A novel derivation of rigorous macroscopic limits from a micro-meso description of signal-triggered cell migration in fibrous environments

Abstract

In this work we upscale a prototypical kinetic transport equation which models a cell population moving in a fibrous environment with a chemo- or haptotactic signal influencing both the direction and the magnitude of the cell velocity. The presented approach to scaling does not rely on orthogonality and treats parabolic and hyperbolic scalings in a unified manner. It is shown that the steps of the formal limit procedures are mirrored by rigorous operations with finite measures provided that the measure-valued position-direction fiber distribution enjoys some spacial continuity.