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Implantation of neuroprosthetic electrodes induces a stereotypical state ofneuroinflammation, which is thought to be detrimental for the neuronssurrounding the electrode. Mechanisms of this type of neuroinflammation arestill not understood well. Recent experimental and theoretical results pointout possible role of the diffusion species in this process. The paper considersa model of anomalous diffusion occurring in the glial scar around a chronicimplant in two simple geometries -- a separable rectilinear electrode and acylindrical electrode, which are solvable exactly. We describe a hypotheticalextended source of diffusing species and study its concentration profile insteady-state conditions. Diffusion transport is assumed to obey afractional-order Fick law, which is derived from physically realisticassumptions using a fractional calculus approach. The derived fractional-orderdistribution morphs into regular order diffusion in the case of integerfractional exponents. The model presented here demonstrates that accumulationof diffusing species can occur and the scar properties (i.e. tortuosity,fractional order, scar thickness) can influence such accumulation. The observedshape of the concentration profile corresponds qualitatively with GFAP profilesreported in the literature. The main difference with respect to the previousstudies is the explicit incorporation of the apparatus of fractional calculuswithout assumption of an ad hoc tortuosity parameter. Intended application ofthe approach is the study of diffusing substances in the glial scar afterimplantation of neural prostheses, although the approach can be adapted toother studies of diffusion in biological tissues, for example of biomoleculesor small drug molecules.

A model of fractional-order diffusion in the glial scar