胰腺癌手术规划与术后评估的数学方法与演化建模

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.

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。

胰腺癌是“癌中之王”，近年来，外科治疗胰腺癌从技术层面进步巨大，但胰腺癌患者总体的预后依旧很差，5年生存率仅为7.5%，重要原因在于胰腺癌早期病变很难在计算机断层扫描（Computedtomography,CT）,磁共振成像（Magneticresonanceimaging, MRI）获得胰腺癌典型特征和周围血管的形态边界的立体可视化信息，而与CT评估比较，三维可视化技术可以提供立体形态学信息，将胰腺癌可切除性提高了12.5%。近年来，关于肿瘤手术规划与术后评估的数学方法与演化建模、肿瘤大数据挖掘与图像处理的计算数学方法，肿瘤模糊弱小目标增强的医学图像处理技术、多模态、多时间序列图像、目标缺损图像的3D/4D非刚性配准与融合算法都有长足发展和进步。然而，胰腺癌手术规划与术后评估的数学方法与演化建模都鲜有研究和文献报道。本项目研究围绕胰腺癌数学方法三维可视化建模手术规划与术后评估、模糊弱小目标增强的医学图像处理技术、胰腺癌大数据挖掘、人工智能及数特征提取、多模态、多时间序列图像、目标缺损图像的3D/4D非刚性配准与融合算法这几个方面，最终目标是研制胰腺癌癌的边界界定、手术规划与术后评估辅助系统，并开展临床应用。研究上，针对图像的增强使用 Proximity 算法求解 ROF 模型对胰腺 CT 图像去噪增强；针对图像的分割我们在U-net的基础上结合boosting的思想，提出了新的网络模块boosting-unet用于胰腺自动分割任务与基于UMRFormer-Net的胰腺癌 CT 图像分割，并且对血管的分割进行了优化；针对图像配准提出了基于深度学习自动特征提取的全自动胰腺癌配准算法。针对胰腺癌的建模与演化，建立的胰腺癌生长的数学模型，将临床和实验相结合来预测病人的肿瘤生长的形状和大小。项目组所建立的胰腺癌生长的数学模型可以和临床和实验相结合来预测病人的肿瘤生长的形状和大小，从而帮助医生的临床诊断和制定个体化的治疗方案。