# An empirical index of insulin sensitivity from short IVGTT: validation against the minimal model and glucose clamp indices in patients with different clinical characteristics

- 1.2k Downloads
- 37 Citations

## Abstract

### Aims/hypothesis

Minimal model analysis for insulin sensitivity has been validated against the glucose clamp and is an accepted method for estimating insulin sensitivity from IVGTT. However minimal model analysis requires a 3 h test and relevant expertise to run the mathematical model. The aim of this study was to suggest a simple predictor of minimal model analysis index using only 1 h IVGTT.

### Methods

We studied participants with different clinical characteristics who underwent 3 h regular (*n* = 336) or insulin-modified (*n* = 160) IVGTT, or 1 h IVGTT and euglycaemic–hyperinsulinaemic clamp (*n* = 247). Measures of insulin sensitivity were insulin sensitivity index estimated by minimal model analysis (S_{I}) and the mean glucose infusion rate (clamp) (*M*). A calculated S_{I} (CS_{I}) predictor, \({\text{CS}}_{{\text{I}}} = {\text{ $ \alpha $ }} \times {K_{\text G} } \mathord{\left/ {\vphantom {{K_{G} } {{\left( {{\Delta {\text{AUC}}_{{{\text{INS}}}} } \mathord{\left/ {\vphantom {{\Delta {\text{AUC}}_{{{\text{INS}}}} } T}} \right. \kern-\nulldelimiterspace} T} \right)}}}} \right. \kern-\nulldelimiterspace} {{\left( {{\Delta {\text{AUC}}_{{{\text{INS}}}} } \mathord{\left/ {\vphantom {{\Delta {\text{AUC}}_{{{\text{INS}}}} } T}} \right. \kern-\nulldelimiterspace} T} \right)}}\), was suggested, based on the calculation of the rate of glucose disappearance *K* _{G} and the suprabasal AUC of insulin concentration ΔAUC_{INS} over *T* = 40 min. For all the participants, *α* was assumed equal to the regression line slope between *K* _{G}/(ΔAUC_{INS}/*T*) and S_{I} in control participants.

### Results

CS_{I} and S_{I} showed high correlation (*R* ^{2} = 0.68–0.96) and regression line slopes of approximately one in the majority of groups. CS_{I} tended to overestimate S_{I} in type 2 diabetic participants, but results were more reliable when CS_{I} was computed with insulin-modified rather than regular IVGTT. CS_{I} showed behaviours similar to S_{I} as regards relationships with BMI, acute insulin response and sex. CS_{I} showed good correlation with *M* (*R* ^{2} = 0.82).

### Conclusions/interpretation

A short test can achieve a good approximation of minimal model analysis and clamp insulin sensitivity. The importance of a method such as CS_{I} is that it allows analysis of IVGTT datasets with samples limited to 1 h.

## Keywords

Glucose tolerance Insulin action Insulin resistance One hour intravenous glucose tolerance test## Abbreviations

- AIR
_{G} Acute insulin response to glucose

- AUC
_{INS} AUC of insulin concentration

- CS
_{I} Calculated S

_{I}- IGM
_{CL} Impaired glucose metabolism (participants subjected to clamp)

- IGT
Impaired glucose tolerance

- INSMOD
Insulin-modified 3 h frequently sampled IVGTT

*M*Mean glucose infusion rate (clamp)

- NGT
Normal glucose tolerance

- NGT
_{CL} NGT participants subjected to clamp

- S
_{I} Insulin sensitivity index estimated by minimal model analysis

## Introduction

Insulin sensitivity is paramount for characterising metabolic states. The glucose clamp is the experimental procedure yielding the gold standard measurement of this variable. Nonetheless, minimal model analysis of IVGTT data, i.e. insulin sensitivity index estimated by minimal model analysis (S_{I}), is also widely used to assess insulin sensitivity [1, 2]. However, despite some efforts to develop automatic procedures and lower the need for user intervention [3], the minimal model procedure requires sophisticated computer programming and relevant expertise to run the mathematical model properly. Furthermore, reliable results based on minimal model require many plasma insulin and glucose samples over a time interval of at least 3 h after glucose injection.

The aims of this study were: (1) to propose an index able to predict minimal model insulin sensitivity values based on direct calculations from easily measurable simple variables and not requiring complex mathematical models, while using IVGTT data limited to 1 h or less, as often happened before introduction of the minimal model [4]; and (2) to validate the new index against minimal model S_{I} and the glucose clamp, by assessing its performance in several groups of participants with different degree of glucose tolerance and specific clinical characteristics.

## Methods

Participants analysed in this study are presented in the following sections. All participants gave their consent to the investigations, which were approved by the Local Ethics Committees.

