DDMODEL00000111: Magni_2004_diabetes_IVGTT

  public model
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.
PharmML 0.8.x (0.8.1)
  • 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
  • Dipartimento di Informatica e Sistemistica, Università degli Studi di Pavia via Ferrata, Pavia, Italy. paolo.magni@unipv.it
  • 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.
Paolo Magni
Context of model development: Variability sources in PK and PD (CYP, Renal, Biomarkers); Clinical end-point; Mechanistic Understanding;
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: estimation; simulation;
Nature of research: Clinical research & Therapeutic use;
Therapeutic/disease area: Endocrinology;
Annotations are correct.
This model is not certified.
  • Model owner: Paolo Magni
  • Submitted: Dec 11, 2015 11:43:47 PM
  • Last Modified: Nov 8, 2017 4:42:03 PM
Revisions
  • Version: 14 public model Download this version
    • Submitted on: Nov 8, 2017 4:42:03 PM
    • Submitted by: Paolo Magni
    • With comment: Updated model annotations.
  • Version: 11 public model Download this version
    • 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 public model Download this version
    • Submitted on: Jul 16, 2016 3:22:58 PM
    • Submitted by: Paolo Magni
    • With comment: Model revised without commit message
  • Version: 4 public model Download this version
    • 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

T

Function Definitions

combinedError1:realadditive:realproportional:realf:real=additive+proportionalf

Covariate Model: cm

Continuous Covariates

GLUC

Parameter Model: pm

Random Variables

eps_RES_CP1vm_err.DV~Normal2mean=0var=1

Population Parameters

data1
data_k_joint
POP_jointvm_mdl.MDL__prior~RandomSample
POP_K01=pm.POP_joint1
POP_K12=pm.POP_joint2
POP_K21=pm.POP_joint3
POP_mvm_mdl.MDL__prior~Normal1mean=pm.MU_POP_mstdev=pm.SIGMA_POP_m
POP_alphavm_mdl.MDL__prior~Normal1mean=pm.MU_POP_alphastdev=pm.SIGMA_POP_alpha
POP_betavm_mdl.MDL__prior~Normal1mean=pm.MU_POP_betastdev=pm.SIGMA_POP_beta
POP_x0vm_mdl.MDL__prior~Normal1mean=pm.MU_POP_x0stdev=pm.SIGMA_POP_x0
POP_hvm_mdl.MDL__prior~Normal1mean=pm.MU_POP_hstdev=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.GB0.03

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.x01000

Structural Model: sm

Variables

ISR=pm.msm.X
dYi={-pm.alphasm.Yi-pm.betacm.GLUC-pm.h0.05551ifcm.GLUC>pm.h-pm.alphasm.Yiotherwise
TCP1=-pm.K01+pm.K21sm.CP1+pm.K12sm.CP2+sm.ISRCP1T=0=0
TCP2=-pm.K12sm.CP2+pm.K21sm.CP1CP2T=0=0
TX=-sm.ISR+sm.YiXT=0=pm.x0new
TYi=sm.dYiYiT=0=0

Observation Model: om1

Continuous Observation

Y=sm.CP1+combinedError1additive=1.0E-4f=sm.CP1proportional=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_joint1
data_k12
pm.data_k_joint2
data_k21
pm.data_k_joint3

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 Initial Value 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
 
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