# DDMODEL00000096: Terranova_2013_oncology_TGI_combo

Short description:
PKPD model of tumor growth kinetics in xenograft mice after administration of anticancer agents given in combination
 Format: PharmML 0.8.x (0.8.1) Related Publication: .hiddenContent {display:none;} A predictive pharmacokinetic-pharmacodynamic model of tumor growth kinetics in xenograft mice after administration of anticancer agents given in combination. Terranova N, Germani M, Del Bene F, Magni P Cancer chemotherapy and pharmacology, 8/2013, Volume 72, Issue 2, pages: 471-482 Affiliation: Dipartimento di Ingegneria Industriale e dell'Informazione, Università degli Studi di Pavia, Via Ferrata 3, Pavia, Italy. paolo.magni@unipv.it Abstract: PURPOSE: In clinical oncology, combination treatments are widely used and increasingly preferred over single drug administrations. A better characterization of the interaction between drug effects and the selection of synergistic combinations represent an open challenge in drug development process. To this aim, preclinical studies are routinely performed, even if they are only qualitatively analyzed due to the lack of generally applicable mathematical models. METHODS: This paper presents a new pharmacokinetic-pharmacodynamic model that, starting from the well-known single agent Simeoni TGI model, is able to describe tumor growth in xenograft mice after the co-administration of two anticancer agents. Due to the drug action, tumor cells are divided in two groups: damaged and not damaged ones. The damaging rate has two terms proportional to drug concentrations (as in the single drug administration model) and one interaction term proportional to their product. Six of the eight pharmacodynamic parameters assume the same value as in the corresponding single drug models. Only one parameter summarizes the interaction, and it can be used to compute two important indexes that are a clear way to score the synergistic/antagonistic interaction among drug effects. RESULTS: The model was successfully applied to four new compounds co-administered with four drugs already available on the market for the treatment of three different tumor cell lines. It also provided reliable predictions of different combination regimens in which the same drugs were administered at different doses/schedules. CONCLUSIONS: A good and quantitative measurement of the intensity and nature of interaction between drug effects, as well as the capability to correctly predict new combination arms, suggest the use of this generally applicable model for supporting the experiment optimal design and the prioritization of different therapies. Contributors: Paolo Magni
 Context of model development: Combination Therapy Dose Selection; Model compliance with original publication: Yes; Model implementation requiring submitter’s additional knowledge: No; Modelling context description: PURPOSE: In clinical oncology, combination treatments are widely used and increasingly preferred over single drug administrations. A better characterization of the interaction between drug effects and the selection of synergistic combinations represent an open challenge in drug development process. To this aim, preclinical studies are routinely performed, even if they are only qualitatively analyzed due to the lack of generally applicable mathematical models. METHODS: This paper presents a new pharmacokinetic-pharmacodynamic model that, starting from the well-known single agent Simeoni TGI model, is able to describe tumor growth in xenograft mice after the co-administration of two anticancer agents. Due to the drug action, tumor cells are divided in two groups: damaged and not damaged ones. The damaging rate has two terms proportional to drug concentrations (as in the single drug administration model) and one interaction term proportional to their product. Six of the eight pharmacodynamic parameters assume the same value as in the corresponding single drug models. Only one parameter summarizes the interaction, and it can be used to compute two important indexes that are a clear way to score the synergistic/antagonistic interaction among drug effects. RESULTS: The model was successfully applied to four new compounds co-administered with four drugs already available on the market for the treatment of three different tumor cell lines. It also provided reliable predictions of different combination regimens in which the same drugs were administered at different doses/schedules. CONCLUSIONS: A good and quantitative measurement of the intensity and nature of interaction between drug effects, as well as the capability to correctly predict new combination arms, suggest the use of this generally applicable model for supporting the experiment optimal design and the prioritization of different therapies.; 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 not certified.
• Model owner: Paolo Magni
• Submitted: Dec 10, 2015 11:21:34 PM
##### Revisions
• Version: 7
• Submitted on: Oct 10, 2016 8:00:38 PM
• Submitted by: Paolo Magni
• With comment: Edited model metadata online.
• Version: 5
• Submitted on: May 24, 2016 11:31:41 PM
• Submitted by: Paolo Magni
• With comment: Updated model annotations.
• Version: 4
• Submitted on: Dec 10, 2015 11:21:34 PM
• Submitted by: Paolo Magni
• With comment: Edited model metadata online.