### Participants, 3 h regular IVGTT

Main characteristics and insulin sensitivity in study groups

Study groups per protocol | Participant characteristics | Insulin sensitivity | ||||||
---|---|---|---|---|---|---|---|---|

| Age (years) | BMI (kg/m | | S | CS | | | |

3 h regular IVGTT | ||||||||

Control | 114 | 34.4 ± 1.6 | 23.6 ± 0.5 | 4.6 ± 0.05 | 5.55 ± 0.25 | 5.81 ± 0.28 | 0.22 | – |

IGT | 128 | 42.8 ± 1.4 | 27.9 ± 0.6 | 4.7 ± 0.09 | 2.58 ± 0.17 | 2.68 ± 0.20 | 0.49 | – |

Type 2 diabetes | 22 | 41.2 ± 4.8 | 23.8 ± 0.5 | 6.3 ± 0.20 | 2.31 ± 0.29 | 4.68 ± 0.69 | 0.0013 | – |

Renal disease | 52 | 44.3 ± 2.9 | 25.7 ± 1.0 | 5.0 ± 0.08 | 4.71 ± 0.32 | 4.34 ± 0.33 | 0.20 | – |

Hyperparathyroidism, pre | 9 | 66.0 ± 3.0 | 25.1 ± 2.5 | 5.2 ± 0.22 | 3.18 ± 0.53 | 3.87 ± 0.58 | 0.26 | – |

Hyperparathyroidism, post | 9 | 66.0 ± 3.0 | 24.4 ± 2.3 | 5.2 ± 0.26 | 5.34 ± 0.67 | 6.66 ± 0.96 | 0.043 | – |

Former type 1 diabetes | 11 | 40.0 ± 3.0 | 26.6 ± 2.0 | 5.2 ± 0.17 | 3.39 ± 0.63 | 2.70 ± 0.49 | 0.11 | – |

3 h INSMOD | ||||||||

Type 2 diabetes INSMOD | 160 | 51.2 ± 1.4 | 29.7 ± 0.4 | 10.3 ± 0.29 | 1.23 ± 0.08 | 1.32 ± 0.08 | 0.05 | – |

1 h IVGTT and clamp | ||||||||

NGT | 171 | 41.3 ± 1.0 | 27.4 ± 0.4 | 4.9 ± 0.05 | – | 5.87 ± 0.25 | – | 7.02 ± 0.23 |

IGM | 55 | 46.1 ± 1.6 | 29.1 ± 0.7 | 5.4 ± 0.08 | – | 4.16 ± 0.39 | – | 6.08 ± 0.32 |

Type 2 diabetes clamp | 21 | 52.4 ± 3.0 | 35.9 ± 3.0 | 6.7 ± 0.46 | – | 3.63 ± 0.54 | – | 4.22 ± 0.54 |

### Type 2 diabetic participants, 3 h insulin-modified IVGTT

We analysed from previous studies [10, 11, 12] 160 type 2 diabetic participants who had undergone an insulin-modified, 3 h, frequently sampled IVGTT (INSMOD) with exogenous intravenous infusion of insulin (0.03 or 0.05 U/kg) at 20 min [9] (Table 1). Some of these participants were under pharmacological treatment, with gemfibrozil [10], sulfonylurea or biguanide preparations [11].

### Participants, 1 h IVGTT and clamp

We analysed 247 participants from the Botnia study [13], the EUGENE2 study [14] and another study [15]. All these participants underwent IVGTT (for at least 1 h) and 2 h euglycaemic–hyperinsulinaemic glucose clamp. Among participants undergoing the clamp, 171 had NGT (NGT_{CL}), 55 had impaired glucose metabolism (IGM_{CL}), i.e. either impaired fasting glucose or IGT or both, and 21 had type 2 diabetes (Table 1). Seven participants in the type 2 diabetes clamp group had severe obesity and subsequently underwent bariatric surgery (here we only report data before surgery).

### Calculation of insulin sensitivity

_{I}). In the participants with the clamp, insulin sensitivity was calculated as the mean glucose infusion rate (

*M*) over the last 40 min of the test. For all participants, we calculated a surrogate index of S

_{I}, called calculated S

_{I}(CS

_{I}), with an expression similar to that originally proposed by Galvin et al. [16]. Justification of the difference between our approach and that of Galvin et al. [16] is discussed later. For the participants with regular IVGTT the expression for CS

_{I}was:

*α*is a constant (scaling factor),

*K*

_{G}is the rate of glucose disappearance (slope of log glucose), ΔAUC

_{INS}is the AUC of insulin concentration above basal value and

*T*is the time interval between 10 and 50 min (=40 min) when

*K*

_{G}and ΔAUC

_{INS}are computed. Initial time interval was not zero to avoid possible confounding effects due to mixing. The

*α*constant was assumed equal to the slope of the regression line between the factor

*K*

_{G}/(ΔAUC

_{INS}/

*T*) and S

_{I}in the control group, i.e.

*α*= 0.276. This value was used to calculate CS

_{I}in all the participants analysed in this study, including those undergoing INSMOD rather than regular IVGTT or clamp.

_{I}was:

*K*

_{G1}and ΔAUC

_{INS1}were computed between 10 and 25 min, whereas

*K*

_{G2}and ΔAUC

_{INS2}were computed between 25 and 50 min.

