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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:	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.

Mandatory file
- Executable_Rocchetti_2013_oncology_TGI_combo.xml

Additional Files

Model owner: Paolo Magni
Submitted: Sep 26, 2014 11:18:04 AM
Last Modified: Oct 10, 2016 7:53:05 PM

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

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

POP_LAMBDA0

POP_LAMBDA1

POP_W0

POP_K1

POP_K2

POP_IC50

POP_IC50COMBO

POP_KA_A

POP_KE_A

POP_FV1_A

POP_KA_B

POP_KE_B

POP_K21

POP_K12

POP_FV1_B

POP_EMAX

CV

Individual Parameters

LAMBDA0 = pm.POP_LAMBDA0

LAMBDA1 = pm.POP_LAMBDA1

W0 = pm.POP_W0

K1 = pm.POP_K1

K2 = pm.POP_K2

IC50 = pm.POP_IC50

IC50COMBO = pm.POP_IC50COMBO

KA_A = pm.POP_KA_A

KE_A = pm.POP_KE_A

FV1_A = pm.POP_FV1_A

KA_B = pm.POP_KA_B

KE_B = pm.POP_KE_B

K21 = pm.POP_K21

K12 = pm.POP_K12

FV1_B = pm.POP_FV1_B

EMAX = pm.POP_EMAX

Structural Model: $sm$

Variables

PSI = 20

C1_A = sm.Q1_A \cdot pm.FV1_A

C1_B = sm.Q1_B \cdot pm.FV1_B

K2INH = pm.K2 \cdot (1 - \frac{sm.C1_A}{(sm.C1_A + pm.IC50COMBO)})

WTOT = sm.Z0 + sm.Z1 + sm.Z2 + sm.Z3

\begin{matrix} \frac{ⅆ}{ⅆ T} Q0_A = - pm.KA_A \cdot sm.Q0_A \\ Q0_A (T = 0) = 0 \end{matrix}

\begin{matrix} \frac{ⅆ}{ⅆ T} Q1_A = pm.KA_A \cdot sm.Q0_A - pm.KE_A \cdot sm.Q1_A \\ Q1_A (T = 0) = 0 \end{matrix}

\begin{matrix} \frac{ⅆ}{ⅆ T} Q0_B = - pm.KA_B \cdot sm.Q0_B \\ Q0_B (T = 0) = 0 \end{matrix}

\begin{matrix} \frac{ⅆ}{ⅆ T} Q1_B = pm.KA_B \cdot sm.Q0_B - (pm.K12 + pm.KE_B) \cdot sm.Q1_B + pm.K21 \cdot sm.Q2_B \\ Q1_B (T = 0) = 0 \end{matrix}

\begin{matrix} \frac{ⅆ}{ⅆ T} Q2_B = pm.K12 \cdot sm.Q1_B - pm.K21 \cdot sm.Q2_B \\ Q2_B (T = 0) = 0 \end{matrix}

\begin{matrix} \frac{ⅆ}{ⅆ T} Z0 = \frac{pm.LAMBDA0 \cdot sm.Z0}{{(1 + {\frac{sm.WTOT \cdot pm.LAMBDA0}{pm.LAMBDA1}}^{sm.PSI})}^{\frac{1}{sm.PSI}}} \cdot (1 - \frac{pm.EMAX \cdot sm.C1_A}{(sm.C1_A + pm.IC50)}) - sm.K2INH \cdot sm.C1_B \cdot sm.Z0 \\ Z0 (T = 0) = pm.W0 \end{matrix}

\begin{matrix} \frac{ⅆ}{ⅆ T} Z1 = sm.K2INH \cdot sm.C1_B \cdot sm.Z0 - pm.K1 \cdot sm.Z1 \\ Z1 (T = 0) = 0 \end{matrix}

\begin{matrix} \frac{ⅆ}{ⅆ T} Z2 = pm.K1 \cdot sm.Z1 - pm.K1 \cdot sm.Z2 \\ Z2 (T = 0) = 0 \end{matrix}

\begin{matrix} \frac{ⅆ}{ⅆ T} Z3 = pm.K1 \cdot sm.Z2 - pm.K1 \cdot sm.Z3 \\ Z3 (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_rocchetti2013_data.csv

Column Definitions

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

Column Mappings

Column Ref	Modelling Mapping
$ID$	$vm_mdl.ID$
$TIME$	$T$
$DV$	$om1.Y$
$AMT$	${\begin{cases} sm.Q0_A & if & CMT = 1 \land AMT > 0 \\ sm.Q0_B & if & CMT = 2 \land AMT > 0 \end{cases}$

Estimation Step

OID	$estimStep_1$
Dataset Reference	$nm_ds$

Parameters To Estimate

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

DDMODEL00000008: Rocchetti_2013_oncology_TGI_combo