Letters to the Editor
 |
ABSTRACT |
The following is an abstract of the article discussed in the
subsequent letter:
Finegood, Diane T., and Dan Tzur. Reduced
glucose effectiveness associated with reduced insulin release: an
artifact of the minimal-model method. Am. J. Physiol. 271 (Endocrinol. Metab. 34): E485-E495, 1996.
We previously
demonstrated that minimal model-derived estimates of glucose
effectiveness (SG), based on the frequently sampled
intravenous glucose tolerance test (SG FSIGT), were
reduced in islet-transplanted or streptozotocin-treated dogs and in
patients with insulin-dependent diabetes mellitus. To ascertain the
validity of our observations, we compared SG FSIGT with
estimates based on a basal hormone replacement glucose clamp
(SG BRCLAMP) and a basal hormone replacement glucose
tolerance test (SG BRGTT) in normal control (CNTL,
n = 12) and streptozotocin-treated dogs with normal fasting
plasma glucose (STZ-Rx, n = 9). SG FSIGT was reduced in STZ-Rx compared with CNTL (P < 0.05). However,
neither SG BRCLAMP nor SG BRGTT was
reduced in the STZ-Rx group (P > 0.05). Comparison of
protocols for each subject indicated that SG FSIGT was
greater than either SG BRCLAMP or
SG BRGTT in control (P < 0.002) but not in
STZ-Rx dogs (P > 0.1). The relationship of
SG FSIGT to insulin secretory function suggests that our
previous conclusion that SG FSIGT was reduced in
subjects with limited insulin release may be an artifact of the
minimal-model method. Our results suggest that caution must be
exercised in the interpretation of differences in minimal-model
estimates of SG between subject groups with significantly different levels of insulin secretory function.
 |
LETTER |
Minimal Model Estimate of Glucose Effectiveness: Role of the
Minimal Model Volume and of the Second Hidden Compartment
To the Editor: The paper by Finegood and Tzur (9) on a
potential artifact of the minimal model (3) in assessing glucose
effectiveness addresses a relevant issue given the important role of
this index (1, 2, 5). In reading their arguments, we think that some
clarification of some of their methodological aspects of data analysis
and some of their conclusions would be helpful for other readers. We
think that our observations and insights are critical, especially in
light of the increasing demand for a better definition of the domain of
validity of the minimal model estimate of glucose effectiveness called
for by recent experimental (10) and theoretical (6-8) results.
The volume issue.
Comparison of the minimal model index of glucose effectiveness,
SG FSIVGTT, measured from a frequently sampled
intravenous glucose tolerance test, FSIVGTT, with the analogous
clamp-based index, SG BRCLAMP, measured from a basal
hormone replacement glucose clamp, BRCLAMP, requires coping with the
fact that the two indexes are not expressed in the same units. Whereas
SG FSIVGTT, a fractional index, is expressed in minutes,
SG BRCLAMP is expressed in milliliters per kilogram per
minute. To convert the two indexes to common units, one must either
multiply SG FSIVGTT or divide SG BRCLAMP by some volume factor. Various approaches have been taken.
Ader et al. (1) divided the mean value of
SG BRCLAMP by Steele's volume (169 ml/kg)
(12). In contrast, Finegood and Tzur (9) chose to divide
SG BRCLAMP by the mean total volume of glucose distribution taken from the literature (250 ml/kg). However, as Finegood and Tzur state in their paper, "the approach taken and the
(volume) estimate used will affect the magnitude of
SG BRCLAMP and could impact on the conclusion that
SG is overestimated by the minimal model method in normal
subjects." Moreover, it is important to recognize that the chosen
approach and volume are likely to affect their correlation plots (Figs.
4 and 5 in Ref. 9) between SG FSIVGTT,
SG BRCLAMP, and the third index of glucose effectiveness
they measured, SG BRGTT, based on a basal hormone replacement glucose tolerance test, BRGTT.
The resolution of the volume issue is thus of paramount importance to
put the comparison between minimal model and clamp indexes of glucose
effectiveness on firm ground. In a previous paper (6) we suggested that
to convert the minimal model and clamp indexes to the same units one
should multiply SG FSIVGTT by the minimal model volume
of glucose distribution, V, because the information leading to an
individualized estimate of the volume is available in each FSIVGTT data
set. We will show formally that this is the correct approach. To do so
we need to return to the definition of glucose effectiveness. Glucose
effectiveness measures the effect of glucose at basal insulin to
enhance its own disappearance from plasma (Rd) and inhibit
its own endogenous production (EGP) (5)
|
(1)
|
where Ib denotes basal insulin concentration.
