model analysis of regular and insulin-modified FSIGT
GIOVANNI PACINI,1 GIANCARLO TONOLO,2 MARIA SAMBATARO,3 MARIO MAIOLI,2 MILCO CICCARESE,2 ENRICO BROCCO,3ANGELO AVOGARO,4AND ROMANO NOSADINI2 1Institute of Systems Science and Biomedical Engineering (LADSEB), Italian National Research Council, 35127 Padua;2Institute of Clinical Medicine, University of Sassari, 07100 Sassari; and 3Institute of Internal Medicine and4Department of Clinical and Experimental Medicine,
University of Padova, 35128 Padua, Italy Pacini, Giovanni, Giancarlo Tonolo, Maria Sam-bataro, Mario Maioli, Milco Ciccarese, Enrico Brocco, Angelo Avogaro, and Romano Nosadini. Insulin
sensitiv-ity and glucose effectiveness: minimal model analysis of regular and insulin-modified FSIGT. Am. J. Physiol. 274 (Endocrinol. Metab. 37): E592–E599, 1998.—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. SIwas 7.1160.80 1024· min21· µU21· ml in rFSIGT and 6.9660.83 in mFSIGT (P50.656), regression r50.92, P, 0.0001; SGwas 0.026060.0028 min21and 0.035760.0052, respectively, statistically different (P50.013) but still with a good regression (r50.66, P50.0051). SGand insulin amount during the early period correlated (r 5 0.6, P 5 0.015 in rFSIGT and r50.76, P50.0006 in mFSIGT). In summary, both FSIGTs with minimal model analysis provide the same SI, which is a very robust index. SGwas different by 28% due probably to the relationship between SGand 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 theb-cell activity.
frequently sampled intravenous glucose tolerance test; glu-cose tolerance; minimal model protocols; insulin action
SINCE ITS FIRST INTRODUCTIONin the late seventies, the minimal model technique has been increasingly ex-ploited 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 consider-ations: it allows a direct stimulation of the b-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 meta-bolic parameters extracted from the test.
Several FSIGT protocols have been proposed in addi-tion 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 situa-tions 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 b-cell activity that can be erroneously interpreted when exogenous insulin or other pharmacological agents are administered.
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.
MATERIALS AND METHODS
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 sub-jects 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. Tests and assays. The experimental protocols started be-tween 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 time210 and21 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,
0193-1849/98 $5.00 Copyrightr1998 the American Physiological Society E592
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, Den-mark) 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).
Sampling tubes contained 10 units powdered heparin and 1 mg NaF; samples were kept on ice until centrifugation. Glucose was immediately measured, whereas insulin, corti-sol, and growth hormone were later determined after storage at220°C. Glucose was measured in duplicate by the glucose oxidase technique on an automated analyzer. The coefficient of variation (CV) of a single determination was 61.5%. Insulin was measured in duplicate by radioimmunoassay (insulin 125I-RIA; Incstar, Stillwater, MN) with intra- and interassay CVs for the quality control #7%. Cortisol was assessed by radioimmunoassay (GammaCoat cortisol, 125 I-RIA; Incstar) with interassay CVs#9% (intra-assay#6.8%). Human growth hormone (hGH-CTK) was measured by immuno-radiometric assay (Sorin Biomedica, Saluggia, Italy), with interas-say CVs#4% (intra-assay#2.5%). Insulin, cortisol, and growth hormone for each single subject for both regular and insulin-modified FSIGT were measured in the same assay.
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 param-eters, 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 disappear-ance, yields two parameters: SI (min21· µU21· ml) and SG (min21). 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).
The area under the insulin concentration curve was com-puted by integrating with the trapezoidal rule. Differences in mean values were tested for significance by paired t-test. Equivalence between parameters estimated from the two tests was evaluated by the Bland-Altman method (12). All data and results are given as means6SE.
