Non-steady-state measurement of glucose turnover
in rats by using a one-compartment
model
J. PROIETTO,
J.-F. SAUTER,
F. ROHNER-JEANRENAUD,
AND B. JEANRENAUD
Laboratoires de Recherches M&taboliques, Faculty
University of Geneva, 1211 Geneva 4, Switzerland
validation;
pool fraction;
lean and genetically
obese ( fa/fa) rats
of tracer techniques in
vivo has been emphasized by Vranic (16) in his review
of tracer methodology. In this respect, there is agreement
that the measurement of glucose turnover using tracer
methods gives meaningful results when employed during
steady-state conditions (1). On the other hand, the difficulty in applying simplified mathematical
models for
the complex non-steady-state in vivo glucose system has
led to the development of several methods (11). One of
these approaches is that proposed by Steele (13). Steele’s
equation is based on a one-pool model and on the initial
assumption of instant mixing of glucose in its entire
space. It can be written as follows
THE NEED FOR THE VALIDATION
R a-
- F - [WG + GPP’ (SA2-SA,M~2- h)l
#A2
+ S&)/2
where Ra equals rate of glucose appearance, F equals
infusion rate of tracer, V equals glucose space or extracellular volume (estimated as being 25% of body wt), and
G1 and GB equal glucose concentrations
at times tl and
and Department
J. TERRETTAZ,
of Medicine,
t2. The
glucose space (V) times the average glucose
concentration
[V x (G, + G2)/2], is the total glucose
pool. SA1 and SA2 are the glucose specific activities at
times tl and t2.
However, the assumption
of instant mixing in the
entire glucose pool did not prove valid, and it was necessary to actually determine and/or choose an empirical
factor that reduces the effective volume of distribution
of glucose, a factor referred to as “p” (13, 17), where p is
a fraction of the whole glucose pool. V now becomes pV.
By using the infusion of inulin as tracer and tracee,
Norwich et al. (9) and Radziuk et al. (10) concluded that
the one-pool model gave the best results when p was
assumed to be between 0.5 and 0.8. However, these
authors agreed that the results based on inulin may not
be directly applicable to in vivo glucose handling. Since
then, only two studies have appeared, directly validating
the one-pool model using glucose (1, 11). These studies,
conducted in dogs, both concluded that the one-pool
model gave reasonable results but they differed in their
determination
of the optimal pool fraction, one concluding that 0.2 was the best pool fraction (l), while the
other found 0.75 to be the best (11). No pool fraction
applicable to glucose handling in the rat has been determined as yet. The aim of this study was therefore to
validate the one-compartment
model in the rat and to
experimentally
determine the best pool fraction to be
used in this species widely used in animal experiments.
MATERIALS
AND
METHODS
Thirteen lean monozygotic (FA/FA ) and six genetically obese ( fa/fa) rats weighing 249 t 4 and 345 t 11
g, respectively, were used. After an overnight fast, anesthesia was induced with 50 mg/kg pentobarbital
(Nembutal, Abbott, Chicago, IL). Two catheters were inserted
into the right jugular vein for infusions. Blood samples
were taken from a catheter inserted in the left carotid
artery. A tracheostomy
tube was placed to allow for
tracheal cleaning. The body temperature of anesthetized
animals was maintained between 36.5 and 37.5C” using
a heating blanket with a rectal probe. These surgical
procedures were followed by a 30.min resting period
before the start of the experiments.
Experimental Designs
The pool fraction to be used in Steele’s (13) equation
in the rat was determined using two different approaches.
0193-1849/87 $1.50 Copyright 0 1987 the American Physiological Society
E77
Downloaded from http://ajpendo.physiology.org/ by 10.220.33.3 on September 13, 2016
PROIETTO, J., F. ROHNER-JEANRENAUD,
E. IONESCU, J.
TERRETTAZ, J.-F. SAUTER, AND B. JEANRENAUD. Non-steadystate measurement
of glucose turnover in rats by using a onecompartment
model. Am. J. Physiol. 252 (Endocrinol.
Metab.
15): E77-E84,
1987.-One
of the tracer methods often employed to measure glucose turnover in the non-steady state
uses the one compartment
model of Steele (Ann. NY Acad Sci
1959). However, this model gives adequate results when it is
assumed that only a fraction of the glucose pool takes part in
rapid changes of glucose specific activity, thereby being necessary to use a correction factor called the “pool fraction.”
