1 Institute of Systems Science
and Biomedical Engineering (LADSEB), The minimal model is widely used to evaluate
insulin action on glucose disappearance from frequently sampled
intravenous glucose tolerance tests (FSIGT). The common protocols are a
regular (rFSIGT, single injection of 0.3 g/kg of glucose) and an
insulin-modified test (mFSIGT, with an additional insulin
administration at 20 min). This study compared the insulin sensitivity
index (SI) and glucose
effectiveness (SG) obtained in
the same individual (16 normal subjects) with the two tests.
SI was 7.11 ± 0.80 10
frequently sampled intravenous glucose tolerance test; glucose
tolerance; minimal model protocols; insulin action
SINCE ITS FIRST INTRODUCTION in the late seventies, the
minimal model technique has been increasingly exploited to determine insulin sensitivity and glucose effectiveness, which have been demonstrated to be important parameters quantifying some of the main
factors controlling glucose disposal (7). This technique uses a
mathematical model to analyze glucose and insulin concentration time
courses after a glucose intravenous injection. The choice of the
intravenous glucose tolerance test with frequent sampling during the
first hour (FSIGT) is justified by several considerations: it allows a
direct stimulation of the Several FSIGT protocols have been proposed in addition to the classic
procedure characterized by a single bolus of glucose (dose of 300 mg/kg) followed by the collection of about 30 samples in 3-4 h. In
particular, it has been suggested to increase the test dynamics by
inducing a second "artificial" insulin peak by injecting either
tolbutamide (10) or insulin (16) 20 min after the glucose bolus. The
second type of experiment (insulin-modified FSIGT) is becoming the
recommended test to estimate insulin sensitivity in a wide variety of
situations especially when the endogenous insulin response is lacking.
However, the standard test or regular FSIGT (only glucose bolus
injection, without any other action) is still widely used because it
also allows inferences on the The use of these two different protocols raised the issue of whether
the FSIGT yields similar metabolic indexes in the same subject when
performed with or without adding insulin. The present study compares
the two tests by estimating the insulin sensitivity index
(SI) and the glucose
effectiveness (SG), obtained
with the regular and the insulin-modified FSIGT, in a group of normal
subjects with various degrees of glucose tolerance.
Subjects.
A total of 16 subjects participated in this study. Each one underwent
two randomly performed FSIGT, one regular and one insulin modified. The
subjects were all healthy as evaluated by a series of independent
tests. The selection was carried out trying to obtain a range of
insulin sensitivity as wide as possible; therefore, we included
subjects already known or expected to exhibit high (young individuals
regularly exercising)- and low-insulin sensitivity (moderate obesity).
The characteristics of the subjects are shown in Table
1. No changes of diet, life-style, and any
other habit were allowed between the first and the second test. The
period between the two tests elapsed from 1 wk to 12 days. The subjects gave their informed consent, and the study was reviewed and authorized by the Ethical Committees of the Schools of Medicine of the
Universities of Padova and Sassari.
ABSTRACT
Top
Abstract
Introduction
Materials & Methods
Results
Discussion
References
4 · min
1 · µU
1 · ml
in rFSIGT and 6.96 ± 0.83 in mFSIGT
(P = 0.656), regression r = 0.92, P < 0.0001;
SG was 0.0260 ± 0.0028 min
1 and 0.0357 ± 0.0052, respectively, statistically different
(P = 0.013) but still with a good
regression (r = 0.66, P = 0.0051). SG and insulin amount during the
early period correlated (r = 0.6, P = 0.015 in rFSIGT and
r = 0.76, P = 0.0006 in mFSIGT). In summary,
both FSIGTs with minimal model analysis provide the same
SI, which is a very robust index.
SG was different by 28% due
probably to the relationship between
SG and the amount of circulating
insulin. In studies comparing groups, the simpler rFSIGT can still be
used with the advantage of accounting for endogenous insulin, thus
offering the possibility of direct inferences on the
-cell activity.
INTRODUCTION
Top
Abstract
Introduction
Materials & Methods
Results
Discussion
References
-cell without the confounding effects of
the gastrointestinal factors proper of the oral test, it provides a
quite high dynamics of both glucose and insulin concentration, and the
given dose of glucose is known as well as the appearance in the
systemic circulation. These factors allow an accurate and precise
evaluation of the metabolic parameters extracted from the test.
