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Short description:

Insulin minimal model (MM) for the Bayesian estimation of insulin secretion rate (ISR) and other physiological indexes (e.g,. beta-cell sensitivity) in presence of a uncertain C-peptide kinetics.

Format:	PharmML 0.8.x (0.8.1)
Related Publication:	Insulin minimal model indexes and secretion: proper handling of uncertainty by a Bayesian approach. Sparacino G, Bellazzi R, Toffolo GM, Cobelli C, Magni Paolo Annals of biomedical engineering, 7/2004, Volume 32, Issue 7, pages: 1027-1037 Affiliation: Dipartimento di Informatica e Sistemistica, Università degli Studi di Pavia via Ferrata, Pavia, Italy. paolo.magni@unipv.it Abstract: The identification of the insulin minimal model (MM) for the estimation of insulin secretion rate (ISR) and physiological indexes (e.g. beta-cell sensitivity) requires the knowledge of C-peptide (CP) kinetics. The four parameters of the two-compartment model of CP kinetics in a given individual can be derived either from an additional bolus experiment or, more frequently, from a population model. However, in both situations, the CP kinetics is uncertain and, in MM identification, it should be treated as such. This paper shows how to handle CP kinetics uncertainty by using a Bayesian methodology. In seven subjects, MM indexes and ISR were estimated together with their confidence intervals, using either the bolus data or the population model to assess CP kinetics. The two main results that arise from the application of the new methodology are: (i) the use of the population model in place of the bolus data to determine CP kinetics does not affect, on average, the point estimates of ISR profile and MM parameters but only the confidence intervals which becomes wider (less than 50%); (ii) in both the bolus and population situation neglecting the uncertainty of CP kinetics, as done in MM literature so far, introduces no bias, on average, on point estimates of MM indexes but only an underestimation of confidence intervals.
Contributors:	Paolo Magni

Context of model development:	Clinical end-point; Mechanistic Understanding; Variability sources in PK and PD (CYP, Renal, Biomarkers);
Discrepancy between implemented model and original publication:	Compared to the model described in the paper, the expression of ISR has been herein simplified as ISR=m*X, instead of using a piecewise function. This assumption has been done for computational problems, exactly as it was carried out in the Matlab target code of the original publication (available from the authors). The described simplification was also adopted in other previous works on the glucose-insulin minimal model (e.g., Toffolo G. et al., 2006, doi:10.1152/ajpendo.00473.2004).;
Model compliance with original publication:	Yes;
Model implementation requiring submitter’s additional knowledge:	No;
Modelling context description:	The identification of the insulin minimal model (MM) for the estimation of insulin secretion rate (ISR) and physiological indexes (e.g. beta-cell sensitivity) requires the knowledge of C-peptide (CP) kinetics. The four parameters of the two-compartment model of CP kinetics in a given individual can be derived either from an additional bolus experiment or, more frequently, from a population model. However, in both situations, the CP kinetics is uncertain and, in MM identification, it should be treated as such. This paper shows how to handle CP kinetics uncertainty by using a Bayesian methodology. In seven subjects, MM indexes and ISR were estimated together with their confidence intervals, using either the bolus data or the population model to assess CP kinetics. The two main results that arise from the application of the new methodology are: (i) the use of the population model in place of the bolus data to determine CP kinetics does not affect, on average, the point estimates of ISR profile and MM parameters but only the confidence intervals which becomes wider (less than 50%); (ii) in both the bolus and population situation neglecting the uncertainty of CP kinetics, as done in MM literature so far, introduces no bias, on average, on point estimates of MM indexes but only an underestimation of confidence intervals.;
Modelling task in scope:	simulation; estimation;
Nature of research:	Clinical research & Therapeutic use;
Therapeutic/disease area:	Endocrinology;

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

Mandatory file
- Executable_Magni_2004_diabetes_IVGTT.xml

Additional Files

Model owner: Paolo Magni
Submitted: Dec 11, 2015 11:43:47 PM
Last Modified: Nov 8, 2017 4:42:03 PM

Revisions

Version: 14
- Submitted on: Nov 8, 2017 4:42:03 PM
- Submitted by: Paolo Magni
- With comment: Updated model annotations.
Version: 11
- Submitted on: Oct 11, 2016 5:41:52 PM
- Submitted by: Paolo Magni
- With comment: Update MDL syntax to the version 1.0 and R script to SEE version 2.0.0. Added prior distributions Code automatically generated/manually modified for WinBUGS
Version: 8
- Submitted on: Jul 16, 2016 3:22:58 PM
- Submitted by: Paolo Magni
- With comment: Model revised without commit message
Version: 4
- Submitted on: Dec 11, 2015 11:43:47 PM
- Submitted by: Paolo Magni
- With comment: Edited model metadata online.

Name

Magni_2004_diabetes_IVGTT

Independent Variables

Function Definitions

combinedError1 : real (additive : real, proportional : real, f : real) = additive + proportional \cdot f

Covariate Model: $cm$

Continuous Covariates

GLUC

Parameter Model: $pm$

Random Variables

{eps_RES_CP1}_{vm_err.DV} ~ Normal2 (mean = 0, var = 1)

Population Parameters

data1

data_k_joint

{POP_joint}_{vm_mdl.MDL__prior} ~ RandomSample ()

POP_K01 = pm.POP_joint (1)

POP_K12 = pm.POP_joint (2)

POP_K21 = pm.POP_joint (3)

{POP_m}_{vm_mdl.MDL__prior} ~ Normal1 (mean = pm.MU_POP_m, stdev = pm.SIGMA_POP_m)