### Name

Generated from MDL. MOG ID: terranova_2013

 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

$\mathrm{LAMBDA0_POP}$
$\mathrm{LAMBDA1_POP}$
$\mathrm{K1a_POP}$
$\mathrm{K2a_POP}$
$\mathrm{K1b_POP}$
$\mathrm{K2b_POP}$
$\mathrm{W0_POP}$
$\mathrm{GAMMA_POP}$
$\mathrm{K10A_POP}$
$\mathrm{K12A_POP}$
$\mathrm{K21A_POP}$
$\mathrm{V1A_POP}$
$\mathrm{K10B_POP}$
$\mathrm{K12B_POP}$
$\mathrm{K21B_POP}$
$\mathrm{V1B_POP}$
$\mathrm{CV}$

#### Individual Parameters

$\mathrm{LAMBDA0}=\mathrm{pm.LAMBDA0_POP}$
$\mathrm{LAMBDA1}=\mathrm{pm.LAMBDA1_POP}$
$\mathrm{K1a}=\mathrm{pm.K1a_POP}$
$\mathrm{K2a}=\mathrm{pm.K2a_POP}$
$\mathrm{K1b}=\mathrm{pm.K1b_POP}$
$\mathrm{K2b}=\mathrm{pm.K2b_POP}$
$\mathrm{W0}=\mathrm{pm.W0_POP}$
$\mathrm{GAMMA}=\mathrm{pm.GAMMA_POP}$
$\mathrm{K10A}=\mathrm{pm.K10A_POP}$
$\mathrm{K12A}=\mathrm{pm.K12A_POP}$
$\mathrm{K21A}=\mathrm{pm.K21A_POP}$
$\mathrm{V1A}=\mathrm{pm.V1A_POP}$
$\mathrm{K10B}=\mathrm{pm.K10B_POP}$
$\mathrm{K12B}=\mathrm{pm.K12B_POP}$
$\mathrm{K21B}=\mathrm{pm.K21B_POP}$
$\mathrm{V1B}=\mathrm{pm.V1B_POP}$

