Christian Faivre

Mathematical Modeling of Tumor Growth and Metastatic Spreading: Validation in Tumor-Bearing Mice

Defining tumor stage at diagnosis is a pivotal point for clinical decisions about patient treatment strategies. In this respect, early detection of occult metastasis invisible to current imaging methods would have a major impact on best care and long-term survival. Mathematical models that describe metastatic spreading might estimate the risk of metastasis when no clinical evidence is available. In this study, we adapted a top-down model to make such estimates. The model was constituted by a transport equation describing metastatic growth and endowed with a boundary condition for metastatic emission. Model predictions were compared with experimental results from orthotopic breast tumor xenograft experiments conducted in Nod/Scidγ mice. Primary tumor growth, metastatic spread and growth were monitored by 3D bioluminescence tomography. A tailored computational approach allowed the use of Monolix software for mixed-effects modeling with a partial differential equation model. Primary tumor growth was described best by Bertalanffy, West, and Gompertz models, which involve an initial exponential growth phase. All other tested models were rejected. The best metastatic model involved two parameters describing metastatic spreading and growth, respectively. Visual predictive check, analysis of residuals, and a bootstrap study validated the model. Coefficients of determination were [Formula: see text] for primary tumor growth and [Formula: see text] for metastatic growth. The data-based model development revealed several biologically significant findings. First, information on both growth and spreading can be obtained from measures of total metastatic burden. Second, the postulated link between primary tumor size and emission rate is validated. Finally, fast growing peritoneal metastases can only be described by such a complex partial differential equation model and not by ordinary differential equation models. This work advances efforts to predict metastatic spreading during the earliest stages of cancer.

Metronomics chemotherapy: time for computational decision support

Over the last decade, metronomic chemotherapy has been increasingly considered as an attractive strategy for treating cancer in a variety of settings. Beside pharmaco-economic considerations making metronomics a unique opportunity in low- or middle-income countries, revisiting dosing schedules using continuous low doses of cytotoxics should theoretically permit to reduce the incidence of treatment-related toxicities, while offering unexpected novel mechanisms of actions such as antiangiogenic or immuno-stimulating properties. Consequently, a number of clinical trials sought to evaluate to what extent switching to metronomic schedules could actually impact indeed on the efficacy/toxicity balance of a variety of anticancer drugs in both adults and pediatric oncology. Vinorelbine is a vinca-alcaloïd that remains the backbone of several regimens to treat patients with metastatic breast cancer or non-small cell lung cancer. Additionally, vinorelbine is widely used to treat a variety of solid tumors in children such as rhabdomyosarcomas and acute leukemia. The recent approval of an oral formulation of vinorelbine has open the way to developing alternative metronomic schedules with this drug. Consequently, a number of clinical trials investigating on metronomic vinorelbine have been performed over the last few years, with seemingly inconsistent results to date. Of note, all the studies published thus far were based upon empirical determination of the metronomic schedule, both in terms of doses, drug-free intervals and repartition of the administrations throughout time. Because the very concept of «low, repeated doses with little or no drug-free interval» covers numerous possible combinations, determining the optimal protocol using traditional under-powered empirical design looks like an unreachable goal. In this context, mathematical modeling offers invaluable in silico tools to help determining the optimal metronomic schedule among a variety of possibilities. This review covers the latest clinical trials investigating on metronomic vinorelbine and proposes alternative strategies for developing computational decision support to make metronomics a scientific-grounded strategy, rather than an empirical practice at the bedside. In particular, mathematical simulations using an original pharmacokinetics/pharmacodynamics constraint models provide clues for exploring new paths in the way metronomic vinorelbine could be scheduled in patients with lung cancer.

