Two-dimensional continuum map of filamentous random networks

Randomly cross-linked fiber networks are the building blocks of many biological systems such as cytoskeleton and tissue scaffolds. Here, we study the elastic properties of these networks at various length scales by mapping their elasticity into heterogeneous two-dimensional continuum media. The inhomogeneous elastic properties of the continuum domain are obtained from a minimization technique. It is shown that elastic modulus of filamentous networks, similar to the gradients of their deformation field, is long-range correlated and follows a power law scaling over the range of scale with upper and lower bounds proportional to the mean fiber segment length and entire fiber length., respectively.