Abstract 402: A new mathematical model for describing metastatic spreading: Validation in tumor-bearing mice, confrontation with clinical data and in silico simulations to optimize treatment modalities.
Authors: Mollard Severine , Ciccolini Joseph , Hartung Niklas , Faivre Christian , Benzekri Sébastien , Chapuisat Guillemette , Benabdallah Assia , Hubert Florence , Barbolosi Dominique 
Published: August 2014

Abstract
Occult metastatic disease is a major concern in clinical oncology because optimal therapy can not been undertaken in a timely manner. Developing mathematical tools for describing and anticipating early metastatic stages would help clinicians to choose the most adequate therapeutic strategy, even if no metastasis is yet detectable at bedside. We have developed a mathematical model that provides a Metastatic Index (MI). We used a phenomenological approach based on a structured transport equation with non local boundary condition for the colony size distribution of metastases. The velocity of this transport was related to a Gompertz law's growth. The colonization rate of the tumors reflects not only the metastatic diffusion but also some fractal dimension of the blood vessels infiltrating the tumors. This model is mostly based upon few parameters and can integrate the impact of surgery or chemotherapies on tumor growth and spreading. Model structure and parameters were first adjusted by fitting the predictions with observed data from several experiments performed in mice bearing the MDA-231LUC+ breast orthotopic xenograft. Three-dimmensional bioluminescence monitoring was carried out so as to detect early metastases as small as 10ˆ5 cells. A pre-validation step was carried out to check the ability of bioluminescence imaging to discriminate small metastatic sites from artifactual signals. Various molecular markers (A-cadherine, alcohol dehydrogenase, metaloproteases) were studied from tumor biopsies to refine some of the model parameters. Data were finally compared using Monolix software and Visual Predictive Check confirmed the ability of the model to predict accuratelly both tumor growth-rate and invasiveness. Additionally, we compared the in silico predictions of the model with clinical data from 2648 breast cancer patients (a.k.a. the Koscielny cohort) with a follow-up of metastatic reccurence depending on the initial tumor size measured upon surgery. Results showed that the model's predictions matched the clinical observations (rˆ2=0.98), thus suggesting that our MI could be a useful tool indeed to forecast metastatic spreading in patients with cancer. Finally, in silico simulations were performed to study the impact of surgery or treatment with cytotoxics alone or combined with antiangiogenics. Marked variations in efficacy were observed depending on the treatment modalities. The resulting simulations suggest therefore that our mathematical model could be used as well to determine in silico the best scheduling and dosing of cancer chemotherapy, especially when anti-angiogenic and cytotoxic drugs are associated.
Citation Format: Severine Mollard, Joseph Ciccolini, Niklas Hartung, Christian Faivre, Sébastien Benzekri, Guillemette Chapuisat, Assia Benabdallah, Florence Hubert, Dominique Barbolosi. A new mathematical model for describing metastatic spreading: Validation in tumor-bearing mice, confrontation with clinical data and in silico simulations to optimize treatment modalities. [abstract]. In: Proceedings of the 104th Annual Meeting of the American Association for Cancer Research; 2013 Apr 6-10; Washington, DC. Philadelphia (PA): AACR; Cancer Res 2013;73(8 Suppl):Abstract nr 402. doi:10.1158/1538-7445.AM2013-402