A phase Ia/Ib clinical trial of metronomic chemotherapy based on a mathematical model of oral vinorelbine in metastatic non-small cell lung cancer and malignant pleural mesothelioma: rationale and study protocol

BackgroundMetronomic oral vinorelbine is effective in metastatic NSCLC and malignant pleural mesothelioma, but all the studies published thus far were based upon a variety of empirical and possibly suboptimal schedules, with inconsistent results. Mathematical modelling showed by simulation that a new metronomic protocol could lead to a better safety and efficacy profile.DesignThis phase Ia/Ib trial was designed to confirm safety (phase Ia) and evaluate efficacy (phase Ib) of a new metronomic oral vinorelbine schedule. Patients with metastatic NSCLC or malignant pleural mesothelioma in whom standard treatments failed and who exhibited ECOG performance status 0–2 and adequate organ function will be eligible. Our mathematical PK-PD model suggested an alternative weekly D1, D2 and D4 schedule (named Vinorelbine Theoretical Protocol) with a respective dose of 60, 30 and 60 mg. Trial recruitment will be two-staged, as 12 patients are planned to participate in phase Ia to confirm safety and consolidate the calibration of the model parameters. Depending on the phase Ia results and after a favourable decision from a consultative committee, the extension phase (phase Ib) will be an efficacy study including 20 patients who will receive the Optimal Vinorelbine Theoretical Protocol. The primary endpoint is the tolerance (assessed by CTC v4.0) for the phase Ia and the objective response according to RECIST 1.1 for phase Ib.An ancillary study on circulating angiogenesis biomarkers will be a subproject of the trial.DiscussionThis ongoing trial is the first to prospectively test a mathematically optimized schedule in metronomic chemotherapy. As such, this trial can be considered as a proof-of-concept study demonstrating the feasibility to run a computational-driven protocol to ensure an optimal efficacy/toxicity balance in patients with cancer.Trial registrationEudraCT N°: 2015-000138-31

Model-based optimization of combined antiangiogenic + cytotoxics modalities: application to the bevacizumab-paclitaxel association in breast cancer models

In clinical practice, antiangiogenic bevacizumab is usually administrated concomitantly to the chemotherapy. Still, pharmacodynamics effect of antiangiogenics lead to a transient state of normalization of the vessels, thus increasing tumor blood perfusion. This could be used as a time-window for administrating cytotoxics, so as to maximize the amount of drugs reaching the tumor eventually. Our group has developed original mathematical models describing the impact of bevacizumab on tumor vasculature. Simulations have demonstrated in silico that a 6-days lag between the administration of bevacizumab and starting the chemotherapy is recommended to achieve antitumoral efficacy. To test this hypothesis, we have used a breast cancer model to compare the efficacy, tolerance and impact on metastatic spreading of a variety of combinations between bevacizumab and paclitaxel. Fifty NSG mice were grafted with resistant MDA-MB-231-LUC+ human breast cancer cells. Animals were next randomized into 6 groups (control, bevacizumab (B), paclitaxel (T) bevacizumab + pacitaxel (B+T), bevacizumab then paclitaxel (B/T), and paclitaxel then bevacizumab (T/B)). Tumor growth and metastatic spreading were monitored by bioluminescence 3D. Main endpoints were overall survival, tolerance, tumor growth and metastatic spreading. At 60 days, survival was 100% (B/T), 85% (B+T), 75% (T), 65% (T/B), 35% (B) and 0% (control). Additionally, sequences proved to have a strong impact on both timing and localization of the metastatic spreading. Bevacizumab alone led to a metastatic acceleration, since lesions appeared earlier, even as compared with untreated animals. Conversely, the (B/T) sequence reduced significantly the risk of lymph-node metastasis, as compared with any other combinations (i.e., 10% (B/T) vs. 25 and 40% for (B+T) and (T/B), respectively), whereas 100% of untreated animals showed lymph node metastasis. Large inter-individual variability within the groups led to non-significant differences in tumor size at study conclusion, despite the fact that marked reduction in tumor volume was achieved in the (B/T) group. Finally, the (B/T) combination proved to be the best tolerated one. Our present data strongly suggest that refining the sequence in the administration of drugs is critical to improve both tolerance and efficacy. Here, the (B/T) association proved to be more efficacious than any other modalities, especially to reduce and to delay metastasis. Conversely, bevacizumab alone proved to accelerate metastatic spreading. Although preliminary, this POC study demonstrates the relevance of our mathematical model, since predictions of the model have been fully confirmed at the bench. This model could be further used to test in silico various combinations with other anti-angiogenic drugs, so as to identify the best modality of combination prior to use those drugs in vivo.