Applying the above definition to a glucose clamp in which one attains a
steady state for plasma glucose concentration, Rd, and EGP,
one
has
|
(2)
|
where GINF is the exogenous glucose infusion rate needed to
compensate for the increase in Rd and the decrease
in EGP.
The minimal model describes glucose dynamics during an intravenous
glucose tolerance test with the well-known equations
|
(3)
|
where D is the injected glucose dose and V is the minimal
model volume of glucose distribution. The index of glucose
effectiveness, SG, will denote SG FSIVGTT or
SG BRGTT, depending on whether a FSIVGTT or a BRGTT is
carried out. Of note is that during a BRGTT insulin action X in Eq. 3 is identically equal to zero. If we express the glucose equation
in terms of glucose mass instead of concentration, its right member
describes the net balance between Rd and
EGP
|
(4)
|
where Q is the glucose mass in the system. Applying the
definition of glucose effectiveness (Eq. 1) to the expression
of Rd-EGP of the minimal model given by Eq. 4, one
obtains
|
(5)
|
Comparing Eqs. 2 and 5, one can see that no
conversion is necessary because the minimal model method provides an
index of glucose effectiveness that has the same units as the
clamp-based index. Of note is that V can be estimated from the same
data that provide SG FSIVGTT or SG BRGTT
and can therefore be individualized in each subject. Because the volume
information is contained in the data, the use instead of Steele's
volume [as in Ader et al. (1)] or of a mean total glucose
distribution volume [as in Finegood and Tzur (9)] is hardly
justifiable. Incidentally, this individualized volume has been already
used in the validation studies of the minimal model insulin sensitivity
index, where SIV has been evaluated against the insulin
sensitivity index measured by the clamp technique (3, 11).
In light of the above considerations, the question arises as to whether
the conclusions drawn in Ref. 9 are confirmed if an individualized
volume is used instead of the mean total distribution volume.
Specifically, two points need to be readdressed.
SG FSIVGTT vs. SG BRGTT.
Finegood and Tzur found that, in normal subjects, the fractional
glucose effectiveness index measured during a traditional FSIVGTT,
SG FSIVGTT, is higher than the one estimated
during a glucose tolerance test at basal insulin,
SG BRGTT. Does this relationship still hold when each
fractional index is multiplied by the companion volume V? The question
arises because in all likelihood the minimal model volume V estimated
from a FSIGT is lower than that estimated from a BRGTT.
Noncorrelation between SG BRGTT and
SG BRCLAMP.
The noncorrelation (r = 0.05) between SG BRGTT
and SG BRCLAMP of Fig. 5 in Ref. 9 is quite a
surprise and would have deserved more discussion in the paper. This
result implies that, even at basal insulin, i.e. under
optimized experimental conditions, the minimal model does not provide a
valid measure of glucose effectiveness. Of the two measures of glucose
effectiveness SG BRCLAMP has more history, so let's
assume for the sake of reasoning that SG BRCLAMP is not
a problem. In calculating glucose effectiveness from the BRGTT, what's
still missing is the volume V estimated in each individual. Thus the
correlation between the BRGTT- and BRCLAMP-based indexes of glucose
effectiveness needs to be reevaluated by comparing SG BRCLAMP to SG BRGTTV.
Role of the hidden compartment.
Finegood and Tzur found that SG FSIVGTT is higher than
SG BRGTT in normal dogs but not in dogs with reduced
insulin secretory function. The result obtained in normal dogs is in
keeping with the results reported by Quon et al. (10), who found in
insulin-dependent diabetic patients a discrepancy between the minimal
model prediction and the experimentally observed profile of glucose
concentration during a BRGTT. Finegood and Tzur formulated the
hypothesis that, when the minimal model is applied to individuals with
a normal insulin secretory function, it is unable to correctly
segregate glucose and insulin effects on glucose disappearance. This is an elegant way of putting the issue, but it does not help much in
clarifying what's wrong with the minimal model.
The finding that SG FSIVGTT is higher than
SG BRGTT in normal dogs is clearly a symptom of model
error, because the value that is taken on by SG should be
independent of the insulin profile during the glucose tolerance test.