The
aim of this study was to experimentally
determine the best pool
fraction needed in the rat for the calculation of glucose turnover
using a one-compartment
model. This is important
as no data
are available so far in this widely used species. For this purpose,
glucose turnover was measured in anesthetized
lean and genetically obese fa/fa rats, using two different experimental
designs.
In all conditions, the error in estimating the total rate of glucose
appearance was lowest when 0.5 was used as the pool fraction.
The error was greater with an increase and a decrease in the
pool fraction value. It is concluded that in the rat the onecompartment
model measures changes in glucose turnover with
reasonable accuracy in non-steady-state
conditions and that a
pool fraction of 0.5 gives the best results.
E. IONESCU,
E78
NON-STEADY-STATE
GLUCOSE
A
Do(~H-~)
Glucose
I
0
2
0
0
’ io
’ 40
0
00
0
0
Glucose
.
6
0 -0
’ $0
TIME
’ 8’0
’ lb0
’ li0
’ 140
(min)
B
.
I
2.
,.‘Y
.*.
,ooGl ucose
“.
.“(14C-ljGlucose=
b
0
I1
..I
20
1
40
TIME
60
I
I
80
I.
IN RATS
pump was calibrated at the end of the study to precisely
measure the rate of unlabeled glucose delivery.
The formula (see Introduction)
of the one pool model
(13) was used to calculate the total rate of glucose appearance (total R,) with the full range of theoretically
possible pool fractions from 0 to 1. It should be noted
that total R, is equal to gut glucose absorption plus
hepatic glucose production plus any other exogenous
source of glucose (i.e., glucose infusion). In this experimental group, hepatic glucose production was completely
suppressed due to the high infusion rate of glucose; gut
glucose absorption was estimated to be nil because of the
overnight fasting; thus it resulted that total R, was equal
to the glucose infusion rate. The variations in glucose
infusion rate were plotted and the true R, at the midpoint
of sequential 5-min intervals was read. These values of
true R, were compared with the tracer calculated Ra.
The difference between the true and the calculated R,
was the error in the calculation of R, at these time points.
Experimental design 2. As these studies did not require
the suppression of hepatic glucose production, they could
be applied to normal as well as insulin resistant geneti-
4
100
11 -
(min)
FIG. 1. Experimental
designs. In both exptl designs, glucose turnover was measured with a primed infusion of D-[3-3H]glucose. In expt
1 (A), endogenous glucose production was suppressed by using an
infusion of glucose. After a steady-state period, glucose infusion rate
was changed every minute and blood was sampled every 5 min to
produce bell shape changes in glycemia. Because endogenous glucose
production was suppressed, tracer-determined rate of glucose appearance (R,) equaled intravenous glucose infusion rate. In expt 2 (B),
endogenous glucose production rate was not suppressed, total R, was
measured using D- [3-3H] glucose, and glucose given intravenously to
produce bell-shape changes in glycemia was labeled with a 2nd tracer
(D[l-'4C]gluCOse).
One-pool model was applied to calculate the directly
verifiable intravenous glucose infusion rate.
Experimental
design 1. The first studies involved the
suppression of endogenous glucose production with an
unlabeled glucose infusion in six lean (FA/FA ) rats.
After the collection of a base-line sample, a primed
constant infusion (Gilson Minipulse 2, Villiers, Le Bel,
France) of D-[3-3H]glucose (New England Nuclear, Boston, MA) was commenced at 15 &i/h,
as depicted by
Fig. lA. At 50 min, three blood samples, each 5 min,
were taken for estimation
of plasma D-[3-3H]glucose
specific activity and plasma glucose and insulin levels.
At 60 min, an unlabeled glucose infusion was commenced
at a rate of 6.5 mg/min (-twice the basal hepatic glucose
production rate), to suppress hepatic glucose production
(see RESULTS). After 1 h of equilibration,
ending by the
collection of three other basal samples, the unlabeled
glucose infusion rate was varied according to a predetermined pattern to produce a bell-shape change in glycemia. Blood was sampled every 5 min for 30 min for
estimation of plasma glucose levels and glucose specific
activity. The total volume of blood taken was 4.4 ml/rat,
which corresponds to -15% of its blood volume. This
volume was replaced by isotonic saline. At the end of the
experiment, 5-min samples of D-[3-3H]glucose infusate
were taken in triplicate to accurately measure the delivery rate of the tracer. For each rat, the glucose infusion
lo-
l-
POOL
FRACTION
2. Plot of squared error between actual and calculated rate of
glucose appearance (RJ as a function of pool fraction used to calculate
R,, in normal rats studied with exptl design 1 (Fig. lA) (see MATERIALS
AND METHODS).
