Admittance Method for Estimating Local Field Potentials Generated in a Multi-Scale Neuron Model of the Hippocampus

Significant progress has been made toward model-based prediction of neral tissue activation in response to extracellular electrical stimulation, but challenges remain in the accurate and efficient estimation of distributed local field potentials (LFP). Analytical methods of estimating electric fields are a first-order approximation that may be suitable for model validation, but they are computationally expensive and cannot accurately capture boundary conditions in heterogeneous tissue. While there are many appropriate numerical methods of solving electric fields in neural tissue models, there isn't an established standard for mesh geometry nor a well-known rule for handling any mismatch in spatial resolution. Moreover, the challenge of misalignment between current sources and mesh nodes in a finite-element or resistor-network method volume conduction model needs to be further investigated. Therefore, using a previously published and validated multi-scale model of the hippocampus, the authors have formulated an algorithm for LFP estimation, and by extension, bidirectional communication between discretized and numerically solved volume conduction models and biologically detailed neural circuit models constructed in NEURON. Development of this algorithm required that we assess meshes of (i) unstructured tetrahedral and grid-based hexahedral geometries as well as (ii) differing approaches for managing the spatial misalignment of current sources and mesh nodes. The resulting algorithm is validated through the comparison of Admittance Method predicted evoked potentials with analytically estimated LFPs. Establishing this method is a critical step toward closed-loop integration of volume conductor and NEURON models that could lead to substantial improvement of the predictive power of multi-scale stimulation models of cortical tissue. These models may be used to deepen our understanding of hippocampal pathologies and the identification of efficacious electroceutical treatments.