Abstract
PURPOSE: To develop and investigate a set of biophysical models based on a mechanically coupled reaction-diffusion model of the spatiotemporal evolution of tumor growth after radiation therapy. METHODS AND MATERIALS: Post-radiation therapy response is modeled using a cell death model (M(d)), a reduced proliferation rate model (M(p)), and cell death and reduced proliferation model (M(dp)). To evaluate each model, rats (n = 12) with C6 gliomas were imaged with diffusion-weighted magnetic resonance imaging (MRI) and contrast-enhanced MRI at 7 time points over 2 weeks. Rats received either 20 or 40 Gy between the third and fourth imaging time point. Diffusion-weighted MRI was used to estimate tumor cell number within enhancing regions in contrast-enhanced MRI data. Each model was fit to the spatiotemporal evolution of tumor cell number from time point 1 to time point 5 to estimate model parameters. The estimated model parameters were then used to predict tumor growth at the final 2 imaging time points. The model prediction was evaluated by calculating the error in tumor volume estimates, average surface distance, and voxel-based cell number. RESULTS: For both the rats treated with either 20 or 40 Gy, significantly lower error in tumor volume, average surface distance, and voxel-based cell number was observed for the M(dp) and M(p) models compared with the M(d) model. The M(dp) model fit, however, had significantly lower sum squared error compared with the M(p) and M(d) models. CONCLUSIONS: The results of this study indicate that for both doses, the M(p) and M(dp) models result in accurate predictions of tumor growth, whereas the M(d) model poorly describes response to radiation therapy.