So where is the error in the minimal model? Finegood and Tzur did not
answer this question. Here we would like to offer our interpretation of
their findings by building on a recent paper in which we theoretically
analyzed the effect of the single-compartment approximation of the
minimal model on SG estimation by using a two-compartment
model as a reference (7). First, Finegood and Tzur showed that glucose
decay during a BRGTT is biexponential and not monoexponential as
dictated by the minimal model, thus confirming our theoretical
prediction (7). They then concluded that the monocompartmental
description of glucose kinetics is sufficiently adequate, since the
minimal model was well able to describe the BRGTT glucose data from 10 min onward. Unfortunately, the finding that the single-pool description is reasonably good when the glucose system is studied at basal insulin
does not ensure that such an approximation is also adequate when
insulin, in addition to glucose, changes during the test. Extrapolating
to the FSIVGTT what has been found with the BRGTT is not only
methodologically questionable but probably fallacious. During the BRGTT
glucose decay is governed only by glucose effectiveness, and
SG is estimated from the whole glucose data set between 10 and 180 min. Because the fast component of glucose disappearance becomes negligible after ~20 min, SG BRGTT
is mainly determined by the slow component. In contrast, during the
FSIVGTT, glucose decay reflects both glucose effectiveness and insulin
sensitivity, and SG is mainly estimated in the initial
portion of the test, when glucose is high and insulin action, albeit
increasing, is low. Because this is the moment when the fast component
of glucose disappearance plays the major role (7), it is easy to
realize that one will obtain higher values of SG FSIVGTT
than SG BRGTT. In other words, we speculate that the
monocompartmental approximation is much more critical during the
FSIVGTT than during the BRGTT, and the higher values observed for
SG FSIVGTT than for SG BRGTT can be explained by the presence of a second, inaccessible compartment. The finding that the gap between SG FSIVGTT and
SG BRGTT is reduced in animals with impaired secretory
function also fits with the above reasoning: when the early insulin
response is absent, the time window crucial for SG
estimation (glucose high and insulin action low) widens, and the
relative importance of the fast vs. the slow component of
Rd in determining the value of SG diminishes. As a result, SG FSIVGTT comes close to the value of the
slow component and thus to SG BRGTT.
 |
REFERENCES |
1.
Ader, M.,
G. Pacini,
Y. J. Yang,
and
R. N. Bergman.
Importance of glucose per se to intravenous tolerance. Comparison of the minimal-model prediction with direct measurement.
Diabetes
34:
1092-1103,
1985[Abstract].
2.
Basu, A.,
A. Caumo,
F. Bettini,
A. Gelisio,
A. Alzaid,
C. Cobelli,
and
R. A. Rizza.
Impaired basal glucose effectiveness in NIDDM. Contribution of defects in glucose disappearance and production, measured using an optimized minimal model independent protocol.
Diabetes
46:
421-432,
1997[Abstract].
3.
Bergman, R. N.,
Y. Z. Ider,
C. R. Bowden,
and
C. Cobelli.
Quantitative estimation of insulin sensitivity.
Am. J. Physiol.
236 (Endocrinol. Metab. Gastrointest. Physiol. 5):
E667-E677,
1979[Abstract/Free Full Text].
4.
Bergman, R. N.,
R. Prager,
A. Volund,
and
J. M. Olefsky.
Equivalence of the insulin-sensitivity index in man derived by the minimal model method and the euglycemic glucose clamp.
J. Clin. Invest.
79:
790-800,
1987[Medline].
5.
Best, J. D.,
S. E. Kahn,
M. Ader,
R. M. Watanabe,
T.-C. Ni,
and
R. N. Bergman.
Role of glucose effectiveness in the determination of glucose tolerance.
Diabetes Care
19:
1018-1030,
1996[Medline].
6.
Caumo, A.,
A. Giacca,
M. Morgese,
G. Pozza,
P. Micossi,
and
C. Cobelli.
Minimal model of glucose disappearance: lessons from the labelled IVGTT.
Diabetic. Med.
8:
822-832,
1991[Medline].
7.
Caumo, A.,
P. Vicini,
and
C. Cobelli.
Is the minimal model too minimal?
Diabetologia
39:
997-1000,
1996[Medline].
8.
Cobelli, C.,
P. Vicini,
and
A. Caumo.
If the minimal model is too minimal, who suffers more: SG or SI?
