Graph-Based Models of Cortical Axons for the Prediction of Neuronal Response to Extracellular Electrical Stimulation

Histology-driven model of the macaque motor hyperdirect pathway

Emerging appreciation for the hyperdirect pathway (HDP) as an important cortical glutamatergic input to the subthalamic nucleus (STN) has motivated a wide range of recent investigations on its role in motor control, as well as the mechanisms of subthalamic deep brain stimulation (DBS). However, the pathway anatomy and terminal arbor morphometry by which the HDP links cortical and subthalamic activity are incompletely understood. One critical hindrance to advancing understanding is the lack of anatomically detailed population models which can help explain how HDP pathway anatomy and neuronal biophysics give rise to spatiotemporal patterns of stimulus-response activity observed in vivo. Therefore, the goal of this study was to establish a population model of motor HDP axons through application of generative algorithms constrained by recent histology and imaging data. The products of this effort include a de novo macaque brain atlas, detailed statistical analysis of histological reconstructions of macaque motor HDP axons, and the generation of 10,000 morphometrically constrained synthetic motor HDP axons. The synthetic HDP axons exhibited a 3.8% mean error with respect to parametric distributions of the fiber target volume, total length, number of bifurcations, bifurcation angles, meander angles, and segment lengths measured in BDA-labeled HDP axon reconstructions. As such, this large population of synthetic motor HDP axons represents an anatomically based foundation for biophysical simulations that can be coupled to electrophysiological and/or behavioral measurements, with the goal of better understanding the role of the HDP in motor system activity.

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.