胰腺癌手术规划与术后评估的数学方法与演化建模

胰腺癌是“癌中之王”，术后5年生存率仅为7.5%。关键原因之一是没有深度挖掘胰腺癌CT/MRI图像信息，基于数学方法对浸润性胰腺癌边界精准界定。基于团队在胰腺癌可视化、影像组学、稀疏机器学习方法和高维偏微分方程数值方法等研究基础，拟开展以下突破性研究：(1)基于胰腺癌大数据，利用核函数逼近方法，精确分割胰腺癌三维图像，研究胰腺癌识别与三维成像，阐明胰腺癌边界界定机理和定量医学成像的不确定性；(2)利用卷积神经网络和在线学习方法，识别周边胰腺微小血管，阐明胰腺癌微小血管浸润机理；(3)结合先验知识，利用Stokes方程，构建胰腺癌边缘演化的数学模型，结合核函数与有限差分方法、有限元方法和有限体积方法，计算胰腺癌三维边缘演化过程，揭示胰腺癌边界演化规律。最终研制具有自主知识产权的胰腺癌手术规划与术后评估辅助系统，开展临床应用。本研究对改善民生和提高人民身心健康有重要的价值。

The content of the application corresponds to the research direction of “Mathematics and Medical Health Cross-Focus Project”. Pancreatic cancer is the “king of cancer”, with a 5-year survival rate of only 7.5%. One of the key reasons is that there is no deep excavation of CT/MRI image information of pancreatic cancer and precise boundary definition of invasive pancreatic cancer based on mathematical methods. According to the our team’s research foundation in pancreatic cancer visualization, photoacoustic imaging, imaging omics, sparse machine learning methods, and numerical methods of high-dimensional partial differential equations, the following breakthrough studies are planned: (1) based on the big data of pancreatic cancer, the kernel function approximation method is used to accurately segment the three-dimensional image of pancreatic cancer, and the recognition and three-dimensional imaging of pancreatic cancer are studied to clarify the boundary definition mechanism of pancreatic cancer and the uncertainty of quantitative medical imaging; (2) convolution neural network and online learning method are used to identify peripheral pancreatic microvessels and elucidate the mechanism of microvascular invasion in pancreatic cancer; (3) combined with prior knowledge and Stokes equation, the mathematical model of pancreatic cancer edge evolution can be constructed. Combined with kernel function, finite difference method, finite element method and finite volume method, the three-dimensional edge evolution process of pancreatic cancer can be calculated, and the evolution law of pancreatic cancer boundary is revealed. Finally, we will develop a pancreatic cancer surgery planning and postoperative evaluation assistant system with independent intellectual property rights, and carry out clinical application. This study is of great value to improve people’s livelihood and physical and mental health.