DDMoRe Model Repository

Overview
Files
History
Model Definition
Trial Design
Modelling Steps

Short description:

This is a model for glucose kinetics in humans, including a physiology-based mechanism for glucose uptake saturation. It is able to describe the relationship between glucose utilization and glucose and insulin concentrations during different tests, such as the clamp, the oral glucose tolerance test and the mixed-meal test. By Roberto Bizzotto, Institute of Neuroscience, CNR, Padua, Italy. Copyright 2016

Format:	PharmML 0.8.x (0.8.1)
Related Publication:	Glucose uptake saturation explains glucose kinetics profiles measured by different tests. Bizzotto R, Natali A, Gastaldelli A, Muscelli E, Krssak M, Brehm A, Roden M, Ferrannini E, Mari A American journal of physiology. Endocrinology and metabolism, 8/2016, Volume 311, Issue 2, pages: E346-57 Affiliation: CNR Institute of Neuroscience, Padua, Italy; roberto.bizzotto@isib.cnr.it. Abstract: It is known that for a given insulin level glucose clearance depends on glucose concentration. However, a quantitative representation of the concomitant effects of hyperinsulinemia and hyperglycemia on glucose clearance, necessary to describe heterogeneous tests such as euglycemic and hyperglycemic clamps and oral tests, is lacking. Data from five studies (123 subjects) using a glucose tracer and including all the above tests in normal and diabetic subjects were collected. A mathematical model was developed in which glucose utilization was represented as a Michaelis-Menten function of glucose with constant Km and insulin-controlled Vmax, consistently with the basic notions of glucose transport. Individual values for the model parameters were estimated using a population approach. Tracer data were accurately fitted in all tests. The estimated Km was 3.88 (2.83-5.32) mmol/l [median (interquartile range)]. Median model-derived glucose clearance at 600 pmol/l insulin was reduced from 246 to 158 ml·min(-1)·m(-2) when glucose was raised from 5 to 10 mmol/l. The model reproduced the characteristic lack of increase in glucose clearance when moderate hyperinsulinemia was accompanied by hyperglycemia. In all tests, insulin sensitivity was inversely correlated with BMI, as expected (R(2) = 0.234, P = 0.0001). In conclusion, glucose clearance in euglycemic and hyperglycemic clamps and oral tests can be described with a unifying model, consistent with the notions of glucose transport and able to reproduce the suppression of glucose clearance due to hyperglycemia observed in previous studies. The model may be important for the design of reliable glucose homeostasis simulators.
Contributors:	Roberto Bizzotto

Context of model development:	Mechanistic Understanding;
Discrepancy between implemented model and original publication:	The model in MDL/PharmML language differs from the one used in the related publication in two aspects: 1) it does not consider that the subject undergoing a paired test is unique; 2) it is used as a simulation model, as performing parameter estimation on the provided dataset ("Simulated_glucoseKinetics.csv") would be meaningless, because of the used model inputs.;
Long technical model description:	Long_technical_model_description_glucoseKinetics.txt;
Model compliance with original publication:	No;
Model implementation requiring submitter’s additional knowledge:	No;
Modelling context description:	This model was developed to be able to describe glucose kinetics during different tests, such as the clamp, the oral glucose tolerance test and the mixed-meal test, with a unique set of equations and a unique parameter distribution. The success of the development process allowed to state that the physiological mechanisms underlying glucose kinetics are similar after oral and intravenous glucose administration. Moreover, the developed model quantitatively explained, for the first time, an important phenomenon: in the presence of hyperglycaemia, hyperinsulinemia fails to increase glucose clearance as would expected if glucose clearance were unaffected by the glucose levels. This model may have future applications in areas such as the development of more accurate insulin sensitivity indices from tests other than the glucose clamp and for the study of insulin sensitivity in circumstances in which the glucose clamp would not be feasible or appropriate. Furthermore, the model may be an essential component of new accurate glucose homeostasis simulators.;
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
- glucoseKinetics.xml

Additional Files

Model owner: Roberto Bizzotto
Submitted: Oct 14, 2016 5:54:08 PM
Last Modified: Jun 30, 2017 8:02:50 AM

Revisions

Version: 15
- Submitted on: Jun 30, 2017 8:02:50 AM
- Submitted by: Roberto Bizzotto
- With comment: Edited model metadata online.
Version: 13
- Submitted on: Oct 14, 2016 6:12:56 PM
- Submitted by: Roberto Bizzotto
- With comment: Edited model metadata online.
Version: 11
- Submitted on: Oct 14, 2016 6:05:42 PM
- Submitted by: Roberto Bizzotto
- With comment: Edited model metadata online.
Version: 9
- Submitted on: Oct 14, 2016 5:54:08 PM
- Submitted by: Roberto Bizzotto
- With comment: Edited model metadata online.

