Author: Xianjin Dai, PhD, Xiang Wan, Lei Xing, Qiuyun Xu, Lewei Zhao, Zeyu Zhou 👨🔬
Affiliation: Department of Radiation Oncology, Stanford University, Carl Zeiss X-ray Microscopy, Department of Mathematics and Statistics, Loyola University Chicago, Department of Radiation Oncology, City of Hope National Medical Center 🌍
Purpose: The purpose of this study is to examine and quantify tumor shrinkage over time in response to fractionated radiotherapy. We seek to establish a predictive model that can provide a systematic understanding of tumor responses to different radiation fraction schedules, providing clinicians with a theoretical tool to optimize patient treatment plans. We use a 2-dimensional (in space) model, by asserting one degree of spatial symmetry of the domain, as a preliminary step toward an ultimate 3-dimensional model.
Methods: We use a tumor response model to simulate the effects of fractionated radiotherapy across various populations. We implemented this model using Gmsh to discretize the geometry grid and then employ the open-source FEniCS/DOLFIN software to construct the mixed finite element method (FEM) space and solve the system of diffusion equations with free boundary within this framework.
Results: The model is simulated for longitudinal symmetric domains with free boundaries, as it is shown that the tumor may decrease in size because of radiation with different strength. The numerical simulation observes (i) the predicted stage-wise tumor shrinkage corresponding to the various radiation fractions; (ii) the ascending rate of shrinkage corresponding to the increasing radiation strength, each quantified and visualized in plots about maximum tumor radii versus time and strength, respectively. It presents an intuitive and clear timeline of tumor shrinkage post treatment, thereby validating our model's capability to predict radiotherapy outcomes.
Conclusion: Our results demonstrate the potential of finite element analysis in predicting tumor responses to fractionated radiotherapy. This study shows how computational modeling can help personalize cancer treatment by predicting and visualizing how individual tumors respond to different radiation treatment schedules. Further validation using clinical data is essential to refine the model's predictive accuracy, opening doors for its potential application in personalized treatment planning for radiotherapy.