Cells and organisms follow aligned structures in their environment, a process that can generate persistent migration paths. Kinetic transport equations are a popular modelling tool for describing biological movements at the mesoscopic level, yet their formulations usually assume a constant turning rate. Here we relax this simplification, extending to include a turning rate that varies according to the anisotropy of a heterogeneous environment. We extend known methods of parabolic and hyperbolic scaling and apply the results to cell movement on micropatterned domains. We show that inclusion of orientation dependence in the turning rate can lead to persistence of motion in an otherwise fully symmetric environment and generate enhanced diffusion in structured domains.

细胞和有机体在其环境中遵循对齐的结构，这一过程可以产生持久的迁移路径。动力学输运方程是一种流行的建模工具，用于在介观水平上描述生物运动，但它们的公式通常假设一个恒定的转动速率。在这里，我们放宽了这种简化，扩展到包括根据异质环境的各向异性而变化的转动速率。我们扩展了已知的抛物线和双曲线缩放方法，并将结果应用于微图案域上的细胞运动。我们表明，在转动速率中包含方向依赖性可以导致运动在完全对称的环境中持续存在，并在结构化域中产生增强的扩散。