COMSOL Multiphysics® modelling of oxygen diffusion through a cellulose nanofibril conduit employed for peripheral nerve repair

Background 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. 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. 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. 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. Results 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. 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. 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. Conclusions 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. 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 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. 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.

COMSOL Multiphysics® Modelling of Oxygen Diffusion Through a Cellulose Nanofibril Conduit Employed for Peripheral Nerve Repair

Background Peripheral nerve injury can cause significant impairment, and the current methods for facilitating repair, particularly over distances greater than approximately 1mm, are not entirely effective. 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. 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. 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. Results 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. 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. 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. Conclusions 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. 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 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. 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.

Formation of Si Nanorods and Discrete Nanophases by Axial Diffusion of Si from Substrate into Au and AuPt Nanoalloy Nanorods

Interdiffusion between Si substrate and nanorod arrays of Au, Pt, and AuPt nanoalloys is investigated at temperatures lower than the AuSi eutectic temperature. When the nanorod is pure Au, Si diffusion from the substrate is very rapid. Au atoms are completely replaced by Si, converting the nanostructure into one of Si nanorod arrays. Au is diffused out to the substrate. The Au nanorod arrays on Si are unstable. When the nanorod is pure Pt, however, no diffusion of Si into the nanorod or any silicide formation is observed. The Pt nanorods are stable on Si substrate. When the nanorods are an alloy of AuPt, interesting interactions occur. Si diffusion into the nanorods is rapid but the diffusing Si readily reacts with Pt forming PtSi while Au diffuses out to the substrate. After annealing, nanophases of Au, Pt, PtSi, and Si may be present within the nanorods. When the Pt content of the alloy is low (12 at%) all Pt atoms are converted to silicide and the extra Si atoms remain in elemental form, particularly near the tip of the nanorods. Hence, the presence of Au accelerates Si diffusion and the ensuing reaction to form PtSi, a phenomenon absents in pure Pt nanorods. When the Au content of the alloy is low, the Si diffusion would cease when all Au atoms have diffused out of the nanorod, thereby arresting the silicide formation resulting in excess Pt in elemental form within the nanorod. This is a technique of making Si nanorods with and without embedded PtSi nanophase consisting of heterojunctions which could have unique properties.