### Statistical analysis

Relationships between S_{I} and CS_{I} were investigated by linear regression analysis with no intercept. Difference between the mean value of S_{I} and CS_{I} in each of the different groups of participants was assessed through the paired *t* test. The same test was used to assess difference in insulin sensitivity in the hyperparathyroidism group before and after surgery. Difference in the mean value of each index among different groups was assessed through ANOVA. Similarly, we analysed the relationship between CS_{I} and *M* by linear regression and used ANOVA to assess differences of both indices among different groups. Relationships between some variables were also investigated by accounting for measurement errors for both variables in the regression [18]. Normality of distributions was assessed before testing for possible differences in insulin sensitivity indices. In case of non-normal distributions, tests were performed on logarithmically transformed values (this applied to the majority of cases, except hyperparathyroidism and former type 1 diabetes groups). *p* < 0.05 was considered statistically significant. Values are reported as mean ± SE.

## Results

### Minimal model and CS_{I} analyses of regular IVGTT

_{I}and CS

_{I}was found in the following groups: control (

*R*

^{2}= 0.89,

*p*< 0.0001, slope = 1.00, 95% CI 0.93–1.07), IGT (

*R*

^{2}= 0.79,

*p*< 0.0001, slope = 0.97, 95% CI 0.89–1.06), renal disease (

*R*

^{2}= 0.85,

*p*< 0.0001, slope = 0.86, 95% CI 0.76-0.97), former type 1 diabetes patients (after kidney pancreas transplantation) (

*R*

^{2}= 0.89,

*p*< 0.0001, slope = 0.75, 95% CI 0.57-0.93) and hyperparathyroidism (

*R*

^{2}= 0.83,

*p*< 0.0001, slope = 1.09, 95% CI 0.68-1.49 before surgery;

*R*

^{2}= 0.96,

*p*< 0.0001, slope = 1.24, 95% CI 1.02–1.46 after surgery) (Fig. 1). In the type 2 diabetes group the correlation between S

_{I}and CS

_{I}, though weaker than in the other groups, was still significant (

*R*

^{2}= 0.68,

*p*< 0.0001), despite the fact that CS

_{I}overestimated S

_{I}(slope = 1.75, 95% CI 1.21-2.29). When the participants were considered all together, the correlation remained highly significant (

*R*

^{2}= 0.84,

*p*< 0.0001, slope = 0.99, 95% CI 0.94-1.04).

_{I}and CS

_{I}(Table 1) were not different except for the type 2 diabetes and hyperparathyroidism after surgery groups, which showed a slight difference as shown by

*p*values (Table 1). Bland–Altman plot for all the participants (Fig. 2a) proved substantial equivalence between the two measurements. The absolute difference between S

_{I}and CS

_{I}in relation to the AUC of insulin in the time interval

*T*(Fig. 2b) showed that only at low insulin levels did S

_{I}and CS

_{I}tend to diverge. ANOVA showed that S

_{I}was different between control and all the other groups (

*p*< 0.03) except for the hyperparathyroidism after surgery group. Significant differences were also found in the renal disease vs IGT and type 2 diabetes groups (

*p*< 0.0001), and in the hyperparathyroidism after surgery vs IGT and type 2 diabetes groups (

*p*< 0.0006). Similar results were found for CS

_{I}(

*p*value range:

*p*< 0.0001 to

*p*= 0.0313), except for comparisons of type 2 diabetes with the other groups. It is worth noting the difference in insulin sensitivity between hyperparathyroidism before and after surgery: as expected, S

_{I}was increased after surgery (

*p*= 0.021) (Table 1) and similar results were found with CS

_{I}(

*p*= 0.008).

_{G}) (mean insulin value above basal in the 0 to 8 min period of the IVGTT). Both S

_{I}and CS

_{I}showed with AIR

_{G}a weak but significant nonlinear inverse relationship, which was better appreciated after performing linear regression analysis on logarithmically transformed values (

*R*

^{2}= 0.19,

*p*= 0.0002 for S

_{I};

*R*

^{2}= 0.09,

*p*= 0.0009 for CS

_{I}) (Fig. 3). According to ordinary least-squares regression analysis, the relationship was not strictly hyperbolic, but it was similar with both indices. However, when the analysis was carried out through a regression method accounting for measurement errors in both variables, the relationship turned out to be hyperbolic, as the 95% CI for the slope included −1 for S

_{I}(slope: −1.33, 95% CI −2.08, −0.59) and CS

_{I}(slope: −1.25, 95% CI −2.15, −0.35).

In all the participants, we also analysed insulin sensitivity with respect to BMI. As expected, S_{I} showed an inverse relationship with BMI; in fact, after log-log transformation, a weak but significant linear regression was observed (*R* ^{2} = 0.19, *p* < 0.0001), although the relationship was not hyperbolic (according to both regression methods). Similar results were found for CS_{I} (*R* ^{2} = 0.18, *p* < 0.0001). Participants were then classified as lean or overweight according to their BMI (threshold 25 kg/m^{2}). Both S_{I} and CS_{I} showed significant differences in insulin sensitivity between the two groups (S_{I} = 4.65 ± 0.32 × 10^{−4} min^{−1} [μU/ml]^{−1} lean; 3.09 ± 0.28 overweight; *p *= 0.0003; CS_{I} = 5.03 ± 0.38 × 10^{−4} min^{−1} [μU/ml]^{−1} lean; 2.99 ± 0.28 overweight; *p* < 0.0001; to convert values for S_{I} and CS_{I} to SI units (× 10^{−4} min^{−1} [pmol/l]^{−1}), multiply by 0.1667).