-cell activity that can be erroneously
interpreted when exogenous insulin or other pharmacological agents are
administered.
MATERIALS AND METHODS
Top
Abstract
Introduction
Materials & Methods
Results
Discussion
References
Table 1.
Characteristics of subjects and Gb and Ib
before rFSIGT and mFSIGT
Tests and assays.
The experimental protocols started between 0800 and 0830 after an
overnight fast. A vein flow needle was inserted in an antecubital vein
for blood sampling, its patency being maintained by slow saline drip.
Basal blood samples were collected at time 10 and
1 min, after which glucose (300 mg/kg body wt) was
infused in a contralateral vein within 30 s, starting at
time 0. For the regular FSIGT
(hereafter called rFSIGT) additional samples were collected at 3, 4, 5, 6, 8, 10, 14, 19, 22, 25, 30, 40, 50, 60, 70, 80, 100, 140, and 180 min. The insulin-modified FSIGT (or mFSIGT) differed from this protocol
by a nonprimed infusion of 0.03 U/kg of insulin (Actrapid;
Novo-Nordisk, Bagsvaerd, Denmark) for 5 min starting at 20 min in the
same vein where glucose was injected. The sampling schedule was 3, 4, 5, 6, 8, 10, 14, 19, 22, 27, 30, 35, 40, 50, 70, 100, 140, and 180 min.
The 25-min sample of rFSIGT was shifted at 27 min in mFSIGT, because at
25 min the insulin infusion ends and mixing effects could still occur. In mFSIGT the sample at 35 min was added for evaluating insulin concentration because no significant change in the glucose pattern is
expected to happen around that time. We have maintained the same
schedule in the tail of the test (from 100 to 180 min) given the
recently appreciated importance of such a period in the estimation of
minimal model parameters (21).
Data analysis and statistics.
Parameter KG, the glucose
tolerance index, was calculated as the slope of the natural logarithm
of glucose concentration versus time from 10 to 20 min for the period
before insulin infusion and from 20 to 40 min for that after the
insulin infusion. FSIGT data were submitted to the computer program
MINMOD (23), which uses a nonlinear least-squares estimation technique
and a constant variance structure for the measurement error to fit the
time course of glucose concentration under insulin control and thus to
calculate the characteristic metabolic parameters, as previously
described in detail (3, 7, 9, 23). In short, it assumes a first order
nonlinear kinetics and, by accounting for the effect of insulin and of
glucose on glucose disappearance, yields two parameters: SI
(min1 · µU
1 · ml)
and SG
(min
1). The accuracy of the
estimated parameters was assessed with the CV, which was given by the
percent ratio between the standard deviation and the absolute value.
The standard deviation was obtained by the square root of the main
diagonal of the covariance matrix calculated during the least-squares
estimation procedure (28).
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RESULTS |
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The measured plasma concentrations of glucose and insulin are
shown in Fig. 1. Fasting glucose and
insulin were virtually the same before the regular and the
insulin-modified experiment (Table 1). In both cases, after glucose
injection, a similar peak was reached (291 ± 12 mg/dl for
rFSIGT and 279 ± 13 for mFSIGT, P = 0.38). Glucose patterns up to 20 min, time of beginning of the
insulin infusion in mFSIGT, were similar in both tests, as also
demonstrated by same parameter KG
calculated from 10 to 20 min (2.74 ± 0.30 %min1 in rFSIGT and 2.79 ± 0.29 in mFSIGT, P = 0.857). Glucose time courses after insulin infusion exhibited different
patterns, as reflected by different
KG, calculated from 20 to 40 min
(Table 2). In rFSIGT glucose returned to
preinjection level by 60 min and exhibited a slight undershoot (nadir
of 73 ± 2 mg/dl in the interval 40-140 min). In mFSIGT glucose
was back to preinjection level at 35 min and kept decreasing between 40 and 70 min, when it reached the lowest value (on average 54 ± 3 mg/dl). By 3 h glucose concentration was again at the
preinjection level. Preinjection insulin levels were the same (Table
1), and the patterns before 20 min were similar both in terms of first
peak (at 4 min 70.6 ± 13.1 µU/ml in rFSIGT and 72.2 ± 12.6 in
mFSIGT, P = 0.69) and of the area
under the curve (0.67 ± 0.10 mU min/ml in rFSIGT and 0.64 ± 0.09 in mFSIGT, P = 0.58).