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

#### Variables

$\mathrm{PSI}=20$
$\mathrm{WTOT}=\mathrm{sm.X00}+\mathrm{sm.X10}+\mathrm{sm.X20}+\mathrm{sm.X30}+\mathrm{sm.X01}+\mathrm{sm.X11}+\mathrm{sm.X21}+\mathrm{sm.X31}+\mathrm{sm.X02}+\mathrm{sm.X12}+\mathrm{sm.X22}+\mathrm{sm.X32}+\mathrm{sm.X03}+\mathrm{sm.X13}+\mathrm{sm.X23}+\mathrm{sm.X33}$
$\mathrm{Ca}=\frac{\mathrm{sm.Q1A}}{\mathrm{pm.V1A}}$
$\begin{array}{c}\frac{d}{dT}\mathrm{Q1A}=\mathrm{pm.K21A}\cdot \mathrm{sm.Q2A}-\left(\mathrm{pm.K10A}+\mathrm{pm.K12A}\right)\cdot \mathrm{sm.Q1A}\\ \mathrm{Q1A}\left(T=0\right)=0\end{array}$
$\begin{array}{c}\frac{d}{dT}\mathrm{Q2A}=\mathrm{pm.K12A}\cdot \mathrm{sm.Q1A}-\mathrm{pm.K21A}\cdot \mathrm{sm.Q2A}\\ \mathrm{Q2A}\left(T=0\right)=0\end{array}$
$\mathrm{Cb}=\frac{\mathrm{sm.Q1B}}{\mathrm{pm.V1B}}$
$\begin{array}{c}\frac{d}{dT}\mathrm{Q1B}=\mathrm{pm.K21B}\cdot \mathrm{sm.Q2B}-\left(\mathrm{pm.K10B}+\mathrm{pm.K12B}\right)\cdot \mathrm{sm.Q1B}\\ \mathrm{Q1B}\left(T=0\right)=0\end{array}$
$\begin{array}{c}\frac{d}{dT}\mathrm{Q2B}=\mathrm{pm.K12B}\cdot \mathrm{sm.Q1B}-\mathrm{pm.K21B}\cdot \mathrm{sm.Q2B}\\ \mathrm{Q2B}\left(T=0\right)=0\end{array}$
$\begin{array}{c}\frac{d}{dT}\mathrm{X00}=\frac{\mathrm{pm.LAMBDA0}\cdot \mathrm{sm.X00}}{{\left(1+{\frac{\mathrm{sm.WTOT}\cdot \mathrm{pm.LAMBDA0}}{\mathrm{pm.LAMBDA1}}}^{\mathrm{sm.PSI}}\right)}^{\frac{1}{\mathrm{sm.PSI}}}}-\mathrm{pm.K2a}\cdot \mathrm{sm.Ca}\cdot \mathrm{sm.X00}-\mathrm{pm.K2b}\cdot \mathrm{sm.Cb}\cdot \mathrm{sm.X00}-\mathrm{pm.GAMMA}\cdot \mathrm{sm.Ca}\cdot \mathrm{sm.Cb}\cdot \mathrm{sm.X00}\\ \mathrm{X00}\left(T=0\right)=\mathrm{pm.W0}\end{array}$
$\begin{array}{c}\frac{d}{dT}\mathrm{X10}=\mathrm{pm.K2a}\cdot \mathrm{sm.Ca}\cdot \mathrm{sm.X00}-\mathrm{pm.K1a}\cdot \mathrm{sm.X10}-\mathrm{pm.K2b}\cdot \mathrm{sm.Cb}\cdot \mathrm{sm.X10}\\ \mathrm{X10}\left(T=0\right)=0\end{array}$
$\begin{array}{c}\frac{d}{dT}\mathrm{X20}=\mathrm{pm.K1a}\cdot \mathrm{sm.X10}-\mathrm{pm.K1a}\cdot \mathrm{sm.X20}-\mathrm{pm.K2b}\cdot \mathrm{sm.Cb}\cdot \mathrm{sm.X20}\\ \mathrm{X20}\left(T=0\right)=0\end{array}$
$\begin{array}{c}\frac{d}{dT}\mathrm{X30}=\mathrm{pm.K1a}\cdot \mathrm{sm.X20}-\mathrm{pm.K1a}\cdot \mathrm{sm.X30}-\mathrm{pm.K2b}\cdot \mathrm{sm.Cb}\cdot \mathrm{sm.X30}\\ \mathrm{X30}\left(T=0\right)=0\end{array}$
$\begin{array}{c}\frac{d}{dT}\mathrm{X01}=\mathrm{pm.K2b}\cdot \mathrm{sm.Cb}\cdot \mathrm{sm.X00}-\mathrm{pm.K2a}\cdot \mathrm{sm.Ca}\cdot \mathrm{sm.X01}-\mathrm{pm.K1b}\cdot \mathrm{sm.X01}\\ \mathrm{X01}\left(T=0\right)=0\end{array}$
$\begin{array}{c}\frac{d}{dT}\mathrm{X11}=\mathrm{pm.K2b}\cdot \mathrm{sm.Cb}\cdot \mathrm{sm.X10}+\mathrm{pm.K2a}\cdot \mathrm{sm.Ca}\cdot \mathrm{sm.X01}-\mathrm{pm.K1a}\cdot \mathrm{sm.X11}-\mathrm{pm.K1b}\cdot \mathrm{sm.X11}+\mathrm{pm.GAMMA}\cdot \mathrm{sm.Ca}\cdot \mathrm{sm.Cb}\cdot \mathrm{sm.X00}\\ \mathrm{X11}\left(T=0\right)=0\end{array}$
$\begin{array}{c}\frac{d}{dT}\mathrm{X21}=\mathrm{pm.K1a}\cdot \mathrm{sm.X11}+\mathrm{pm.K2b}\cdot \mathrm{sm.Cb}\cdot \mathrm{sm.X20}-\mathrm{pm.K1a}\cdot \mathrm{sm.X21}-\mathrm{pm.K1b}\cdot \mathrm{sm.X21}\\ \mathrm{X21}\left(T=0\right)=0\end{array}$
$\begin{array}{c}\frac{d}{dT}\mathrm{X31}=\mathrm{pm.K1a}\cdot \mathrm{sm.X21}+\mathrm{pm.K2b}\cdot \mathrm{sm.Cb}\cdot \mathrm{sm.X30}-\mathrm{pm.K1a}\cdot \mathrm{sm.X31}-\mathrm{pm.K1b}\cdot \mathrm{sm.X31}\\ \mathrm{X31}\left(T=0\right)=0\end{array}$
$\begin{array}{c}\frac{d}{dT}\mathrm{X02}=\mathrm{pm.K1b}\cdot \mathrm{sm.X01}-\mathrm{pm.K2a}\cdot \mathrm{sm.Ca}\cdot \mathrm{sm.X02}-\mathrm{pm.K1b}\cdot \mathrm{sm.X02}\\ \mathrm{X02}\left(T=0\right)=0\end{array}$
$\begin{array}{c}\frac{d}{dT}\mathrm{X12}=\mathrm{pm.K1b}\cdot \mathrm{sm.X11}+\mathrm{pm.K2a}\cdot \mathrm{sm.Ca}\cdot \mathrm{sm.X02}-\mathrm{pm.K1a}\cdot \mathrm{sm.X12}-\mathrm{pm.K1b}\cdot \mathrm{sm.X12}\\ \mathrm{X12}\left(T=0\right)=0\end{array}$
$\begin{array}{c}\frac{d}{dT}\mathrm{X22}=\mathrm{pm.K1a}\cdot \mathrm{sm.X12}+\mathrm{pm.K1b}\cdot \mathrm{sm.X21}-\mathrm{pm.K1a}\cdot \mathrm{sm.X22}-\mathrm{pm.K1b}\cdot \mathrm{sm.X22}\\ \mathrm{X22}\left(T=0\right)=0\end{array}$
$\begin{array}{c}\frac{d}{dT}\mathrm{X32}=\mathrm{pm.K1a}\cdot \mathrm{sm.X22}+\mathrm{pm.K1b}\cdot \mathrm{sm.X31}-\mathrm{pm.K1a}\cdot \mathrm{sm.X32}-\mathrm{pm.K1b}\cdot \mathrm{sm.X32}\\ \mathrm{X32}\left(T=0\right)=0\end{array}$
$\begin{array}{c}\frac{d}{dT}\mathrm{X03}=\mathrm{pm.K1b}\cdot \mathrm{sm.X02}-\mathrm{pm.K2a}\cdot \mathrm{sm.Ca}\cdot \mathrm{sm.X03}-\mathrm{pm.K1b}\cdot \mathrm{sm.X03}\\ \mathrm{X03}\left(T=0\right)=0\end{array}$
$\begin{array}{c}\frac{d}{dT}\mathrm{X13}=\mathrm{pm.K1b}\cdot \mathrm{sm.X12}+\mathrm{pm.K2a}\cdot \mathrm{sm.Ca}\cdot \mathrm{sm.X03}-\mathrm{pm.K1a}\cdot \mathrm{sm.X13}-\mathrm{pm.K1b}\cdot \mathrm{sm.X13}\\ \mathrm{X13}\left(T=0\right)=0\end{array}$
$\begin{array}{c}\frac{d}{dT}\mathrm{X23}=\mathrm{pm.K1a}\cdot \mathrm{sm.X13}+\mathrm{pm.K1b}\cdot \mathrm{sm.X22}-\mathrm{pm.K1a}\cdot \mathrm{sm.X23}-\mathrm{pm.K1b}\cdot \mathrm{sm.X23}\\ \mathrm{X23}\left(T=0\right)=0\end{array}$
$\begin{array}{c}\frac{d}{dT}\mathrm{X33}=\mathrm{pm.K1a}\cdot \mathrm{sm.X23}+\mathrm{pm.K1b}\cdot \mathrm{sm.X32}-\mathrm{pm.K1a}\cdot \mathrm{sm.X33}-\mathrm{pm.K1b}\cdot \mathrm{sm.X33}\\ \mathrm{X33}\left(T=0\right)=0\end{array}$

