Belfatto Antonella, Riboldi Marco, Ciardo Delia, Cattani Federica, Cecconi Agnese, Lazzari Roberta, Jereczek-Fossa Barbara Alicja, Orecchia Roberto, Baroni Guido, Cerveri Pietro
Department of Electronics, Information and Bioengineering, Politecnico di Milano University, Milan, Italy
Department of Electronics, Information and Bioengineering, Politecnico di Milano University, Milan, Italy Bioengineering Unit, Centro Nazionale di Adroterapia Oncologica, Pave, Italy.
Technol Cancer Res Treat. 2016 Feb;15(1):146-58. doi: 10.1177/1533034615573796. Epub 2015 Mar 10.
This article describes a macroscopic mathematical modeling approach to capture the interplay between solid tumor evolution and cell damage during radiotherapy. Volume regression profiles of 15 patients with uterine cervical cancer were reconstructed from serial cone-beam computed tomography data sets, acquired for image-guided radiotherapy, and used for model parameter learning by means of a genetic-based optimization. Patients, diagnosed with either squamous cell carcinoma or adenocarcinoma, underwent different treatment modalities (image-guided radiotherapy and image-guided chemo-radiotherapy). The mean volume at the beginning of radiotherapy and the end of radiotherapy was on average 23.7 cm(3) (range: 12.7-44.4 cm(3)) and 8.6 cm(3) (range: 3.6-17.1 cm(3)), respectively. Two different tumor dynamics were taken into account in the model: the viable (active) and the necrotic cancer cells. However, according to the results of a preliminary volume regression analysis, we assumed a short dead cell resolving time and the model was simplified to the active tumor volume. Model learning was performed both on the complete patient cohort (cohort-based model learning) and on each single patient (patient-specific model learning). The fitting results (mean error: ∼ 16% and ∼ 6% for the cohort-based model and patient-specific model, respectively) highlighted the model ability to quantitatively reproduce tumor regression. Volume prediction errors of about 18% on average were obtained using cohort-based model computed on all but 1 patient at a time (leave-one-out technique). Finally, a sensitivity analysis was performed and the data uncertainty effects evaluated by simulating an average volume perturbation of about 1.5 cm(3) obtaining an error increase within 0.2%. In conclusion, we showed that simple time-continuous models can represent tumor regression curves both on a patient cohort and patient-specific basis; this discloses the opportunity in the future to exploit such models to predict how changes in the treatment schedule (number of fractions, doses, intervals among fractions) might affect the tumor regression on an individual basis.
本文描述了一种宏观数学建模方法，用于捕捉放疗期间实体瘤演变与细胞损伤之间的相互作用。从为图像引导放疗获取的系列锥形束计算机断层扫描数据集中重建了15例子宫颈癌患者的体积退缩曲线，并通过基于遗传的优化用于模型参数学习。被诊断为鳞状细胞癌或腺癌的患者接受了不同的治疗方式（图像引导放疗和图像引导放化疗）。放疗开始时和放疗结束时的平均体积分别平均为23.7 cm³（范围：12.7 - 44.4 cm³）和8.6 cm³（范围：3.6 - 17.1 cm³）。模型中考虑了两种不同的肿瘤动态：存活（活跃）癌细胞和坏死癌细胞。然而，根据初步体积退缩分析的结果，我们假设死细胞的消解时间较短，模型被简化为活跃肿瘤体积。在完整的患者队列上（基于队列的模型学习）和每个患者个体上（患者特异性模型学习）都进行了模型学习。拟合结果（基于队列的模型和患者特异性模型的平均误差分别约为16%和6%）突出了模型定量再现肿瘤退缩的能力。使用一次对除1例患者外的所有患者计算的基于队列的模型（留一法技术），平均获得约18%的体积预测误差。最后，进行了敏感性分析，并通过模拟约1.5 cm³的平均体积扰动来评估数据不确定性影响，误差增加在0.2%以内。总之，我们表明简单的时间连续模型可以在患者队列和患者特异性基础上表示肿瘤退缩曲线；这揭示了未来利用此类模型预测治疗方案（分次次数、剂量、分次间隔）的变化如何可能在个体基础上影响肿瘤退缩的机会。
