Abstract A09: Predicting response to whole brain radiotherapy in a murine model of glioma
Authors: Hormuth David A. , Weis Jared A. , Eldridge Stephanie B. , Miga Michael I. , Rericha Erin C. , Quaranta Vito , Yankeelov Thomas E. 
Published: March 2017

Abstract
Introduction: Glioblastoma is a highly invasive and aggressive brain tumor which accounts for nearly 82% of all gliomas. One promising direction for improving the clinical care of cancer, in general, and glioblastomas, in particular, is the development of accurate and precise predictive mathematical models of tumor growth. Specifically, models that can accurately characterize tumor response to radiotherapy could improve the design and optimization of individual radiotherapy plans. Using non-invasive imaging measurements from magnetic resonance imaging (MRI), a biophysical model of tumor growth has been shown to accurately predict future tumor growth on an individual basis in a murine model of glioma. In this work, we have expanded upon this biophysical model to incorporate the effects of radiotherapy. Furthermore, we evaluate the accuracy of model predictions relative to in vivo measurements of tumor growth.
Methods: Untreated tumor growth was modeled using a mechanically-coupled reaction-diffusion model incorporating a voxel-specific carrying capacity, a voxel-specific tumor cell proliferation rate, and a global value for tumor cell diffusion. The effects of radiotherapy were modeled as resulting in either instantaneous cell death (Md model), the reduction in the net proliferation rate (Mp model), or a combination of the two effects (Mdp ). Instantaneous cell death was incorporated into the Md and Mdp models by estimating a death rate that was applied only during treatment. Similarly, decreased proliferation was incorporated into the Mp and Mdp models by estimating a proliferation fraction that was applied during and after treatment. To evaluate these models, rats with C6 gliomas were imaged over twelve days with diffusion-weighted MRI (DW-MRI) and contrast enhanced MRI (CE-MRI). Rats were imaged at three time points prior to receiving whole brain radiation therapy with a dose of either 20 Gy (N = 5) or 40 Gy (N = 7), and were imaged an additional four times following treatment. Tumor cellularity was estimated within enhancing regions in CE-MRI images using DW-MRI data. The pre-treatment measurements of cellularity were used to estimate tumor cell proliferation rate, carrying capacity, and the tumor cell diffusion coefficient. Two post-treatment measurements were used to estimate the post-treatment model parameters. The estimated model parameters were then used in a finite difference simulation to predict tumor growth at the remaining (6th through 7th) imaging time points. Error between the predicted radiotherapy response and the observed radiotherapy response was assessed by calculating the percent error in tumor volume, percent error in voxel cell number, and the normalized root mean square error (nRMSE).
Results: For the 20 Gy rats no statistically significant differences were observed for model error in tumor volume (ranging from 7.7 to 21.2%), voxel cell number (ranging from 14.0 to 18.4%), or nRMSE (ranging from 0.14 to 0.16) between models. For the 40 Gy rats, the error in tumor volume prediction was significantly lower (p &lt; 0.05) for the Mp and Mdp models (ranging from 22.2 to 36.3%) compared to the Md model (error greater than 54%). Error in voxel cell number ranged from 17.2 to 23.3% for all three models. The Mp and Mdp models had statistically lower nRMSE (nRMSE &lt; 0.30, p = 0.05) compared to the Md model (nRMSE = 0.64).
Conclusion: For 20 Gy whole brain radiotherapy, all three models demonstrated accurate prediction of future bulk tumor growth. However, at 40 Gy the model predictions of future bulk tumor growth were poor, although the Mp and Mdp models provide lower error in predictions than the Md model. Additionally, all three models fail to capture the development of low cell density, potentially necrotic, regions following radiotherapy for both the 20 and 40 Gy groups. Further work is needed to better characterize intra-tumor response at all doses.
Citation Format: David A. Hormuth, II, Jared A. Weis, Stephanie B. Eldridge, Michael I. Miga, Erin C. Rericha, Vito Quaranta, Thomas E. Yankeelov. Predicting response to whole brain radiotherapy in a murine model of glioma. [abstract]. In: Proceedings of the AACR Special Conference on Engineering and Physical Sciences in Oncology; 2016 Jun 25-28; Boston, MA. Philadelphia (PA): AACR; Cancer Res 2017;77(2 Suppl):Abstract nr A09.