Number of expts is 6 k SE. Errors between actual and
calculated rate of R, have been determined for each animal at each
time point shown in Table 2. Number of time points was G/animal,
thus 36 observations for 6 animals tested. Errors were squared to
remove minus or plus individual values, a procedure that provides an
error that is not underestimated as it would be if not squared. By using
a paired t test, 0.5 was significantly different from 0, 0.1, 0.2, 0.7, 0.8,
and 1.0 as pool fractions.
FIG.
Downloaded from http://ajpendo.physiology.org/ by 10.220.33.3 on September 13, 2016
Dd3H-3)Glucose
TURNOVER
NON-STEADY-STATE
GLUCOSE
TURNOVER
IN
E79
RATS
1. Percent error between true glucose R, and calculated R, with 0.5 as a pool fraction:
mean of different animals as a function of time
TABLE
Time, min
Exptl
design
110-115
115-120
120-125
6t2
6t2
7t3
1 (6)
Means f SE
125 -130
130-135
16k2
llt2
135-140
21t4
Time, min
o-5
5-10
10-15
15-20
20-25
11.2k1.4
Means + SE
25-30
design 2
Lean rats (7)
14t2
23k5
17t3
15t3
13*3
15t5
Obese rats (6)
lOt4
24k3
1427
B&3
9t3
15k4
Number of rats is in parentheses. For details of the experimental designs, see MATERIALS
Fig. lA, exptl design 2 is that depicted by Fig. 1B. R,, rate of glucose appearance.
30-35
35-40
20t5
14k3
29k6
43t8
40-45
Exptl
AND
METHODS.
55tll
5Ok18
Ecptl
22.3zk2.3
20.7t3.1
design I is that depicted by
1
F = R,(SA:! + SA1)/2 + [pV(G1 + G2)/2
x @A2- SMI(t2 - h)l
00
110
120
TIME
130
140
(min)
3. Example of 1 experiment performed with exptl design 1 (Fig.
IA). True rate of glucose appearance (R,) shown by continuous line
(0) and calculated R,s by using 0.2 (0), 0.5 (*), and 0.75 (0) as pool
fractions.
FIG.
tally obese (fa/fa) rats. As in expt I, the two groups of
animals [7 lean (FA/FA) and 6 obese ( fa/fa) rats] received a primed constant infusion of D-[3-3H]glucose
during 50 min, ended by the collection of three basal
samples. At the end of this period, the infusion of a
glucose solution (20%) mixed with trace amounts of D[ 1-14C]glucose (Amersham, Amersham, UK) was commenced and varied every minute according to predetermined patterns, as depicted by Fig. 1B. Blood samples
were withdrawn each 5 min for 45 min for measurement
of plasma glucose and glucose specific activities. At the
end of each experiment, the glucose infusion pump was
precisely calibrated. The Steele equation (13) was applied
and total R, was determined as mentioned above using
the full range of theoretically possible pool fractions from
0 to 1. Taking into consideration that total R, is equal
to gut glucose absorption (gut R,) plus hepatic glucose
production (HGP) plus any other exogenous source of
glucose (i.e.. glucose infused) and that gut R, was as-
where F equals appearance rate of D-[ l-14C]ghcOse,
R,
equals previously determined total rate of appearance of
glucose (total RJ, and SA1 and SAZ equal specific activities of D-[lJ4C]glucose
in the blood at times tl and t2,
respectively. Other abbreviations, see above.
Knowing the appearance rate of [l-14C]glucose in the
blood, one can determine the appearance rate of exogenously infused cold glucose from the known specific
activity of the infusate. The infusion rates of glucose
thus calculated, using the full range of pool fractions (Ol), were compared with the actually measured true glucose infusion rate. Note that HGP, i.e., endogenous glucose production, can additionally
be calculated as being
the difference between total R, and exogenously infused
labeled [ 1J4C]glucose, although this parameter is not
needed for actual determinations
of the various p values.
