DDMODEL00000008: Rocchetti_2013_oncology_TGI_combo

Short description:
PKPD model of tumor growth after administration of an anti-angiogenic agent, bevacizumab, as single-agent and combination therapy in tumor xenografts
 Format: PharmML 0.8.x (0.8.1) Related Publication: .hiddenContent {display:none;} Predictive pharmacokinetic-pharmacodynamic modeling of tumor growth after administration of an anti-angiogenic agent, bevacizumab, as single-agent and combination therapy in tumor xenografts. Rocchetti M, Germani M, Del Bene F, Poggesi I, Magni P, Pesenti E, De Nicolao G Cancer chemotherapy and pharmacology, 5/2013, Volume 71, Issue 5, pages: 1147-1157 Affiliation: Pharmacokinetics and Modeling, Accelera S.r.l., Nerviano, MI, Italy. Università degli Studi di Pavia, Pavia, Italy. Abstract: PURPOSE: Pharmacokinetic-pharmacodynamic (PK-PD) models able to predict the action of anticancer compounds in tumor xenografts have an important impact on drug development. In case of anti-angiogenic compounds, many of the available models show difficulties in their applications, as they are based on a cell kill hypothesis, while these drugs act on the tumor vascularization, without a direct tumor cell kill effect. For this reason, a PK-PD model able to describe the tumor growth modulation following treatment with a cytostatic therapy, as opposed to a cytotoxic treatment, is proposed here. METHODS: Untreated tumor growth was described using an exponential growth phase followed by a linear one. The effect of anti-angiogenic compounds was implemented using an inhibitory effect on the growth function. The model was tested on a number of experiments in tumor-bearing mice given the anti-angiogenic drug bevacizumab either alone or in combination with another investigational compound. Nonlinear regression techniques were used for estimating the model parameters. RESULTS: The model successfully captured the tumor growth data following different bevacizumab dosing regimens, allowing to estimate experiment-independent parameters. A combination model was also developed under a 'no-interaction' assumption to assess the effect of the combination of bevacizumab with a target-oriented agent. The observation of a significant difference between model-predicted and observed tumor growth curves was suggestive of the presence of a pharmacological interaction that was further accommodated into the model. CONCLUSIONS: This approach can be used for optimizing the design of preclinical experiments. With all the inherent limitations, the estimated experiment-independent model parameters can be used to provide useful indications for the single-agent and combination regimens to be explored in the subsequent development phases. Contributors: Paolo Magni
 Context of model development: Combination Therapy Dose Selection; Candidate Comparison, Selection, Human Dose Prediction; Model compliance with original publication: Yes; Model implementation requiring submitter’s additional knowledge: No; Modelling context description: PURPOSE: Pharmacokinetic-pharmacodynamic (PK-PD) models able to predict the action of anticancer compounds in tumor xenografts have an important impact on drug development. In case of anti-angiogenic compounds, many of the available models show difficulties in their applications, as they are based on a cell kill hypothesis, while these drugs act on the tumor vascularization, without a direct tumor cell kill effect. For this reason, a PK-PD model able to describe the tumor growth modulation following treatment with a cytostatic therapy, as opposed to a cytotoxic treatment, is proposed here. METHODS: Untreated tumor growth was described using an exponential growth phase followed by a linear one. The effect of anti-angiogenic compounds was implemented using an inhibitory effect on the growth function. The model was tested on a number of experiments in tumor-bearing mice given the anti-angiogenic drug bevacizumab either alone or in combination with another investigational compound. Nonlinear regression techniques were used for estimating the model parameters. RESULTS: The model successfully captured the tumor growth data following different bevacizumab dosing regimens, allowing to estimate experiment-independent parameters. A combination model was also developed under a 'no-interaction' assumption to assess the effect of the combination of bevacizumab with a target-oriented agent. The observation of a significant difference between model-predicted and observed tumor growth curves was suggestive of the presence of a pharmacological interaction that was further accommodated into the model. CONCLUSIONS: This approach can be used for optimizing the design of preclinical experiments. With all the inherent limitations, the estimated experiment-independent model parameters can be used to provide useful indications for the single-agent and combination regimens to be explored in the subsequent development phases.; 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 not certified.
• Model owner: Paolo Magni
• Submitted: Sep 26, 2014 11:18:04 AM
Revisions
• Version: 6
• Submitted on: Oct 10, 2016 7:53:05 PM
• Submitted by: Paolo Magni
• With comment: Edited model metadata online.
• Version: 4
• Submitted on: May 24, 2016 11:17:40 PM
• Submitted by: Paolo Magni
• With comment: Updated model annotations.
• Version: 3
• Submitted on: Dec 10, 2015 10:37:36 PM
• Submitted by: Paolo Magni
• With comment: Edited model metadata online.
• Version: 1
• Submitted on: Sep 26, 2014 11:18:04 AM
• Submitted by: Paolo Magni
• With comment: Import of Rocchetti_2013_oncology_TGI_antiangiogenic_combo