Name

Glucose kinetics in humans: a unique model for different tests

Description

Independent Variables

Function Definitions

additiveError : real (additive : real) = additive

Parameter Model: $pm$

Random Variables

{eta_KmG}_{vm_mdl.ID} ~ Normal2 (mean = 0, var = pm.var_KmG)

{eta_Vmax0}_{vm_mdl.ID} ~ Normal2 (mean = 0, var = pm.var_Vmax0)

{eta_Emax}_{vm_mdl.ID} ~ Normal2 (mean = 0, var = pm.var_Emax)

{eta_gamma}_{vm_mdl.ID} ~ Normal2 (mean = 0, var = pm.var_gamma)

{eta_KmI}_{vm_mdl.ID} ~ Normal2 (mean = 0, var = pm.var_KmI)

{eta_t12I}_{vm_mdl.ID} ~ Normal2 (mean = 0, var = pm.var_t12I)

{eta_t12G}_{vm_mdl.ID} ~ Normal2 (mean = 0, var = pm.var_t12G)

{eta_V}_{vm_mdl.ID} ~ Normal2 (mean = 0, var = pm.var_V)

{eta_flambda3}_{vm_mdl.ID} ~ Normal2 (mean = 0, var = pm.var_flambda3)

{eta_flambda2}_{vm_mdl.ID} ~ Normal2 (mean = 0, var = pm.var_flambda2)

{eta_w1}_{vm_mdl.ID} ~ Normal2 (mean = 0, var = pm.var_w1)

{eta_fw2}_{vm_mdl.ID} ~ Normal2 (mean = 0, var = pm.var_fw2)

{eta_F}_{vm_mdl.ID} ~ Normal2 (mean = 0, var = pm.var_F)

{epsilon}_{vm_err.DV} ~ Normal2 (mean = 0, var = pm.sigma)

Population Parameters

typ_KmG

typ_Vmax0

typ_Emax

typ_gamma

typ_KmI

typ_t12I

typ_t12G

typ_V

typ_flambda3

typ_flambda2

typ_w1

typ_fw2

typ_F

var_KmG

var_Vmax0

var_Emax

var_gamma

var_KmI

var_t12I

var_t12G

var_V

var_flambda3

var_flambda2

var_w1

var_fw2

var_F

corr_gamma_KmI

alpha

sigma

Individual Parameters

\ln (KmG) = \ln (pm.typ_KmG) + pm.eta_KmG

\ln (Vmax0) = \ln (pm.typ_Vmax0) + pm.eta_Vmax0

\ln (Emax) = \ln (pm.typ_Emax) + pm.eta_Emax

\ln (gamma) = \ln (pm.typ_gamma) + pm.eta_gamma

\ln (KmI) = \ln (pm.typ_KmI) + pm.eta_KmI

\ln (t12I) = \ln (pm.typ_t12I) + pm.eta_t12I

\ln (t12G) = \ln (pm.typ_t12G) + pm.eta_t12G

\ln (V) = \ln (pm.typ_V) + pm.eta_V

logit (flambda3) = logit (pm.typ_flambda3) + pm.eta_flambda3

logit (flambda2) = logit (pm.typ_flambda2) + pm.eta_flambda2

logit (w1) = logit (pm.typ_w1) + pm.eta_w1

logit (fw2) = logit (pm.typ_fw2) + pm.eta_fw2

\ln (F) = \ln (pm.typ_F) + pm.eta_F

Random Variable Correlation

corr (eta_gamma, eta_KmI) = pm.corr_gamma_KmI

Structural Model: $sm$

Variables

INS

GLU

TOBS

T1

GLU1

INS1

VHL = 700

deltaHL = 15

delta = 10

w2 = (1 - pm.w1) \cdot pm.fw2

w3 = 1 - pm.w1 - sm.w2

lambda1 = \frac{\frac{(pm.w1 \cdot pm.flambda2 \cdot pm.flambda3 + sm.w2 \cdot pm.flambda3 + sm.w3)}{pm.flambda2 \cdot pm.flambda3} \cdot sm.delta \cdot pm.F}{(sm.delta \cdot (pm.V - sm.VHL) - pm.F)}