The recycling of [14C]glucose was measured by the
method of Reichard and co-workers (12), which isolates
the carbon in the position 6 of the glucose molecule. The
14C counts isolated in position 6 were then multiplied by
4 to yield an estimate of the 14C recycled in the entire
glucose molecule. In these studies, the recycled [‘“Clglucose counts were found to be low (~10% of total 14C
counts at the end of the experiment) but were nevertheless subtracted from the total [ “C]glucose radioactivity,
to yield the true [ 1-14C]glucose radioactivity.
In experimental designs 1 and 2 the data have purposely not been
smoothed to keep to real data without minimizing
“noise
from experimental
error” and to further strengthen the
comparison between the two different protocols insofar
that the curve-fitting
procedures are not standardized
and/or not unequivocally accepted.
Analytical Procedures
Glucose was measured with a Beckman
lvzer 2 (Beckman Instruments.
Fullerton.
glucose anaCA). Plasma
Downloaded from http://ajpendo.physiology.org/ by 10.220.33.3 on September 13, 2016
sumed to be zero as for the first experimental
design, it
was therefore obvious that total R, was equal to HGP
plus exogenously [ 1-14C]glucose infused. Total R, was
determined
by using D-[ 3-3H] glucose, as mentioned
above. To determine the rate of exogenous [lJ4C]glucose
infusion, Steele’s formula was transposed as follows
18
E80
NON-STEADY-STATE
GLUCOSE
TURNOVER
IN RATS
TABLE 2. Actual glucose infusion rates, calculated glucose R, MCRG, and actual and calculated
glucose areas in individual lean rats
Time, min
Expt
b,
MC%
110-115
115-120
120-125
125-130
130-135
135-140
Glucose Areas
Over Base
Lines, mg/45
min
Infusion rate,
7.4
10.6
13.2
13.1
11.4
8.0
318.5*
mg/min
Calculated rate,
8.4
10.0
11.8
11.7
10.9
6.3
295.47
mg/min
MCI&, ml/min
3.2
2.7
3.3
3.7
4.0
3.3
14
Infusion rate,
7.8
11.2
14.0
14.0
12.3
8.5
339.0*
mg/min
Calculated rate,
8.2
11.3
13.7
11.7
12.0
6.1
298.2-f
mg/min
MC&, ml/min
3.1
2.7
3.2
3.0
3.9
3.5
15
Infusion rate,
7.4
10.6
13.2
13.1
11.4
8.0
318.5”
mg/min
Calculated rate,
7.5
10.3
10.4
10.9
9.4
5.4
269.2 t
mg/min
MC&, ml/min
2.5
2.6
2.8
3.1
3.1
3.2
16
Infusion rate,
7.8
11.2
14.0
14.0
12.3
8.5
339.0*
mg/min
Calculated rate,
8.1
11.1
14.1
12.1
10.7
6.9
315.ot
mg/min
MC&, ml/min
2.6
3.0
3.6
3.5
3.5
3.4
17
Infusion rate,
7.4
10.6
13.2
13.1
11.4
8.0
3 18.5’
mg/min
Calculated rate,
11.7
7.6
12.4
10.2
9.9
6.3
290.97
mg/min
MC&, ml/min
2.4
2.6
2.9
3.2
3.5
3.3
18
Infusion rate,
7.8
11.2
14.0
14.0
12.3
8.5
339.0*
mg/min
Calculated rate,
8.5
12.8
13.7
11.4
10.6
7.9
324.97
mg/min
MC&, ml/min
2.2
2.5
2.5
2.6
2.7
3.0
Values are means t SE. For details of the experimental design, see MATERIALS
AND METHODS.
Exptl design 1 is depicted by Fig 1A. R,, rate
of glucose appearance; MCR,o, metabolic clearance rate of glucose; p = 0.5 for calculated glucose R,. * Actual glucose areas over base lines;
t calculated glucose areas over base lines.
13
Statistical Analysis
For both experimental
designs, statistical
analyses
were performed using a two-tailed paired t test. All
calculations were performed on a Cyber 180-830 computer (CDC) and a Hewlett-Packard
97 calculator.
