"Investigating the impact tumor heterogeneity has on patient response to radiotherapy via mathematical modeling"
The overall purpose of this study is to determine how different assumptions of radiotherapy efficacy affect predictions of tumor cell count using a biology-based mathematical model describing the spatiotemporal evolution of tumor growth and response to radiotherapy. Models seeking to predict patient-specific response have yet to characterize intratumoral heterogeneity in response to radiotherapy. To address this limitation, we acquired quantitative magnetic resonance imaging (MRI) data on four patients with high-grade gliomas at the MD Anderson Cancer Center being treated with fractionated radiotherapy. This longitudinal data was then used to inform a two-species mechanically-coupled reaction diffusion model  describing the spatiotemporal change of tumor growth and response to therapy. Tumor cell proliferation rates, tumor diffusion coefficients, and response to radiotherapy (estimated as the surviving fraction following a single radiotherapy session) were calibrated from data up to 1-month post-radiotherapy using the Levenberg-Marquardt approach in MATLAB. With these patient-specific calibrated parameters, our model simulated tumor growth and response assuming treatment efficacy varies homogeneously (globally) or heterogeneously (as a function of vasculature and cell density). We calculated and compared the percent change in tumor cell count three months after initial treatment for surviving fractions of 0.2 to 1 (in increments of 0.05) for four patients. Treatment response as observed at 3-months post-radiotherapy varied greatly (from eradication to residual disease) depending on each assumption on the spatial variations in efficacy. For example, a surviving fraction of 0.6 resulted in complete eradication of the tumor under both homogenous and heterogenous (cell density) assumptions. However, when radiotherapy efficacy was related to vasculature, only an average 55% decrease in tumor cell count was observed. Thus, we have developed an approach to quantify the impact of different assumptions of heterogeneity in response to radiation on percent change in tumor cell count. Future efforts will extend this approach to a larger cohort of patients.
Additional authors: Tarini Thiagarajan; Thomas E. Yankeelov (1-6); David A. Hormuth, II (1-2); Caroline Chung (7)
1 Oden Institute for Computational Engineering and Sciences, 2 Livestrong Cancer Institutes, 3 Biomedical Engineering, 4 Diagnostic Medicine, and 5 Oncology, The University of Texas at Austin. 6 Department of Imaging Physics, 7 Radiation Oncology MD Anderson Cancer Center.