{POP_alpha}_{vm_mdl.MDL__prior} ~ Normal1 (mean = pm.MU_POP_alpha, stdev = pm.SIGMA_POP_alpha)

{POP_beta}_{vm_mdl.MDL__prior} ~ Normal1 (mean = pm.MU_POP_beta, stdev = pm.SIGMA_POP_beta)

{POP_x0}_{vm_mdl.MDL__prior} ~ Normal1 (mean = pm.MU_POP_x0, stdev = pm.SIGMA_POP_x0)

{POP_h}_{vm_mdl.MDL__prior} ~ Normal1 (mean = pm.MU_POP_h, stdev = pm.SIGMA_POP_h)

CV = 0.06

GB = 87

MU_POP_m = 0.5

MU_POP_alpha = 0.06

MU_POP_beta = 11

MU_POP_x0 = 1.8

MU_POP_h = pm.GB

SIGMA_POP_m = 0.5

SIGMA_POP_alpha = 0.06

SIGMA_POP_beta = 11

SIGMA_POP_x0 = 1.8

SIGMA_POP_h = pm.GB \cdot 0.03

Individual Parameters

K01 = pm.POP_K01

K12 = pm.POP_K12

K21 = pm.POP_K21

m = pm.POP_m

alpha = pm.POP_alpha

beta = pm.POP_beta

x0 = pm.POP_x0

h = pm.POP_h

x0new = pm.x0 \cdot 1000

Structural Model: $sm$

Variables

ISR = pm.m \cdot sm.X

dYi = {\begin{cases} - pm.alpha \cdot (sm.Yi - pm.beta \cdot (cm.GLUC - pm.h) \cdot 0.05551) & if & cm.GLUC > pm.h \\ - pm.alpha \cdot sm.Yi & otherwise \end{cases}

\begin{matrix} \frac{ⅆ}{ⅆ T} CP1 = - (pm.K01 + pm.K21) \cdot sm.CP1 + pm.K12 \cdot sm.CP2 + sm.ISR \\ CP1 (T = 0) = 0 \end{matrix}

\begin{matrix} \frac{ⅆ}{ⅆ T} CP2 = - pm.K12 \cdot sm.CP2 + pm.K21 \cdot sm.CP1 \\ CP2 (T = 0) = 0 \end{matrix}

\begin{matrix} \frac{ⅆ}{ⅆ T} X = - sm.ISR + sm.Yi \\ X (T = 0) = pm.x0new \end{matrix}

\begin{matrix} \frac{ⅆ}{ⅆ T} Yi = sm.dYi \\ Yi (T = 0) = 0 \end{matrix}

Observation Model: $om1$

Continuous Observation

Y = sm.CP1 + combinedError1 (additive = 1.0E-4, f = sm.CP1, proportional = pm.CV) + pm.eps_RES_CP1

External Dataset

OID

data1

File Specification

Format	$csv$
Delimiter	comma
File Location	prior_magni2004.csv

Column Definitions

Column ID	Position	Column Type	Value Type
$data_k01$	$1$	$undefined$	$real$
$data_k12$	$2$	$undefined$	$real$
$data_k21$	$3$	$undefined$	$real$

Column Mappings

Column Ref	Modelling Mapping
$data_k01$	$pm.data_k_joint (1)$
$data_k12$	$pm.data_k_joint (2)$
$data_k21$	$pm.data_k_joint (3)$

External Dataset

OID	$nm_ds$
Tool Format	NONMEM

File Specification

Format	$csv$
Delimiter	comma
File Location	Simulated_magni2004_data.csv

Column Definitions

Column ID	Position	Column Type	Value Type
$ID$	$1$	$id$	$int$
$TIME$	$2$	$idv$	$real$
$DV$	$3$	$dv$	$real$
$GLUC$	$4$	$covariate$	$real$
$EVID$	$5$	$evid$	$real$

Column Mappings

Column Ref	Modelling Mapping
$TIME$	$T$
$DV$	$om1.Y$
$GLUC$	$cm.GLUC$

Estimation Step

OID	$estimStep_1$
Dataset Reference	$nm_ds$

Parameters To Estimate

Parameter	Fixed?	Limits
pm.POP_joint	false	$()$
pm.POP_m	false	$()$
pm.POP_alpha	false	$()$
pm.POP_beta	false	$()$
pm.POP_x0	false	$()$
pm.POP_h	false	$()$

Operations

Operation: $1$

Op Type

generic

Operation Properties

Name	Value
algo	$mcmc$

Operation: $2$

Op Type

BUGS

Operation Properties

Name	Value
burnin	$1000$
inits	$POP_m=0.73, POP_beta=10.07, POP_x0=1.5, POP_alpha=0.044, POP_h=88.83$
nchains	$1$
niter	$20000$
odesolver	$LSODA$
parameters	$POP_K01, POP_K12, POP_K21$
winbugsgui	$false$

Step Dependencies

Step OID	Preceding Steps
$estimStep_1$

DDMODEL00000111: Magni_2004_diabetes_IVGTT

Revisions

Name

Independent Variables

Function Definitions

Covariate Model: cm

Continuous Covariates

Parameter Model: pm

Random Variables

Population Parameters

Individual Parameters

Structural Model: sm

Variables

Observation Model: om1

Continuous Observation

External Dataset

File Specification

Column Definitions

Column Mappings

External Dataset

File Specification

Column Definitions

Column Mappings

Estimation Step

Parameters To Estimate

Operations

Operation: 1

Operation Properties

Operation: 2

Operation Properties

Step Dependencies

Covariate Model: $cm$

Parameter Model: $pm$

Structural Model: $sm$

Observation Model: $om1$

Operation: $1$

Operation: $2$