RESULTS
In the first experimental
design (Fig. lA), the basal
glycemia of the lean monozygotic (FA/FA) rats was 126
+ 3 mg/dl. Basal insulinemia
was 1.0 t 0.2 rig/ml and
basal hepatic glucose production
1.8 t 0.08 mg/min.
After 1 hour of unlabeled glucose infusion (6.7 t 0.14
mg/min) to suppress endogenous glucose production, the
stable plasma glucose levels were 240 t 8 mg/dl and the
insulin levels 5.03 t 0.32 rig/ml. By using the steadystate formula, it was found that in all rats the hepatic
glucose production was suppressed (-0.55 $- 0.15 mg/
min, n = 6). Starting at this time and for the next 30
min the unlabeled glucose infusion rate was changed
every minute according to a previously determined algorithm that induced an increase and a subsequent decrease in glucose appearance. The tracer-determined
R,,
calculated by using the full range of possible pool fractions, was then compared with the true R, (see details in
MATERIALS
AND METHODS).
Figure 2 is a plot of the
squared error between the true and the calculated R, as
a function of the pool fraction used. As can be seen,
although there was obvious spreading around the nadir
of the curve, the smallest apparent squared error appeared to be 0.5, the error increasing both with an
increase and a decrease in the pool fraction. By choosing
0.5 as the best pool fraction, the mean percent error of
Downloaded from http://ajpendo.physiology.org/ by 10.220.33.3 on September 13, 2016
insulin concentrations
were determined using dextrancharcoal separation of the bound and free fractions (4).
For the determination
of D- [3-3H]glucose specific activity, 30 ~1 of plasma were deproteinized in duplicate using
60 ~1 of ZnS04 (0.3 M) and 60 ~1 of Ba(OH)2 (0.3 M).
One hundred microliters of the supernatant were evaporated to dryness to eliminate tritiated water. The samples were then reconstituted
with 4 ml of water and
counted using 10 ml of Luma Gel (Lumac/3 M, Schaesberg, The Netherlands). In the samples from expt 2, after
the deproteinization,
the loo-p1 samples were passed
through an ion-exchange resin (Bio-Rad Ag-2X8, BioRad Laboratories, CA) to remove [14C]-labeled charged
metabolites of glucose. Half of the sample was counted
in a liquid scintillation
counter using a dual-label counting program that corrected for spillover of the [‘“Cl
counts in the 3H channel and vice versa, The remainder
was stored for the subsequent determination
of the rate
of Cori cycling, namely the rate of randomization
of the
[‘“Cl to carbons 1, 3,4, and 6, as described above.
NON-STEADY-STATE
I1
0
02
I1
04
11
06
11
08
v
t
1-O
POOL
FRACTION
Plot of squared error between infused and calculated rate of
glucose appearance (R,,) as a function of pool fraction in 13 rats studied
using the two-isotope exptl design 2 (Fig. 1B) (see MATERIALS
AND
METHODS).
Number of expts is 13 k SE. Errors between actual and
calculated rate of & have been determined for each animal at each
time point shown in Table 3. Number of time points was S/animal,
thus 117 observations for the 13 animals were tested. Errors were
squared to remove minus or plus individual values, a procedure that
provides an error that is not underestimated as it would be if not
squared. A paired t test showed that 0.5 gave significantly different
(2P < 0.05) results than all other pool fractions.
FIG.
4.
the calculated Ra compared with the infused R, was 11.2
t 1.4%, as shown by Table 1. It can further be seen in
Table 1 that the percent error was not constant as a
function of time, being smallest at the ascending part of
glucose infusion. This is illustrated by Fig. 3, showing a
representative experiment in which the true R, as well
as the calculated R,s using pool fractions of 0.2, 0.5, and
0.75, respectively, are represented; while the error is
negligible in the ascending part of glucose infusion with
a pool fraction of 0.5, it becomes greater in the second
phase of the study. The raw data of the first experimental
design just described, including the metabolic clearance
rates of glucose (MC&)
as well as the glucose areas
under the curves given as milligram per 45 min of infused
versus calculated values (with p = 0.5), are provided in
Table 2.
