Diffusion anisotropy in collagen gels and tumors: the effect of fiber network orientation.

The interstitial matrix is comprised of cross-linked collagen fibers, generally arranged in nonisotropic orientations. Spatial alignment of matrix components within the tissue can affect diffusion patterns of drugs. In this study, we developed a methodology for the calculation of diffusion coefficients of macromolecules and nanoparticles in collagenous tissues. The tissues are modeled as three-dimensional, stochastic, fiber networks with varying degrees of alignment. We employed a random walk approach to simulate diffusion and a Stokesian dynamics method to account for hydrodynamic hindrance. We performed our analysis for four different structures ranging from nearly isotropic to perfectly aligned. We showed that the overall diffusion coefficient is not affected by the orientation of the network. However, structural anisotropy results in diffusion anisotropy, which becomes more significant with increase in the degree of alignment, the size of the diffusing particle, and the fiber volume fraction. To test our model predictions we performed diffusion measurements in reconstituted collagen gels and tumor xenografts. We measured fiber alignment and diffusion with second harmonic generation and multiphoton fluorescent recovery after photobleaching techniques, respectively. The results showed for the first time in tumors that the structure and orientation of collagen fibers in the extracellular space leads to diffusion anisotropy.