Modeling the emergence of resistance in low-grade glioma patients treated with temozolomide, and simulations using a stochastic approach
P. Mazzocco (1), F. Ducray (2), A. Leclercq-Samson (3)
(1) Inria, Project-team NUMED, Ecole Normale Supérieure de Lyon, 46 allée d’Italie, 69007 Lyon Cedex 07, France ; (3) Hospices Civils de Lyon, Hôpital Neurologique, Neuro-oncologie,Lyon, 69003 France; Inserm U1028 ; CNRS UMR5292 ; LyonNeuroscience Research Center, Neuro-oncology and Neuro- inflammation team, Lyon,F-69000, France; University Lyon 1, Lyon, F-69000, France (3) Université Joseph Fourier, Grenoble, UFR IM2AG, Laboratoire Jean Kuntzmann, UMR CNRS 5224; 38 041 Grenoble Cedex 09.
Objectives: To develop a mixed-effect modeling framework to describe the emergence of resistance in low-grade glioma (LGG) patients treated with temozolomide (TMZ).
Methods: We analyzed a dataset containing mean tumor diameters (MTD) in 77 LGG patients, treated with first-line TMZ, representing a total of 952 observations. TMZ is known to induce DNA mutations that decrease chemo sensibility of the tumor. Almost half of the patients (n = 34, 44%) experienced tumor progression during treatment.
We proposed a mixed-effect model, using ordinary differential equations (ODE), to describe the observed MTD, especially the resistance phenomenon. To this purpose, we modified a previously published model [1] and added a sub-population of resistant cells to describe the emergence of resistance in a more mechanistic manner. We tested different hypotheses for the emergence of resistance, including mutations due to TMZ and random mutations that can occur at any time. The best model was chosen according to the regular selection criteria. Model parameters were estimated in a population context, using Monolix [2] (Lixoft [3]).
ODE model parameter estimates were then used to simulate tumor dynamics through a stochastic approach. That later introduced some randomness that compensated effects of factors that were not included in the model, such as environmental factors. We implemented stochastic differential equations (SDE) in Matlab to allow for some randomness in the processes involved in tumor evolution, before, during and after the treatment.
Results: We found that the best ODE model includes mutations due to TMZ, as well as random mutations that can occur before, during and after treatment. The model reproduced the different tumor dynamics observed in our population, including tumor progression during treatment.
We then added noise on the TMZ clearance and on the mutation parameters. Empirical distributions for time to progression, time to tumor growth and minimal tumor size were then derived from these distributions.
Conclusions: Our results indicated that two different processes were involved in the emergence of resistance: random mutations and mutations due to TMZ chemotherapy. Thanks to simulations with SDEs, empirical distributions were build for time to tumor growth, time to progression and minimal tumor size. This modeling framework could be used to test different therapeutic protocols for TMZ administration, in order to delay the emergence of resistance and prolong tumor response to treatment.
References:
[1] Ribba B, Kaloshi G, Peyre M, Ricard D, Calvez V, Tod M, et al. A Tumor Growth Inhibition Model For Low-Grade Glioma Treated With Chemotherapy or Radiotherapy. Clin Cancer Res. 2012;18: 5071–80. doi:10.1158/1078-0432.CCR-12-0084
[2] E. Kuhn and M. Lavielle. Maximum likelihood estimation in nonlinear mixed effects models. Comput. Statist. Data Anal., 49:1020–1038, 2005.
[3] Lixoft. Monolix methodology. Available at http://www.lixoft.com/wp-content/resources/docs/monolixMethodology.pdf, March 2013. Version 4.2.2.