Name

Generated from MDL. MOG ID: rocchetti2013

 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

$\mathrm{POP_LAMBDA0}$
$\mathrm{POP_LAMBDA1}$
$\mathrm{POP_W0}$
$\mathrm{POP_K1}$
$\mathrm{POP_K2}$
$\mathrm{POP_IC50}$
$\mathrm{POP_IC50COMBO}$
$\mathrm{POP_KA_A}$
$\mathrm{POP_KE_A}$
$\mathrm{POP_FV1_A}$
$\mathrm{POP_KA_B}$
$\mathrm{POP_KE_B}$
$\mathrm{POP_K21}$
$\mathrm{POP_K12}$
$\mathrm{POP_FV1_B}$
$\mathrm{POP_EMAX}$
$\mathrm{CV}$

Individual Parameters

$\mathrm{LAMBDA0}=\mathrm{pm.POP_LAMBDA0}$
$\mathrm{LAMBDA1}=\mathrm{pm.POP_LAMBDA1}$
$\mathrm{W0}=\mathrm{pm.POP_W0}$
$\mathrm{K1}=\mathrm{pm.POP_K1}$
$\mathrm{K2}=\mathrm{pm.POP_K2}$
$\mathrm{IC50}=\mathrm{pm.POP_IC50}$
$\mathrm{IC50COMBO}=\mathrm{pm.POP_IC50COMBO}$
$\mathrm{KA_A}=\mathrm{pm.POP_KA_A}$
$\mathrm{KE_A}=\mathrm{pm.POP_KE_A}$
$\mathrm{FV1_A}=\mathrm{pm.POP_FV1_A}$
$\mathrm{KA_B}=\mathrm{pm.POP_KA_B}$
$\mathrm{KE_B}=\mathrm{pm.POP_KE_B}$
$\mathrm{K21}=\mathrm{pm.POP_K21}$
$\mathrm{K12}=\mathrm{pm.POP_K12}$
$\mathrm{FV1_B}=\mathrm{pm.POP_FV1_B}$
$\mathrm{EMAX}=\mathrm{pm.POP_EMAX}$

