Global Analysis of the Dynamics of a Piecewise Linear Vector Field Model for Prostate Cancer Treatment |
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Authors: | Carvalho Tiago Cristiano Rony Rodrigues Diego S. Tonon Durval J. |
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Affiliation: | 1.Department of Computing and Mathematics, Faculty of Philosophy, Sciences and Letters of Ribeir?o Preto, University of S?o Paulo, Ribeir?o Preto, 14040-901, SP, Brazil ;2.Institute of Mathematics and Statistics, Federal University of Goiás, Goiania, 74001-970, GO, Brazil ;3.School of Technology, University of Campinas, Limeira, 13484-332, SP, Brazil ; |
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Abstract: | Oncological therapies usually are applied intermittently, i.e., not continuously over time. In the periods in between, though, the cancer cells are usually left free to grow. This intermittency is a key issue in prostate cancer hormonal therapies based on androgen suppression. Here, we address this treatment modality by analyzing a piecewise smooth vector field approach. In fact, using the PSA (prostate-specific antigen) serum level as a control variable to switch between treatment and no-treatment periods of hormone therapy (androgen withdrawal), by means of typical parameter values, our theoretical analysis supports the idea that intermittent androgen suppression may prevent a prostate cancer relapse for a specific class of patients. |
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