The second experimental
design (Fig. 1B) was performed on both normal [lean monozygotic (FA/FA )] and
genetically obese ( fa/fa) rats. Basal plasma glucose values of lean rats were 128 t 2 mg/dl, those of insulin were
0.7 t 0.11 rig/ml, while basal hepatic glucose production
was 2.2 t 0.2 mg/min. The obese fa/fa rats had a basal
plasma glucose level of 196 t 9 mg/dl, with an insuline-
TURNOVER
ES1
IN RATS
mia of 14.3 t 1.5 rig/ml, while basal glucose turnover
was 3.7 k 0.2 mg/min. Figure 4 illustrates that in the 13
animals studied by using this protocol, the least error in
the measurement
of the intravenous glucose infusion
rate was obtained when 0.5 was used as the pool fraction.
By using a paired t test, 0.5 gave a significantly smaller
error than all other pool fractions, including 0.4 and 0.6.
When lean and obese rats were analyzed separately, 0.5
gave the smallest error in both groups.
The error in lean and obese rats between the infused
and the calculated R, using 0.5 as pool fraction is shown
in Table 1. As can be seen, although the mean percent
error was 22 and 21% for the two groups of animals,
respectively, it was variable but lower (lo-15%) in the
ascending part of glucose infusion. This is well illustrated
by Fig. 5, showing the results of one lean and one obese
rat, with the true R, and R,s calculated with 0.2,0.5, and
0.75. Whereas 0.5 is certainly the best amongst these 3pool fractions for both experiments, it can be seen that,
even with 0.5, the error is greater at the end of the
glucose algorithm. The raw data of the second experimental design just described, including the metabolic
clearance rates of glucose (MC&)
as well as the glucose
areas under the curves given as milligram
per 45 min of
infused versus calculated values (with p = 0.5) are provided in Table 3. It can be observed from such raw data
that the MC&, of individual
normal rats increases in
lean rats, while such an increase is obviously blunted in
the obese insulin-resistant
ones.
e
Le
.
TIME(min)
5. True rate of glucose appearance (R*) shown by continuous
line (0) and calculated R,s by using 0.2 (0), 0.5 (*), and 0.75 (o) as pool
fractions for 1 expt performed on lean normal rats and 1 expt performed
on genetically obese animals using in both cases exptl design 2 (Fig.
1B).
FIG.
Downloaded from http://ajpendo.physiology.org/ by 10.220.33.3 on September 13, 2016
t
GLUCOSE
E82
NON-STEADY-STATE
GLUCOSE
TURNOVER
IN RATS
3. Actual glucose infusion rates, calculated glucose R, MCRC, and actual and calculated glucose areas
in individual lean and genetically obeserats
TABLE
Time, min
Expt
fk
MCRc
Basal HGP,
mg/min
o-5
5-10
10-15
1.8
1.5
0.8
1.9
1.5
1.6
1.8
1.5
0.6
1.9
1.7
2.2
1.8
2.9
2.6
1.6
3.0
2.4
2.1
2.9
2.5
1.7
3.0
2.2
0.5
2.9
1.9
1.6
2.4
1.8
1.7
1.0
3.0
2.0
1.0
3.0
2.7
1.1
4.3
3.2
1.1
4.4
3.4
1.1
4.3
3.4
1.2
4.4
4.0
1.4
4.3
3.8
1.1
4.4
3.5
1.4
4.6
4.2
1.2
15-20
20-25
25-30
30-35
35-40
40-45
5.7
4.5
1.2
5.9
5.3
2.4
5.7
4.8
1.4
5.9
4.4
2.0
5.7
4.6
0.9
5.9
5.9
2.2
6.2
5.5
1.4
6.9
7.0
4.9
2.3
7.2
6.4
2.3
7.0
4.5
1.7
7.2
7.3
2.5
7.0
7.5
2.5
7.2
7.1
2.9
7.7
6.4
1.9
6.8
6.1
2.3
7.0
7.4
3.3
6.8
6.6
3.0
7.0
4.7
1.8
6.8
4.2
1.6
7.0
4.8
2.4
7.5
6.1
2.2
5.4
3.4
2.5
5.6
3.1
1.8
5.4
4.7
2.8
5.6
4.0
1.9
5.4
3.2
1.5
5.6
5.7
3.1
5.9
3.8
2.0
2.6
0.8
2.1
2.8
2.5
2.7
2.6
0.1
2.1
2.8
1.5
1.9
2.6
0.6
2.1
2.8
1.6
2.8
2.7
1.6
1.8
Glucose Areas
Over
Base Lines,
mg/45 min
Lean
1
2
3
5
6
11
1.7
2.6
1.9
2.5
2.0
2.5
1.4
6.2
2.1
7.2
6.8
2.5
6.9
6.3
2.2
7.2
5.8
1.8
6.9
6.7
2.3
7.2
5.3
1.9
7.6
6.4
1.6
217.0”
166.2-k
224.9*
194.0t
217.0”
171.9t
224.9*
178.0t
217.0”
171.0t
224.9*
187.5t
217.0”
192.0t
Obese
8.1
8.0
Infusion rate, mg/min
1.9
3.2
4.9
6.7
8.3
6.3
2.9
251.5”
7.6
6.8
8.4
4.1
2.8
