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Modeling the Treatment of Glioblastoma Multiforme and Cancer Stem Cells with Ordinary Differential Equations


Affiliations
1 Department of Mathematics,Winthrop University, Rock Hill, SC 29733, United States
2 Department of Mathematics, Vassar College, Poughkeepsie, NY 12604, United States
 

Despite improvements in cancer therapy and treatments, tumor recurrence is a common event in cancer patients. One explanation of recurrence is that cancer therapy focuses on treatment of tumor cells and does not eradicate cancer stem cells (CSCs). CSCs are postulated to behave similar to normal stem cells in that their role is to maintain homeostasis. That is, when the population of tumor cells is reduced or depleted by treatment, CSCs will repopulate the tumor, causing recurrence. In this paper, we study the application of the CSC Hypothesis to the treatment of glioblastoma multiforme by immunotherapy. We extend the work of Kogan et al. (2008) to incorporate the dynamics of CSCs, prove the existence of a recurrence state, and provide an analysis of possible cancerous states and their dependence on treatment levels.
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  • Modeling the Treatment of Glioblastoma Multiforme and Cancer Stem Cells with Ordinary Differential Equations

Abstract Views: 76  |  PDF Views: 1

Authors

Kristen Abernathy
Department of Mathematics,Winthrop University, Rock Hill, SC 29733, United States
Jeremy Burke
Department of Mathematics, Vassar College, Poughkeepsie, NY 12604, United States

Abstract


Despite improvements in cancer therapy and treatments, tumor recurrence is a common event in cancer patients. One explanation of recurrence is that cancer therapy focuses on treatment of tumor cells and does not eradicate cancer stem cells (CSCs). CSCs are postulated to behave similar to normal stem cells in that their role is to maintain homeostasis. That is, when the population of tumor cells is reduced or depleted by treatment, CSCs will repopulate the tumor, causing recurrence. In this paper, we study the application of the CSC Hypothesis to the treatment of glioblastoma multiforme by immunotherapy. We extend the work of Kogan et al. (2008) to incorporate the dynamics of CSCs, prove the existence of a recurrence state, and provide an analysis of possible cancerous states and their dependence on treatment levels.