Evolution and remodeling of fiber distributions in homogenized constrained mixture models of soft tissue

The changes in soft tissue growth and remodeling generally alter the orientation distribution of collagen fibers within the tissue, yet the underlying principles remain incompletely understood. Recently a new theoretical framework based on the homogenized constrained mixture theoryof soft tissue growth and remodeling has been proposed. By making some simplifying assumptions, analytical solutions have been derived to better comprehend how collagen fiber distribution evolves during growth and remodeling under uniaxial loading. The analysis reveals a natural inclination for collagen fibers to peak in the direction of loading and spread out, with the spread increasing in proportion to the ratio of the fiber half-life time to the time constant governing loading-related fiber production. This finding sheds light on why collagen fiber reinforcement in vivo typically exhibits distributions resembling von Mises distributions with finite spreads. Additionally, the analysis highlights a significant dependence on the history of fiber distribution evolution, potentially explaining why tissues under similar loading conditions can exhibit considerably different fiber orientation distributions. The theoretical analysis covered both the angular space-time and the angular phase space. These combinations brought several interesting insights that confirm a tendency of fiber reorientation towards the direction of loading that has been observed both in experiments and hypothesized in previous modeling work.

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