Towards an Image-Informed Mathematical Model of In Vivo Response to Fractionated Radiation Therapy

Abstract

Fractionated radiation therapy is central to the treatment of numerous malignancies, including high-grade gliomas where complete surgical resection is often impractical due to its highly invasive nature. Development of approaches to forecast response to fractionated radiation therapy may provide the ability to optimize or adapt treatment plans for radiotherapy. Towards this end, we have developed a family of 18 biologically-based mathematical models describing the response of both tumor and vasculature to fractionated radiation therapy. Importantly, these models can be personalized for individual tumors via quantitative imaging measurements. To evaluate this family of models, rats (n = 7) with U-87 glioblastomas were imaged with magnetic resonance imaging (MRI) before, during, and after treatment with fractionated radiotherapy (with doses of either 2 Gy/day or 4 Gy/day for up to 10 days). Estimates of tumor and blood volume fractions, provided by diffusion-weighted MRI and dynamic contrast-enhanced MRI, respectively, were used to calibrate tumor-specific model parameters. The Akaike Information Criterion was employed to select the most parsimonious model and determine an ensemble averaged model, and the resulting forecasts were evaluated at the global and local level. At the global level, the selected model’s forecast resulted in less than 16.2% error in tumor volume estimates. At the local (voxel) level, the median Pearson correlation coefficient across all prediction time points ranged from 0.57 to 0.87 for all animals. While the ensemble average forecast resulted in increased error (ranging from 4.0% to 1063%) in tumor volume predictions over the selected model, it increased the voxel wise correlation (by greater than 12.3%) for three of the animals. This study demonstrates the feasibility of calibrating a model of response by serial quantitative MRI data collected during fractionated radiotherapy to predict response at the conclusion of treatment.

A Multi-Compartment Model of Glioma Response to Fractionated Radiation Therapy Parameterized via Time-Resolved Microscopy Data

“…To the best of our knowledge, this study is the first mechanism-based fractionated radiation model verified by the cell experimental data at high temporal-resolution. We have constructed this approach by building on previous time-resolved dynamic radiation models that either calibrated to a single dose of radiation (46), or to data collected every several days (23) or weeks (47). We hope that the current effort can provide motivation for focusing on factors that describe the dynamics of radiobiology as a function of time, thereby potentially providing a new way to guide and optimize radiation dose scheduling.…”

“…This study demonstrates a promising experimental-mathematical approach based on radiobiology mechanisms that can accurately predict the temporal dynamics of the response of glioma cells to radiation. Future efforts include linking the model to our tissue scale formalism for predicting response in patients (23), and employing the methods of optimal control theory to optimize treatment outcomes in pre-clinical murine studies (59).…”

“…More recently, several studies have constructed radiation response models that account for temporal changes in hypoxia (20), DNA repair (21), and fractionation (22). Hormuth et al contributed a tissue-scale model that employed the oxygen enhancement ratio to adjust the radiation efficacy during fractionation treatment and tested model predictions against in vivo MRI data (23,24). Brüningk et al (25) proposed a cell-scale decision tree model that accounted for conversion between cell cycle compartments after radiation.…”

Biologically-Based Mathematical Modeling of Tumor Vasculature and Angiogenesis via Time-Resolved Imaging Data

“…The influence of vasculature on tumor response to radiotherapy was considered by Hormuth et al [ 32 , 85 , 144 ], who used a coupled PDE-based model of tumor growth and angiogenesis in a murine model of glioma. Quantitative MRI collected before and after radiation therapy were used to initialize estimates of tumor cellularity (from diffusion-weighted MRI [ 145 ]) and blood volume fraction (from DCE-MRI) as well as to calibrate model parameters.…”

“…Similarly, a previous study assessing the validity of 39 models of tumor growth and radiotherapy response [ 137 ] was used to guide modeling of tumor and vasculature response to radiotherapy. When response to radiotherapy was considered, Hormuth et al observed that spatially varying the efficacy of radiotherapy as a function of local blood volume fraction also improved predictions of tumor response [ 85 , 144 ].…”