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Short description:

PKPD model of tumor growth inhibition and toxicity outcome after administration of anticancer agents in xenograft mice

Format:	PharmML 0.8.x (0.8.1)
Related Publication:	Evaluation of a PK/PD DEB-based model for tumor-in-host growth kinetics under anticancer treatment E.M.Tosca, E.Borella, N.Terranova, M.Rocchetti, P.Magni PAGE 25, 6/2015 Affiliation: Department of Electrical, Computer and Biomedical Engineering, University of Pavia, via Ferrata 5, Pavia, I-27100, Italy Abstract: Objectives: Mathematical models for describing the tumor growth in animals often neglect the relationship between tumor and host organism. To overcome this limitation, a more mechanistic model, based on energy balance between tumor and host, was developed. This PK/PD model, combining the Dynamic Energy Budget (DEB) theory with the Simeoni tumor growth inhibition (TGI) model, describes both the dynamics of the tumor-host interaction and the effect of anticancer treatments. Here a slightly revised model formulation and a new implementation are proposed. Moreover, a comparative study on the tumor growth in control groups between the DEB-TGI model and the widely used Simeoni TGI model is presented. Methods: Data used for model validation refer to xenograft experiments conducted on Harlan Sprague Dawley mice. Average data of tumor weight and mice net body weight were considered for the control and treated groups. The PKs were derived from separated studies. Monolix 4.3.3 was used for model identification, while Simulx was used to confirm the hypothesis emerged from a dynamic system analysis. Results: First of all, the model was identified on different experimental datasets with the following strategy: 1) physiological parameters of the tumor-free model were estimated on growth data of typical HSD mice; 2) estimated values were used to find the initial value for the energy reserve at the beginning of the experiment; 3) once fixed the tumor-free model parameters and energy initial value, the tumor-related and the drug-related parameters were simultaneously estimated. The mathematical analysis of the dynamic system showed that, as the Simeoni model, the DEB-TGI model predicts an exponential growth of the tumor in the early phases of its development. The exponential growth rate depends on several model parameters some of them related to the tumor cell lines and other to the host. We investigated also the relationship between the DEB-TGI model parameters and the decreasing of the tumor growth rate. Conclusions: The tumor-in-host DEB-based model confirmed its good capability in describing tumor growth and host body growth even when an anticancer drug is administered. Moreover, the affinities emerged from the comparative analysis with the Simenoni model provide a possible biological interpretation of the assumptions underlying the Simeoni model unperturbed (control) growth curve.
Contributors:	Elena Maria Tosca

Context of model development:	Candidate Comparison, Selection, Human Dose Prediction;
Discrepancy between implemented model and original publication:	Among the drugs considered in the paper, only PACLITAXEL has been used;
Model compliance with original publication:	Yes;
Model implementation requiring submitter’s additional knowledge:	No;
Modelling context description:	Host features, such as cell proliferation rates, caloric intake, metabolism and energetic conditions, significantly influence tumor growth; at the same time, tumor growth may have a dramatic impact on the host conditions. For example, in clinics, at certain stages of the tumor growth, cachexia (body weight reduction) may become so relevant to be considered as responsible for around 20% of cancer deaths. Unfortunately, anticancer therapies may also contribute to the development of cachexia due to reduced food intake (anorexia), commonly observed during the treatment periods. For this reason, cachexia is considered one of the major toxicity findings to be evaluated also in preclinical studies. However, although various pharmacokinetic-pharmacodynamic (PK-PD) tumor growth inhibition (TGI) models are currently available, the mathematical modelling of cachexia onset and TGI after an anticancer administration in preclinical experiments is still an open issue. To cope with this, a new PK-PD model, based on a set of tumor-host interaction rules taken from Dynamic Energy Budget (DEB) theory and a set of drug tumor inhibition equations taken from the well-known Simeoni TGI model, was developed. The model is able to describe the body weight reduction, splitting the cachexia directly induced by tumor and that caused by the drug treatment under study. It was tested in typical preclinical studies, essentially designed for efficacy evaluation and routinely performed as a part of the industrial drug development plans. For the first time, both the dynamics of tumor and host growth could be predicted in xenograft mice untreated or treated with different anticancer agents and following different schedules. ;
Modelling task in scope:	estimation; simulation;
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
- Terranova_2017_oncology_TGI.xml

Additional Files

Model owner: Elena Maria Tosca
Submitted: Dec 22, 2017 8:10:56 AM
Last Modified: Dec 22, 2017 8:10:56 AM

Revisions

Version: 5
- Submitted on: Dec 22, 2017 8:10:56 AM
- Submitted by: Elena Maria Tosca
- With comment: Model revised without commit message

Name

Terranova_2017_oncology_TGI

Description

PKPD model of tumor growth inhibition and toxicity outcome after administration of anticancer agents in xenograft mice