RESULTS
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 (291612 mg/dl for rFSIGT and 279 613 for mFSIGT, P 5 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 (2.7460.30 %min21in rFSIGT and 2.796 0.29 in mFSIGT, P50.857). Glucose time courses after insulin infusion exhibited different patterns, as re-flected 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 7362 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 5463 mg/dl). By 3 h glucose concentration was again at the preinjec-tion level. Preinjecpreinjec-tion insulin levels were the same (Table 1), and the patterns before 20 min were similar both in terms of first peak (at 4 min 70.6613.1 µU/ml in rFSIGT and 72.2612.6 in mFSIGT, P50.69) and of the area under the curve (0.67 6 0.10 mU min/ml in rFSIGT and 0.64 6 0.09 in mFSIGT, P 5 0.58). The insulin peak induced by the exogenous infusion was 353695 µU/ml at 27 min. The areas under the whole insulin curves were 2.6 6 0.2 mU min/ml in rFSIGT and 5.360.7 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.
The SIand SGestimated in every subject are reported in Table 2. Regarding SI, the mean values were not different (P50.66) and a good correlation was observed (r5 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 Table 1. Characteristics of subjects and Gband Ib
before rFSIGT and mFSIGT
Subject No. Gender Age, yr BMI, kg/m2 rFSIGT mFSIGT Gb Ib Gb Ib 1 M 46 22.7 86 3 84 8 2 M 32 25.3 93 11 96 4 3 M 32 28.4 85 6 98 9 4 F 41 21.6 71 6 79 6 5 M 46 28.0 86 5 85 4 6 M 38 24.7 91 6 94 7 7 F 27 25.5 93 20 89 13 8 F 37 23.0 83 8 85 14 9 M 54 24.7 80 9 83 9 10 M 28 20.8 87 3 86 2 11 M 64 29.4 102 9 104 8 12 M 58 28.4 97 7 99 7 13 F 56 25.7 93 4 99 7 14 F 25 22.1 87 1 80 3 15 F 36 20.8 78 2 83 6 16 F 29 23.1 77 4 79 8 Means6SE 4163 24.660.7 8762 661 8962 761 Other characteristics of subjects: body weight, 7063 kg; height, 16863 cm; systolic pressure, 12664 mmHg; and diastolic pressure, 7563 mmHg. Basal levels of glucose (Gb, mg/dl) and insulin (Ib,
µU/ml) were not different between the 2 tests: P.0.09 and P.0.44 for Gb and Ib, respectively. rFSIGT and mFSIGT, regular and
insulin-modified frequently sampled intravenous glucose tolerance tests; BMI, body mass index.
higher with the rFSIGT (12.162.66% vs. 4.1960.44, P , 0.005). Regarding SG, the mean value from the rFSIGT was lower (P50.0134) than that from mFSIGT. A good correlation, although weaker than that of SI, was still observed (r 5 0.66, P5 0.0051, Fig. 2). The slope was 1.2260.37, not different from that of the unit line, and the intercept was 0.004 min21. 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 (42.7610.61% vs. 7.2260.80, P,0.003).
To interpret the differences of SGin the two tests, we looked for possible relationships between this param-eter and those aspects for which the two tests differ, i.e., the insulin and glucose patterns due to the insulin
infusion. SGwas thus correlated with several param-eters describing concentration time course. In Table 3 the regression coefficients along with their statistics are reported. SGof rFSIGT correlated with the insulin area under the curve during the interval 0–14 min (Fig. 3) and with the KGat 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.