Diabetologia
40:
362-363,
1997[Medline].
9.
Finegood, D. T.,
and
D. Tzur.
Reduced glucose effectiveness associated with reduced insulin release: an artifact of the minimal-model method.
Am. J. Physiol.
271 (Endocrinol. Metab. 34):
E485-E495,
1996[Abstract/Free Full Text].
10.
Quon, M. J.,
C. Cochran,
S. I. Taylor,
and
R. C. Eastman.
Non-insulin mediated glucose disappearance in subjects with IDDM: discordance between experimental results and minimal model analysis.
Diabetes
43:
890-896,
1994[Abstract].
11.
Saad, M. F.,
R. L. Anderson,
A. Laws,
for the IRAS. A comparison between the minimal model and the glucose clamp in the assessment of insulin sensitivity across the spectrum of glucose tolerance.
Diabetes
43:
1114-1121,
1994[Abstract].
12.
Steele, R.,
J. Wall,
R. DeBodo,
and
N. Altszuler.
Measurement of size and turnover rate of body glucose pool by the isotope dilution method.
Am. J. Physiol.
187:
15-24,
1956.
| | | | |
Andrea Caumo
San Raffaele Scientific Institute Milan, Italy
|
| | | | |
Claudio Cobelli
Department of
Electronics and Informatics University of Padua Padua, Italy
|
 |
REPLY |
To the Editor: Drs. Caumo and Cobelli have raised several
issues with regard to our 1996 publication on artifacts in minimal model-derived glucose effectiveness (3). We appreciate this opportunity
to expand on explanations given in our 1996 paper. Caumo and Cobelli
raise two issues and consider them independently: 1) the means
by which we corrected for the volume of distribution and 2) the
two-compartment nature of glucose kinetics. These two issues are not
independent. If, as they argue in the second part of their letter, a
second compartment is responsible for the observed artifact, then it is
not consistent to assume that a single time-invariant volume of
distribution, estimated from the initial slope of glucose fall during
an intravenous glucose tolerance test, is the best way to put clamp and
frequently sampled intravenous glucose tolerance (FSIGT) data on the
same unit basis.
The correspondents argue that it is more correct to multiply
SG FSIGT estimates by the initial distribution volume
than to divide the clamp-based estimate,
SG BRCLAMP, by a steady-state glucose
distribution volume. Their argument is based on the fact that an
individualized volume of distribution can be obtained from each FSIGT
experiment and a tautological manipulation of the one-compartment
glucose kinetics equation. Although we agree that it would be helpful
to be able to use a volume of distribution that is based on each
individual subject's data, we reject the notion that this is
theoretically more correct. Furthermore, we believe this approach is
not optimal because of the so-called "hidden compartment."
Caumo and Cobelli perform some algebraic manipulations, which they
provide as proof that minimal-model glucose effectiveness must be
calculated as SGV. In their manipulations, the distribution volume comes up on the right side of the equation because their starting definition of glucose effectiveness lacks consideration of the
distribution volume and is, in fact, different from the original
definition put forth by Bergman et al. (1), including Dr. Cobelli. In
the original minimal-model paper, SG was defined as
|
(1-1)
|
If we start with the basic mass balance equation governing
both the clamp and the FSIGT situation, we
have
|
(1-2)
|
Because it has been assumed both by ourselves and by Caumo
and Cobelli that, in this instance, the hidden compartment
is not important and that the volume of distribution is time invariant, this equation is equivalent
to
|
(1-3)
|
In an FSIGT, GINF(t) = 0, so
|
(1-4)
|
Combining Eqs. 1 and 4
|
(1-5)
|
As Caumo and Cobelli have stated, clamp glucose
effectiveness is defined as
|
(1-6)
|
Combining Eqs. 5 and 6, we have
|
(1-7)
|
or the equivalent expression
|
(1-8)
|
Clearly the result of this algebraic manipulation depends on
your starting point, and from a theoretical point of view both equations are correct. The form of the equation that first emerges is
determined by whether you start with the original definition of glucose
effectiveness or with a definition that lacks consideration of the
distribution volume.
