title: Mathematical modeling of tumor growth and metastatic spreading: validation in tumor-bearing mice.
abstract: 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.
authors.affiliation: I2M UMR 7373 Aix-Marseille Université, CNRS, Centrale Marseille, Marseille, France.
authors.forename: Niklas
authors.initials: N
authors.lastname: Hartung
authors.affiliation: SMARTc Pharmacokinetics Unit, Inserm S_911 CRO2, Aix Marseille University, Marseille, France.
authors.forename: Séverine
authors.initials: S
authors.lastname: Mollard
authors.affiliation: SMARTc Pharmacokinetics Unit, Inserm S_911 CRO2, Aix Marseille University, Marseille, France.
authors.forename: Dominique
authors.initials: D
authors.lastname: Barbolosi
authors.affiliation: I2M UMR 7373 Aix-Marseille Université, CNRS, Centrale Marseille, Marseille, France.
authors.forename: Assia
authors.initials: A
authors.lastname: Benabdallah
authors.affiliation: I2M UMR 7373 Aix-Marseille Université, CNRS, Centrale Marseille, Marseille, France.
authors.forename: Guillemette
authors.initials: G
authors.lastname: Chapuisat
authors.affiliation: I2M UMR 7373 Aix-Marseille Université, CNRS, Centrale Marseille, Marseille, France.
authors.forename: Gerard
authors.initials: G
authors.lastname: Henry
authors.affiliation: SMARTc Pharmacokinetics Unit, Inserm S_911 CRO2, Aix Marseille University, Marseille, France.
authors.forename: Sarah
authors.initials: S
authors.lastname: Giacometti
authors.affiliation: SMARTc Pharmacokinetics Unit, Inserm S_911 CRO2, Aix Marseille University, Marseille, France.
authors.forename: Athanassios
authors.initials: A
authors.lastname: Iliadis
authors.affiliation: SMARTc Pharmacokinetics Unit, Inserm S_911 CRO2, Aix Marseille University, Marseille, France.
authors.forename: Joseph
authors.initials: J
authors.lastname: Ciccolini
authors.affiliation: SMARTc Pharmacokinetics Unit, Inserm S_911 CRO2, Aix Marseille University, Marseille, France.
authors.forename: Christian
authors.initials: C
authors.lastname: Faivre
authors.affiliation: I2M UMR 7373 Aix-Marseille Université, CNRS, Centrale Marseille, Marseille, France. florence.hubert@univ-amu.fr.
authors.forename: Florence
authors.initials: F
authors.lastname: Hubert
mesh_terms: D000818:Animals; D045744:Cell Line, Tumor; D049109:Cell Proliferation; D005260:Female; D008163:Luminescent Measurements; D008175:Lung Neoplasms / Q000473:pathology; D051379:Mice; D008962:Models, Theoretical; D009362:Neoplasm Metastasis / Q000473:pathology; D009368:Neoplasm Transplantation; D009374:Neoplasms, Experimental / Q000473:pathology*; D010534:Peritoneal Neoplasms / Q000556:secondary