DDMODEL00000094: Insulin sensitivity from labeled IVGTT
Short description:
Model of glucose kinetics and insulin action for a labeled IVGTT
PharmML (0.6.1) 



Roberto Bizzotto

Context of model development:  Mechanistic Understanding; Clinical endpoint; 
Discrepancy between implemented model and original publication:  See the three numbered points in the “Implementation remarks” section of the ivgtt.txt file; 
Long technical model description:  ivgtt.txt; 
Model compliance with original publication:  No; 
Model implementation requiring submitter’s additional knowledge:  Yes; 
Modelling context description:  The model describes glucose kinetics and insulin action during a labeled intravenous glucose tolerance test (IVGTT). The modeling analysis exploits the use of a glucose tracer and is based on a representation that is more accurate than the minimal model. An essential physical representation of the glucose system, i.e. a circulatory model, is used. From this improved modeling analysis the characterization of insulin sensitivity is enriched, providing multiple parameters with clear physiological interpretation.; 
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 10, 2015 7:35:59 PM
 Last Modified: May 18, 2016 4:16:15 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
$\mathrm{Vhl}=\mathrm{0.017}$
$\mathrm{CO}=\mathrm{0.065}$
$\mathrm{lambda}=\frac{\mathrm{CO}}{\mathrm{Vhl}}$
$I=\left(\right(\frac{(T\mathrm{T1})}{(\mathrm{TOBS}\mathrm{T1})}\times (\mathrm{INS}\mathrm{INS1}))+\mathrm{INS1})$
$\mathrm{t0}=0$
$\frac{\mathrm{dtmp}}{\mathrm{dT}}=\left(\right(\mathrm{lambda}\times \mathrm{tmp})+((\mathrm{lambda}\times \mathrm{Vhl})\times \mathrm{Gra}\left)\right)$
$\mathrm{Ga}=\frac{\mathrm{tmp}}{\mathrm{Vhl}}$
$\frac{\mathrm{dG1}}{\mathrm{dT}}=\left(\right(\mathrm{alpha1}\times \mathrm{G1})+(\left(\right(\mathrm{alpha1}\times \mathrm{thetaa})\times (1E\left)\right)\times \mathrm{Ga}\left)\right)$
$\frac{\mathrm{dG2}}{\mathrm{dT}}=\left(\right(\mathrm{alpha2}\times \mathrm{G2})+(\left(\right(\mathrm{alpha2}\times (1\mathrm{thetaa}))\times (1E\left)\right)\times \mathrm{Ga}\left)\right)$
$\mathrm{Gmv}=(\mathrm{G1}+\mathrm{G2})$
$\mathrm{Gra}=(\mathrm{Gmv}+\frac{J}{\mathrm{CO}})$
$\frac{\mathrm{dZ}}{\mathrm{dT}}=\left(\right(\mathrm{beta}\times Z)+(\mathrm{beta}\times (I\mathrm{Ib})\left)\right)$
$E=(\mathrm{Eb}+(\mathrm{gamma}\times Z\left)\right)$
Initial conditions
$\mathrm{tmp}=0$
$\mathrm{G1}=0$
$\mathrm{G2}=0$
$Z=0$
Variability Model
Level  Type 

DV 
residualError 
ID 
parameterVariability 
Covariate Model
Continuous covariate TOBS
Continuous covariate INS
Continuous covariate Ib
Continuous covariate T1
Continuous covariate INS1
Continuous covariate J
Parameter Model
Parameters$alpha1$;
$alpha2$;
$gamma$;
$thetaa$;
$beta$;
$Eb$;
$aa$;
$b$;
$sigma$;
$\mathrm{epsilon}\sim N(\mathrm{0.0},\mathrm{sigma})$ — DV
Observation Model
Observation Y
Continuous / Residual Data
Parameters $Y=(\mathrm{Ga}+(combinedError2(\mathrm{Ga},\mathrm{aa},b)\times \mathrm{epsilon}\left)\right)$
Estimation Steps
Estimation Step estimStep_1
Estimation parameters
Fixed parameters
 $b=0$
 $\mathrm{sigma}=1$
Initial estimates for nonfixed parameters
 $\mathrm{alpha1}=\mathrm{1.4}$
 $\mathrm{alpha2}=\mathrm{0.13}$
 $\mathrm{gamma}=\mathrm{1.6E4}$
 $\mathrm{thetaa}=\mathrm{0.73}$
 $\mathrm{beta}=\mathrm{0.085}$
 $\mathrm{Eb}=\mathrm{0.044}$
 $\mathrm{aa}=\mathrm{0.3}$
Estimation operations
1) Estimate the population parameters
Step Dependencies
 estimStep_1