The insulin peak induced by the exogenous infusion was 353 ± 95 µU/ml at 27 min. The areas under the whole insulin curves were
2.6 ± 0.2 mU min/ml in rFSIGT and 5.3 ± 0.7 in
mFSIGT, P < 0.001. In both protocols
insulin concentration at the end of the 3-h observation period was
again at the preinjection value.
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|
The SI and
SG estimated in every subject are
reported in Table 2. Regarding SI,
the mean values were not different (P = 0.66) and a good correlation was observed
(r = 0.92, P < 0.0001, Fig. 2). The slope was 0.89, not different from
the unit line, and the intercept was not different from zero. The
Bland-Altman test confirmed that the measurements of
SI obtained with the two different methods were equivalent. The CVs of the single estimates, which describe their accuracy, were higher with the rFSIGT (12.1 ± 2.66% vs. 4.19 ± 0.44, P < 0.005).
Regarding SG, the mean value from the rFSIGT was lower (P = 0.0134) than
that from mFSIGT. A good correlation, although weaker than
that of SI, was still observed (r = 0.66, P = 0.0051, Fig. 2). The slope was
1.22 ± 0.37, not different from that of the unit line, and the
intercept was 0.004 min1.
The Bland-Altman test confirmed that the measurements of
SG obtained with the two different
methods were not equivalent. The CVs were much higher with the
rFSIGT (42.7 ± 10.61% vs. 7.22 ± 0.80, P < 0.003).
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To interpret the differences of SG in the two tests, we looked for possible relationships between this parameter and those aspects for which the two tests differ, i.e., the insulin and glucose patterns due to the insulin infusion. SG was thus correlated with several parameters describing concentration time course. In Table 3 the regression coefficients along with their statistics are reported. SG of rFSIGT correlated with the insulin area under the curve during the interval 0-14 min (Fig. 3) and with the KG at any interval during which it was calculated. SG of mFSIGT correlated with the first insulin peak, the area under the insulin curve [both that of the initial phase (Fig. 3) and the total], and KG calculated in the interval 10-20 min. No relationship was found with the hypoglycemic undershoot.
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In Fig. 4 the time courses of cortisol and growth hormone during the two tests are reported. The concentration of both hormones decreased with hyperglycemia and hyperinsulinemia and remained at low levels for the entire test. For every hormone, the two patterns were not different at any data point.
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DISCUSSION |
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The minimal model of glucose disappearance, since its first introduction (8), has been gaining increasing attention for its ability to yield an index of whole body insulin sensitivity from a simple experiment such as a 3-h intravenous glucose tolerance test with frequent blood sampling during the first hour (7). Whereas the structure of the model has remained the same, the experimental protocol that provides glucose and insulin data to the model analysis has been subject of further studies and several variations have been proposed. The aim of these changes has always been the amelioration of the accuracy and precision of those model parameters that represent insulin sensitivity. Theoretical studies showed that increasing the dynamics of the insulin pattern plays a very important role in improving the calculation of SI (15). In particular, when a sharp, high, and well-defined second phase is present, parameter SI is better and more precisely estimated (34). For this reason, it has been suggested to enhance the endogenous insulin response by injecting tolbutamide 20 min after glucose injection (10). With this experiment the value of SI given by the minimal model is equivalent to that obtained with the widely accepted "gold standard" glucose clamp experiment (10). However, tolbutamide often is not available and may have extra pancreatic metabolic effects. The possibility of reaching the same result by just directly injecting insulin led to the currently most adopted protocol with an exogenous intravenous administration of insulin after the regular 0.3 g/kg injection of glucose (16). However, the exogenous administration either of tolbutamide or insulin makes it very hard to obtain also a clear view of the pancreatic function, often as important as the peripheral insulin sensitivity to elucidate the metabolic condition of a subject. This latter bias can be overcome by the 20-min delay of the insulin infusion that allows the possibility of evaluating the first peak pancreatic response immediately after the glucose stimulation. Nevertheless, to assess first- and second-phase insulin secretion and hepatic extraction, many studies still exploit the rFSIGT (e.g., Refs. 4 and 20). The aim of this study was therefore that of comparing glucose disappearance parameters obtained with the two protocols.
