David A Hormuth1, Jared A Weis2, Stephanie L Barnes3, Michael I Miga4, Vito Quaranta5, Thomas E Yankeelov6. 1. Institute for Computational and Engineering Sciences, The University of Texas at Austin, Austin, Texas. Electronic address: david.hormuth@utexas.edu. 2. Department of Biomedical Engineering, Wake Forest School of Medicine, Winston-Salem, North Carolina; Comprehensive Cancer Center, Wake Forest Baptist Medical Center, Winston-Salem, North Carolina. 3. Institute for Computational and Engineering Sciences, The University of Texas at Austin, Austin, Texas. 4. Department of Biomedical Engineering, Vanderbilt University, Nashville, Tennessee; Department of Radiology and Radiological Sciences, Vanderbilt University, Nashville, Tennessee; Department of Neurological Surgery, Vanderbilt University, Nashville, Tennessee. 5. Department of Cancer Biology, Vanderbilt University, Nashville, Tennessee. 6. Institute for Computational and Engineering Sciences, The University of Texas at Austin, Austin, Texas; Department of Biomedical Engineering, The University of Texas at Austin, Austin, Texas; Department of Internal Medicine, The University of Texas at Austin, Austin, Texas.
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 (Md), a reduced proliferation rate model (Mp), and cell death and reduced proliferation model (Mdp). 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 Mdp and Mp models compared with the Md model. The Mdp model fit, however, had significantly lower sum squared error compared with the Mp and Md models. CONCLUSIONS: The results of this study indicate that for both doses, the Mp and Mdp models result in accurate predictions of tumor growth, whereas the Md model poorly describes response to radiation therapy.
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 (Md), a reduced proliferation rate model (Mp), and cell death and reduced proliferation model (Mdp). 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 Mdp and Mp models compared with the Md model. The Mdp model fit, however, had significantly lower sum squared error compared with the Mp and Md models. CONCLUSIONS: The results of this study indicate that for both doses, the Mp and Mdp models result in accurate predictions of tumor growth, whereas the Md model poorly describes response to radiation therapy.
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