We also studied possible differences in insulin sensitivity due to sex: neither S_{I} nor CS_{I} were different: S_{I} = 3.87 ± 0.17 × 10^{−4} min^{−1} (μU/ml)^{−1} men; 4.09 ± 0.28 women; *p* > 0.4; CS_{I} = 4.11 ± 0.20 × 10^{−4} min^{−1} (μU/ml)^{−1} men; 4.77 ± 0.33 women; *p* > 0.07.

### Minimal model and CS_{I} analyses of insulin-modified IVGTT

_{I}and CS

_{I}showed strong significant correlation, with the slope of the regression line virtually equal to 1 (

*R*

^{2}= 0.85,

*p*< 0.0001, slope = 0.96, 95% CI 0.89-1.02) (Fig. 4a). Bland–Altman plot showed that only a few samples were outside the limits for equivalence (Fig. 4b). The paired

*t*test showed a borderline

*p*value (Table 1). We also classified the participants as obese or non-obese. Since BMI was quite high on average (BMI = 29.7 ± 0.4 kg/m

^{2}), we assumed 27.5 as threshold between the two groups. As expected, S

_{I}was higher in the non-obese group, with similar results found for CS

_{I}(S

_{I}= 1.77 ± 0.18 × 10

^{−4}min

^{−1}[μU/ml]

^{−1}non-obese; 0.94 ± 0.08 obese;

*p*< 0.0001; CS

_{I}= 1.73 ± 0.17 × 10

^{−4}min

^{−1}[μU/ml]

^{−1}non-obese; 1.10 ± 0.08 obese;

*p*= 0.0002). Neither S

_{I}nor CS

_{I}were different between men and women (S

_{I}= 1.19 ± 0.11 × 10

^{−4}min

^{−1}[μU/ml]

^{−1}men; 1.04 ± 0.14 women;

*p*> 0.5; CS

_{I}= 1.30 ± 0.10 × 10

^{−4}min

^{−1}[μU/ml]

^{−1}men; 1.03 ± 0.11 women;

*p*> 0.2).

### Glucose clamp and CS_{I} analyses

*M*and CS

_{I}showed good correlation (

*R*

^{2}= 0.82,

*p*< 0.0001) (Fig. 5a). When analysing the participants divided according to glucose tolerance, correlation remained significant (NGT

_{CL}:

*R*

^{2}= 0.84,

*p*< 0.0001; IGM

_{CL}:

*R*

^{2}= 0.74,

*p*< 0.0001; type 2 diabetes clamp:

*R*

^{2}= 0.81,

*p*< 0.0001) (Fig. 5b).

*M*(Table 1) was different in each group (

*p*< 0.03). Similar differences (

*p*< 0.002) were found with CS

_{I}(Table 1) except in the IGM

_{CL}and type 2 diabetes clamp groups, where statistical significance was not reached.

*M*was higher in lean than in overweight participants (8.72 ± 0.33 and 5.58 ± 0.18 mg min

^{−1}kg

^{−1},

*p*< 0.0001; to convert values for

*M*to SI units [mmol min

^{−1}kg

^{−1}], multiply by 0.005551), as was the case for CS

_{I}(7.56 ± 0.38 and 4.26 ± 0.20 × 10

^{−4}min

^{−1}[μU/ml]

^{−1},

*p*< 0.0001). As regards possible differences related to sex, neither

*M*nor CS

_{I}showed any difference (

*p*> 0.07). In a subgroup of participants, we corrected

*M*for the steady-state insulin level, but results did not change significantly (not shown). It is worth noting that in the small group of type 2 diabetes clamp participants with severe obesity, 3 h IVGTT data were available, thus S

_{I}was computed. As expected, we found agreement between S

_{I}and

*M*, with regression coefficient value (

*R*

^{2}= 0.63,

*p*= 0.018) similar to those observed between CS

_{I}and

*M*, as reported above. In this specific subgroup, CS

_{I}showed a very strong relationship with

*M*(

*R*

^{2}= 0.95,

*p*< 0.0001).

