DDMODEL00000132: Minimal model

  public model
Short description:
Simplified model of glucose kinetics and insulin action designed for the determination of insulin sensitivity form an intravenous glucose test.
PharmML (0.6.1)
  • Quantitative estimation of insulin sensitivity.
  • Bergman RN, Ider YZ, Bowden CR, Cobelli C
  • The American journal of physiology, 6/1979, Volume 236, Issue 6, pages: E667-77
  • Northwestern University Technological Institute, Illinois
  • We have evaluated the feasibility of using a mathematical model of glucose disappearance to estimate insulin sensitivity. Glucose was injected into conscious dogs at 100, 200, or 300 mg/kg. The measured time course of insulin was regarded as the "input," and the falling glucose concentration as the "output" of the physiological system storing and using glucose. Seven mathematical models of glucose uptake were compared to identify the representation most capable of simulating glucose disappearance. One specific nonlinear model was superior in that it 1) predicted the time course of glucose after glucose injection, 2) had four parameters that could be precisely estimated, and 3) described individual experiments with similar parameter values. Insulin sensitivity index (SI), defined as the dependence of fractional glucose disappearance on plasma insulin, was the ratio of two parameters of the chosen model and could be estimated with good reproducibility from the 300 mg/kg injection experiments (SI = 7.00 X 10(-4) +/- 24% (coefficient of variation) min-1/(microU/ml) (n = 8)). Thus, from a single glucose injection it is possible to obtain a quantitative index of insulin sensitivity that may have clinical applicability.
Roberto Bizzotto
Context of model development: Clinical end-point; Mechanistic Understanding;
Discrepancy between implemented model and original publication: The equations of the original publication were simplified in this work: “Bergman RN, Phillips LS, Cobelli C: 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 68:1456-1467, 1981”. The equations were then reformulated in the following paper, used to implement the model implemented here: “Mari A: Assessment of insulin sensitivity with minimal model: role of model assumptions. Am J Physiol 272:E925-934, 1997”. Data for validation have been taken from a published study in dogs: “Finegood DT, Pacini G, Bergman RN: 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”. See the file minimalModel.txt for details.;
Long technical model description: minimalModel.txt;
Model compliance with original publication: No;
Model implementation requiring submitter’s additional knowledge: Yes;
Modelling context description: The minimal model was designed for the determination of insulin sensitivity form an intravenous glucose test;
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 4:11:32 PM
  • Last Modified: May 18, 2016 3:49:43 PM
  • Version: 10 public model Download this version
    • Submitted on: May 18, 2016 3:49:43 PM
    • Submitted by: Roberto Bizzotto
    • With comment: Modified accommodations
  • Version: 2 public model Download this version
    • Submitted on: Dec 29, 2015 4:11:32 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

I=(((T-T1)(TOBS-T1) ×(INS-INS1))+INS1)
dtmpdT=((-(SG+(SI ×Z)) ×tmp)+((VWGT ×SG) ×Gb))
GLU=(WGTV ×tmp)
dZdT=((-lambda ×Z)+(lambda ×(I-Ib)))

Initial conditions

tmp=(VWGT ×Gb)

Variability Model

Level Type





Covariate Model

Continuous covariate TOBS

Continuous covariate INS

Continuous covariate Gb

Continuous covariate Ib

Continuous covariate WGT

Continuous covariate T1

Continuous covariate INS1

Parameter Model

SI SG V lambda alpha b sigma
epsilonN(0.0,sigma) — DV

Observation Model

Observation Y
Continuous / Residual Data

Y=(GLU+(combinedError2(GLU,alpha,b) ×epsilon))

Estimation Steps

Estimation Step estimStep_1

Estimation parameters

Fixed parameters

  • b=0
  • sigma=1

Initial estimates for non-fixed parameters

  • SI=5.0E-4
  • SG=0.05
  • V=50
  • lambda=0.05
  • alpha=2
Estimation operations
1) Estimate the population parameters
    Algorithm FO

    Step Dependencies

    • estimStep_1