ESTIMATION OF HEPATIC INSULIN EXTRACTION DURING IM-IVGTT: INDIVIDUAL VS STANDARD KINETIC PARAMETERS

M. Campioni*, G. Toffolo*, R. Rizza** and C. Cobelli*

* Department of Information Engineering, University of Padova, Padova, Italy
** Division of Endocrinology, Diabetes, Metabolism and Nutrition, Department of Internal Medicine, Mayo Clinic and Foundation, Rochester, MN, USA

cobelli@dei.unipd.it

Abstract: A priori knowledge of C-peptide and insulin kinetics is a requisite for a reliable assessment of pre- and post-hepatic insulin secretion, and thus of hepatic insulin extraction, from C-peptide and insulin plasma concentration data measured during a glucose perturbation. Aim of this study is to develop a model to calculate standard insulin kinetic parameters from subject anthropometric characteristics. To this purpose we analysed IM-IVGTT (Insulin-Modified Intravenous Glucose tolerance Test) data with the minimal model of insulin secretion and kinetics [7] in 132 healthy subjects heterogeneous in term of age, sex and body weight. Using a statistical analysis, based on ANOVA, ANCOVA and stepwise linear regression, we proposed a model to calculate standard insulin kinetic parameters from age and from Body Surface Area (n(min^-1)=-0.0005·Age(yr)+0.252; R=0.22; P=0.0097; VI(l)=exp(0.5358·BSA(m²)+1); R=0.35; P<0.001). We also demonstrated that standard values of kinetic parameters can be used to estimate post-hepatic secretion and hepatic extraction indices in an individual without significant loss of accuracy.

Introduction

Hepatic insulin extraction during a glucose perturbation can be assessed by comparing pre- and post-hepatic insulin secretion profiles. The rationale is illustrated in Fig.1: insulin and C-peptide are equimolarly secreted from the ß-cells and pass through the liver, where insulin, but not C-peptide, undergoes hepatic extraction. Pre-hepatic secretion (SR) during an intravenous or an oral glucose tolerance test can be estimated non invasively in humans by identifying the minimal model of C-peptide secretion and kinetics [3],[4], [8]. Since the simultaneous estimation of secretion and kinetics is difficult, due to undesired compensations between the two processes [3], a method was proposed in [2] to calculate standard kinetic parameters for C-peptide clearance from individual anthropometric characteristics. Post-hepatic secretion (SR^post) can be calculated by applying a modelling approach to insulin data, but this requires to model both secretion and kinetics. However, information on insulin kinetics is not still available. The aim here is to determine standard parameters for insulin clearance, to be used to assess post-hepatic insulin secretion from plasma insulin data. To this purpose, we analysed Insulin-Modified Intravenous Glucose Tolerance Test (IM-IVGTT) in 132 healthy subjects heterogeneous in term of age, sex and body weight with the minimal model of insulin secretion and kinetics [7]. This protocol combines a glucose bolus with a short insulin infusion from 20 to 25 minutes after the glucose bolus and is advantageous with respect to the standard IVGTT since the decay of insulin concentration observed after the exogenous insulin administration allows a reliable description of insulin kinetics in each individual [4]. Based on these data, linear regressions models to calculate standard insulin kinetic parameters from individual anthropometric characteristics were developed. Finally, the impact on post-hepatic insulin secretion and hepatic extraction indices of using standard rather than individually derived insulin kinetic parameters was evaluated.

Materials and Methods

Subjects: Study was performed on 132 healthy subjects (72 males, 60 females). Mean age of the subjects was 55±23 (SD) yr (42 young, mean age 23±3 yr, and 90 old, mean age 70±6 yr), mean body surface area BSA 1.89±0.22 m², mean body mass index BMI 26.6±3.5 kg/m², mean body weight BW 78±14 kg. A subject was considered obese if his/her BMI > 27.

Experimental Protocol: The IM-IVGTT study consisted of an intravenous glucose injection (dose=300mg/kg) followed by an exogenous insulin infusion (dose=0.03 U/kg) in the 20-25 min interval after the glucose dose. 21 blood samples were collected from the arterialised venous site at time t= 0, 2, 4, 6, 8, 10, 15, 20, 22, 25, 26, 28, 31, 35, 45, 60, 75, 90, 120, 180, 240 min after the glucose dose glucose, insulin and C-peptide concentrations measurement.

