# DDMODEL00000006: Simeoni_2004_oncology_TGI

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: .hiddenContent {display:none;} 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: In vivo; Preclinical development; 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).
• Model owner: Paolo Magni
• Submitted: Sep 25, 2014 5:40:49 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

 T

### Function Definitions

 $\mathrm{proportionalError}:\mathrm{real}\left(\mathrm{proportional}:\mathrm{real},f:\mathrm{real}\right)=\mathrm{proportional}\cdot f$

### Parameter Model: $\mathrm{pm}$

#### Random Variables

${\mathrm{eps_RES_W}}_{\mathrm{vm_err.DV}}~\mathrm{Normal2}\left(\mathrm{mean}=0,\mathrm{var}=1\right)$

#### Population Parameters

$\mathrm{LAMBDA0_POP}$
$\mathrm{LAMBDA1_POP}$
$\mathrm{K1_POP}$
$\mathrm{K2_POP}$
$\mathrm{W0_POP}$
$\mathrm{K10_POP}$
$\mathrm{K12_POP}$
$\mathrm{K21_POP}$
$\mathrm{V1_POP}$
$\mathrm{CV}$

#### Individual Parameters

$\mathrm{LAMBDA0}=\mathrm{pm.LAMBDA0_POP}$
$\mathrm{LAMBDA1}=\mathrm{pm.LAMBDA1_POP}$
$\mathrm{K1}=\mathrm{pm.K1_POP}$
$\mathrm{K2}=\mathrm{pm.K2_POP}$
$\mathrm{W0}=\mathrm{pm.W0_POP}$
$\mathrm{K10}=\mathrm{pm.K10_POP}$
$\mathrm{K12}=\mathrm{pm.K12_POP}$
$\mathrm{K21}=\mathrm{pm.K21_POP}$
$\mathrm{V1}=\mathrm{pm.V1_POP}$

### Structural Model: $\mathrm{sm}$

#### Variables

$\mathrm{PSI}=20$
$C=\frac{\mathrm{sm.Q1}}{\mathrm{pm.V1}}$
$\mathrm{WTOT}=\mathrm{sm.X1}+\mathrm{sm.X2}+\mathrm{sm.X3}+\mathrm{sm.X4}$
$\begin{array}{c}\frac{d}{dT}\mathrm{Q1}=\mathrm{pm.K21}\cdot \mathrm{sm.Q2}-\left(\mathrm{pm.K10}+\mathrm{pm.K12}\right)\cdot \mathrm{sm.Q1}\\ \mathrm{Q1}\left(T=0\right)=0\end{array}$
$\begin{array}{c}\frac{d}{dT}\mathrm{Q2}=\mathrm{pm.K12}\cdot \mathrm{sm.Q1}-\mathrm{pm.K21}\cdot \mathrm{sm.Q2}\\ \mathrm{Q2}\left(T=0\right)=0\end{array}$
$\begin{array}{c}\frac{d}{dT}\mathrm{X1}=\frac{\mathrm{pm.LAMBDA0}\cdot \mathrm{sm.X1}}{{\left(1+{\frac{\mathrm{sm.WTOT}\cdot \mathrm{pm.LAMBDA0}}{\mathrm{pm.LAMBDA1}}}^{\mathrm{sm.PSI}}\right)}^{\frac{1}{\mathrm{sm.PSI}}}}-\mathrm{pm.K2}\cdot \mathrm{sm.C}\cdot \mathrm{sm.X1}\\ \mathrm{X1}\left(T=0\right)=\mathrm{pm.W0}\end{array}$
$\begin{array}{c}\frac{d}{dT}\mathrm{X2}=\mathrm{pm.K2}\cdot \mathrm{sm.C}\cdot \mathrm{sm.X1}-\mathrm{pm.K1}\cdot \mathrm{sm.X2}\\ \mathrm{X2}\left(T=0\right)=0\end{array}$
$\begin{array}{c}\frac{d}{dT}\mathrm{X3}=\mathrm{pm.K1}\cdot \mathrm{sm.X2}-\mathrm{pm.K1}\cdot \mathrm{sm.X3}\\ \mathrm{X3}\left(T=0\right)=0\end{array}$
$\begin{array}{c}\frac{d}{dT}\mathrm{X4}=\mathrm{pm.K1}\cdot \mathrm{sm.X3}-\mathrm{pm.K1}\cdot \mathrm{sm.X4}\\ \mathrm{X4}\left(T=0\right)=0\end{array}$

### Observation Model: $\mathrm{om1}$

#### Continuous Observation

$Y=\mathrm{sm.WTOT}+\mathrm{proportionalError}\left(\mathrm{proportional}=\mathrm{pm.CV},f=\mathrm{sm.WTOT}\right)+\mathrm{pm.eps_RES_W}$

## External Dataset

 OID $\mathrm{nm_ds}$ Tool Format NONMEM

### File Specification

 Format $\mathrm{csv}$ Delimiter comma File Location Simulated_simeoni2004_data.csv

### Column Definitions

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

### Column Mappings

Column Ref Modelling Mapping
$TIME$
$T$
$DV$
$\mathrm{om1.Y}$
$AMT$
$\left\{\begin{array}{lll}\mathrm{sm.Q1}& \text{if}& \mathrm{AMT}>0\end{array}$

## Estimation Step

 OID $\mathrm{estimStep_1}$ Dataset Reference $\mathrm{nm_ds}$

### Parameters To Estimate

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

### Operations

#### Operation: $1$

 Op Type generic
##### Operation Properties
Name Value
algo
$\text{foce}$

## Step Dependencies

Step OID Preceding Steps
$\mathrm{estimStep_1}$