Theoretical framework for estimating the conductivity map of the retina through finite element analysis

A mathematical framework for estimation of the conductivity map of the retina is presented. The problem is formulated and solved in two-dimensional space considering hypothetical inhomogeneity in the conductivity profile at each layer of the retina in x and y directions. Finite element analysis is used to solve the equation of continuity in steady state to simulate voltage measurements as well as estimate the conductivity map. The results of simulated noisy data for an inhomogeneous retina layer and the fovea, which has a more complicated geometry, are presented. The error study of the estimated conductivity map shows that the error for an inhomogeneous conductivity profile is approximately 2% and the error for calculating the fovea conductivity map is just above 8%. This method can be extended to three-dimensions and can also be used to measure the impedance of different layers of the retina for alternating currents.