The results showed that the SI is equivalent in both tests, although it is worth noting that the CV of the estimate, i.e., an index of the precision of the parameter, is much lower in the mFSIGT, confirming a better estimate of SI in the presence of a higher insulin and glucose dynamics. To the best of our knowledge, only a few studies already exist about the comparison of results obtained in the same subjects with different minimal model protocols. Beard et al. (6) found no difference in average SI in normal men when estimated with the regular and the tolbutamide-modified FSIGT, although a careful observation of the single comparisons shows a weak and nonsignificant regression (r = 0.55, P = 0.1). Finegood et al. (16) analyzed the possibility of replacing tolbutamide with a short insulin infusion and found that in normal volunteers SI was not different, at variance with a study of Welch et al. (33), who detected a 15% increase in SI when an insulin bolus replaced tolbutamide. Recently Saad et al. (26), comparing insulin- and tolbutamide-modified FSIGT, saw a good correlation between the SIs in the two cases, but a lower SI was observed with insulin. Prigeon et al. (24) found a consistent decrease of SI with increasing dose of exogenous insulin with the modified FSIGT in obese adults. In both of these latter studies the regular test was, however, not performed.
The present study showed no difference in SI with the two tests despite a wide change in circulating insulin concentration. The reason accounting for this different finding is not clearly understood. Nonetheless, a possible responsibility can be ascribed to a likely transient saturation of the insulin action when the hormone is given as a bolus at high doses (24). Because the minimal model can envision the saturation of the insulin action as a decrease in insulin sensitivity (24), in the present study we adopted the 5-min low-dose insulin infusion (0.03 U/kg) for the modified experiment to maintain the insulin concentration in the physiological range. Furthermore, this low-rate insulin infusion was adopted to try to avoid a deep hypoglycemic nadir, which in our study reached a minimum level of only 20 mg/dl lower than in the regular test. The same SI found in this study with the two protocols suggests that moderate glucose nadir plays no role in the estimation of insulin sensitivity. Our results confirm those obtained from a study similar to the present one by Quon et al. (25) who found no difference in SI when both the regular and the modified FSIGT with 5-min insulin infusion (0.02 U/kg) were used in normal men. These authors found also a regression line very close to the unit line in 8 of 10 cases. Interestingly, the two exceptions were subjects somehow different from the others because of the lowest insulin response during the regular test. The other finding confirmed by our study was the reduced percent CV of SI with the modified test. The CV of SI found by Quon et al. (25) from the modified FSIGT (3.6 ± 1.0%) was similar to that of our study, whereas that from the regular test was much higher (22.2 ± 9.0%). Quon et al. (25) used the standard 30 samples, whereas we adopted a reduced schedule with only 19 samples, which lies between the standard protocol and the minimum allowed number for a reliable estimation [12 samples (27)]. It is not possible to ascertain why our estimation routine [original MINMOD of Pacini and Bergman (23)] does not yield a higher CV, as in theory it should do with a lower number of samples (28). For this purpose it would be necessary to test the two identification softwares with the same identical data set, maintaining the same initial conditions, weighting scheme, and convergence criteria. In fact, all these factors, as well as the measurement noise, contribute to the final covariance matrix and thus to the final accuracy of the estimates.