## Discussion

The simple index of insulin sensitivity introduced and validated here (CS_{I}) was revealed to be a good surrogate of that from the well accepted and widely used minimal model (S_{I}). To our knowledge, only the study of Galvin et al. [16] suggested a simple index for the assessment of insulin sensitivity from IVGTT limited to 1 h. CS_{I} reflects similar concepts, i.e. the quantification of glucose disappearance rate per changes of insulin, but it overcomes some limitations of that study. In fact, Galvin et al. [16] studied the correlation of their index with S_{I} (and also with insulin sensitivity by the glucose clamp), but they did not seek to obtain indices really comparable, their units being different. In addition, they did not present any strategy to correct their index and make it comparable with S_{I} derived from insulin-modified IVGTT. In contrast, CS_{I} includes a time (*T*) factor (see Eq. 1) yielding the same units as S_{I} and was adapted to be used also with the insulin-modified test (Eq. 2). Furthermore, in Galvin et al. [16], the slopes of the regression lines were far from one and different in every group. Moreover, only small groups of participants were studied (with no diabetic patients) and it was not shown whether their index has abilities, similar to S_{I}, to discriminate between groups or clinical conditions with different degrees of insulin resistance. The Galvin index [16] was then used by Anderson et al. [19], but with essentially the same limitations, which probably prevented its diffusion. Prior to this study, we used calculations similar to those for CS_{I} to compute a sensitivity index in mice [20], although not with exactly the same formula and without comparison with the clamp.

After correcting our index with a factor derived from regression analysis of the control group (quite a large group, with a wide range of insulin sensitivity), several other groups of participants with different degrees of glucose tolerance and heterogeneous clinical characteristics were analysed. In the majority of groups, we found a good correlation between S_{I} and CS_{I}, and also CS_{I} values similar to S_{I}, as mirrored both by the slope of the regression lines, which were not (or only slightly) different from 1 (see 95% CI), and by the not significantly different mean values.

The correction factor *α* included in the CS_{I} expression was introduced to scale the values of our new index to those calculated with the minimal model. Thus, the interpretation of results obtained by CS_{I} will be facilitated, given the previous wide experience with S_{I}. This correction factor does not have a specific physiological meaning, similarly to the variables included in other empirical methods for the calculation of insulin sensitivity, such as HOMA-insulin resistance (IR) [21] or Stumvoll’s index [22]. The relevant aspect of the scaling operation was that the same value of the correction factor (*α* = 0.276) was proved to be appropriate in every group of participants (except type 2 diabetes, as discussed below). In fact, all the results were obtained by using the same correction factor in each group that underwent the regular IVGTT. The same *α* value was also proved correct in those groups of participants who underwent INSMOD (type 2 diabetes INSMOD) or the clamp (NGT_{CL}, IGM_{CL}, type 2 diabetes clamp).

The comparison between S_{I} and CS_{I} was not completely satisfactory in type 2 diabetes (regular IVGTT). The fact that in situations of high insulin resistance CS_{I} tended to overestimate S_{I} is an important issue and should be discussed within the frame of basic questions, such as: how reliable is a low S_{I}? This has been much debated among investigators using IVGTT [23, 24]. Thus, we acknowledge that, in situations of low insulin sensitivity, CS_{I} may suffer from inaccuracy, but S_{I} may also exhibit inaccuracy in those conditions [24, 25]. As regards our data, insulin levels in the type 2 diabetes group were usually low, but tended to remain higher than the fasting value: i.e. insulin levels did not return to the basal value during the whole 3 h IVGTT time interval. Thus, in the minimal model approach, the analysis of the last part of the IVGTT tended to decrease the S_{I} value. Since the last part of the complete test is not accounted for by CS_{I}, some discrepancy between the two indices may occur. On the other hand, the finding that in the majority of groups CS_{I} behaves similarly to S_{I} suggests that the information provided by the last part of the IVGTT is usually consistent with that provided by the first part, where CS_{I} is calculated.

Due to the unsatisfactory results in the type 2 diabetes group, we adapted the CS_{I} expression to make it usable with data from the insulin-modified IVGTT as recommended in conditions of poor insulin response [26]. We analysed a large group of type 2 diabetic patients subjected to INSMOD where, as expected, CS_{I} and S_{I} showed low values of insulin sensitivity. They also exhibited a strong correlation with regression slope almost identical with 1, confirming that when dealing with low insulin sensitivity it is recommended to carry out the insulin-modified test even with the short 1 h protocol. We also analysed 208 insulin-modified IVGTT from 146 women with a history of gestational diabetes, who were non-diabetic at the time of examination [27]. We found strong relationship between S_{I} and CS_{I}, with *R* ^{2} = 0.93 and slope of the regression almost equal to 1 (not shown). However, in non-diabetic participants the regular IVGTT has proven adequate for calculating CS_{I} with sufficient accuracy; hence the insulin-modified protocol is not strictly necessary in these participants. It should be noted that other possible expressions were tested for the calculation of CS_{I} with the insulin-modified IVGTT, such as the average between \({{\left( {{\text{ $ \alpha $ }} \times K_{{{\text{G1}}}} } \right)}} \mathord{\left/ {\vphantom {{{\left( {{\text{ $ \alpha $ }} \times K_{{{\text{G1}}}} } \right)}} {{\left( {{\Delta {\text{AUC}}_{{{\text{INS1}}}} } \mathord{\left/ {\vphantom {{\Delta {\text{AUC}}_{{{\text{INS1}}}} } T}} \right. \kern-\nulldelimiterspace} T1} \right)}}}} \right. \kern-\nulldelimiterspace} {{\left( {{\Delta {\text{AUC}}_{{{\text{INS1}}}} } \mathord{\left/ {\vphantom {{\Delta {\text{AUC}}_{{{\text{INS1}}}} } T}} \right. \kern-\nulldelimiterspace} T1} \right)}}\) and \({{\left( {{\text{ $ \alpha $ }} \times K_{{{\text{G2}}}} } \right)}} \mathord{\left/ {\vphantom {{{\left( {{\text{ $ \alpha $ }} \times K_{{{\text{G2}}}} } \right)}} {{\left( {{\Delta {\text{AUC}}_{{{\text{INS2}}}} } \mathord{\left/ {\vphantom {{\Delta {\text{AUC}}_{{{\text{INS2}}}} } T}} \right. \kern-\nulldelimiterspace} T2} \right)}}}} \right. \kern-\nulldelimiterspace} {{\left( {{\Delta {\text{AUC}}_{{{\text{INS2}}}} } \mathord{\left/ {\vphantom {{\Delta {\text{AUC}}_{{{\text{INS2}}}} } T}} \right. \kern-\nulldelimiterspace} T2} \right)}}\), with *T*1 = 15 and *T*2 = 25 min, and also the second expression alone (i.e. only post-injection information). However, the best results in diabetic and non-diabetic participants were obtained by combining pre- and post-injection information as in Equation (2).