Structural Model: $\mathrm{sm}$

Variables

$\mathrm{PSI}=20$
$\mathrm{C1_A}=\mathrm{sm.Q1_A}\cdot \mathrm{pm.FV1_A}$
$\mathrm{C1_B}=\mathrm{sm.Q1_B}\cdot \mathrm{pm.FV1_B}$
$\mathrm{K2INH}=\mathrm{pm.K2}\cdot \left(1-\frac{\mathrm{sm.C1_A}}{\left(\mathrm{sm.C1_A}+\mathrm{pm.IC50COMBO}\right)}\right)$
$\mathrm{WTOT}=\mathrm{sm.Z0}+\mathrm{sm.Z1}+\mathrm{sm.Z2}+\mathrm{sm.Z3}$
$\begin{array}{c}\frac{d}{dT}\mathrm{Q0_A}=-\mathrm{pm.KA_A}\cdot \mathrm{sm.Q0_A}\\ \mathrm{Q0_A}\left(T=0\right)=0\end{array}$
$\begin{array}{c}\frac{d}{dT}\mathrm{Q1_A}=\mathrm{pm.KA_A}\cdot \mathrm{sm.Q0_A}-\mathrm{pm.KE_A}\cdot \mathrm{sm.Q1_A}\\ \mathrm{Q1_A}\left(T=0\right)=0\end{array}$
$\begin{array}{c}\frac{d}{dT}\mathrm{Q0_B}=-\mathrm{pm.KA_B}\cdot \mathrm{sm.Q0_B}\\ \mathrm{Q0_B}\left(T=0\right)=0\end{array}$
$\begin{array}{c}\frac{d}{dT}\mathrm{Q1_B}=\mathrm{pm.KA_B}\cdot \mathrm{sm.Q0_B}-\left(\mathrm{pm.K12}+\mathrm{pm.KE_B}\right)\cdot \mathrm{sm.Q1_B}+\mathrm{pm.K21}\cdot \mathrm{sm.Q2_B}\\ \mathrm{Q1_B}\left(T=0\right)=0\end{array}$
$\begin{array}{c}\frac{d}{dT}\mathrm{Q2_B}=\mathrm{pm.K12}\cdot \mathrm{sm.Q1_B}-\mathrm{pm.K21}\cdot \mathrm{sm.Q2_B}\\ \mathrm{Q2_B}\left(T=0\right)=0\end{array}$
$\begin{array}{c}\frac{d}{dT}\mathrm{Z0}=\frac{\mathrm{pm.LAMBDA0}\cdot \mathrm{sm.Z0}}{{\left(1+{\frac{\mathrm{sm.WTOT}\cdot \mathrm{pm.LAMBDA0}}{\mathrm{pm.LAMBDA1}}}^{\mathrm{sm.PSI}}\right)}^{\frac{1}{\mathrm{sm.PSI}}}}\cdot \left(1-\frac{\mathrm{pm.EMAX}\cdot \mathrm{sm.C1_A}}{\left(\mathrm{sm.C1_A}+\mathrm{pm.IC50}\right)}\right)-\mathrm{sm.K2INH}\cdot \mathrm{sm.C1_B}\cdot \mathrm{sm.Z0}\\ \mathrm{Z0}\left(T=0\right)=\mathrm{pm.W0}\end{array}$
$\begin{array}{c}\frac{d}{dT}\mathrm{Z1}=\mathrm{sm.K2INH}\cdot \mathrm{sm.C1_B}\cdot \mathrm{sm.Z0}-\mathrm{pm.K1}\cdot \mathrm{sm.Z1}\\ \mathrm{Z1}\left(T=0\right)=0\end{array}$
$\begin{array}{c}\frac{d}{dT}\mathrm{Z2}=\mathrm{pm.K1}\cdot \mathrm{sm.Z1}-\mathrm{pm.K1}\cdot \mathrm{sm.Z2}\\ \mathrm{Z2}\left(T=0\right)=0\end{array}$
$\begin{array}{c}\frac{d}{dT}\mathrm{Z3}=\mathrm{pm.K1}\cdot \mathrm{sm.Z2}-\mathrm{pm.K1}\cdot \mathrm{sm.Z3}\\ \mathrm{Z3}\left(T=0\right)=0\end{array}$

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_rocchetti2013_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
$ID$
$\mathrm{vm_mdl.ID}$
$TIME$
$T$
$DV$
$\mathrm{om1.Y}$
$AMT$
$\left\{\begin{array}{lll}\mathrm{sm.Q0_A}& \text{if}& \mathrm{CMT}=1\wedge \mathrm{AMT}>0\\ \mathrm{sm.Q0_B}& \text{if}& \mathrm{CMT}=2\wedge \mathrm{AMT}>0\end{array}$

Estimation Step

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

Parameters To Estimate

Parameter Initial Value Fixed? Limits
pm.POP_LAMBDA0
$0.14$
true
$\left(,\right)$
pm.POP_LAMBDA1
$0.129$
true
$\left(,\right)$
pm.POP_W0
$0.062$
true
$\left(,\right)$
pm.POP_K1
$3.54$
true
$\left(,\right)$
pm.POP_K2
$0.221$
true
$\left(,\right)$
pm.POP_IC50
$2.02$
true
$\left(,\right)$
pm.POP_IC50COMBO
$7$
false
$\left(0,\right)$
pm.POP_KA_A
$2.69$
true
$\left(,\right)$
pm.POP_KE_A
$0.115$
true
$\left(,\right)$
pm.POP_FV1_A
$8.4$
true
$\left(,\right)$
pm.POP_KA_B
$18.8$
true
$\left(,\right)$
pm.POP_KE_B
$49.2$
true
$\left(,\right)$
pm.POP_K21
$10.4$
true
$\left(,\right)$
pm.POP_K12
$141.1$
true
$\left(,\right)$
pm.POP_FV1_B
$0.469$
true
$\left(,\right)$
pm.POP_EMAX
$1$
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
$\mathrm{estimStep_1}$