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.

我们考虑了一个具有异质流动性和增殖率的细胞群生长动力学模型。细胞表型状态由连续结构变量描述，局部细胞群密度函数（即每个空间位置的细胞表型分布）的演变由非局部平流-反应-扩散方程控制。我们报告了数值模拟的结果，表明在细胞移动性有限的情况下，出现了紧凑支撑的移动前沿。更多的移动表型变体占据前沿，而更多增殖的表型变体被选择在前面的后面。为了解释这样的数值结果，我们使用 Hamilton-Jacobi 方法对模型方程进行形式渐近分析。总之，我们证明了局部显性表型特征（即沿表型维度的局部细胞群密度函数的最大值）满足具有源项的广义 Burgers 方程，我们构造了这种传输方程的旅行前沿解并表征了相应的最小速度。此外，我们表明，当细胞迁移率不受限制时，可能会发生前沿加速和拉伸前沿的形成。我们简要讨论了我们的结果对胶质瘤生长的影响。此外，我们表明，当细胞迁移率不受限制时，可能会发生前沿加速和拉伸前沿的形成。我们简要讨论了我们的结果对胶质瘤生长的影响。此外，我们表明，当细胞迁移率不受限制时，可能会发生前沿加速和拉伸前沿的形成。我们简要讨论了我们的结果对胶质瘤生长的影响。