Department of Mechanical and Industrial Engineering, University of Toronto, 5 King's College Road, Toronto, Ontario M5S 3G8, Canada.
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.
Med Phys. 2014 Feb;41(2):021705. doi: 10.1118/1.4859355.
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.
开发数学模型以预测宫颈癌放疗中肿瘤几何形状的演变。
作者开发了两种数学模型来估计肿瘤几何形状的变化：马尔可夫模型和同构收缩模型。马尔可夫模型通过研究肿瘤表面体素状态（肿瘤或非肿瘤）的变化来描述肿瘤的演变。它假设演化遵循马尔可夫过程。转移概率通过最大似然估计获得，并且取决于相邻体素的状态。同构收缩模型根据肿瘤表面体素层来描述肿瘤的收缩或生长，而不是对单个体素进行建模。将这两种拟议模型应用于在玛嘉烈公主癌症中心治疗的 29 名宫颈癌患者的数据，然后与恒体积方法进行比较。使用灵敏度和特异性来衡量模型性能。
在灵敏度（靶区覆盖）和特异性（正常组织保护）之间的权衡方面，马尔可夫模型优于同构收缩模型和恒体积模型。一般来说，与其他模型相比，马尔可夫模型在灵敏度或特异性方面都有几个百分点的提高。在某些参数设置下，同构收缩模型与马尔可夫方法相当。凸形肿瘤形状更容易预测。
通过在体素水平上使用概率模型对肿瘤几何形状的变化进行建模，可以提高靶区覆盖和正常组织保护的效果。我们的马尔可夫模型灵活且具有可调参数，可以调整模型性能以满足一系列标准。这种模型可能支持宫颈癌放射治疗的自适应范式的发展。
