title: A stochastic model for tumor geometry evolution during radiation therapy in cervical cancer.
abstract: OBJECTIVE
  To develop mathematical models to predict the evolution of tumor geometry in cervical cancer undergoing radiation therapy.
  
  
  METHODS
  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.
  
  
  RESULTS
  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.
  
  
  CONCLUSIONS
  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.
authors: Department of Mechanical and Industrial Engineering, University of Toronto, 5 King's College Road, Toronto, Ontario M5S 3G8, Canada.
authors: Yifang
authors: Y
authors: Liu
authors: Department of Mechanical and Industrial Engineering, University of Toronto, 5 King's College Road, Toronto, Ontario M5S 3G8, Canada and Techna Institute for the Advancement of Technology for Health, 124-100 College Street Toronto, Ontario M5G 1P5, Canada.
authors: Timothy C Y
authors: TC
authors: Chan
authors: Department of Mechanical and Industrial Engineering, University of Toronto, 5 King's College Road, Toronto, Ontario M5S 3G8, Canada.
authors: Chi-Guhn
authors: CG
authors: Lee
authors: Department of Radiation Physics, Radiation Medicine Program, Princess Margaret Cancer Centre, University Health Network, 610 University of Avenue, Toronto, Ontario M5T 2M9, Canada and Department of Radiation Oncology, University of Toronto, 148-150 College Street, Toronto, Ontario M5S 3S2, Canada.
authors: Young-Bin
authors: YB
authors: Cho
authors: Department of Radiation Physics, Radiation Medicine Program, Princess Margaret Cancer Centre, University Health Network, 610 University of Avenue, Toronto, Ontario M5T 2M9, Canada; Department of Radiation Oncology, University of Toronto, 148-150 College Street, Toronto, Ontario M5S 3S2, Canada; and Techna Institute for the Advancement of Technology for Health, 124-100 College Street, Toronto, Ontario M5G 1P5, Canada.
authors: Mohammad K
authors: MK
authors: Islam
mesh_terms: D005260:Female; D006801:Humans; D008279:Magnetic Resonance Imaging; D008390:Markov Chains; D008954:Models, Biological; D058958:Organs at Risk / Q000528:radiation effects; D013269:Stochastic Processes; D002583:Uterine Cervical Neoplasms / Q000473:pathology* / Q000532:radiotherapy*