Independent Variables

Function Definitions

additiveError : real (additive : real) = additive

Parameter Model: $pm$

Random Variables

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

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

Population Parameters

K10_POP

K12_POP

K21_POP

V1_POP

En_initial_POP

rho_b_POP

xi_POP

ni_POP

gr_POP

V1inf_POP

mu_POP

mu_u_POP

gu_POP

delta_Vmax_POP

W_initial_POP

Vu1_initial_POP

IC50_POP

k1_POP

k2_POP

b_W

b_Wu

Individual Parameters

K10 = pm.K10_POP

K12 = pm.K12_POP

K21 = pm.K21_POP

V1 = pm.V1_POP

En_initial = pm.En_initial_POP

rho_b = pm.rho_b_POP

xi = pm.xi_POP

ni = pm.ni_POP

gr = pm.gr_POP

V1inf = pm.V1inf_POP

mu = pm.mu_POP

mu_u = pm.mu_u_POP

gu = pm.gu_POP

delta_Vmax = pm.delta_Vmax_POP

W_initial = pm.W_initial_POP

Vu1_initial = pm.Vu1_initial_POP

IC50 = pm.IC50_POP

k1 = pm.k1_POP

k2 = pm.k2_POP

density_V = 1

density_Vu = 1

omeg = 0.75

m = \frac{pm.ni}{{pm.V1inf}^{\frac{1}{3}} \cdot pm.gr}

Z_initial = \frac{pm.W_initial}{(1 + pm.En_initial \cdot pm.xi)}

Structural Model: $sm$

Variables

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

\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}

rho = pm.rho_b \cdot (1 - \frac{sm.C}{(pm.IC50 + sm.C)})

ku = \frac{pm.mu_u \cdot sm.Vu1}{(sm.Z + pm.mu_u \cdot sm.Vu1)}

switch1 = \frac{((1 - sm.ku) \cdot pm.ni \cdot sm.En \cdot {sm.Z}^{\frac{2}{3}} - pm.gr \cdot pm.m \cdot sm.Z)}{(pm.gr + (1 - \frac{pm.mu_u \cdot sm.Vu1}{(sm.Z + pm.mu_u \cdot sm.Vu1)}) \cdot sm.En)}

switch2 = \frac{((1 - sm.ku) \cdot pm.ni \cdot sm.En \cdot {sm.Z}^{\frac{2}{3}} - pm.gr \cdot pm.m \cdot sm.Z)}{(1 - \frac{pm.mu_u \cdot sm.Vu1}{(sm.Z + pm.mu_u \cdot sm.Vu1)}) \cdot (sm.En + pm.omeg \cdot pm.gr)}

Wu = pm.density_Vu \cdot (sm.Vu1 + sm.Vu2 + sm.Vu3 + sm.Vu4)

W = pm.density_V \cdot (1 + pm.xi \cdot sm.En) \cdot sm.Z

W_err = pm.b_W \cdot \sqrt{sm.W}

Wu_err = pm.b_Wu \cdot \sqrt{sm.Wu}

\begin{matrix} \frac{ⅆ}{ⅆ T} Z = {\begin{cases} \frac{((1 - sm.ku) \cdot pm.ni \cdot sm.En \cdot {sm.Z}^{\frac{2}{3}} - pm.gr \cdot pm.m \cdot sm.Z)}{(pm.gr + (1 - sm.ku) \cdot sm.En)} & if & sm.switch1 \geq 0 \\ \frac{((1 - sm.ku) \cdot pm.ni \cdot sm.En \cdot {sm.Z}^{\frac{2}{3}} - pm.gr \cdot pm.m \cdot sm.Z)}{(1 - sm.ku) \cdot (sm.En + pm.omeg \cdot pm.gr)} & if & sm.switch1 < 0 \land sm.switch2 \leq - pm.delta_Vmax \\ - pm.delta_Vmax & otherwise \end{cases} \\ Z (T = 0) = pm.Z_initial \end{matrix}

\begin{matrix} \frac{ⅆ}{ⅆ T} En = \frac{pm.ni}{{sm.Z}^{\frac{1}{3}}} \cdot (sm.rho \cdot {\frac{pm.V1inf}{(sm.Vu1 + sm.Z)}}^{\frac{2}{3}} - sm.En) \\ En (T = 0) = pm.En_initial \end{matrix}

