A Particle Interaction Model for the Simulation of Biological, Cross-Linked Fiber Networks Inspired From flocking Theory

Abstract

Dynamic, cross-linked, biological fiber networks play major roles in cell and tissue function. They are challenging structures to model due to the vast number of components and the complexity of the interactions within the structure. We present here a particle-based model for fiber networks inspired from flocking theory, where fibers are modeled as point particles and cross-link interactions are modeled via distance-based potential functions. The frictional potential in flocking models takes on the form of a function that decays with increasing inter-particle distance, with the specific form of this function fit for a particular model. We determined, by conducting full microscopic fiber network simulations, that for the case of a cross-linked fiber network, this function takes on the form of a Gaussian. The basic flocking model is also modified to include an elastic potential as well as drag from the surrounding fluid. Conceptually, the proposed model can be understood as a distributed Kelvin–Voigt particle model. The model is able to simulate behaviors such as strain hardening, viscoelastic creep, stress relaxation, network rupture, and network reformation, which are common characteristics of biological fiber networks. The numerical experiments shown in this paper utilize experimentally-derived parameters for actin fiber networks (as a test case), and produce biologically reasonable results. The benefits of this particle model over polymer-based models are that they are computationally simple to implement and can be easily connected to kinetic and continuum-level models.