In Fig. 4 the time courses of cortisol and growth hormone during the two tests are reported. The concen-tration of both hormones decreased with hyperglyce-mia and hyperinsulinehyperglyce-mia and remained at low levels
Table 2. Metabolic and model-estimated parameters from regular and insulin-modified tests
Subject No. rFSIGT mFSIGT KG SI SG KG SI SG 1 1.46 4.82 0.0213 3.23 5.23 0.0322 2 3.48 10.01 0.0365 4.66 12.01 0.0260 3 2.42 4.43 0.0359 3.03 2.86 0.0496 4 3.07 8.79 0.0499 7.21 7.15 0.0578 5 1.31 6.96 0.0185 2.20 5.59 0.0345 6 1.42 11.17 0.0125 5.19 11.08 0.0325 7 1.45 7.40 0.0293 5.00 9.59 0.0243 8 1.12 8.41 0.0189 5.24 7.52 0.0172 9 1.83 3.09 0.0208 3.77 4.42 0.0253 10 0.81 4.88 0.0068 2.39 6.11 0.0168 11 1.97 3.45 0.0426 2.34 3.16 0.0881 12 2.53 5.11 0.0301 3.23 4.06 0.0725 13 1.23 10.61 0.0191 6.41 11.26 0.0240 14 2.88 13.82 0.0285 4.86 11.92 0.0209 15 1.47 7.46 0.0170 4.15 6.47 0.0182 16 1.75 3.29 0.0280 3.48 2.61 0.0220 Means6SE 1.8960.19 7.1160.80 0.026060.0028 4.1560.36 6.9660.83 0.035760.0052 Glucose tolerance index (KG, %min21) was calculated in time period 20–40 min, when glucose patterns diverge due to exogenous insulin
infusion in mFSIGT (P50.0001, comparing 2 tests). SI(1024· min21· µU21· ml), insulin sensitivity index (P50.656); SG(min21), glucose
effectiveness (P50.013).
Fig. 1. Time course of glucose and insulin concen-tration during insulin-modified (mFSIGT, A and B) and regular (rFSIGT, C and D) frequently sampled intravenous glucose tolerance tests (FSIGT). In both cases glucose (0.3 g/kg) was injected at time 0. In mFSIGT insulin (0.03 U/kg) was also infused from 20 to 25 min.
for the entire test. For every hormone, the two patterns were not different at any data point.
DISCUSSION
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
param-eters that represent insulin sensitivity. Theoretical studies showed that increasing the dynamics of the insulin pattern plays a very important role in improv-ing 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 tolbuta-mide 20 min after glucose injection (10). With this Fig. 2. Linear regression between insulin sensitivity index [SI,
1024· min21· µU21· ml, A, r50.92, P,0.0001] and glucose
effective-ness (SG, min21, B, r50.66, P50.0051) obtained with rFSIGT and
mFSIGT. Dotted line in B represents unit line, which coincides with regression line in A.
Table 3. Correlation coefficients and statistics from linear regressions between SGestimated with rFSIGT
and mFSIGT and parameters describing time courses of insulin and glucose concentration
rFSIGT mFSIGT
r P r P
Insulin pattern
Insulin peak, first phase 0.438 0.0896 0.864 0.0001 Insulin area, first phase 0.596 0.0149 0.759 0.0006 Insulin area, total 0.331 0.2109 0.849 0.0001 Glucose pattern
KG, 10–20 0.626 0.0095 0.679 0.0038
KG, 20–40 0.780 0.0004 0.210 0.4339
KG, 10–40 0.900 0.0001 0.044 0.8709
Gnadir 0.426 0.0995 0.016 0.9520
Insulin peak is maximum value of insulin concentration after glucose bolus. Areas under insulin concentration curve are su-prabasal. For calculation of KGseeMATERIALS AND METHODS. Gnadiris
difference between basal glucose and minimum value of glucose concentration.
Fig. 3. Linear regression between SG(min21) and area under insulin
concentration curve (AUC, mU · ml21· min) in early phase (from 0 to
14 min) during rFSIGT (A, r50.60, P50.015) and mFSIGT (B, r5 0.76, P50.0006).