231.0-k
Calculated rate, mg/min
2.7
1.9
3.8
2.6
8.2
1.5
1.5
1.5
1.5
1.5
MC&, ml/min
1.4
1.5
1.5
1.5
8.1
8.3
8.0
6.3
2.9
251.5”
12
Infusion rate, mg/min
1.9
3.2
4.9
6.7
2.0
3.8
7.6
6.1
7.0
4.2
3.2
226.5-f
Calculated rate, mg/min
2.3
4.7
6.7
1.5
1.6
1.8
1.9
1.9
2.0
2.0
2.0
2.1
MC&, ml/min
1.6
3.0
4.7
6.4
7.9
8.0
7.8
6.0
2.5
239.0”
19
Infusion rate, mg/min
Calculated rate, mg/min
3.9
1.7
3.9
5.2
5.9
8.4
6.4
6.4
3.3
0.3
207.3 t
1.3
1.3
1.4
1.4
1.4
1.4
1.1
1.0
1.1
MC&, ml/min
20
Infusion rate, mg/min
2.1
3.4
5.0
6.7
8.1
8.2
7.9
6.4
3.2
255.0*
Calculated rate, mg/min
3.5
2.2
4.6
5.1
6.1
8.3
8.1
5.9
3.2
2.1
228.0t
MCb, ml/min
1.7
1.3
1.4
1.8
1.4
2.3
0.5
1.3
0.9
21
Infusion rate, mg/min
1.6
3.0
4.7
6.4
7.9
8.0
7.8
6.0
2.5
239.0*
Calculated rate, mg/min
2.7
1.8
2.3
5.0
6.1
6.2
7.2
7.4
1.4
1.3
193.5t
MC&, ml/min
1.2
1.1
1.1
1.4
1.5
1.6
1.5
0.9
1.2
6.4
3.2
22
Infusion rate, mg/min
2.1
3.4
5.0
6.7
8.1
8.2
7.9
255.0”
9.1
6.8
6.3
5.4
0
Calculated rate, mg/min
3.8
2.6
3.9
4.5
6.6
226.0t
1.5
1.8
2.4
1.6
1.9
1.6
1.1
MCRG, ml/min
1.2
1.8
For details of the experimental design, see MATERIALS
AND METHODS.
Exptl design 2 is depicted by Fig 1B. I&, rate of glucose appearance;
HGP, hepatic glucose production; MC&, metabolic clearance rate of glucose.
p = 0.5 for calculated glucose R*. * Actual glucose areas over base
lines; t calculated glucwe areas over base lines.
10
DISCUSSION
The laboratory rat is increasingly used to perform in
vivo metabolic studies. Thus rat models of obesity, insulin resistance, and inappropriate
regulation of glucose
handling are now studied using techniques previously
applied to humans. These include the euglycemic and
hyperglycemic clamps and the measurement of glucose
turnover under steady-state conditions by using tracer
dilution techniques (7, 8, 15). The measurement of glucose turnover during non-steady-state
in the rat [most
important in assessing glucose handling during spontaneous glucose ingestion as recently described (5)] can
only be performed using the one-pool model proposed by
Steele, since the alternative model, independent of any
pool fraction (possibly better on theoretical grounds),
requires blood sampling during the first 2 h of a constant
tracer infusion to determine the constants in the formulas (11). This is not possible in a small animal with a
limited blood volume. However, one of the problems with
the one-compartment
model is that it requires the assumption of a rapidly mixing part of the total glucose
pool. The rapidity with which glucose mixes in its compartment, and hence the “pool fraction” that quantifies
this rapidly mixing glucose pool, will depend partly on
physical factors such as cardiac output, circulation time,
and the absolute size of the glucose space. It cannot
therefore be assumed that the pool fraction needed in
the rat will necessarily be the same as that in larger
animals and in humans. Furthermore,
although 0.65 is
widely used as the pool fraction, the only two studies
performed in dogs that have actually validated the model
using glucose have given conflicting results. Hence Allsop
et al. (1) found that a pool fraction of 0.2 gave the best
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4
Infusion rate, mg/min
Calculated rate, mg/min
MC&, ml/min
Infusion rate, mg/min
Calculated rate, mg/min
MC&, ml/min
Infusion rate, mg/min
Calculated rate, mg/min
MC&, ml/min
Infusion rate, mg/min
Calculated rate, mg/min
MC&, ml/min
Infusion rate, mg/min
Calculated rate, mg/min
MC&, ml/min
Infusion rate, mg/min
Calculated rate, mg/min
MC&, ml/min
Infusion rate, mg/min
Calculated rate, mg/min
MC&, ml/min
NON-STEADY-STATE
GLUCOSE
IN RATS
E83
greater than the errors on the rising part of the protocol.
