论文标题
低级神经胶质瘤进化的随机分层模型
A stochastic hierarchical model for low grade glioma evolution
论文作者
论文摘要
提出了低级神经胶质瘤进化的随机分层模型。从使用分段扩散Markov过程（PDIFMP）对细胞运动的描述开始，我们使用广义的Fokker-Planck方程得出了该Markov过程的过渡概率密度的方程。然后，宏观模型是通过抛物线限制和矩方程中的希尔伯特膨胀得出的。设置模型后，我们执行了几项数值测试，以研究局部特征和PDIFMP的扩展发生器在肿瘤进展过程中的作用。主要目的侧重于了解该过程在微观尺度上的跳跃速率函数的变化以及宏观尺度上的扩散系数与神经胶质瘤细胞的扩散行为以及恶性肿瘤的扩散行为有关，即从低级gliomas到高级gliomas。
A stochastic hierarchical model for the evolution of low grade gliomas is proposed. Starting with the description of cell motion using piecewise diffusion Markov processes (PDifMPs) at the cellular level, we derive an equation for the density of the transition probability of this Markov process using the generalised Fokker-Planck equation. Then a macroscopic model is derived via parabolic limit and Hilbert expansions in the moment equations. After setting up the model, we perform several numerical tests to study the role of the local characteristics and the extended generator of the PDifMP in the process of tumour progression. The main aim focuses on understanding how the variations of the jump rate function of this process at the microscopic scale and the diffusion coefficient at the macroscopic scale are related to the diffusive behaviour of the glioma cells and to the onset of malignancy, i.e., the transition from low-grade to high-grade gliomas.