Fig. 4. Time course of counterregulatory hormones [cortisol (A) and growth hormone (B)] during mFSIGT (s) and rFSIGT (r). hGH, human growth hormone.
experiment the value of SIgiven by the minimal model is equivalent to that obtained with the widely accepted ‘‘gold standard’’ glucose clamp experiment (10). How-ever, 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 tolbu-tamide or insulin makes it very hard to obtain also a clear view of the pancreatic function, often as impor-tant 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 SIis equivalent in both tests, although it is worth noting that the CV of the estimate, i.e., an index of the precision of the param-eter, 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 SIin normal men when estimated with the regular and the tolbutamide-modified FSIGT, although a careful observation of the single compari-sons shows a weak and nonsignificant regression (r5 0.55, P 5 0.1). Finegood et al. (16) analyzed the possibility of replacing tolbutamide with a short insulin infusion and found that in normal volunteers SIwas 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 SIwas observed with insulin. Prigeon et al. (24) found a consistent decrease of SIwith 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 SIwith the two tests despite a wide change in circulating insulin concentration. The reason accounting for this different finding is not clearly understood. Nonetheless, a pos-sible 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 experi-ment to maintain the insulin concentration in the
physiological range. Furthermore, this low-rate insulin infusion was adopted to try to avoid a deep hypoglyce-mic 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 con-firm 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 6 1.0%) was similar to that of our study, whereas that from the regular test was much higher (22.269.0%). Quon et al. (25) used the standard 30 samples, whereas we adopted a re-duced schedule with only 19 samples, which lies be-tween 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 measure-ment noise, contribute to the final covariance matrix and thus to the final accuracy of the estimates.
At variance with SI, a statistically significant differ-ence was found concerning the SG. Parameter SGfrom 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 SGquantifies the actions of glu-cose per se, independent of increased insulin, to normal-ize glucose concentration through actions on glucose production and utilization (3). The importance of this variable on the evaluation of the overall glucose homeo-stasis 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 com-ments. First, this study provided further evidence about an association between SGand insulin concentra-tion, as already suggested by other investigations in nondiabetic subjects (19, 29). Finegood and Tzur (18), from the conclusions of a study performed in streptozoto-cin-treated dogs, pointed out that the minimal model overestimates SGin normal dogs compared with that obtained in animals pharmacologically lacking insulin. It is interesting to notice that SIremains unchanged in
their streptozotocin-treated dogs despite the difference in insulin secretion (18, 32), as in our study. Basu et al. (5) reported that SGis 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 concen-tration and an unchanged insulin sensitivity.
In addition, Finegood and Tzur (18) speculated that the lower SGin 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 SGis 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 SGand insulin. Thomaseth and Cobelli (30) showed that the estimation of SGin 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 result-ing SG value is very sensitive to dynamic changes in concentration occurring in these periods. Parameter SG therefore does not depend only on the prevailing insu-lin 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 estima-tion of SGin 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 exog-enously 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 param-eter SGcorrectly 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 stan-dard and tolbutamide-modified tests (3, 17, 34). An-other 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 produc-tion (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 produc-tion 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 regard-less 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 SGbetween the two competing protocols was found. This is not surprising when insulin-modified and tolbutamide-insulin-modified FSIGT are com-pared (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 tolbuta-mide (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 SGwith the regular test exists also in the studies of Quon et al. (25) (0.0244 vs. 0.0253 min21) and Beard et al. (6) (0.016 vs. 0.017). None of these studies reported the CV of SGestimates, 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 SGfrom 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, SGand SIcan 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 con-firmed that SIis 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 SGfrom 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 SGis 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 ac-counts for the endogenous insulin action for the whole length of the experiment, therefore offering the possibil-ity of direct inferences on theb-cell activity.
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 statisti-cal issues of the minimal model. Gianluigi Fenu and Margherita Porcu (University of Sassari) were invaluable in running the measure-ment assays. The commeasure-ments of Richard Watanabe (University of Michigan) are also acknowledged.
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.