Given that true glucose kinetics are approximated only by a single
compartment and that a second so-called hidden compartment may be
important, we must also consider the effect of the hidden compartment
on estimates of the distribution volume. Wolfe (5) clearly demonstrated
that, in the nonsteady state, a single-compartment volume of
distribution varies with time, with the greatest time dependence
occurring at the beginning of a perturbation such as glucose
administration. In contrast, as the system approaches steady state, the
distribution volume varies less in time and approximates the original
value determined by Steele at 25% of body weight (4). For this reason,
we believe the nonindividualized steady-state estimate of distribution
volume used to correct the clamp calculation may be more accurate than
the individualized, but highly time-dependent estimate of the initial
distribution volume obtained during the FSIGT. Because the assumption
that the distribution volume does not vary is incorporated in the
definition of glucose effectiveness, we believe use of the steady-state
estimate to correct the steady-state experiment is less subject to
error.
The correspondents suggest that, if we correct
SG FSIGT and SG BRGTT by the
individual estimates of the distribution volume, these two parameters
will become equivalent, because they believe that the volume estimated
from an FSIGT will be lower than that estimated from a BRGTT. The
reason why they believe that the volume estimated from the FSIGT would
be lower than that from the BRGTT was not explained. Contrary to their
expectations, the distribution volume estimates from these two types of
experiments are identical (1.32 ± 0.13 vs. 1.31 ± 0.13 dl/kg,
P = 0.89 by paired t-test), and the relationship
between SG BRGTT × V and SG FSIGT × V
is the same as in Fig. 4B of our original manuscript (3).
Drs. Caumo and Cobelli also speculated that if we correct
SG BRGTT rather than SG BRCLAMP, the
correlation in Fig. 5 might improve. In fact, SG BRGTT × V is also not correlated with SG BRCLAMP (r = 0.28, P = 0.43), and the previously equivalent
estimates of glucose effectiveness are no longer equivalent
(SG BRGTT = 1.9 ± 0.2 vs.
SG BRCLAMP = 4.3 ± 0.5
ml · min
1 · kg
1,
P < 0.001). We take this as further proof that
correction of SG BRCLAMP is more appropriate than that
of SG BRGTT or SG FSIGT with
individualized values of the distribution volume. The lack of
correlation between SG BRCLAMP and
SG BRGTT is more likely due to the rather small
(~3-fold) range of normal values and the fact that the estimate of
SG BRCLAMP is not very precise. As we indicated in our paper (3), the coefficient of variation for SG BRCLAMP was 60 ± 15%. Although the coefficient of
variation for SG BRGTT was not determined, we expect
that it would be similar to that of SG FSIGT, which was
found to be 23 ± 4%.
Finally, we agree with the correspondents that their subsequent
model-based analysis (2) of the role of the hidden compartment helps to
explain the reason for the artifact identified in our paper (3). Their
arguments provide a theoretical basis for our contention that the
inadequacy of the one-compartment representation of the BRGTT
experiments in control animals but not in streptozotocin-treated animals might provide at least a partial explanation for the observed artifact. The correspondents' demonstration that the hidden
compartment is important (2) was beyond the scope of our original paper (3).
 |
REFERENCES |
1.
Bergman, R. N.,
Y. Z. Ider,
C. R. Bowden,
and
C. Cobelli.
Quantitative estimation of insulin sensitivity.
Am. J. Physiol.
236 (Endocrinol. Metab. Gastrointest. Physiol. 5):
E667-E677,
1979[Abstract/Free Full Text].
2.
Caumo, A.,
P. Vicini,
and
C. Cobelli.
Is the minimal-model too minimal?
Diabetologia
39:
997-1000,
1996[Medline].
3.
Finegood, D. T.,
and
D. Tzur.
Reduced glucose effectiveness associated with reduced insulin release: an artifact of the minimal-model method.
Am. J. Physiol.
271 (Endocrinol. Metab. 34):
E485-E495,
1996[Abstract/Free Full Text].
4.
Steele, R.,
J. S. Wall,
R. C. deBodo,
and
N. Altszuler.
Measurement of size and turnover rate of body glucose pool by the isotope dilution method.
Am. J. Physiol.
187:
15-24,
1956.
5.
Wolfe, R. R.
Radioactive and Stable Isotope Tracers in Biomedicine. Principles and Practice of Kinetic Analysis. New York: Wiley-Liss, 1992, p. 133-137.
| | | | |
Diane T. Finegood
Diabetes Research Laboratory School of Kinesiology Simon Fraser University Burnaby, BC, Canada V5A 1S6
|
AJP Endocrinol Metab 274(3):E573-E576
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Copyright © 1998 the American Physiological Society