IEEE Trans Med Imaging. 2014 Apr;33(4):995-1003. doi: 10.1109/TMI.2014.2301892.
We propose a patient-specific model based on partial differential equation to predict the evolution of lung tumors during radiotherapy. The evolution of tumor cell density is formulated by three terms: 1) advection describing the advective flux transport of tumor cells, 2) proliferation representing the tumor cell proliferation modeled as Gompertz differential equation, and 3) treatment quantifying the radiotherapeutic efficacy from linear quadratic formulation. We consider that tumor cell density variation can be derived from positron emission tomography images, the novel idea is to model the advection term by calculating 3D optical flow field from sequential images. To estimate patient-specific parameters, we propose an optimization between the predicted and observed images, under a global constraint that the tumor volume decreases exponentially as radiation dose increases. A thresholding on the predicted tumor cell densities is then used to define tumor contours, tumor volumes and maximum standardized uptake values (SUVmax). Results obtained on seven patients show a satisfying agreement between the predicted tumor contours and those drawn by an expert.
我们提出了一种基于偏微分方程的个体化模型来预测放疗过程中肺肿瘤的演变。肿瘤细胞密度的演变由三个项来描述：1）描述肿瘤细胞对流通量输运的对流项，2）增殖项，代表肿瘤细胞增殖，采用 Gompertz 微分方程建模，3）治疗项，从线性二次公式量化放射治疗效果。我们认为肿瘤细胞密度的变化可以从正电子发射断层扫描图像中得到，新的想法是通过从连续图像中计算三维光流场来模拟对流项。为了估计个体化参数，我们提出了一种在全局约束下的预测图像和观察图像之间的优化方法，该约束条件是随着辐射剂量的增加，肿瘤体积呈指数下降。然后对预测的肿瘤细胞密度进行阈值处理，以定义肿瘤轮廓、肿瘤体积和最大标准化摄取值（SUVmax）。对七名患者的研究结果表明，预测的肿瘤轮廓与专家绘制的轮廓之间具有令人满意的一致性。
