Rheology of the cytoskeleton as a fractal network

We model the cytoskeleton as a fractal network by identifying each segment with a simple Kelvin-Voigt element with a well defined equilibrium length. The final structure retains the elastic characteristics of a solid or a gel, which may support stress, without relaxing. By considering a very simple regular self-similar structure of segments in series and in parallel, in one, two, or three dimensions, we are able to express the viscoelasticity of the network as an effective generalized Kelvin-Voigt model with a power law spectrum of retardation times L∼τα. We relate the parameter α with the fractal dimension of the gel. In some regimes (0<α<1), we recover the weak power law behaviors of the elastic and viscous moduli with the angular frequencies G'∼G'′∼wα that occur in a variety of soft materials, including living cells. In other regimes, we find different power laws for G' and G''.