论文标题
模型中的入侵前线和自适应动力学，用于具有异质迁移率的细胞群体的生长
Invasion fronts and adaptive dynamics in a model for the growth of cell populations with heterogeneous mobility
论文作者
论文摘要
我们考虑了一种具有异质迁移率和增殖率的细胞群体动力学的模型。细胞表型态通过连续的结构变量和局部细胞种群密度函数的演变（即每个空间位置处的细胞表型分布）的演变由非本地对流反应扩散方程控制。我们报告数值模拟的结果，表明，在细胞迁移率有界的情况下，出现了紧凑的行进前部。更多的移动表型变体占据了前边缘，而在前面的后面选择了更多的增殖表型变体。为了解释这种数值结果，我们使用汉密尔顿 - 雅各比方法对模型方程进行了形式的渐近分析。总而言之，我们表明，局部主导的表型性状（即沿表型维度的局部细胞种群密度函数的最大点）满足具有源术语的广义汉堡方程，我们构建了此类传输方程的travelling-front解决方案，并表征了相应的最小速度。此外，我们表明，当细胞迁移率无限制时，可能会发生前边缘加速度和伸展前端的形成。我们简要讨论了我们的结果在神经胶质瘤生长的背景下的含义。
We consider a model for the dynamics of growing cell populations with heterogeneous mobility and proliferation rate. The cell phenotypic state is described by a continuous structuring variable and the evolution of the local cell population density function (i.e. the cell phenotypic distribution at each spatial position) is governed by a non-local advection-reaction-diffusion equation. We report on the results of numerical simulations showing that, in the case where the cell mobility is bounded, compactly supported travelling fronts emerge. More mobile phenotypic variants occupy the front edge, whereas more proliferative phenotypic variants are selected at the back of the front. In order to explain such numerical results, we carry out formal asymptotic analysis of the model equation using a Hamilton-Jacobi approach. In summary, we show that the locally dominant phenotypic trait (i.e. the maximum point of the local cell population density function along the phenotypic dimension) satisfies a generalised Burgers' equation with source term, we construct travelling-front solutions of such transport equation and characterise the corresponding minimal speed. Moreover, we show that, when the cell mobility is unbounded, front edge acceleration and formation of stretching fronts may occur. We briefly discuss the implications of our results in the context of glioma growth.
