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In addition to laying down myelin during the regeneration phase, during the degeneration process Schwann cells phagocytose debris and produce growth factors, which leads to macrophage recruitment for further phagocytosis and commencement of nerve regeneration. Briefly, an influx of calcium to the injury site initiates degeneration of the distal stump by activating the protease calpain. The process entails Wallerian degeneration, which begins shortly after nerve transection and initiates eventual regeneration. Peripheral nerves have the innate ability to regenerate over short distances. As such the modeling results may be employed to predict and control the amount and distribution of oxygenation throughout the conduit, and hence to guide experimental conduit design. The length of the conduit did not alter the mechanism of diffusion, but rather had an inverse relationship with the magnitude of the overall concentration profile. At low wall permeabilities the axial diffusion is dominant for all configurations, while for higher wall permeabilities the radial diffusion became dominant for smaller diameters. The results of this study suggest that there is a complex relationship between axial and radial diffusion as the properties of the conduit such as length, diameter, and permeability are altered and when investigating various locations within the model. When the walls of the CNF conduit were modeled to have significant oxygen permeability, oxygen diffusion across the conduit was shown to dominate relative to axial diffusion of oxygen along the length of the conduit, which was otherwise the controlling diffusion mechanism. Various CNF wall permeabilities, conduit lengths, and nerve-to-conduit diameter ratios have been examined all of which were shown to have an impact on the resultant oxygen profile within the conduit.
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The current work employs 3D modelling and analysis via COMSOL Multiphysics® to determine how the CNF conduit facilitates oxygen movement both radially through the conduit walls and axially along the length of the conduit. Preliminary testing in multiple animal models has yielded positive results, but more information is needed regarding how the CNF conduit facilitates nutrient and gas flow. A potential new method for promoting peripheral nerve repair that addresses the shortcomings of current interventions is a biocompatible cellulose nanofibril (CNF) conduit that degrades in-vivo over time.
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Allografts, autografts, and synthetic conduits are three of the most common surgical interventions for peripheral nerve repair however, each has limitations including poor biocompatibility, adverse immune responses, and the need for successive surgeries. Aufl., 2005.Peripheral nerve injury can cause significant impairment, and the current methods for facilitating repair, particularly over distances greater than approximately 1 mm, are not entirely effective. Partielle Differentialgleichungen und numerische Methoden. Society for Industrial and Applied Mathematics, 2. The Finite Element Method for Elliptic Problems. The Mathematical Theory of Finite Element Methods. Freezing Rotating Waves in Damped Wave Equationsĭamped cubic-quintic complex Ginzburg-Landau equation Freezing Traveling Waves in Damped Wave EquationsĨ. Further coherent structures in Reaction Diffusion Systemsįreezing Relative Equilibria in Equivariant Second-Order Evolution Equations (with Comsol Multiphysics 5.1 and 5.2) 7. Spinning 3-soliton (rotating multisoliton)Ħ. Spinning 2-soliton (rotating multisoliton) Traveling oscillating 2-front (traveling oscillating multifront) Oscillating pulse and traveling oscillating front Oscillating 2-pulse (oscillating multipulse) Traveling 2-front (collision, colliding fronts)
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Traveling 2-front (traveling multifront, repelling fronts) Freezing Multistructures (Multifronts, Multipulses and Multisolitons) and Wave Interactions in Reaction Diffusion Systems Freezing Waves with Several Symmetries in Reaction Diffusion Systemsĥ. Spinning soliton, dissipative soliton, rotating solitonĤ. Freezing Rotating Waves in Reaction Diffusion Systems Freezing Oscillating Waves in Reaction Diffusion EquationsĬubic-quintic complex Ginzburg-Landau equationģ. Freezing Traveling Waves in Reaction Diffusion EquationsĢ. Freezing traveling waves with Comsol Multiphysics: The Nagumo equationįreezing Relative Equilibria in Equivariant First-Order Evolution Equations (with Comsol Multiphysics 5.1 and 5.2) 1.8.3 Numerical approximation of rotating waves via freezing methodįor the implementation we suggest the following tutorials