The "SafeSpace" Radial Diffusion Coefficients Database: Dependencies and application to simulations

Radial diffusion has been established as one of the most important mechanisms contributing to both the acceleration and loss of relativistic electrons in the outer radiation belt. In the framework of the SafeSpace project we have used 9 years (2011–2019) of multi-point magnetic and electric field measurements from THEMIS A, D and E satellites to create a database of accurately calculated radial diffusion coefficients (DLL) spanning an L* range from 3 to 8. In this work we investigate the dependence of the DLL on the various solar wind parameters, geomagnetic indices and coupling functions, and moreover, on the spatial parameters L* and Magnetic Local Time (MLT), during the solar cycle 24. The spatial distribution of the DLL reveals important MLT dependence rising from the various Ultra Low Frequency (ULF) wave generation mechanisms. Furthermore, we investigate via a superposed analysis, the dependence of the DLL on solar wind drivers. We show that the Interplanetary Coronal Mass Ejections (ICME) driven disturbances accompanied by high solar wind pressure values combined with intense magnetospheric compression produce DLLB values comparable or even greater than the ones of DLLE. This feature cannot be captured by semi-empirical models and introduces a significant energy dependence on the DLL. Finally, we show the advantages of the use of accurately calculated DLL by means of numerical simulations of relativistic electron fluxes performed with the Salammbô code and significant deviations of several semi-empirical model predictions depending on the level of geomagnetic activity and L-shell.

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.