### 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_terranova_2013_data.csv

### Column Definitions

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

### Column Mappings

Column Ref Modelling Mapping
$TIME$
$T$
$DV$
$\mathrm{om1.Y}$
$AMT$
$\left\{\begin{array}{lll}\mathrm{sm.Q1A}& \text{if}& \mathrm{CMT}=1\wedge \mathrm{AMT}>0\\ \mathrm{sm.Q1B}& \text{if}& \mathrm{CMT}=3\wedge \mathrm{AMT}>0\end{array}$

## Estimation Step

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

### Parameters To Estimate

Parameter Initial Value Fixed? Limits
pm.LAMBDA0_POP
$0.149$
true
$\left(,\right)$
pm.LAMBDA1_POP
$0.203$
true
$\left(,\right)$
pm.K1a_POP
$2.24$
true
$\left(,\right)$
pm.K2a_POP
$0.0512$
true
$\left(,\right)$
pm.K1b_POP
$1.68$
true
$\left(,\right)$
pm.K2b_POP
$0.0984$
true
$\left(,\right)$
pm.W0_POP
$0.0566$
true
$\left(,\right)$
pm.GAMMA_POP
$-2$
false
$\left(,\right)$
pm.K10A_POP
$28.1$
true
$\left(,\right)$
pm.K12A_POP
$4.94$
true
$\left(,\right)$
pm.K21A_POP
$5.58$
true
$\left(,\right)$
pm.V1A_POP
$1.42$
true
$\left(,\right)$
pm.K10B_POP
$97.3$
true
$\left(,\right)$
pm.K12B_POP
$20.4$
true
$\left(,\right)$
pm.K21B_POP
$45.2$
true
$\left(,\right)$
pm.V1B_POP
$0.887$
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
$\mathrm{estimStep_1}$