Towards Patient-Specific Mathematical Radiation Oncology
Rockne, Russell Christian
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The war against cancer continues to take its toll on society, even after many decades of focused, intensive research into its origins and cures. Increasingly, efforts are being made to incorporate physical sciences and mathematical approaches in this battle. The term "integrated mathematical oncology" has been coined, which serves to unify the biological and quantitative sciences to bring a fresh perspective to cancer research. In this vein, mathematical modeling is beginning to serve many purposes, from providing a theoretical framework for biological hypothesis testing, to producing data-driven predictions of future disease behavior, to ultimately laying a foundation for personalized medicine. Glioblastoma is an aggressive primary brain tumor which presents a particularly significant opportunity for personalized medicine. Glioblastoma is a diffusely invading cancer which blurs the lines between normal brain and malignant tumor. The disease is formally named glioblastoma multiforme (GBM), to emphasize the pathogenic and morphologic heterogeneity of the disease. Despite this heterogeneity, treatment options are limited and somewhat algorithmic. Nearly all patients diagnosed with GBM will receive radiation and chemo-therapy following surgery. The diverse nature of the disease combined with a 12--14 month prognosis and a "one size fits all" approach to treatment, leads to a unique opportunity for integrated mathematical oncology in the form of patient-specific modeling. I present studies and analysis of mathematical models of radiation therapy-induced DNA damage and repair kinetics, as well as a clinically targeted mathematical model of glioblastoma growth and invasion which incorporates the effects of radiation therapy that links to the concept of personalized medicine by way of estimating patient-specific parameters in a mechanistic model. Specifically, I present analytic solutions for a nonlinear, two-compartment ODE model of radiation-induced DNA damage and repair, which illustrates orders of magnitude differences between the linearized solution used pervasively in the literature, and the analytic solution to the fully nonlinear model. Further, data-driven parameterization of the DNA damage and repair model reveals superior model prediction and parameter stability across a wide range of experimental conditions compared to current model paradigms. I also present the implications of a patient-specific calibration of a reaction-diffusion model for glioblastoma growth. This patient-specific model is expanded to include delivery and temporally delayed response to radiation therapy to yield a predictive relationship between the net rate of proliferation and radiation sensitivity. The patient-specific radiation therapy model is expanded to include spatially and temporally defined treatment delivery and hypoxia-mediated treatment resistance. This extension advances the patient-specific radiation response model into 3D, improves model accuracy, and demonstrates a multifaceted application of patient-specific mathematical modeling for translation to the clinical setting.
- Applied mathematics