lambda2 = sm.lambda1 \cdot pm.flambda2

lambda3 = sm.lambda2 \cdot pm.flambda3

c1 = \frac{sm.deltaHL \cdot pm.F}{(sm.deltaHL \cdot sm.VHL - 2 \cdot pm.F)}

c2 = \frac{- sm.deltaHL \cdot pm.F}{(sm.deltaHL \cdot sm.VHL - pm.F)}

I = \frac{(T - sm.T1)}{(sm.TOBS - sm.T1)} \cdot (sm.INS - sm.INS1) + sm.INS1

GL = \frac{(T - sm.T1)}{(sm.TOBS - sm.T1)} \cdot (sm.GLU - sm.GLU1) + sm.GLU1

t0 = 0

\begin{matrix} \frac{ⅆ}{ⅆ T} X1 = \frac{(sm.GL - sm.X1) \cdot \ln (2)}{pm.t12G} \\ X1 (T = sm.t0) = 0 \end{matrix}

\begin{matrix} \frac{ⅆ}{ⅆ T} X = \frac{(sm.X1 - sm.X) \cdot \ln (2)}{pm.t12G} \\ X (T = sm.t0) = 0 \end{matrix}

\begin{matrix} \frac{ⅆ}{ⅆ T} Z1 = \frac{(sm.I - sm.Z1) \cdot \ln (2)}{pm.t12I} \\ Z1 (T = sm.t0) = 0 \end{matrix}

\begin{matrix} \frac{ⅆ}{ⅆ T} Z = \frac{(sm.Z1 - sm.Z) \cdot \ln (2)}{pm.t12I} \\ Z (T = sm.t0) = 0 \end{matrix}

Vmax = pm.Vmax0 + \frac{pm.Emax \cdot {sm.Z}^{pm.gamma}}{({pm.KmI}^{pm.gamma} + {sm.Z}^{pm.gamma})}

cl = \frac{sm.Vmax}{(pm.KmG + sm.X)}

E = \frac{sm.cl}{pm.F}

\begin{matrix} \frac{ⅆ}{ⅆ T} xHL1 = sm.c2 \cdot sm.xHL1 + sm.Gv \\ xHL1 (T = sm.t0) = 0 \end{matrix}

\begin{matrix} \frac{ⅆ}{ⅆ T} xHL2 = - sm.deltaHL \cdot sm.xHL2 + sm.Gv \\ xHL2 (T = sm.t0) = 0 \end{matrix}

G = sm.c1 \cdot sm.xHL1 - sm.c1 \cdot sm.xHL2

\begin{matrix} \frac{ⅆ}{ⅆ T} xPER1 = - sm.lambda1 \cdot sm.xPER1 + pm.w1 \cdot (1 - sm.E) \cdot sm.G \\ xPER1 (T = sm.t0) = 0 \end{matrix}

\begin{matrix} \frac{ⅆ}{ⅆ T} xPER2 = - sm.lambda2 \cdot sm.xPER2 + sm.w2 \cdot (1 - sm.E) \cdot sm.G \\ xPER2 (T = sm.t0) = 0 \end{matrix}

\begin{matrix} \frac{ⅆ}{ⅆ T} xPER3 = - sm.lambda3 \cdot sm.xPER3 + sm.w3 \cdot (1 - sm.E) \cdot sm.G \\ xPER3 (T = sm.t0) = 0 \end{matrix}

\begin{matrix} \frac{ⅆ}{ⅆ T} xPER4 = sm.lambda1 \cdot sm.xPER1 + sm.lambda2 \cdot sm.xPER2 + sm.lambda3 \cdot sm.xPER3 - sm.delta \cdot sm.xPER4 \\ xPER4 (T = sm.t0) = 0 \end{matrix}

