A Mathematical Model for Growing Metastases on Oncologists’s Service

Abstract : 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.
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https://hal.inria.fr/hal-01087708
Contributor : Sebastien Benzekry <>
Submitted on : Wednesday, November 26, 2014 - 3:22:07 PM
Last modification on : Thursday, November 7, 2019 - 1:20:37 AM
Long-term archiving on : Friday, February 27, 2015 - 12:27:17 PM

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Dominique Barbolosi, Assia Benabdallah, Sébastien Benzekry, Joseph Ciccolini, Christian Faivre, et al.. A Mathematical Model for Growing Metastases on Oncologists’s Service. Computational Surgery and Dual Training, Springer, pp.331 - 338, 2014, ⟨10.1007/978-1-4614-8648-0_21⟩. ⟨hal-01087708⟩

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