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Model Definition
Estimation Steps

Short description:

Preclinical Biomarker/tumor growth inhibition model for targeted agents The model integrates the (i) pharmacokinetics drug properties, (ii) drug effect on biomarker turnover, (iii) propagation of the inhibitory tumor growth signal resulted from the biomarker effects, and (iv) tumor growth dynamics.

Format:	PharmML (0.6.1)
Related Publication:	Semi-mechanistic modelling of the tumour growth inhibitory effects of LY2157299, a new type I receptor TGF-beta kinase antagonist, in mice. Bueno L, de Alwis DP, Pitou C, Yingling J, Lahn M, Glatt S, Trocóniz IF European journal of cancer (Oxford, England : 1990), 1/2008, Volume 44, Issue 1, pages: 142-150 Affiliation: Department of Pharmacy and Pharmaceutical Technology, School of Pharmacy, University of Navarra, Pamplona, Spain. Abstract: Human xenografts Calu6 (non-small cell lung cancer) and MX1 (breast cancer) were implanted subcutaneously in nude mice and LY2157299, a new type I receptor TGF-beta kinase antagonist, was administered orally. Plasma levels of LY2157299, percentage of phosphorylated Smad2,3 (pSmad) in tumour, and tumour size were used to establish a semi-mechanistic pharmacokinetic/pharmacodynamic model. An indirect response model was used to relate plasma concentrations with pSmad. The model predicts complete inhibition of pSmad and rapid turnover rates [t(1/2) (min)=18.6 (Calu6) and 32.0 (MX1)]. Tumour growth inhibition was linked to pSmad using two signal transduction compartments characterised by a mean signal propagation time with estimated values of 6.17 and 28.7 days for Calu6 and MX1, respectively. The model provides a tool to generate experimental hypothesis to gain insights into the mechanisms of signal transduction associated to the TGF-beta membrane receptor type I.
Contributors:	Niklas Hartung

Context of model development:	Disease Progression model;
Long technical model description:	Plasma pharmacokinetics of the TGF-beta kinase antagonist were best described with a two compartment model. Phosphorylated Smad2 and Smad3 (pSmad) was used as a biomarker for tumour growth inhibition. An indirect response model was used to relate the predicted plasma concentrations with the observed pSmad data. Tumour growth was described by an exponential model with a switch from exponential to linear growth. The inhibitory growth signal exerted by pSmad was described by a 0-1 normalised effect on tumour growth rate.;
Model compliance with original publication:	Yes;
Model implementation requiring submitter’s additional knowledge:	No;
Modelling context description:	tumour growth inhibitory effects of a TGF-beta kinase antagonist;
Modelling task in scope:	estimation;
Nature of research:	Preclinical development;
Therapeutic/disease area:	Oncology;

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

Mandatory file
- Executable_Bueno.xml

Additional Files

Model owner: Niklas Hartung
Submitted: Dec 15, 2015 7:30:52 PM
Last Modified: Jul 15, 2016 10:19:49 AM

Revisions

Version: 10
- Submitted on: Jul 15, 2016 10:19:49 AM
- Submitted by: Niklas Hartung
- With comment: Edited model metadata online.
Version: 7
- Submitted on: May 20, 2016 2:07:25 PM
- Submitted by: Niklas Hartung
- With comment: Model revised without commit message
Version: 4
- Submitted on: Dec 15, 2015 7:30:52 PM
- Submitted by: Niklas Hartung
- With comment: Edited model metadata online.

Independent variable T

Function Definitions

proportionalError (proportional, f) = (proportional \times f)

Structural Model sm

Variable definitions

KA = (8 \times 24)

V = 0.443

CL = (0.551 \times 24)

VT = 1.29

Q = (1.28 \times 24)

KOUT = (2.24 \times 24)

E0 = 100

KSYN = (KOUT \times E0)

EMAX = 1

C50 = 0.79

NN = 1.4

GA = 20

KE0 = \frac{3}{MTT}

CP = (\frac{CENTRAL}{V} + 1.0E-4)

IT = (1 - \frac{(EMAX \times {CP}^{NN})}{({CP}^{NN} + {C50}^{NN})})

SNL = \frac{((E0 - SMAD) + 1.0E-5)}{E0}

TDCC = (1 - SINL2)

\frac{dDEPOT}{dT} = (- KA \times DEPOT)

\frac{dCENTRAL}{dT} = ((((KA \times DEPOT) + (\frac{Q}{VT} \times PERPH)) - (\frac{Q}{V} \times CENTRAL)) - (\frac{CL}{V} \times CENTRAL))

\frac{dPERPH}{dT} = ((\frac{Q}{V} \times CENTRAL) - (\frac{Q}{VT} \times PERPH))

\frac{dSMAD}{dT} = ((KSYN \times IT) - (KOUT \times SMAD))

\frac{dTUMOUR}{dT} = (\frac{(KIN \times TUMOUR)}{{(1 + {\frac{(KIN \times TUMOUR)}{KB}}^{GA})}^{\frac{1}{GA}}} \times TDCC)

\frac{dSINL1}{dT} = (KE0 \times (SNL - SINL1))

\frac{dSINL2}{dT} = (KE0 \times (SINL1 - SINL2))

Initial conditions

DEPOT = 0

CENTRAL = 0

PERPH = 0

SMAD = 100

TUMOUR = N0

SINL1 = 0

SINL2 = 0

Variability Model

Level	Type
DV	residualError
ID	parameterVariability

Parameter Model

Parameters

POP_KIN

;

POP_N0

;

POP_KB

;

POP_MTT

;

RUV

;

PPV_KIN

;

PPV_N0

;

ETA_KIN \sim N (0.0, PPV_KIN)

— ID

ETA_N0 \sim N (0.0, PPV_N0)

— ID

EPS_Y \sim N (0.0, 1.0)

— DV

log (KIN) = (log (POP_KIN) + ETA_KIN)

log (N0) = (log (POP_N0) + ETA_N0)

KB = POP_KB

MTT = POP_MTT

Observation Model

Observation Y
Continuous / Residual Data

Parameters

Y = (TUMOUR + (proportionalError (RUV, TUMOUR) \times EPS_Y))

Estimation Steps

Estimation Step estimStep_1

Estimation parameters

Initial estimates for non-fixed parameters

$POP_KIN = 0.137$
$POP_N0 = 39$
$POP_KB = 111$
$POP_MTT = 6.17$
$RUV = 0.0322$
$PPV_KIN = 0.0358$
$PPV_N0 = 0.0469$

Estimation operations

1) Estimate the population parameters

Algorithm FOCEI

Step Dependencies

estimStep_1

DDMODEL00000127: Bueno_PreclinicalBiomarkerTGI