Gv = sm.delta \cdot sm.xPER4

Variables

depot (ADM = 1, TARGET = sm.X1)

depot (ADM = 2, TARGET = sm.X)

depot (ADM = 3, TARGET = sm.Z1)

depot (ADM = 4, TARGET = sm.Z)

depot (ADM = 5, TARGET = sm.xHL1, P = \frac{1}{pm.F})

depot (ADM = 6, TARGET = sm.xHL2, P = \frac{1}{pm.F})

Observation Model: $om1$

Continuous Observation

Y = sm.G + additiveError (additive = pm.alpha) + pm.epsilon

External Dataset

OID	$nm_ds$
Tool Format	Monolix

File Specification

Format	$csv$
Delimiter	comma
File Location	Simulated_glucoseKinetics.csv

Column Definitions

Column ID	Position	Column Type	Value Type
$TIME$	$1$	$idv$	$real$
$DV$	$2$	$dv$	$real$
$MDV$	$3$	$mdv$	$int$
$AMT$	$4$	$dose$	$real$
$RATE$	$5$	$rate$	$real$
$ID$	$6$	$id$	$int$
$INS$	$7$	$reg$	$real$
$GLU$	$8$	$reg$	$real$
$CMT$	$9$	$adm$	$int$
$TOBS$	$10$	$reg$	$real$
$T1$	$11$	$reg$	$real$
$GLU1$	$12$	$reg$	$real$
$INS1$	$13$	$reg$	$real$

Column Mappings

Column Ref	Modelling Mapping
$TIME$	$T$
$DV$	$om1.Y$
$AMT$	${\begin{cases} blk: sm, adm: 1 & if & AMT = 1 \\ blk: sm, adm: 2 & if & AMT = 2 \\ blk: sm, adm: 3 & if & AMT = 3 \\ blk: sm, adm: 4 & if & AMT = 4 \\ blk: sm, adm: 5 & if & AMT = 5 \\ blk: sm, adm: 6 & if & AMT = 6 \end{cases}$
$ID$	$vm_mdl.ID$
$INS$	$sm.INS$
$GLU$	$sm.GLU$
$TOBS$	$sm.TOBS$
$T1$	$sm.T1$
$GLU1$	$sm.GLU1$
$INS1$	$sm.INS1$

Simulation Step

OID	$simulStep_1$

Variable Assignments

Variable	Value
pm.typ_KmG	$3.88$
pm.typ_Vmax0	$338$
pm.typ_Emax	$4812$
pm.typ_gamma	$1.62$
pm.typ_KmI	$784$
pm.typ_t12I	$15.9$
pm.typ_t12G	$0.7$
pm.typ_V	$12648$
pm.typ_flambda3	$0.0582$
pm.typ_flambda2	$0.154$
pm.typ_w1	$0.609$
pm.typ_fw2	$0.901$
pm.typ_F	$2688$
pm.var_KmG	$0.219$
pm.var_Vmax0	$0$
pm.var_Emax	$0.112$
pm.var_gamma	$0.111$
pm.var_KmI	$0.263$
pm.var_t12I	$0.151$
pm.var_t12G	$0$
pm.var_V	$0.0557$
pm.var_flambda3	$0.179$
pm.var_flambda2	$0$
pm.var_w1	$0.773$
pm.var_fw2	$0$
pm.var_F	$0$
pm.corr_gamma_KmI	$- 0.44$
pm.alpha	$0.014$
pm.sigma	$1$

Operations

Operation: $1$

Op Type

generic

Operation Properties

Name	Value

Step Dependencies

Step OID	Preceding Steps
$simulStep_1$

DDMODEL00000227: Glucose kinetics in humans: a unique model for different tests

Revisions

Name

Description

Independent Variables

Function Definitions

Parameter Model: pm

Random Variables

Population Parameters

Individual Parameters

Random Variable Correlation

Structural Model: sm

Variables

Variables

Observation Model: om1

Continuous Observation

External Dataset

File Specification

Column Definitions

Column Mappings

Simulation Step

Variable Assignments

Operations

Operation: 1

Operation Properties

Step Dependencies

Parameter Model: $pm$

Structural Model: $sm$

Observation Model: $om1$

Operation: $1$