\begin{matrix} \frac{ⅆ}{ⅆ T} Vu1 = {\begin{cases} \frac{(pm.ni \cdot {sm.Z}^{\frac{2}{3}} + pm.m \cdot sm.Z) \cdot pm.gr \cdot sm.ku \cdot sm.En}{(pm.gr \cdot pm.gu + (1 - sm.ku) \cdot pm.gu \cdot sm.En)} - pm.mu \cdot sm.Vu1 - pm.k2 \cdot sm.Vu1 \cdot sm.C & if & sm.switch1 \geq 0 \\ \frac{pm.gr \cdot pm.m \cdot pm.mu_u \cdot sm.Vu1}{pm.gu} - pm.mu \cdot sm.Vu1 - pm.k2 \cdot sm.C \cdot sm.Vu1 & if & sm.switch1 < 0 \land sm.switch2 < 0 \land sm.switch2 \geq - pm.delta_Vmax \\ \frac{sm.ku}{pm.gu} \cdot (sm.En \cdot pm.ni \cdot {sm.Z}^{\frac{2}{3}} + pm.delta_Vmax \cdot sm.En + pm.delta_Vmax \cdot pm.omeg \cdot pm.gr) - pm.mu \cdot sm.Vu1 - pm.k2 \cdot sm.C \cdot sm.Vu1 & otherwise \end{cases} \\ Vu1 (T = 0) = pm.Vu1_initial \end{matrix}

\begin{matrix} \frac{ⅆ}{ⅆ T} Vu2 = pm.k2 \cdot sm.C \cdot sm.Vu1 - pm.k1 \cdot sm.Vu2 \\ Vu2 (T = 0) = 0 \end{matrix}

\begin{matrix} \frac{ⅆ}{ⅆ T} Vu3 = pm.k1 \cdot sm.Vu2 - pm.k1 \cdot sm.Vu3 \\ Vu3 (T = 0) = 0 \end{matrix}

\begin{matrix} \frac{ⅆ}{ⅆ T} Vu4 = pm.k1 \cdot sm.Vu3 - pm.k1 \cdot sm.Vu4 \\ Vu4 (T = 0) = 0 \end{matrix}

Observation Model: $om1$

Continuous Observation

Y1 = sm.W + additiveError (additive = sm.W_err) + pm.eps_RES_W

Observation Model: $om2$

Continuous Observation

Y2 = sm.Wu + additiveError (additive = sm.Wu_err) + pm.eps_RES_Wu

External Dataset

OID	$nm_ds$
Tool Format	NONMEM

File Specification

Format	$csv$
Delimiter	comma
File Location	Simulated_DEB_TGI_data.csv

Column Definitions

Column ID	Position	Column Type	Value Type
$ID$	$1$	$id$	$int$
$TIME$	$2$	$idv$	$real$
$DV$	$3$	$dv$	$real$
$DVID$	$4$	$dvid$	$int$
$AMT$	$5$	$dose$	$real$
$EVID$	$6$	$evid$	$real$
$CMT$	$7$	$cmt$	$int$

Column Mappings

Column Ref	Modelling Mapping
$TIME$	$T$
$DV$	${\begin{cases} om1.Y1 & if & DVID = 1 \\ om2.Y2 & if & DVID = 2 \end{cases}$
$AMT$	${\begin{cases} sm.Q1 & if & AMT > 0 \end{cases}$

Estimation Step

OID	$estimStep_1$
Dataset Reference	$nm_ds$

Parameters To Estimate

Parameter	Initial Value	Fixed?	Limits
pm.K10_POP	$20.832$	true	$()$
pm.K12_POP	$0.144$	true	$()$
pm.K21_POP	$2.011$	true	$()$
pm.V1_POP	$813.1$	true	$()$
pm.En_initial_POP	$1.3$	true	$()$
pm.xi_POP	$0.184$	true	$()$
pm.ni_POP	$1.2242$	true	$()$
pm.gr_POP	$12.2$	true	$()$
pm.V1inf_POP	$22.6$	true	$()$
pm.rho_b_POP	$1$	true	$()$
pm.mu_POP	$0.0223$	false	$(0)$
pm.mu_u_POP	$13.3$	false	$(0)$
pm.gu_POP	$11.7$	false	$(0)$
pm.delta_Vmax_POP	$0.185$	false	$(0)$
pm.W_initial_POP	$21.2$	false	$(0)$
pm.Vu1_initial_POP	$0.0023$	false	$(0)$
pm.IC50_POP	$0.461$	false	$(0)$
pm.k1_POP	$0.462$	false	$(0)$
pm.k2_POP	$6.53E-4$	false	$(0)$
pm.b_W	$0.101$	false	$(0)$
pm.b_Wu	$0.134$	false	$(0)$

Operations

Operation: $1$

Op Type

generic

Operation Properties

Name	Value
algo	$foce$

Step Dependencies

Step OID	Preceding Steps
$estimStep_1$

DDMODEL00000274: Terranova_2017_oncology_TGI

Revisions

Name

Description

Independent Variables

Function Definitions

Parameter Model: pm

Random Variables

Population Parameters

Individual Parameters

Structural Model: sm

Variables

Observation Model: om1

Continuous Observation

Observation Model: om2

Continuous Observation

External Dataset

File Specification

Column Definitions

Column Mappings

Estimation Step

Parameters To Estimate

Operations

Operation: 1

Operation Properties

Step Dependencies

Parameter Model: $pm$

Structural Model: $sm$

Observation Model: $om1$

Observation Model: $om2$

Operation: $1$