# DDMODEL00000128: Ribba_2012_PCV

Short description:
The model is a tumor growth inhibition model for adult diffuse low-grade gliomas (LGGs). The model describes tumor size evolution in patients treated with PCV (procarbazine, 1-(2-chloroethyl)-3-cyclohexyl-l-nitrosourea (CCNU) and vincristine). The data set includes longitudinal mean tumor diameter data obtained from 21. The model is developed in a mixed-effects fashion and consists of non-linear ordinary differential equations. Parameters are fit using the SAEM algorithm implemented in Monolix. The PCV protocol consisted of up to 6 cycles of the following treatment, with intervals of 6 weeks between cycles: CCNU (110 mg/m2) administered on day 1, procarbazine (60 mg/m2) administered on days 8 to 21, and vincristine (1.4 mg/m2, max. 2 mg) administered on days 8 and 29.
 Format: PharmML (0.6.1) Related Publication: .hiddenContent {display:none;} A tumor growth inhibition model for low-grade glioma treated with chemotherapy or radiotherapy. Ribba B, Kaloshi G, Peyre M, Ricard D, Calvez V, Tod M, Cajavec-Bernard B, Idbaih A, Psimaras D, Dainese L, Pallud J, Cartalat-Carel S, Delattre JY, Honnorat J, Grenier E, Ducray F Clinical cancer research : an official journal of the American Association for Cancer Research, 9/2012, Volume 18, Issue 18, pages: 5071-5080 Affiliation: Ribba, INRIA, Project-team NUMED, Ecole Normale Superieure de Lyon, 46 allee d0Italie, 69007 Lyon Cedex 07, France. benjamin.ribba@inria.fr Abstract: PURPOSE: To develop a tumor growth inhibition model for adult diffuse low-grade gliomas (LGG) able to describe tumor size evolution in patients treated with chemotherapy or radiotherapy. EXPERIMENTAL DESIGN: Using longitudinal mean tumor diameter (MTD) data from 21 patients treated with first-line procarbazine, 1-(2-chloroethyl)-3-cyclohexyl-l-nitrosourea, and vincristine (PCV) chemotherapy, we formulated a model consisting of a system of differential equations, incorporating tumor-specific and treatment-related parameters that reflect the response of proliferative and quiescent tumor tissue to treatment. The model was then applied to the analysis of longitudinal tumor size data in 24 patients treated with first-line temozolomide (TMZ) chemotherapy and in 25 patients treated with first-line radiotherapy. RESULTS: The model successfully described the MTD dynamics of LGG before, during, and after PCV chemotherapy. Using the same model structure, we were also able to successfully describe the MTD dynamics in LGG patients treated with TMZ chemotherapy or radiotherapy. Tumor-specific parameters were found to be consistent across the three treatment modalities. The model is robust to sensitivity analysis, and preliminary results suggest that it can predict treatment response on the basis of pretreatment tumor size data. CONCLUSIONS: Using MTD data, we propose a tumor growth inhibition model able to describe LGG tumor size evolution in patients treated with chemotherapy or radiotherapy. In the future, this model might be used to predict treatment efficacy in LGG patients and could constitute a rational tool to conceive more effective chemotherapy schedules. Contributors: Christian Laveille
 Validation Status: Annotations have not been checked. Certification Comment: This model is not certified.
• Model owner: Christian Laveille
• Submitted: Dec 16, 2015 8:06:02 AM
##### Revisions
• Version: 4
• Submitted on: Dec 16, 2015 8:06:02 AM
• Submitted by: Christian Laveille
• With comment: Edited model metadata online.

Independent variable TIME

### Function Definitions

$combinedError1(additive,proportional,f)=(additive+(proportional ×f))$

### Structural Model sm

Variable definitions

$K=100$
$C=C_m$
$PT=PT_m$
$Q=Q_m$
$QP=QP_m$
$DPSTAR=((PT+Q)+QP)$
$dC_mdTIME=(-KDE ×C)$
$dPT_mdTIME=(((((LAMBDAP ×PT) ×(1-DPSTARK))+(KQPP ×QP))-(KPQ ×PT))-(((GAMA ×PT) ×KDE) ×C))$
$dQ_mdTIME=((KPQ ×PT)-(((GAMA ×Q) ×KDE) ×C))$
$dQP_mdTIME=(((((GAMA ×Q) ×KDE) ×C)-(KQPP ×QP))-(DELTAQP ×QP))$
$EFF=((PT_m+Q_m)+QP_m)$

Initial conditions

$C_m=0$
$PT_m=PT0$
$Q_m=Q0$
$QP_m=0$

### Variability Model

Level Type

DV

residualError

ID

parameterVariability

### Parameter Model

Parameters
$TVPT0$ $TVQ0$ $TVLAMBDAP$ $TVKPQ$ $TVKQPP$ $TVDELTAQP$ $TVGAMA$ $TVKDE$ $SDADD$ $SDPROP$ $OMPT0$ $OMQ0$ $OMLAMBDAP$ $OMKPQ$ $OMKQPP$ $OMDELTAQP$ $OMGAMA$ $OMKDE$ $SIGMA$
$ETA_PT0∼N(0.0,OMPT0)$ — ID
$ETA_Q0∼N(0.0,OMQ0)$ — ID
$ETA_LAMBDAP∼N(0.0,OMLAMBDAP)$ — ID
$ETA_KPQ∼N(0.0,OMKPQ)$ — ID
$ETA_KQPP∼N(0.0,OMKQPP)$ — ID
$ETA_DELTAQP∼N(0.0,OMDELTAQP)$ — ID
$ETA_GAMA∼N(0.0,OMGAMA)$ — ID
$ETA_KDE∼N(0.0,OMKDE)$ — ID
$EPS_Y∼N(0.0,SIGMA)$ — DV
$log(PT0)=(log(TVPT0)+ETA_PT0)$
$log(Q0)=(log(TVQ0)+ETA_Q0)$
$log(LAMBDAP)=(log(TVLAMBDAP)+ETA_LAMBDAP)$
$log(KPQ)=(log(TVKPQ)+ETA_KPQ)$
$log(KQPP)=(log(TVKQPP)+ETA_KQPP)$
$log(DELTAQP)=(log(TVDELTAQP)+ETA_DELTAQP)$
$log(GAMA)=(log(TVGAMA)+ETA_GAMA)$
$log(KDE)=(log(TVKDE)+ETA_KDE)$

### Observation Model

#### Observation YContinuous / Residual Data

Parameters
$Y=(EFF+(combinedError1(SDADD,SDPROP,EFF) ×EPS_Y))$

### Estimation Steps

#### Estimation Step estimStep_1

##### Estimation parameters

Fixed parameters

• $SDPROP=0$
• $OMKDE=0.49$
• $SIGMA=1$

Initial estimates for non-fixed parameters

• $TVPT0=10$
• $TVQ0=50$
• $TVLAMBDAP=0.15$
• $TVKPQ=0.05$
• $TVKQPP=0.005$
• $TVDELTAQP=0.01$
• $TVGAMA=1$
• $TVKDE=0.3$
• $SDADD=3$
• $OMPT0=0.25$
• $OMQ0=0.25$
• $OMLAMBDAP=0.25$
• $OMKPQ=0.25$
• $OMKQPP=0.25$
• $OMDELTAQP=0.25$
• $OMGAMA=0.25$
##### Estimation operations
1) Estimate the population parameters
Algorithm SAEM

### Step Dependencies

• estimStep_1