Abstract 4506: Computational-driven metronomics: application to gemcitabine in neuroblastoma-bearing mice

Metronomics (i.e., repeated administration of small doses of drugs over a long period of time) is an attractive strategy to reduce treatment-related toxicities while possibly offering unexpected novel mechanisms of action such as anti-angiogenesis or immuno-stimulatory properties. Defining an optimal metronomic schedule remains uneasy because of the variety of possible combinations between dosing, frequency and duration. Our group has developed innovative modeling tools to optimize metronomic schedules. Here, we have used this computational approach to test whether metronomics gemcitabine would make better than standard gemcitabine in mice bearing human neuroblastoma. In silico simulation suggested that shifting from standard 100 mg/kg/w over 4 consecutive weeks to the metronomic 1 mg/kg/d schedule for 28 consecutive days would achieve higher antitumoral efficacy while being well tolerated. To test this hypothesis, 100 000 human GI-ME-N neuroblastoma cells stably transfected with luciferase were subcutaneously grafted in 40 nude mice. Mice were next split in 3 groups: control, 100 mg/kg/w gemcitabine (STD-GEM) and 1 mg/kg/d gemcitabine (MetroGem-1). An additional satellite group was treated with 0.5 mg/kg/d (MetroGem-0.5). Metro-Gem was administrated using an osmotic pump implanted subcutaneously. Efficacy (i.e., comparison in tumor growth) was the main endpoint. Pharmacokinetics, tumor inflammation, and vascular density were the secondary endpoints. Gemcitabine assay showed that whereas Cmax up to 80 μg/ml were reached in mice treated with STD-GEM, steady-state concentrations of 0.1 μg/ml only were observed in animals undergoing MetroGem-1. Measuring cathepsin expression by fluorescence imaging suggested reduced inflammation in mice treated with the metronomic schedule. Similarly, fluorescence imaging showed smaller vascular density in mice treated with MetroGem-1 or -0.5 as compared with control or STD-GEM animals. To further check a possible anti-angiogenic effect, tumor perfusion rate was measuring next using luciferine, and fully confirmed that mice treated with Metro-Gem exhibited reduced blood flow as compared with other groups. Finally, bioluminescence monitoring of tumor growth showed that whereas STD-GEM was totally ineffective, both MetroGem-1 and MetroGem-0.5 achieved 60% reduction in tumor mass at the end of the treatment (p Citation Format: Joseph Ciccolini, Eddy Pasquier, Aurelie Lombard, Sarah Giacometti, Christian Faivre, Raphaelle Fanciullino, Cindy Serdjebi, Dominique Barbolosi, Nicolas Andre. Computational-driven metronomics: application to gemcitabine in neuroblastoma-bearing mice. [abstract]. In: Proceedings of the 106th Annual Meeting of the American Association for Cancer Research; 2015 Apr 18-22; Philadelphia, PA. Philadelphia (PA): AACR; Cancer Res 2015;75(15 Suppl):Abstract nr 4506. doi:10.1158/1538-7445.AM2015-4506

A Mathematical Model for Growing Metastases on Oncologists’s Service

The dual classification of cancer as localized or metastatic disease is one of the key point in the elaboration of the best therapy for each patient. Neverthe-less, many studies reveal that part of these localized diseases are already metastatic. The presence of undetectable or micro-metastases explains the necessity of adjuvant chemotherapies after resection of the primary tumor even for some T1N0M0 cancer. There is probably a continuum between these two stages. We expose here how a mathematical model of growing metastases could reflect this continuum of the disease and how such a model could help the oncologists in the choice of the treatment. This phenomenological model is based on a structured transport equations with non local boundary condition describing the evolution of the density of metastasis. Thanks to this model, we forge a new numerical index, that we call Metastatic Index, able to reveal either the micro-metastatic state of the patient, or the visible metastatic one. Numerical illustrations show how this new index can be used.

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.

Proceedings: AACR 104th Annual Meeting 2013; Apr 6-10, 2013; Washington, DC 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 laws 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 models 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, Sebastien 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