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Grill, W. M.

Publications and source records attributed to Grill, W. M..

2 recordsLinked to original sources

Biophysically Realistic Neuron Models for Simulation of Cortical Stimulation

1.ObjectiveWe implemented computational models of human and rat cortical neurons for simulating the neural response to cortical stimulation with electromagnetic fields.\n\nApproachWe adapted model neurons from the library of Blue Brain models to reflect biophysical and geometric properties of both adult rat and human cortical neurons and coupled the model neurons to exogenous electric fields (E-fields). The models included 3D reconstructed axonal and dendritic arbors, experimentally-validated electrophysiological behaviors, and multiple, morphological variants within cell types. Using these models, we characterized the single-cell responses to intracortical microstimulation (ICMS) and uniform E-field with dc as well as pulsed currents.\n\nMain resultsThe strength-duration and current-distance characteristics of the model neurons to ICMS agreed with published experimental results, as did the subthreshold polarization of cell bodies and axon terminals by uniform dc E-fields. For all forms of stimulation, the lowest threshold elements were terminals of the axon collaterals, and the dependence of threshold and polarization on spatial and temporal stimulation parameters was strongly affected by morphological features of the axonal arbor, including myelination, diameter, and branching.\n\nSignificanceThese results provide key insights into the mechanisms of cortical stimulation. The presented models can be used to study various cortical stimulation modalities while incorporating detailed spatial and temporal features of the applied E-field.

bioengineering

Coupling magnetically induced electric fields to neurons: longitudinal and transverse activation

We present a theory and computational models to couple the electric field induced by magnetic stimulation to neuronal membranes. The response of neuronal membranes to induced electric fields is examined under different time scales, and the characteristics of the primary and secondary electric fields from electromagnetic induction and charge accumulation on conductivity boundaries, respectively, are analyzed. Based on the field characteristics and decoupling of the longitudinal and transverse field components along the neural cable, quasi-potentials are a simple and accurate approximation for coupling of magnetically induced electric fields to neurons and a modified cable equation provides theoretical consistency for magnetic stimulation. The conventional and modified cable equations are used to simulate magnetic stimulation of long peripheral nerves by circular and figure-8 coils. Activation thresholds are obtained over a range of lateral and vertical coil positions for two nonlinear membrane models representing unmyelinated and myelinated axons and also for undulating myelinated axons. For unmyelinated straight axons, the thresholds obtained with the modified cable equation are significantly lower due to transverse polarization, and the spatial distributions of thresholds as a function of coil position differ significantly from predictions by the activating function. For myelinated axons, the transverse field contributes negligibly to activation thresholds, whereas axonal undulation can increase or decrease thresholds depending on coil position. The analysis provides a rigorous theoretical foundation and implementation methods for the use of the cable equation to model neuronal response to magnetically induced electric fields. Experimentally observed stimulation with the electric fields perpendicular to the nerve trunk cannot be explained by transverse polarization alone and is likely due to nerve fiber undulation and other geometrical inhomogeneities.

bioengineering