# DDMODEL00000131: Dose-response characteristics of insulin action on glucose metabolism

Short description:
Model of glucose kinetics and insulin action from non-steady-state labeled data
 Format: PharmML (0.6.1) Related Publication: .hiddenContent {display:none;} Dose-response characteristics of insulin action on glucose metabolism: a non-steady-state approach. Natali A, Gastaldelli A, Camastra S, Sironi AM, Toschi E, Masoni A, Ferrannini E, Mari A American journal of physiology. Endocrinology and metabolism, 5/2000, Volume 278, Issue 5, pages: E794-801 Affiliation: Metabolism Unit of the Consiglio Nazionale delle Ricerche Institute of Clinical Physiology and Department of Internal Medicine, University of Pisa, 56126 Pisa, Italy. anatali@ifc.pi.cnr.it Abstract: The traditional methods for the assessment of insulin sensitivity yield only a single index, not the whole dose-response curve information. This curve is typically characterized by a maximally insulin-stimulated glucose clearance (Cl(max)) and an insulin concentration at half-maximal response (EC(50)). We developed an approach for estimating the whole dose-response curve with a single in vivo test, based on the use of tracer glucose and exogenous insulin administration (two steps of 20 and 200 mU x min(-1) x m(-2), 100 min each). The effect of insulin on plasma glucose clearance was calculated from non-steady-state data by use of a circulatory model of glucose kinetics and a model of insulin action in which glucose clearance is represented as a Michaelis-Menten function of insulin concentration with a delay (t(1/2)). In seven nondiabetic subjects, the model predicted adequately the tracer concentration: the model residuals were unbiased, and their coefficient of variation was similar to the expected measurement error (approximately 3%), indicating that the model did not introduce significant systematic errors. Lean (n = 4) and obese (n = 3) subjects had similar half-times for insulin action (t(1/2) = 25 +/- 9 vs. 25 +/- 8 min) and maximal responses (Cl(max) = 705 +/- 46 vs. 668 +/- 259 ml x min(-1) x m(-2), respectively), whereas EC(50) was 240 +/- 84 microU/ml in the lean vs. 364 +/- 229 microU/ml in the obese (P < 0.04). EC(50) and the insulin sensitivity index (ISI, initial slope of the dose-response curve), but not Cl(max), were related to body adiposity and fat distribution with r of 0.6-0.8 (P < 0.05). Thus, despite the small number of study subjects, we were able to reproduce information consistent with the literature. In addition, among the lean individuals, t(1/2) was positively related to the ISI (r = 0.72, P < 0.02). We conclude that the test here presented, based on a more elaborate representation of glucose kinetics and insulin action, allows a reliable quantitation of the insulin dose-response curve for whole body glucose utilization in a single session of relatively short duration. Contributors: Roberto Bizzotto
 Context of model development: Mechanistic Understanding; Clinical end-point; Discrepancy between implemented model and original publication: See the four numbered points in the “Implementation remarks” section of the insulinAction.txt file; Long technical model description: insulinAction.txt; Model compliance with original publication: No; Model implementation requiring submitter’s additional knowledge: Yes; Modelling context description: The method allows the estimation of the whole-body dose-response curve relating glucose clearance to insulin concentration - an elaborate characterization of insulin sensitivity - from a single in vivo test exploring non-steady-state conditions. The test is a isoglycemic hyperinsulinemic glucose clamp with two levels of exogenous insulin administration and the use of a stable-isotope glucose tracer.; Modelling task in scope: estimation; Nature of research: Clinical research & Therapeutic use; Therapeutic/disease area: Metabolism;
 Validation Status: Annotations are correct. Certification Comment: This model is not certified.
• Model owner: Roberto Bizzotto
• Submitted: Dec 29, 2015 3:56:12 PM
##### Revisions
• Version: 7
• Submitted on: May 18, 2016 4:11:44 PM
• Submitted by: Roberto Bizzotto
• With comment: Updated model annotations.
• Version: 4
• Submitted on: Dec 29, 2015 3:56:12 PM
• Submitted by: Roberto Bizzotto
• With comment: Edited model metadata online.

Independent variable T

### Function Definitions

$combinedError2(additive,proportional,f)=(proportional2+(additive2 ×f2))$

### Structural Model sm

Variable definitions

$CO=(0.84 ×(3200-(30 ×(age-40))))1000$
$omegaa=(beta ×CO)((beta ×Vlung)-CO)$
$I=(((T-T1)(TOBS-T1) ×(INS-INS1))+INS1)$
$t0=0$
$dx1dT=((-omegaa ×x1)+(CO ×trra))$
$dx2dT=((-beta ×x2)+(omegaa ×x1)CO)$
$tra=(beta ×x2)$
$dx3dT=((-lambd1 ×x3)+((w1 ×(1-E)) ×tra))$
$dx4dT=((-lambd2 ×x4)+((w2 ×(1-E)) ×tra))$
$dx5dT=((-lambd3 ×x5)+((((1-w1)-w2) ×(1-E)) ×tra))$
$dx6dT=((((-gamma ×x6)+(lambd1 ×x3))+(lambd2 ×x4))+(lambd3 ×x5))$
$trv=(gamma ×x6)$
$trra=(trv+RinfCO)$
$dZdT=((-alpha ×Z)+(alpha ×(I-Ib)))$
$E=(Eb+(((1-Eb) ×Emax) ×Z)(EC50+Z))$

Initial conditions

$x1=0$
$x2=0$
$x3=0$
$x4=0$
$x5=0$
$x6=0$
$Z=0$

### Variability Model

Level Type

DV

residualError

ID

parameterVariability

### Covariate Model

Continuous covariate TOBS

Continuous covariate INS

Continuous covariate Ib

Continuous covariate age

Continuous covariate T1

Continuous covariate INS1

Continuous covariate Rinf

### Parameter Model

Parameters
$lambd1$ $lambd2$ $lambd3$ $w1$ $w2$ $alpha$ $Eb$ $Emax$ $EC50$ $aa$ $b$ $sigma$
$epsilon∼N(0.0,sigma)$ — DV
$beta=15$
$gamma=10$
$Vlung=0.7$

### Observation Model

#### Observation YContinuous / Residual Data

Parameters
$Y=(tra+(combinedError2(tra,aa,b) ×epsilon))$

### Estimation Steps

#### Estimation Step estimStep_1

##### Estimation parameters

Fixed parameters

• $b=0$
• $sigma=1$

Initial estimates for non-fixed parameters

• $lambd1=1$
• $lambd2=0.3$
• $lambd3=0.02$
• $w1=0.4$
• $w2=0.5$
• $alpha=0.03$
• $Eb=0.03$
• $Emax=0.3$
• $EC50=150$
• $aa=0.004$
##### Estimation operations
1) Estimate the population parameters
Algorithm FO

### Step Dependencies

• estimStep_1