At variance with SI, a statistically significant difference was found concerning the SG. Parameter SG from the rFSIGT was lower, although a positive correlation was found between the two protocols. The CV with rFSIGT was much higher, indicating also a less precise estimate. Parameter SG quantifies the actions of glucose per se, independent of increased insulin, to normalize glucose concentration through actions on glucose production and utilization (3). The importance of this variable on the evaluation of the overall glucose homeostasis has been recently widely recognized (2, 11). It was therefore noteworthy trying to understand why SG differed between the two tests and in particular to relate this parameter to those other factors that were different in the two tests. The regression analysis indicated a direct relationship between SG and the circulating insulin. This fact deserves several comments. First, this study provided further evidence about an association between SG and insulin concentration, as already suggested by other investigations in nondiabetic subjects (19, 29). Finegood and Tzur (18), from the conclusions of a study performed in streptozotocin-treated dogs, pointed out that the minimal model overestimates SG in normal dogs compared with that obtained in animals pharmacologically lacking insulin. It is interesting to notice that SI remains unchanged in their streptozotocin-treated dogs despite the difference in insulin secretion (18, 32), as in our study. Basu et al. (5) reported that SG is dependent on insulin levels in non-insulin-dependent diabetes mellitus (NIDDM). Our results confirm in humans that a decrease of SG is accompanied by a reduction of systemic insulin concentration and an unchanged insulin sensitivity.
In addition, Finegood and Tzur (18) speculated that the lower SG in the streptozotocin-treated dogs, and in general the relationship between insulin concentration and SG is a result of the performance of the minimal model, whereas Basu et al. (5) indicated that decreased SG is a defect associated with NIDDM rather than an artifact of the model. From our study it is not possible to clarify this issue; however, there are some aspects that can help the understanding of the model behavior and the correlation between SG and insulin. Thomaseth and Cobelli (30) showed that the estimation of SG in normal subjects depends mainly on the concentration patterns during the first 20 min of the test and around 60 min and Thomaseth and Pacini (31) showed that the resulting SG value is very sensitive to dynamic changes in concentration occurring in these periods. Parameter SG therefore does not depend only on the prevailing insulin levels during the first phase, as we and others have shown, but also on the qualitative time course of glucose and insulin. In fact, the marked variations in both patterns, induced by the insulin infusion from 20 to 60 min, occur together with a more precise estimation of SG in the mFSIGT. Moreover, in the rFSIGT only the regression with the area under the first phase is statistically significant, whereas in the mFSIGT the regression holds both with the first phase and with the total area. This is further evidence that SG, in addition to depending on the initial insulin response, is more sensitive to the amount and dynamics of insulin in the so-called second phase. The above considerations led to the concept that being the first phase insulin response important for a good estimate of SG, caution is required in those subjects lacking the acute insulin response, for instance in NIDDM. However, the second phase is a determinant for calculating SG, and thus the exogenously induced elevated insulin concentration during mFSIGT compensates the low first peak and allows an acceptable estimate of SG.
Another important issue that currently is the subject of debate regards the physiological meaning of glucose effectiveness and the question of whether model parameter SG correctly measures this process. Finegood and Tzur (18) compared clamp-derived measurements with SG obtained with the insulin-modified test, whereas Ader et al. (2) measured in dogs the fractional glucose disappearance in the somatostatin-induced absence of a significant dynamic insulin response, which is by definition the glucose effectiveness. In both of these elegant studies, the authors saw that the directly measured values were similar and consistent with published minimal model estimates obtained from standard and tolbutamide-modified tests (3, 17, 34). Another interesting result of the study of Ader et al. (2) has been the partitioning of glucose effectiveness in the contribution of glucose uptake and hepatic glucose production (HGO). In our study we did not use any tracer, so that we could not factor out those two processes. Being unable to distinguish the contribution of the various organs from cold glucose measurements in plasma, we can obtain only figures of "global" glucose disposition. The model in fact has been designed such that glucose disappearance, described by SI and SG, includes peripheral uptake and net hepatic glucose balance (8, 10). Because liver production is not directly accounted for by the model, but is hidden in the global changes of concentration, we checked some counterregulatory hormones to have an idea of liver behavior. The concentration of cortisol and growth hormone remained constant and lower than basal during the whole test, even when glucose reached levels far below the fasting ones. We are aware that we have no measurement of glucagon, the most potent stimulator of HGO, but we still accept that cortisol and growth hormone reflect changes in glucose production as well. These results confirm evidence from studies with labeled FSIGT, which showed that the rFSIGT markedly suppresses HGO (2, 13), thus a fortiori does the insulin-modified test. This is in line with the demonstration of a similar suppression of HGO regardless of intraportal insulin delivery or systemic infusion (1). Given no significant differences of HGO in the two tests, changes in glucose production are not responsible for the differences in SG. Furthermore, according to other investigators, SI and SG are not expected to strongly depend on changes in HGO (10, 21).
