose pool by the isotope dilution method.
Am J Physiol
187:
15-24,
1956[Abstract/Free Full Text].
27.
Stumboll, M,
Chintalapudi U,
Perriello G,
Welle S,
Gutierrez O,
and
Gerich J.
Uptake and release of glucose by the human kidney.
J Clin Invest
96:
2528-2533,
1995[ISI][Medline].
28.
Taylor, R,
Magnusson I,
Rothman DL,
Cline GW,
Caumo A,
Cobelli C,
and
Shulman GI.
Direct assessment of liver glucogen storage by 13C nuclear magnetic resonance spectroscopy and regulation of glucose homeostasis after a mixed meal in normal subjects.
J Clin Invest
126:
126-132,
1996.
29.
Thorburn, A,
Litchfield A,
Fabris S,
and
Proietto J.
Abnormal transient rise in hepatic glucose production after oral glucose in non-insulin-dependent diabetic subjects.
Diabetes Res Clin Pract
28:
127-135,
1995[ISI][Medline].
Am J Physiol Endocrinol Metab 284(1):E55-E69
0193-1849/03 $5.00
Copyright © 2003 the American Physiological Society