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Model Definition
Estimation Steps

Short description:

Model of glucose kinetics and insulin action from non-steady-state labeled data

Format:	PharmML (0.6.1)
Related Publication:	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 Affiliation: 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 Abstract: 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.
Contributors:	Roberto Bizzotto

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

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

Mandatory file
- Executable_insulinAction.xml

Additional Files

Model owner: Roberto Bizzotto
Submitted: Dec 29, 2015 3:56:12 PM
Last Modified: May 18, 2016 4:11:44 PM

Revisions

Version: 7
- Submitted on: May 18, 2016 4:11:44 PM
- Submitted by: Roberto Bizzotto
- With comment: Updated model annotations.
Version: 4
- 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) = \sqrt{({proportional}^{2} + ({additive}^{2} \times f^{2}))}

Structural Model sm

Variable definitions

CO = \frac{(0.84 \times (3200 - (30 \times (age - 40))))}{1000}

omegaa = \frac{(beta \times CO)}{((beta \times Vlung) - CO)}

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

t0 = 0

\frac{dx1}{dT} = ((- omegaa \times x1) + (CO \times trra))

\frac{dx2}{dT} = ((- beta \times x2) + \frac{(omegaa \times x1)}{CO})

tra = (beta \times x2)

\frac{dx3}{dT} = ((- lambd1 \times x3) + ((w1 \times (1 - E)) \times tra))

\frac{dx4}{dT} = ((- lambd2 \times x4) + ((w2 \times (1 - E)) \times tra))

\frac{dx5}{dT} = ((- lambd3 \times x5) + ((((1 - w1) - w2) \times (1 - E)) \times tra))

\frac{dx6}{dT} = ((((- gamma \times x6) + (lambd1 \times x3)) + (lambd2 \times x4)) + (lambd3 \times x5))

trv = (gamma \times x6)

trra = (trv + \frac{Rinf}{CO})

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

E = (Eb + \frac{(((1 - Eb) \times Emax) \times Z)}{(EC50 + Z)})

Initial conditions

x1 = 0

x2 = 0

x3 = 0

x4 = 0

x5 = 0

x6 = 0

Z = 0

Variability Model

Level	Type
DV	residualError
ID	parameterVariability

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

Parameters

lambd1

;

lambd2

;

lambd3

;

w1

;

w2

;

alpha

;

Eb

;

Emax

;

EC50

;

aa

;

b

;

sigma

;

epsilon \sim N (0.0, sigma)

— DV

beta = 15

gamma = 10

Vlung = 0.7

Observation Model

Observation Y
Continuous / Residual Data

Parameters

Y = (tra + (combinedError2 (tra, aa, b) \times 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

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