All the reports reviewed on SI
comparisons among different minimal model protocols (6, 16, 24-26,
33) showed also the estimated SG.
In all these studies no difference in
SG between the two competing
protocols was found. This is not surprising when insulin-modified and
tolbutamide-modified FSIGT are compared (16, 26, 33), because in both
cases a large amount of insulin is present. On the contrary, when the
regular FSIGT is compared with the modified test, with tolbutamide (6)
or insulin (25) the results differ from what we have found in our
study. This should not depend on the subjects who exhibited both
SI and
KG values very similar in the
three studies. Also the different protocol does not play a role:
insulin dose of Quon et al. (25) was lower than ours (0.02 vs. 0.03 U/kg) and Beard et al. (6) used tolbutamide, but the resulting areas
under the insulin curve were all similar. The reason remains unclear,
and we can only observe that although very minor and definitely not
significant a trend toward a lower SG with the regular test exists
also in the studies of Quon et al. (25) (0.0244 vs. 0.0253 min1) and Beard et al.
(6) (0.016 vs. 0.017). None of these studies reported the CV of
SG estimates, and therefore it is
hard to interpret the effective power of those differences.
In summary, it must be stressed that it is not yet known in humans
whether the SG from rFSIGT or that
from the mFSIGT is the one equivalent to the "true" glucose
effectiveness. In any case, if a study is focused on evaluating
differences among groups, e.g., before and after a specific treatment,
because of the good linear correlation seen above,
SG and
SI can be reliably employed, regardless of the protocol used, providing it is the same type of test
in both groups. Given the importance of this issue, more studies are
necessary to further debate on the meaning of the real glucose
effectiveness (2, 5, 18), on its dependency on the specific test (14),
and on the effect that the estimating model has on its calculation (13,
22). From our study we conclude that both the regular and the
insulin-modified FSIGT with minimal model analysis provide the same
figure for SI. It is possible that
the asymptotic formulas to evaluate the statistical differences, i.e.,
valid for large sample sizes, are not totally adequate to our situation
(16 subjects). However, other kinds of tests, such as the Bland-Altman
method, have confirmed that it is unlikely that possible approximation
errors would have changed the conclusions. Thus our study confirmed
that SI is a very robust index
being independent of the prevailing levels of insulin concentration. The modified test, because of its high dynamics, yields more accurate estimates, and it is the test to be used in those situations where the
endogenous insulin response is lacking. Assuming therefore that the modified test is the reference protocol, it resulted that
SG from rFSIGT is underestimated
on average by 28%, the reason for this underestimation being a linear
relationship found between SG and
the amount of insulin present in the systemic circulation during the
test. Finally, whether the true
SG is that from the regular or
from the modified FSIGT remains to be determined; however, in studies
comparing groups, the regular FSIGT can still be used with the
advantage of simplicity. In addition, it accounts for the endogenous
insulin action for the whole length of the experiment, therefore
offering the possibility of direct inferences on the -cell activity.
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ACKNOWLEDGEMENTS |
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The authors kindly thank the colleagues of LADSEB-Consiglio Nazionale delle Ricerche (CNR) Andrea Mari and Karl Thomaseth for their useful suggestions on some methodological aspects and statistical issues of the minimal model. Gianluigi Fenu and Margherita Porcu (University of Sassari) were invaluable in running the measurement assays. The comments of Richard Watanabe (University of Michigan) are also acknowledged.
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FOOTNOTES |
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Romano Nosadini is also affiliated with the Institute of Internal Medicine and with the CNR Centre for Studies on Aging, University of Padova. Maria Sambataro is currently affiliated with the Division of Medicine of the Hospital of Porto Viro (Rovigo).
A portion of this work was presented at the 32nd Congress of the European Association for the Study of Diabetes in Vienna, Austria (September 1996) and was published as abstract 600 in Diabetologia 39, Suppl. 1: 158A, 1996.
Address for reprint requests: G. Pacini, LADSEB-CNR, Corso Stati Uniti, 4, 35127 Padova, Italy.
Received 2 September 1997; accepted in final form 16 December 1997.
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