Insulin Model: The model of post-hepatic insulin secretion and kinetics is here briefly described. A linear mono-compartmental model was assumed to describe insulin kinetics (Fig.1), according to the following equation:

(1)

where I (pmol/l) denotes the insulin concentration above basal, n (min^-1) the constant rate of insulin disappearance, SR^post (pmol·l^-1·min^-1) the post-hepatic insulin secretion normalized to the insulin volume of distribution V_I and expressed as deviation from basal, U(t) the exogenous input, i.e. the intravenous insulin infusion. SR^post, reflecting the combined effect of pancreatic secretion and hepatic extraction, was described by the following equations:

	(2)
	(3)
	(4)

where X (pmol/l) and Y (pmol/l/min) denote respectively insulin amount and provision in the ß-cells, both normalized to the distribution volume of insulin; m (min^-1), a (min^-1), ß (min^-1), h (mg of glucose/dl) are the secretory parameters. First and second phase of insulin secretion derive respectively from X₀, representing the amount of insulin stored in the ß-cells in a promptly releasable form (labile insulin), and provision Y, controlled by glucose concentration G (mg/dl) through parameter ß according to eq. (4). The model allows to predict post-hepatic insulin secretion profile SR^post (eq. (2)) and to define four indices to quantify the sensitivity to glucose of post-hepatic insulin secretion. First-phase sensitivity index 1post (10⁹) is a measure of the stimulatory effect of the glucose bolus upon the secretion of stored insulin and is defined as the amount of insulin (per unit of insulin distribution volume) X₀ released in response to the maximum glucose concentration above basal (G_max-G_b) achieved during the experiment:

(5)

The second-phase sensitivity index 2^post (10⁹ · min^-1) is a measure of the effect of glucose concentration (above the threshold level h) on ß-cell secretion at the steady state:

(6)

The basal sensitivity index b^post (109·min^-1) measures basal insulin secretion rate over basal glucose concentration:

(7)

where SR_b^post (pmol/l/min) is the basal post-hepatic insulin secretion and I_b the insulin end-test basal value. Finally, the total sensitivity index ^post (10⁹·min^-1) measures the area under curve of insulin secretion rate over the area under curve of plasma glucose concentration:

(8)

where T=240 (min) is the experiment period.

Assessment of Hepatic Extraction: Pre-hepatic secretion can be evaluated from the minimal model of C-peptide secretion and kinetics [4] together with pre-hepatic sensitivity indices ₁, ₂, _b, . By comparing pre- and post-hepatic sensitivity indices it is possible to evaluate the fraction of secreted insulin which is extracted by the liver in the basal state and during the IM-IVGTT, denoted as HEb and HE respectively:

	(9)
	(10)

where V_C is the C-peptide distribution volume.

Model Identification: Parameters of the insulin minimal model, i.e. kinetic parameters n and V_I and secretory parameters a, ß, X₀, h were a priori uniquely identifiable [1]. Model parameters were estimated, together with a measure of their precision, by non-linear least squares using SAAM II software [5]. Relative weights were chosen, equal to the inverse of the variance of the measurement errors, which were assumed to be independent, gaussian, and zero mean with a constant standard deviation, which has been estimated a posteriori.

Standard Parameters of Insulin Kinetics: The subjects were grouped according to their anthropometric characteristics: sex (male and female), age (young and old), and BMI (lean and obese). The significance of differences of insulin kinetic parameters n and VI between the groups was estimated with analysis of variance (ANOVA). The dependence of insulin kinetic parameters on age, weight, BMI and BSA was tested in all groups with analysis of covariance (ANCOVA) and stepwise linear regression. Application of ANOVA and ANCOVA requires normality and equivalence of n and V_I variance in all groups, that were tested by using respectively the Shapiro and the Bartlett test. A p-value P<0.05 was considered significant. Statistical analysis was performed with software R.

Kinetic Population Model Validation: To quantify the impact of using standard rather than individually estimated insulin kinetic parameters, IM-IVGTT data of 10 subjects, heterogeneous in term of age (45±22 yr , 3 young 24±6 yr and 7 old 66±3 yr), sex (7 male and 3 female), body weight (76±14 kg) and BSA (1.88±0.22 m²) were analysed twice: first, both post-hepatic secretion and insulin kinetic parameters were estimated with the insulin model, second, insulin kinetic parameters were fixed to the values calculated with the linear regression models (Tab. 1) and only post-hepatic secretion parameters were estimated.

Results

Estimates of kinetic parameters n and V_I in 132 subjects are reported in Tab.1 as mean±SD, with the % coefficient of variation (CV) within parentheses, representing the inter-individual variability. These values are for n and V_I respectively 23% and 32% and indicate a low inter-individual variability in a population heterogeneous in term of age, sex and body weight.