CS_{I} was able to reproduce known findings related to insulin sensitivity. The existence of nonlinear inverse (hyperbolic) relationship between insulin sensitivity and insulin release was postulated some years ago [28] and several subsequent studies [29] have confirmed this finding, although it has recently been suggested that the hyperbola may not be evident in some groups of participants [30, 31, 32]. Our control group exhibited a weak, but still significant inverse relationship between insulin sensitivity and AIR_{G}. According to traditional regression analysis, the relationship was not strictly hyperbolic, but when a more refined regression model was used the hyperbolic relationship emerged. It is worth noting that S_{I} and CS_{I} provided similar results in both cases. Insulin sensitivity was higher in lean than in overweight or obese participants with both indices, which also showed a nonlinear inverse relationship (though weak) with BMI, in agreement with previous studies [33]. As regards the effect of sex on insulin sensitivity, results from S_{I} and CS_{I} were again similar and in agreement with previous studies [34].

Even though a good agreement was found between S_{I} and CS_{I}, we aimed to validate CS_{I} against the measurement obtained from the glucose clamp. CS_{I} exhibited a good degree of correlation with *M* and a similar ability to discriminate between participants with different glucose tolerance, as well as between lean and overweight participants. This agreement with the clamp further strengthened the ability of CS_{I} to describe insulin sensitivity in different metabolic conditions.

In this study we included three groups of type 2 diabetic patients. As regards the type 2 diabetes and type 2 diabetes INSMOD groups, it must be noted (Table 1) that both S_{I} and CS_{I} were higher in the former than the latter (*p* < 0.0001 by ANOVA). This possible inconsistency warrants further comment. First, it cannot be excluded that this difference in insulin sensitivity was real, since type 2 diabetic populations may be significantly heterogeneous [35]. On the other hand, as already pointed out, S_{I} may be inaccurate in participants with low insulin values, and CS_{I} exhibits similar limitations in those conditions. Another confounding factor may be the fact that the type 2 diabetes and type 2 diabetes INSMOD groups were studied in different laboratories, probably using different insulin assays: this remains a problem known to be a possible source of error [36]. In any case, we believe that the lower insulin sensitivity in the type 2 diabetes INSMOD than in the type 2 diabetes group may not be an artefact: in fact, HOMA-IR was also clearly higher in the former (7.85 vs 3.47 [non-dimensional], *p* < 0.007), possibly also due the much higher BMI (Table 1). Similar comments hold for the significant difference in CS_{I} values (*p* < 0.0001) between IGT and IGM_{CL}.

In conclusion, although the minimal model analysis remains the reference method to assess insulin sensitivity from the 3 h IVGTT, the proposed simple, empirical index CS_{I} generally proved to be a reliable index. In the condition of low insulin sensitivity, quite common in type 2 diabetes, analysis of insulin-modified rather than regular IVGTT data should be performed to obtain more reliable estimations, although it is known that in such conditions the assessment of insulin sensitivity becomes intrinsically more uncertain and possibly inaccurate. The great advantage of CS_{I} is that it allows assessment of insulin sensitivity from IVGTT data limited to 1 h, which cannot be analysed with the minimal model. The possibility of analysing less expensive short IVGTTs makes performance of the test easier and less of a burden for participants and investigators, allowing in larger populations the simultaneous assessment of insulin sensitivity and beta cell function (e.g. AIR_{G} variable) with a simple approach. CS_{I} also allows retrospective studies on all the short IVGTTs commonly performed before the introduction of the minimal model.

## Notes

### Acknowledgements

The Botnia study was supported by a grant from the Sigrid Juselius Foundation. The EUGENE2 study was supported by the European Community (EUGENE2, n. LSHM-CT-2004-512013). We would like to thank A. Mari (ISIB-CNR, Padova, Italy), G. Mingrone (Università Cattolica Sacro Cuore, Rome, Italy), S. Salinari (University of Rome La Sapienza, Rome, Italy) and A. Kautzky-Willer (Medical University of Vienna, Vienna, Austria) for their help and suggestions. Preliminary results were presented at the EASD 2008 Annual Meeting in Rome, Italy.