REFERENCES
1. Ader, M., and R. N. Bergman. Peripheral effects of insulin domi-nate suppression of fasting hepatic glucose production. Am. J. Physiol. 258 (Endocrinol. Metab. 21): E1020–E1032, 1990. 2. Ader, M., T.-C. Ni, and R. N. Bergman. Glucose effectiveness
assessed under dynamic and steady state conditions. Comparabil-ity of uptake versus production components. J. Clin. Invest. 99: 1187–1199, 1997.
3. Ader, M., G. Pacini, Y. Yang, and R. N. Bergman. Importance of glucose per se to intravenous glucose tolerance. Comparison of the minimal-model prediction with direct measurements. Diabe-tes 34: 1092–1103, 1985.
4. Ahre´n, B., and G. Pacini. Impaired adaptation of first-phase insulin secretion in postmenopausal women with glucose intoler-ance. Am. J. Physiol. 273 (Endocrinol. Metab. 36): E701–E707, 1997.
5. Basu, A., A. Caumo, F. Bettini, A. Gelisio, A. Alzaid, C.
Cobelli, and R. Rizza. Impaired basal glucose effectiveness in
NIDDM. Diabetes 46: 421–432, 1997.
6. Beard, J. C., R. N. Bergman, W. K. Ward, and D. Porte, Jr. The insulin sensitivity index in nondiabetic man. Correlation between clamp-derived and IVGTT-derived values. Diabetes 35: 362–369, 1986.
7. Bergman, R. N. Toward physiological understanding of glucose tolerance. Minimal model approach. Diabetes 38: 1512–1527, 1989.
8. 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.
9. Bergman, R. N., L. S. Phillips, and C. Cobelli. Physiologic evaluation of factors controlling glucose tolerance in man. J. Clin. Invest. 68: 1456–1467, 1981.
10. Bergman, R. N., R. Prager, A. Vølund, 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.
11. Best, J., S. E. Kahn, M. Ader, R. M. Watanabe, T.-C. Ni, and
R. N. Bergman. Role of glucose effectiveness in the
determina-tion of glucose tolerance. Diabetes Care 19: 1018–1030, 1996. 12. Bland, J. M., and D. G. Altman. Statistical methods for
assessing agreement between two methods of clinical measure-ments. Lancet i: 307–310, 1986.
13. Caumo, A., and C. Cobelli. Hepatic glucose production during the labeled IVGTT: estimation by deconvolution with a new minimal model. Am. J. Physiol. 264 (Endocrinol. Metab. 27): E829–E841, 1993.
14. Cobelli, C., G. Pacini, G. Toffolo, and L. Sacca` . Estimation of
insulin sensitivity and glucose clearance from minimal model: new insights from labeled IVGTT. Am. J. Physiol. 250 (Endocri-nol. Metab. 13): E591–E598, 1986.
15. Cobelli, C., and K. Thomaseth. The minimal model of glucose disappearance: optimal input studies. Math. Biosci. 83: 127–155, 1987.
16. Finegood, D. T., I. M. Hramiak, and J. Dupre. A modified protocol for estimation of insulin sensitivity with the minimal model of glucose kinetics in patients with insulin-dependent diabetes. J. Clin. Endocrinol. Metab. 70: 1538–1549, 1990. 17. Finegood, D. T., G. Pacini, and R. N. Bergman. The insulin
sensitivity index: correlation in dogs between values determined from the intravenous glucose tolerance test and the euglycemic glucose clamp. Diabetes 33: 362–368, 1984.
18. Finegood, D. T., and D. Tzur. Reduced glucose effectiveness associated with reduced insulin release: an artifact of the mini-mal-model method. Am. J. Physiol. 271 (Endocrinol. Metab. 34): E485–E495, 1996.
19. Kahn, S. E., L. J. Klaff, M. W. Schwartz, J. C. Beard, R. N.
Bergman, and J. Taborsky, Jr. Treatment with a somatostatin
analog decreases pancreatic B-cell and whole body sensitivity to glucose. J. Clin. Endocrinol. Metab. 71: 994–1002, 1990. 20. Kautzky-Willer, A., G. Pacini, U. Barnas, B. Ludvik, C.
