Quantitative characterization of the microstructure and transport properties of biopolymer networks

Biopolymer networks are of fundamental importance to many biological processes in normal and tumorous tissues. In this paper, we employ the panoply of theoretical and simulation techniques developed for characterizing heterogeneous materials to quantify the microstructure and effective diffusive transport properties (diffusion coefficient D_e and mean survival time τ) of collagen type I networks at various collagen concentrations. In particular, we compute the pore-size probability density function P(δ) for the networks and present a variety of analytical estimates of the effective diffusion coefficient D_e for finite-sized diffusing particles, including the low-density approximation, the Ogston approximation and the Torquato approximation. The Hashin-Strikman upper bound on the effective diffusion coefficient D_e and the pore-size lower bound on the mean survival time τ are used as benchmarks to test our analytical approximations and numerical results. Moreover, we generalize the efficient first-passage-time techniques for Brownian-motion simulations in suspensions of spheres to the case of fiber networks and compute the associated effective diffusion coefficient D_e as well as the mean survival time τ, which is related to nuclear magnetic resonance relaxation times. Our numerical results for D_e are in excellent agreement with analytical results for simple network microstructures, such as periodic arrays of parallel cylinders. Specifically, the Torquato approximation provides the most accurate estimates of D_e for all collagen concentrations among all of the analytical approximations we consider. We formulate a universal curve for τ for the networks at different collagen concentrations, extending the work of Torquato and Yeong (1997 J. Chem. Phys. 106 8814). We apply rigorous cross-property relations to estimate the effective bulk modulus of collagen networks from a knowledge of the effective diffusion coefficient computed here. The use of cross-property relations to link other physical properties to the transport properties of collagen networks is also discussed.