Modeling the Dynamics of Glioblastoma Multiforme and Cancer Stem Cells
College
College of Arts and Sciences
Department
Mathematics
Faculty Mentor
Dr. Zach Abernathy & Dr. Kristen Abernathy
Abstract
We extend the work of Kronik, Kogan, Vainstein, and Agur (2008) by incorporating the cancer stem cell hypothesis into a treatment model for Glioblastoma Multiforme. Cancer Stem Cells (CSCs) are a specialized form of tumor cell with normal adult stem cell properties. CSCs are believed to be one of the primary reasons for cancer recurrence since they are more resilient to current treatment practices and are able to repopulate the tumor. We present a system of nonlinear ordinary differential equations that describes the interaction between cancer stem cells, tumor cells, and alloreactive cytotoxic-T-lymphocytes (CTLs). Under the assumption of constant treatment, we present conditions on the treatment amount that leads to a locally stable cure state. We also explore a more biologically accurate treatment schedule in which CTLs are injected periodically. In the case of periodic treatment, we numerically establish treatment schedules that lead to cancer persistence, cancer recurrence, and cancer eradication. We conclude with a sensitivity analysis of our parameters and a discussion of biological implications.
Recognized with an Award?
Winner, Outstanding Undergraduate Student Presentation Award, Regional Mathematics and Statistics Conference, Greensboro, North Carolina, November 2015
Previously Presented/Performed?
11th Annual Regional Mathematics and Statistics Conference, University of North Carolina, Greensboro, November 2015
Grant Support?
Supported by a grant from the National Institutes of Health IDeA Networks for Biomedical Research Excellence (NIH INBRE)
Start Date
22-4-2016 3:00 PM
End Date
22-4-2016 3:15 PM
Modeling the Dynamics of Glioblastoma Multiforme and Cancer Stem Cells
DiGorgio Campus Center, Room 222
We extend the work of Kronik, Kogan, Vainstein, and Agur (2008) by incorporating the cancer stem cell hypothesis into a treatment model for Glioblastoma Multiforme. Cancer Stem Cells (CSCs) are a specialized form of tumor cell with normal adult stem cell properties. CSCs are believed to be one of the primary reasons for cancer recurrence since they are more resilient to current treatment practices and are able to repopulate the tumor. We present a system of nonlinear ordinary differential equations that describes the interaction between cancer stem cells, tumor cells, and alloreactive cytotoxic-T-lymphocytes (CTLs). Under the assumption of constant treatment, we present conditions on the treatment amount that leads to a locally stable cure state. We also explore a more biologically accurate treatment schedule in which CTLs are injected periodically. In the case of periodic treatment, we numerically establish treatment schedules that lead to cancer persistence, cancer recurrence, and cancer eradication. We conclude with a sensitivity analysis of our parameters and a discussion of biological implications.