These errors would be reduced if a smaller effective
volume of distribution
were assumed, i.e., a smaller pool
fraction. The apparent decrease in the volume of distribution of glucose from the start of the decrease in the
glucose infusion rate has also been described by Allsop
et al. (1) in their validation. It is interesting to note that
this is not consistent with the suggestion of Issekutz et
al. (6) that p increases exponentially
with time from the
start of a perturbation.
Because changes in the apparent
volume of distribution
cannot be predicted, it is advisable, even when considering the above-mentioned
considerations, to use the “average” best pool fraction of 0.5
when doing experiments in rats. It should be stated in
this regard that for the purpose of the validation large
changes in glucose turnover were induced (Figs. 3 and
5). In more physiological
situations with more gradual
changes, the errors can be expected to be smaller.
Although not apparent in Table 1, the fact that the
average percent error for the lean and obese rats studied
with the second experimental
approach is double than
that seen for the first one is entirely due to the fact that
the absolute values of glucose turnover were half those
in the first experimental
design (see Tables 2 and 3). In
fact, the absolute minimal
errors (i.e., with a p of 0.5)
are very similar in the two experimental
designs used,
being 1.2 t 0.3 mg/min in the first experimental
design
and 1.0 t 0.14 and 1.0 t 0.23 mg/min in lean and obese
rats, respectively, in the second experimental design.
In conclusion, the recent introduction
of techniques to
perform metabolic studies in vivo in laboratory rats has
opened a potentially fruitful area of research. Among the
methods used are the euglycemic and hyperglycemic
clamps (7, 8, 15) and the measurement of glucose turnover using labeled tracers. This study demonstrates that
the one-pool model can be used to measure non-steadystate glucose turnover in the rat with an optimal pool
fraction of 0.5. In fact, despite its limitations
and inherent errors, the one-compartment
model appears to be the
only one, at the moment, to be applicable to small
rodents.
The technical help of C. Camenzind is gratefully acknowledged as
is the secretarial assistance of C. McVeigh.
This work has been supported by Grants 3.851.0.83 and 3822.086
from the Swiss National Science Foundation (Berne, Switzerland) and
by a grant-in-aid from Nestle S. A. (Vevey, Switzerland). This work
was also supported in part by Novo Laboratories (Australia) and by a
Roche Fellowship from the Royal Australasian College of Physicians.
J. Proietto holds a National Health and Medical Research Council
(Australia) Neil Hamilton Fairley Fellowship.
Received 6 March 1986; accepted in final form 15 August 1986.
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compare time-coincident
values in estimating the errors.
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hyperglycemia,
but was actually found to be negative
(-0.55 mg/min). This is of course a physiological impossibility, as pointed out earlier by others (2), which remains unexplained as yet. However, this enigmatic phenomenon (which could be related to isotope effects, i.e.,
implying
that the clearance of labeled glucose could
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unlikely to affect the finding of the optimal pool fraction
of 0.5, since the latter is also obtained when using a
completely different protocol (see Fig. 1B).
There is, however, one source of error that is intrinsic
to the model and that is seen in all three groups of
animals. Inspection of Table 1 shows that the errors in
the downward part of the bell-shaped algorithm
are
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9.
NON-STEADY-STATE