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Short description:

PKPD model of Tumor Growth Kinetics in xenograft models after administration of anticancer agents

Format:	PharmML 0.8.x (0.8.1)
Related Publication:	Predictive pharmacokinetic-pharmacodynamic modeling of tumor growth kinetics in xenograft models after administration of anticancer agents. Simeoni M, Magni P, Cammia C, De Nicolao G, Croci V, Pesenti E, Germani M, Poggesi I, Rocchetti M Cancer research, 2/2004, Volume 64, Issue 3, pages: 1094-1101 Affiliation: Dipartimento di Informatica e Sistemistica, University of Pavia, Pavia, and Pharmacia Italia S.p.A., Nerviano. Milan, Italy. Abstract: The available mathematical models describing tumor growth and the effect of anticancer treatments on tumors in animals are of limited use within the drug industry. A simple and effective model would allow applying quantitative thinking to the preclinical development of oncology drugs. In this article, a minimal pharmacokinetic-pharmacodynamic model is presented, based on a system of ordinary differential equations that link the dosing regimen of a compound to the tumor growth in animal models. The growth of tumors in nontreated animals is described by an exponential growth followed by a linear growth. In treated animals, the tumor growth rate is decreased by a factor proportional to both drug concentration and number of proliferating tumor cells. A transit compartmental system is used to model the process of cell death, which occurs at later times. The parameters of the pharmacodynamic model are related to the growth characteristics of the tumor, to the drug potency, and to the kinetics of the tumor cell death. Therefore, such parameters can be used for ranking compounds based on their potency and for evaluating potential differences in the tumor cell death process. The model was extensively tested on discovery candidates and known anticancer drugs. It fitted well the experimental data, providing reliable parameter estimates. On the basis of the parameters estimated in a first experiment, the model successfully predicted the response of tumors exposed to drugs given at different dose levels and/or schedules. It is, thus, possible to use the model prospectively, optimizing the design of new experiments.
Contributors:	Paolo Magni

Context of model development:	Candidate Comparison, Selection, Human Dose Prediction;
Model compliance with original publication:	Yes;
Model implementation requiring submitter’s additional knowledge:	No;
Modelling context description:	The available mathematical models describing tumor growth and the effect of anticancer treatments on tumors in animals are of limited use within the drug industry. A simple and effective model would allow applying quantitative thinking to the preclinical development of oncology drugs. In this article, a minimal pharmacokinetic-pharmacodynamic model is presented, based on a system of ordinary differential equations that link the dosing regimen of a compound to the tumor growth in animal models. The growth of tumors in nontreated animals is described by an exponential growth followed by a linear growth. In treated animals, the tumor growth rate is decreased by a factor proportional to both drug concentration and number of proliferating tumor cells. A transit compartmental system is used to model the process of cell death, which occurs at later times. The parameters of the pharmacodynamic model are related to the growth characteristics of the tumor, to the drug potency, and to the kinetics of the tumor cell death. Therefore, such parameters can be used for ranking compounds based on their potency and for evaluating potential differences in the tumor cell death process. The model was extensively tested on discovery candidates and known anticancer drugs. It fitted well the experimental data, providing reliable parameter estimates. On the basis of the parameters estimated in a first experiment, the model successfully predicted the response of tumors exposed to drugs given at different dose levels and/or schedules. It is, thus, possible to use the model prospectively, optimizing the design of new experiments.;
Modelling task in scope:	estimation;
Nature of research:	Preclinical development; In vivo;
Therapeutic/disease area:	Oncology;

Validation Status:

Annotations are correct.

Certification Comment:

This model is appropriately and completely documented, can be executed using the DDMoRe Interoperability Framework and is able to reproduce the key findings reported in the related publication. The submitter has demonstrated that the uploaded model is executable and described and coded in agreement with the related publication as follows: 1. parameter estimation using the Interoperability Product 5 - Release Candidate 4 (aka SEE 2.0.0), with NONMEM as the target software and both the real original data provided by the submitter to the reviewer and the simulated data uploaded to the repository; 2. reasonable reproduction of the values in Table 2 from the publication using SEE 2.0.0, with NONMEM as the target software and the real original data (the validation did not consider experiment 1 and coefficient of variations); 3. reproduction of Figure 7 from the publication after parameter estimation as detailed in point 2 above (the validation did not consider experiment 1).

