Deterministic and Explicit: A Quantitative Characterization of the Matrix and Collagen Influence on the Stiffening of Peripheral Nerves Under Stretch

The structural organization of peripheral nerves enables them to adapt to different body postures and movements by varying their stiffness. Indeed, they could become either compliant or stiff in response to the amount of external solicitation. In this work, the global response of nerves to axial stretch was deterministically derived from the interplay between the main structural constituents of the nerve connective tissue. In particular, a theoretical framework was provided to explicitly decouple the action of the ground matrix and the contribution of the collagen fibrils on the macroscopic stiffening of stretched nerves. To test the overall suitability of this approach, as a matter of principle, the change of the shape of relevant curves was investigated for changes of numerical parameters, while a further sensitivity study was performed to better understand the dependence on them. In addition, dimensionless stress and curvature were used to quantitatively account for both the matrix and the fibril actions. Finally, the proposed framework was used to investigate the stiffening phenomenon in different nerve specimens. More specifically, the proposed approach was able to explicitly and deterministically model the nerve stiffening of porcine peroneal and canine vagus nerves, closely reproducing (R2>0.997) the experimental data.