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/Scidg 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 R 2 ¼ 0:94 for primary tumor growth and R 2 ¼ 0:57 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. Cancer Res; 74(22); 6397-407. Ó2014 AACR.

Experimental method and statistical analysis to fit tumor growth model using SPECT/CT imaging: a preclinical study

“…Recently preclinical experiments to predict volume (7) and metastasis (8) have been performed. In (7) several classical existing tumorvolume growth models (such as logistic, Gompertzian etc.)…”

“…For lung-tumor Gompertz and power-law prediction was best, however with prediction rate ≤70% and required prior information on parameter distribution to improve. In (8) primary and metastatic tumor growth models were compared with measurements from preclinical images of breast-tumor bearing mice, with mixed results: coefficients of determination were R 2 =0.94…”

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“…Individualized medicine is mostly based on huge resources to identify markers that are likely to predict the level of aggressiveness of a newly diagnosed cancer, and next to search for predictive markers of response to a given therapy. Such preliminary information can be used subsequently to help clinicians to select the best strategies (ie, administrating systemic adjuvant therapy or not) and the best drug or drugs combination to be given, should they be given 66,67. Avoiding unnecessary treatments is now a critical issue in oncology, both because of the cost of the drugs (ie, with targeted therapies) and the possible treatment-related severe toxicities (ie, with cytotoxics), thereby negatively impacting the quality of life and efficacy–toxicity balance eventually.…”

Three-Dimensional Spatiotemporal Modeling of Colon Cancer Organoids Reveals that Multimodal Control of Stem Cell Self-Renewal is a Critical Determinant of Size and Shape in Early Stages of Tumor Growth

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