To develop mathematical models to predict the evolution of tumor geometry in cervical cancer undergoing radiation therapy.
The authors develop two mathematical models to estimate tumor geometry change: a Markov model and an isomorphic shrinkage model. The Markov model describes tumor evolution by investigating the change in state (either tumor or nontumor) of voxels on the tumor surface. It assumes that the evolution follows a Markov process. Transition probabilities are obtained using maximum likelihood estimation and depend on the states of neighboring voxels. The isomorphic shrinkage model describes tumor shrinkage or growth in terms of layers of voxels on the tumor surface, instead of modeling individual voxels. The two proposed models were applied to data from 29 cervical cancer patients treated at Princess Margaret Cancer Centre and then compared to a constant volume approach. Model performance was measured using sensitivity and specificity.
The Markov model outperformed both the isomorphic shrinkage and constant volume models in terms of the trade-off between sensitivity (target coverage) and specificity (normal tissue sparing). Generally, the Markov model achieved a few percentage points in improvement in either sensitivity or specificity compared to the other models. The isomorphic shrinkage model was comparable to the Markov approach under certain parameter settings. Convex tumor shapes were easier to predict.
By modeling tumor geometry change at the voxel level using a probabilistic model, improvements in target coverage and normal tissue sparing are possible. Our Markov model is flexible and has tunable parameters to adjust model performance to meet a range of criteria. Such a model may support the development of an adaptive paradigm for radiation therapy of cervical cancer.
The authors gratefully acknowledge the support of and helpful suggestions from Dr. Michael Milosevic in this research project and in particular for providing access to the patient data used in this paper. This research was supported in part by the Ontario Consortium for Adaptive Interventions in Radiation Oncology (OCAIRO) funded by the Ontario Research Fund (ORF) and the MITACS Accelerate Internship Program.
II. METHODS AND MATERIALS
II.A. Patient data
II.B. Data processing
II.C. A Markov model: Modeling individual voxels on the tumor surface
II.C.1. Voxel states and geometries
II.C.2. Transition probability estimation
II.D. An isomorphic shrinkage model: Modeling voxel layers on the tumor surface
II.E. A constant volume model
II.F. Performance metrics
III.A. Comparing the three models
III.B. A statistical comparison between the Markov and isomorphic shrinkage models
- Markov processes
- Biomedical modeling
- Medical imaging
- Magnetic resonance imaging
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