DDMODEL00000132: Minimal 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) 



Roberto Bizzotto

Context of model development:  Mechanistic Understanding; Clinical endpoint; 
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 betacell glucose sensitivity from the response to intravenous glucose. J Clin Invest 68:14561467, 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:E925934, 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 33:362368, 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
Revisions
Independent variable T
Function Definitions
$\mathrm{combinedError2}(\mathrm{additive},\mathrm{proportional},f)=\sqrt{({\mathrm{proportional}}^{2}+({\mathrm{additive}}^{2}\times {f}^{2}\left)\right)}$
Structural Model sm
Variable definitions
$I=\left(\right(\frac{(T\mathrm{T1})}{(\mathrm{TOBS}\mathrm{T1})}\times (\mathrm{INS}\mathrm{INS1}))+\mathrm{INS1})$
$\frac{\mathrm{dtmp}}{\mathrm{dT}}=\left(\right((\mathrm{SG}+(\mathrm{SI}\times Z\left)\right)\times \mathrm{tmp})+((\frac{V}{\mathrm{WGT}}\times \mathrm{SG})\times \mathrm{Gb}\left)\right)$
$\mathrm{GLU}=(\frac{\mathrm{WGT}}{V}\times \mathrm{tmp})$
$\frac{\mathrm{dZ}}{\mathrm{dT}}=\left(\right(\mathrm{lambda}\times Z)+(\mathrm{lambda}\times (I\mathrm{Ib})\left)\right)$
Initial conditions
$\mathrm{tmp}=(\frac{V}{\mathrm{WGT}}\times \mathrm{Gb})$
$Z=0$
Variability Model
Level  Type 

DV 
residualError 
ID 
parameterVariability 
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
Parameters$SI$;
$SG$;
$V$;
$lambda$;
$alpha$;
$b$;
$sigma$;
$\mathrm{epsilon}\sim N(\mathrm{0.0},\mathrm{sigma})$ — DV
Observation Model
Observation Y
Continuous / Residual Data
Parameters $Y=(\mathrm{GLU}+(combinedError2(\mathrm{GLU},\mathrm{alpha},b)\times \mathrm{epsilon}\left)\right)$
Estimation Steps
Estimation Step estimStep_1
Estimation parameters
Fixed parameters
 $b=0$
 $\mathrm{sigma}=1$
Initial estimates for nonfixed parameters
 $\mathrm{SI}=\mathrm{5.0E4}$
 $\mathrm{SG}=\mathrm{0.05}$
 $V=\mathrm{50}$
 $\mathrm{lambda}=\mathrm{0.05}$
 $\mathrm{alpha}=2$
Estimation operations
1) Estimate the population parameters
Step Dependencies
 estimStep_1