Mandatory file
- Executable_Simeoni_2004_oncology_TGI.xml

Additional Files

Model owner: Paolo Magni
Submitted: Sep 25, 2014 5:40:49 PM
Last Modified: Oct 5, 2016 11:16:01 PM

Revisions

Version: 9
- Submitted on: Oct 5, 2016 11:16:01 PM
- Submitted by: Paolo Magni
- With comment: Edited model metadata online.
Version: 7
- Submitted on: Oct 5, 2016 10:45:35 PM
- Submitted by: Paolo Magni
- With comment: Update MDL syntax to the version 1.0 and R script to SEE version 2.0.0. Code automatically generated for NONMEM and MONOLIX
Version: 6
- Submitted on: May 24, 2016 11:10:38 PM
- Submitted by: Paolo Magni
- With comment: Updated model annotations.
Version: 5
- Submitted on: May 24, 2016 11:00:52 PM
- Submitted by: Paolo Magni
- With comment: Updated model annotations.
Version: 3
- Submitted on: Dec 10, 2015 9:38:58 PM
- Submitted by: Paolo Magni
- With comment: Edited model metadata online.
Version: 1
- Submitted on: Sep 25, 2014 5:40:49 PM
- Submitted by: Paolo Magni
- With comment: Import of Simeoni_2004_oncology_TGI

Name

Generated from MDL. MOG ID: simeoni2004

Independent Variables

Function Definitions

proportionalError : real (proportional : real, f : real) = proportional \cdot f

Parameter Model: $pm$

Random Variables

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

Population Parameters

LAMBDA0_POP

LAMBDA1_POP

K1_POP

K2_POP

W0_POP

K10_POP

K12_POP

K21_POP

V1_POP

CV

Individual Parameters

LAMBDA0 = pm.LAMBDA0_POP

LAMBDA1 = pm.LAMBDA1_POP

K1 = pm.K1_POP

K2 = pm.K2_POP

W0 = pm.W0_POP

K10 = pm.K10_POP

K12 = pm.K12_POP

K21 = pm.K21_POP

V1 = pm.V1_POP

Structural Model: $sm$

Variables

PSI = 20

C = \frac{sm.Q1}{pm.V1}

WTOT = sm.X1 + sm.X2 + sm.X3 + sm.X4

\begin{matrix} \frac{ⅆ}{ⅆ T} Q1 = pm.K21 \cdot sm.Q2 - (pm.K10 + pm.K12) \cdot sm.Q1 \\ Q1 (T = 0) = 0 \end{matrix}

\begin{matrix} \frac{ⅆ}{ⅆ T} Q2 = pm.K12 \cdot sm.Q1 - pm.K21 \cdot sm.Q2 \\ Q2 (T = 0) = 0 \end{matrix}

\begin{matrix} \frac{ⅆ}{ⅆ T} X1 = \frac{pm.LAMBDA0 \cdot sm.X1}{{(1 + {\frac{sm.WTOT \cdot pm.LAMBDA0}{pm.LAMBDA1}}^{sm.PSI})}^{\frac{1}{sm.PSI}}} - pm.K2 \cdot sm.C \cdot sm.X1 \\ X1 (T = 0) = pm.W0 \end{matrix}

\begin{matrix} \frac{ⅆ}{ⅆ T} X2 = pm.K2 \cdot sm.C \cdot sm.X1 - pm.K1 \cdot sm.X2 \\ X2 (T = 0) = 0 \end{matrix}

\begin{matrix} \frac{ⅆ}{ⅆ T} X3 = pm.K1 \cdot sm.X2 - pm.K1 \cdot sm.X3 \\ X3 (T = 0) = 0 \end{matrix}

\begin{matrix} \frac{ⅆ}{ⅆ T} X4 = pm.K1 \cdot sm.X3 - pm.K1 \cdot sm.X4 \\ X4 (T = 0) = 0 \end{matrix}

Observation Model: $om1$

Continuous Observation

Y = sm.WTOT + proportionalError (proportional = pm.CV, f = sm.WTOT) + pm.eps_RES_W

External Dataset

OID	$nm_ds$
Tool Format	NONMEM

File Specification

Format	$csv$
Delimiter	comma
File Location	Simulated_simeoni2004_data.csv

Column Definitions

Column ID	Position	Column Type	Value Type
$ID$	$1$	$id$	$int$
$TIME$	$2$	$idv$	$real$
$DV$	$3$	$dv$	$real$
$AMT$	$4$	$dose$	$real$
$MDV$	$5$	$mdv$	$int$
$CMT$	$6$	$cmt$	$int$

Column Mappings

Column Ref	Modelling Mapping
$TIME$	$T$
$DV$	$om1.Y$
$AMT$	${\begin{cases} sm.Q1 & if & AMT > 0 \end{cases}$

Estimation Step

OID	$estimStep_1$
Dataset Reference	$nm_ds$

Parameters To Estimate

Parameter	Initial Value	Fixed?	Limits
pm.LAMBDA0_POP	$0.3$	false	$(0)$
pm.LAMBDA1_POP	$0.7$	false	$(0)$
pm.K1_POP	$0.7$	false	$(0)$
pm.K2_POP	$0.5$	false	$(0)$
pm.W0_POP	$0.02$	false	$(0)$
pm.K10_POP	$20.832$	true	$()$
pm.K12_POP	$0.144$	true	$()$
pm.K21_POP	$2.011$	true	$()$
pm.V1_POP	$0.81$	true	$()$
pm.CV	$0.1$	false	$(0)$

Operations

Operation: $1$

Op Type

generic

Operation Properties

Name	Value
algo	$foce$

Step Dependencies

Step OID	Preceding Steps
$estimStep_1$

DDMODEL00000006: Simeoni_2004_oncology_TGI