Streli, H. Graf, and R. Prager. Intravenous calcitriol
normal-izes insulin sensitivity in uremic patients. Kidney Int. 47: 200–206, 1995.
21. Mari, A. Assessment of insulin sensitivity with minimal model: role of model assumptions. Am. J. Physiol. 272 (Endocrinol. Metab. 35): E925–E934, 1997.
22. Ni, T.-C., M. Ader, and R. N. Bergman. Reassessment of glucose effectiveness and insulin sensitivity from minimal model analysis: a theoretical evaluation of the single-compartment glucose distribution assumption. Diabetes 46: 1813–1821, 1997. 23. Pacini, G., and R. N. Bergman. MINMOD: a computer pro-gram to calculate insulin sensitivity and pancreatic responsivity from the frequently sampled intravenous glucose tolerance test. Comput. Methods Programs Biomed. 23: 113–122, 1986. 24. Prigeon, R. L., M. E. Røder, D. Porte, Jr., and S. E. Kahn.
sensitiv-ity by the minimal model technique. Evidence for saturable insulin transport in humans. J. Clin. Invest. 97: 501–507, 1996. 25. Quon, M. J., C. Cochran, S. I. Taylor, and R. C. Eastman.
Direct comparison of standard and insulin modified protocols for minimal model estimation of insulin sensitivity in normal sub-jects. Diabetes Res. 25: 139–149, 1994.
26. Saad, M. F., G. M. Steil, W. W. Kades, M. F. Ayad, W. A.
Elsewafy, R. Boyadjian, S. D. Jinagouda, and R. N. Berg-man. Differences between the tolbutamide-boosted and the
insulin-modified minimal model protocols. Diabetes 46: 1167– 1171, 1997.
27. Steil, G. M., A. Vølund, S. E. Kahn, and R. N. Bergman. Reduced sample number for calculation of insulin sensitivity and glucose effectiveness from the minimal model. Diabetes 42: 250–256, 1993.
28. So¨ derstro¨ m, T., and P. Stoica. System Identification. New
York: Prentice Hall, 1989.
29. Taniguchi, A., Y. Nakai, M. Fukushima, H. Imura, H.
Kawamura, and I. Nagata. Insulin sensitivity, insulin
secre-tion, and glucose effectiveness in subjects with impaired glucose tolerance: a minimal model analysis. Metab. Clin. Exp. 43: 714–718, 1994.
30. Thomaseth, K., and C. Cobelli. Parameter information con-tent during model identification experiments. In: Modelling and Control in Biomedical Systems, edited by D. A. Linkens and E. R. Carson. Oxford: Pergamon, 1997, p. 107–112.
31. Thomaseth, K., and G. Pacini. Effects of measured glucose and insulin concentration on the accuracy of SI and SG. In: The
Minimal Model Approach and Determinants of Glucose Toler-ance, edited by R. N. Bergman and J. C. Lovejoy. Baton Rouge, LA: Louisiana State University Press, 1997, p. 187–201. 32. Tobin, B. L., and D. T. Finegood. Reduced insulin secretion by
repeated low doses of STZ impairs glucose effectiveness but does not induce insulin resistance in dogs. Diabetes 42: 474–483, 1993.
33. Welch, S., S. S. P. Gebhart, R. N. Bergman, and L. S.
Phillips. Minimal model analysis of intravenous glucose
toler-ance test-derived insulin sensitivity in diabetic subjects. J. Clin. Endocrinol. Metab. 71: 1508–1518, 1990.
34. Yang, Y. J., J. H. Youn, and R. N. Bergman. Modified protocols improve insulin sensitivity estimation using the minimal model. Am. J. Physiol. 253 (Endocrinol. Metab. 16): E595–E602, 1987.