Normality of distribution, a prerequisite of ANOVA, was verified for parameter n in all groups of subjects, but the male group where p-value was not too far from significant (P=0.0152). V_I was not normally distributed in most groups, while natural logarithm of V_I (ln(V_I)) was normally distributed in all groups, therefore ln(V_I) was used in our analysis. Results of Bartlett test showed that the insulin kinetic parameters n and ln(V_I) had the same variance in all groups of subjects.

ANOVA indicated that differences of parameter n between groups of subjects were not significant, while parameter ln(V_I) was significantly higher (P<0.001) in males (2.12±0.29) than in females (1.89±0.33).

Stepwise linear regression analysis indicated that a) an increase of age was related with a significant (P=0.0097) decrease of parameter n, b) an increase of BSA and BW was related with a significant (respectively P<0.001 and P<0.001) increase of parameter ln(V_I), c) ln(V_I) was more strongly correlated with BSA (R=0.35) than with BW (R=0.31).

ANCOVA indicated that d) sex differences for mean values of ln(V_I) were related to differences of BSA, and were not significant (P=0.1696) if considered in the linear regression with BSA.

The linear regression models to calculate the insulin kinetic parameters n and V_I from age and from BSA are showed in Fig.2 and in Tab.1.

In order to quantify the impact of using standard rather than individually estimated insulin kinetic parameters, a kinetic population model validation was performed on 10 subjects. Results are shown in Tab. 2 and indicate that the two sets of indices are very similar, since values well correlate and their averages do not differ significantly.

Table 2: Indices of post-hepatic sensitivity and hepatic insulin extraction estimated with individual and standard insulin kinetic parameters (R: coefficient of correlation; P: p-value of Wilcoxon signed rank test).

	individual Mean SD	standard Mean SD	P R
1post 2post bpost post HEb HE	87.8 47.1 4.71 1.42 0.94 0.38 2.36 0.74 0.61 0.17 0.42 0.23	86.6 50.5 4.40 2.21 0.93 0.47 2.30 0.94 0.65 0.12 0.47 0.17	0.39 0.99 0.39 0.85 0.65 0.98 0.54 0.94 0.16 0.95 0.20 0.85

Discussion

In this study we have estimated insulin kinetic parameters from an IM-IVGTT protocol with the minimal model of insulin secretion and kinetics [7] in a population of 132 healthy subjects, heterogeneous in term of age, sex and body weight. The main purpose was to develop a model to calculate standard insulin kinetic parameters from anthropometric characteristics and to verify the impact of using standard rather than individual insulin kinetic parameters on post-hepatic sensitivity to glucose and hepatic extraction indices.

Estimated values for insulin kinetic parameters n and VI were respectively 0.22±0.05 (min^-1) and 7.9±2.6 (l) (Tab. 2), resulting in an insulin plasma clearance (1.70±0.49 (l/min)) very similar to values reported by some authors [6], thus confirming that the linear, single compartment model provides a reasonable description of insulin kinetics.

Inter-individual variability for insulin kinetic parameters n and VI, respectively 23% and 32%, was low, if heterogeneity of subjects in term of age, sex and body weight is considered, and thus insulin kinetics appear to be reproducible with standard population parameters.

Statistical analysis, based on ANOVA, ANCOVA and stepwise linear regression, indicated that insulin kinetic parameters were affected significantly from age and BSA and that the differences between groups of subjects, i.e. male and female, young and old, lean and obese, were not significant when effects of age and BSA were taken into account. In particular, an increase of age was related with a significant (P=0.0097) decrease of parameter n and an increase of BSA was related with a significant (P<0.001) increase of parameter ln(V_I). It's worth nothing that our database didn't include subjects with age ranging from 30 to 60 years, but other results from separate studies, that included subjects with age in this range, confirmed the relation between n and age here reported. These results suggest the use of linear regression models to calculate insulin kinetic parameters n and V_I respectively from age and from BSA (Tab.1 and Fig.2).

Finally, a validation study on 10 subjects indicated that standard values can be used to estimate post-hepatic secretion parameters and hepatic extraction indices in an individual without significant loss of accuracy.

In conclusion, in this study we have demonstrated, using a statistical analysis, that standard population values can be calculated for insulin kinetic parameters from subject age and BSA, and that these standard values can be used to calculate post-hepatic secretion and hepatic extraction indices in an individual without significant loss of accuracy. The linear regression models thus provide a priori knowledge on insulin kinetics, a requisite to derive reliable estimates of post-hepatic secretion and insulin hepatic extraction in experimental protocol like standard IVGTT, meal-like and oral glucose tolerance test, where the simultaneous estimation of kinetic and secretion parameters is critical.

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