In contact with flat adhesive substrates, most biological cells form a thin membrane protrusion called the lamellipodium. The lamellipodium, with actin filaments as major components, is an important organelle responsible for the crawling motion of cells. To understand this phenomenon, the so-called Filament Based Lamellipodium Model was developed in a series of works, see e.g. [MOSS15]. It is a two-dimensional continuum model derived from several mechanical and biochemical effects such as cell-to-substrate adhesion, filament bending, cross-link dynamics, and filament-to-filament interactions. In contrast to the previous works, we incorporate the assumption of short, and consequently, rigid filaments. This allows us to obtain a mathematically simpler and computationally less expensive model.

[MOSS15] A. Manhart, D. Oelz, C. Schmeiser, and N. Sfakianakis. An extended filament based lamellipodium model produces various moving cell shapes in the presence of chemotactic signals. Journal of theoretical biology, 382:244–258, 2015 - DOI: 10.1016/j.jtbi.2015.06.044.