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

  public model
Short description:
Model of glucose kinetics and insulin action from non-steady-state labeled data
PharmML (0.6.1)
  • 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
  • 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
  • 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.
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;
Annotations are correct.
This model is not certified.
  • Model owner: Roberto Bizzotto
  • Submitted: Dec 29, 2015 3:56:12 PM
  • Last Modified: May 18, 2016 4:11:44 PM
  • Version: 7 public model Download this version
    • Submitted on: May 18, 2016 4:11:44 PM
    • Submitted by: Roberto Bizzotto
    • With comment: Updated model annotations.
  • Version: 4 public model Download this version
    • 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)
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)
dZdT=((-alpha ×Z)+(alpha ×(I-Ib)))
E=(Eb+(((1-Eb) ×Emax) ×Z)(EC50+Z))

Initial conditions


Variability Model

Level Type





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

lambd1 lambd2 lambd3 w1 w2 alpha Eb Emax EC50 aa b sigma
epsilonN(0.0,sigma) — DV

Observation Model

Observation Y
Continuous / Residual Data

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