### Duality of interest

L. Groop has been a consultant for and served on advisory boards for sanofi-aventis, GSK, Novartis, Merck, Tethys Bioscience and Xoma, and received lecture fees from Lilly and Novartis. G. Pacini is currently consultant for Novo-Nordisk. All other authors declare that there is no duality of interest associated with this manuscript.

## References

- 1.Bergman RN (1989) Toward physiological understanding of glucose tolerance. Minimal model approach. Diabetes 38:1512–1527CrossRefPubMedGoogle Scholar
- 2.Saad MF, Anderson RL, Laws A et al (1994) A comparison between the minimal model and the glucose clamp in the assessment of insulin sensitivity across the spectrum of glucose tolerance. Diabetes 43:1114–1121CrossRefPubMedGoogle Scholar
- 3.Morbiducci U, Di Benedetto G, Kautzky-Willer A, Pacini G, Tura A (2007) Improved usability of the minimal model of insulin sensitivity based on an automated approach and genetic algorithms for parameter estimation. Clin Sci (Lond) 112:257–263CrossRefGoogle Scholar
- 4.Amatuzio DS, Stutzman FL, Vanderbilt MJ, Nesbitt S (1953) Interpretation of the rapid intravenous glucose tolerance test in normal individuals and in mild diabetes mellitus. J Clin Invest 32:428–435CrossRefPubMedGoogle Scholar
- 5.Viviani GL, Pacini G (1999) Reduced glucose effectiveness as a feature of glucose intolerance: evidence in elderly type-2 diabetic subjects. Aging 11:169–175PubMedGoogle Scholar
- 6.Fliser D, Pacini G, Engelleiter R et al (1998) Insulin resistance and hyperinsulinemia are already present in patients with incipient renal disease. Kidney Int 53:1343–1347CrossRefPubMedGoogle Scholar
- 7.Kautzky-Willer A, Pacini G, Niederle B, Schernthaner G, Prager R (1992) Insulin secretion, insulin sensitivity and hepatic insulin extraction in primary hyperparathyroidism before and after surgery. Clin Endocrinol (Oxf) 37:147–155CrossRefGoogle Scholar
- 8.Rigotti P, Pacini G, Baldan N et al (1998) Insulin secretion in IDDM patients who have undergone successful pancreas–kidney transplantation. Transplant Proc 30:615–617CrossRefPubMedGoogle Scholar
- 9.Pacini G, Tonolo G, Sambataro et al (1998) Insulin sensitivity and glucose effectiveness: minimal model analysis of regular and insulin-modified IVGTT. Am J Physiol Endocrinol Metab 274:E592–E599Google Scholar
- 10.Avogaro A, Miola M, Favaro A et al (2001) Gemfibrozil improves insulin sensitivity and flow-mediated vasodilatation in type 2 diabetic patients. Eur J Clin Invest 31:603–609CrossRefPubMedGoogle Scholar
- 11.Avogaro A, Watanabe RM, Dall’Arche A, de Kreutzenberg SV, Tiengo A, Pacini G (2004) Acute alcohol consumption improves insulin action without affecting insulin secretion in type 2 diabetic subjects. Diabetes Care 27:1369–1374CrossRefPubMedGoogle Scholar
- 12.Ludvik B, Hanefeld M, Pacini G (2008) Improved metabolic control by
*Ipomoea batatas*(Caiapo) is associated with increased adiponectin and decreased fibrinogen levels in type 2 diabetic subjects. Diabetes Obes Metab 10:586–592CrossRefPubMedGoogle Scholar - 13.Groop L, Forsblom C, Lehtovirta M et al (1996) Metabolic consequences of a family history of NIDDM (the Botnia study): evidence for sex-specific parental effects. Diabetes 45:1585–1593CrossRefPubMedGoogle Scholar
- 14.Laakso M, Zilinskaite J, Hansen T et al (2008) EUGENE2 consortium: insulin sensitivity, insulin release and glucagon-like peptide-1 levels in persons with impaired fasting glucose and/or impaired glucose tolerance in the EUGENE2 study. Diabetologia 51:502–511CrossRefPubMedGoogle Scholar
- 15.Salinari S, Bertuzzi A, Asnaghi S, Guidone C, Manco M, Mingrone G (2009) First-phase insulin secretion restoration and differential response to glucose load depending on the route of administration in type 2 diabetic subjects after bariatric surgery. Diabetes Care 32:375–380CrossRefPubMedGoogle Scholar
- 16.Galvin P, Ward G, Walters J et al (1992) A simple method for quantitation of insulin sensitivity and insulin release from an intravenous glucose tolerance test. Diabet Med 9:921–928CrossRefPubMedGoogle Scholar
- 17.Sherwin RS, Kramer KJ, Tobin JD et al (1974) A model of the kinetics of insulin in man. J Clin Invest 53:1481–1492CrossRefPubMedGoogle Scholar
- 18.Combleet PJ, Gochman N (1979) Incorrect least-squares regression coefficients in method-comparison analysis. Clin Chem 25:432–438Google Scholar
