阐明癌症发病机理和开发有效的癌症治疗方法是人类健康的重大需求。癌症组学数据呈几何增长，急需发展新的数学理论和方法来解析这些数据以便更系统地理解癌症动态演变机制。本项目旨在发展新的多尺度随机建模框架和计算工具研究癌症的异质性和随机性如何影响免疫系统和癌症的演变。研究内容包括：在张量计算框架下发展高维组学数据的定量描述与集成方法，提取癌症演变过程重要的特征信息；利用微分方程和种群动力学建模理论，结合优化算法与并行计算等方法，探索从分子、细胞和组织不同层次耦合来刻画癌症演变动力学过程的新随机混合模型的建立；运用多尺度分析、区域控制理论与随机模拟等技术，研究癌症异质性的随机动力学。综合以上数据驱动和模型驱动方法所识别的关键基因、分子、信号通路和生物标记物等理论预测结果，进行生物学实验验证，揭示肝癌发生演变与肝炎病毒感染及免疫微环境的关系和调控机制，为创新癌症免疫治疗方法和药物研发提供新思路和新方法

Elucidating cancer pathogenesis and developing novel anti-cancer therapies are of great significance for human health. It is urgently needed that revolutionary mathematical theories and methods be developed for analyzing cancer multi-omics data with exponentially growth in order to achieve a more reliable and comprehensive understanding of dynamically evolutionary mechanisms of cancer. This project aims at developing novel multiscale and stochastic modeling framework as well as computational tools to investigate the spatial and temporal dynamics of cancer development in order to understand how tumor heterogeneity and stochasticity affect the immune system and cancer progression. Specifically, under the framework of tensor computation and decomposition, computational approaches to quantitatively describe and integrate multi-omics datasets of cancer are developed and main features and key information are extracted. Then, based on this integrated information, we will explore new multi-scale stochastic modeling that describe the dynamics of cancer evolution at the molecular, cellular and tissue scales by combining modeling techniques for differential equations and population dynamics and algorithms for optimization and parallel computations. Furthermore, we will integrate multi-scale analysis, domain control theory and stochastic simulations to study stochastic dynamics in cancer heterogeneity. These systematic predictions of critical factors, including genes, molecular, signal pathways and biomarkers, derived from the above integrative data-driven and model-driven approaches will be validated by biological experiments. These results will be used to reveal the interplay between the evolution of hepatocellular carcinoma and hepatitis virus infection and the immune microenvironment and the regulation mechanisms. These results will provide novel ideas and new approaches for innovating cancer immunotherapies and developing effective therapeutic strategies.