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Model Definition
Estimation Steps

Short description:

Model of glucose kinetics and insulin action for a labeled IVGTT

Format:	PharmML (0.6.1)
Related Publication:	Assessment of insulin sensitivity and secretion with the labelled intravenous glucose tolerance test: improved modelling analysis. Mari A Diabetologia, 9/1998, Volume 41, Issue 9, pages: 1029-1039 Affiliation: Institute of Systems Science and Biomedical Engineering, National Research Council, Padova, Italy. Abstract: A new modelling analysis was developed to assess insulin sensitivity with a tracer-modified intravenous glucose tolerance test (IVGTT). IVGTTs were performed in 5 normal (NGT) and 7 non-insulin-dependent diabetic (NIDDM) subjects. A 300 mg/kg glucose bolus containing [6,6-(2)H2]glucose was given at time 0. After 20 min, insulin was infused for 5 min (NGT, 0.03; NIDDM, 0.05 U/kg). Concentrations of tracer, glucose, insulin and C-peptide were measured for 240 min. A circulatory model for glucose kinetics was used. Glucose clearance was assumed to depend linearly on plasma insulin concentration delayed. Model parameters were: basal glucose clearance (Cl(b)), glucose clearance at 600 pmol/l insulin concentration (Cl600), basal glucose production (Pb), basal insulin sensitivity index (BSI = Cl(b)/basal insulin concentration); incremental insulin sensitivity index (ISI = slope of the relationship between insulin concentration and glucose clearance). Insulin secretion was calculated by deconvolution of C-peptide data. Indices of basal pancreatic sensitivity (PSIb) and first (PSI1) and second-phase (PSI2) sensitivity were calculated by normalizing insulin secretion to the prevailing glucose levels. Diabetic subjects were found to be insulin resistant (BSI: 2.3 +/- 0.6 vs 0.76 +/- 0.18 ml x min(-1) x m(-2) x pmol/l(-1), p < 0.02; ISI: 0.40 +/- 0.06 vs 0.13 +/- 0.05 ml x min(-1) x m(-2) x pmol/l(-1), p < 0.02; Cl600: 333 +/- 47 vs 137 +/- 26 ml x min(-1) x m(-2), p < 0.01; NGT vs NIDDM). Pb was not elevated in NIDDM (588 +/- 169 vs 606 +/- 123 micromol x min(-1) x m(-2), NGT vs NIDDM). Hepatic insulin resistance was however present as basal glucose and insulin were higher. PSI1 was impaired in NIDDM (67 +/- 15 vs 12 +/- 7 pmol x min x m(-2) x mmol/l(-1), p < 0.02; NGT vs NIDDM). In NGT and in a subset of NIDDM subjects (n = 4), PSIb was inversely correlated with BSI (r = 0.95, p < 0.0001, log transformation). This suggests the existence of a compensatory mechanism that increases pancreatic sensitivity in the presence of insulin resistance, which is normal in some NIDDM subjects and impaired in others. In conclusion, using a simple test the present analysis provides a rich set of parameters characterizing glucose metabolism and insulin secretion, agrees with the literature, and provides some new information on the relationship between insulin sensitivity and secretion.
Contributors:	Roberto Bizzotto

Context of model development:	Clinical end-point; Mechanistic Understanding;
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;

Validation Status:	Annotations are correct.
Certification Comment:	This model is not certified.

Mandatory file
- Executable_ivgttNGT.xml

Additional Files

Model owner: Roberto Bizzotto
Submitted: Dec 10, 2015 7:35:59 PM
Last Modified: May 18, 2016 4:16:15 PM

Revisions

Version: 7
- Submitted on: May 18, 2016 4:16:15 PM
- Submitted by: Roberto Bizzotto
- With comment: Updated model annotations.
Version: 4
- Submitted on: Dec 10, 2015 7:35:59 PM
- Submitted by: Roberto Bizzotto
- With comment: Edited model metadata online.

Independent variable T

Function Definitions

combinedError2 (additive, proportional, f) = \sqrt{({proportional}^{2} + ({additive}^{2} \times f^{2}))}

Structural Model sm

Variable definitions

Vhl = 0.017

CO = 0.065

lambda = \frac{CO}{Vhl}

I = ((\frac{(T - T1)}{(TOBS - T1)} \times (INS - INS1)) + INS1)

t0 = 0

\frac{dtmp}{dT} = ((- lambda \times tmp) + ((lambda \times Vhl) \times Gra))

Ga = \frac{tmp}{Vhl}

\frac{dG1}{dT} = ((- alpha1 \times G1) + (((alpha1 \times thetaa) \times (1 - E)) \times Ga))

\frac{dG2}{dT} = ((- alpha2 \times G2) + (((alpha2 \times (1 - thetaa)) \times (1 - E)) \times Ga))

Gmv = (G1 + G2)

Gra = (Gmv + \frac{J}{CO})

\frac{dZ}{dT} = ((- beta \times Z) + (beta \times (I - Ib)))

E = (Eb + (gamma \times Z))

Initial conditions

tmp = 0

G1 = 0

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

;

epsilon \sim N (0.0, sigma)

— DV

Observation Model

Observation Y
Continuous / Residual Data

Parameters

Y = (Ga + (combinedError2 (Ga, aa, b) \times epsilon))

Estimation Steps

Estimation Step estimStep_1

Estimation parameters

Fixed parameters

$b = 0$
$sigma = 1$

Initial estimates for non-fixed parameters

$alpha1 = 1.4$
$alpha2 = 0.13$
$gamma = 1.6E-4$
$thetaa = 0.73$
$beta = 0.085$
$Eb = 0.044$
$aa = 0.3$

Estimation operations

1) Estimate the population parameters

Algorithm FO

Step Dependencies

estimStep_1

DDMODEL00000094: Insulin sensitivity from labeled IVGTT