- 19.Anderson RL, Hamman RF, Savage PJ et al (1995) Exploration of simple insulin sensitivity measures derived from frequently sampled intravenous glucose tolerance (FSIGT) tests. The Insulin Resistance Atherosclerosis Study. Am J Epidemiol 142:724–732PubMedGoogle Scholar
- 20.Pacini G, Ahrén M, Ahren B (2009) Reappraisal of the intravenous glucose tolerance index for a simple assessment of insulin sensitivity in mice. Am J Physiol Regul Integr Comp Physiol 296:R1316–R1324PubMedGoogle Scholar
- 21.Matthews DR, Hosker JP, Rudenski AS, Naylor BA, Treacher DF, Turner RC (1985) Homeostasis model assessment: insulin resistance and beta-cell function from fasting plasma glucose and insulin concentrations in man. Diabetologia 28:412–419CrossRefPubMedGoogle Scholar
- 22.Stumvoll M, Mitrakou A, Pimenta W et al (2000) Use of the oral glucose tolerance test to assess insulin release and insulin sensitivity. Diabetes Care 23:295–301CrossRefPubMedGoogle Scholar
- 23.Haffner SM, D’Agostino R Jr, Festa A et al (2003) Low insulin sensitivity (S(i) = 0) in diabetic and nondiabetic subjects in the insulin resistance atherosclerosis study: is it associated with components of the metabolic syndrome and nontraditional risk factors? Diabetes Care 26:2796–2803CrossRefPubMedGoogle Scholar
- 24.Mari A (1997) Assessment of insulin sensitivity with minimal model: role of model assumptions. Am J Physiol Endocrinol Metab 272:E925–E934Google Scholar
- 25.Ferrannini E, Mari A (1998) How to measure insulin sensitivity. J Hypertens 16:895–906CrossRefPubMedGoogle Scholar
- 26.Finegood DT, Hramiak IM, Dupre J (1990) 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 70:1538–1549CrossRefPubMedGoogle Scholar
- 27.Kautzky-Willer A, Krssak M, Winzer C et al (2003) Increased intramyocellular lipid concentration identifies impaired glucose metabolism in women with previous gestational diabetes. Diabetes 52:244–251CrossRefPubMedGoogle Scholar
- 28.Bergman RN, Phillips LS, Cobelli C (1981) Physiologic evaluation of factors controlling glucose tolerance in man: measurement of insulin sensitivity and beta-cell glucose sensitivity from the response to intravenous glucose. J Clin Invest 68:1456–1467CrossRefPubMedGoogle Scholar
- 29.Kahn SE, Prigeon RL, McCulloch DK et al (1993) Quantification of the relationship between insulin sensitivity and beta-cell function in human subjects. Evidence for a hyperbolic function. Diabetes 42:1663–1672CrossRefPubMedGoogle Scholar
- 30.Ferrannini E, Mari A (2004) Beta cell function and its relation to insulin action in humans: a critical appraisal. Diabetologia 47:943–956CrossRefPubMedGoogle Scholar
- 31.Pacini G (2006) The hyperbolic equilibrium between insulin sensitivity and secretion. Nutr Metab Cardiovasc Dis 16(Suppl 1):S22–S27CrossRefPubMedGoogle Scholar
- 32.Tura A, Mari A, Prikoszovich T, Pacini G, Kautzky-Willer A (2008) Value of the intravenous and oral glucose tolerance tests for detecting subtle impairments in insulin sensitivity and beta-cell function in former gestational diabetes. Clin Endocrinol (Oxf) 69:237–243CrossRefGoogle Scholar
- 33.Garca-Estévez DA, Araújo-Vilar D, Saavedra-González A, Fiestras-Janeiro G, Cabezas-Cerrato J (2004) Analysis of the relationship between body mass index, insulin resistance, and beta-cell function: a cross-sectional study using the minimal model. Metabolism 53:1462–1466CrossRefPubMedGoogle Scholar
- 34.Clausen JO, Borch-Johnsen K, Ibsen H et al (1996) Insulin sensitivity index, acute insulin response, and glucose effectiveness in a population-based sample of 380 young healthy Caucasians. Analysis of the impact of gender, body fat, physical fitness, and life-style factors. J Clin Invest 98:1195–1209CrossRefPubMedGoogle Scholar
- 35.Zhang Y, Wat N, Stratton IM et al (1996) UKPDS 19: heterogeneity in NIDDM: separate contributions of IRS-1 and beta 3-adrenergic-receptor mutations to insulin resistance and obesity respectively with no evidence for glycogen synthase gene mutations. UK Prospective Diabetes Study. Diabetologia 39:1505–1511CrossRefPubMedGoogle Scholar
- 36.Marcovina S, Bowsher RR, Miller WG et al (2007) Standardization of insulin immunoassays: report of the American Diabetes Association Workgroup. Clin Chem 53:711–716CrossRefPubMedGoogle Scholar