Simulating bidirectional peripheral neural interfaces in EIDORS

Abstract

Bioelectronic neural interfaces that deliver adaptive therapeutic stimulation in an intelligent manner must be able to sense and stimulate activity within the same nerve. Existing minimally-invasive peripheral neural interfaces can provide a read-out of the aggregate level of activity via electrical recordings of nerve activity, but these recordings are limited in terms of their specificity. Computational simulations can provide fine-grained insight into the contributions of different neural populations to the extracellular recording, but integration of the signals from individual nerve fibers requires knowledge of spread of current in the complex (heterogenous, anisotropic) extracellular space. We have developed a model which uses the open-source EIDORS package for extracellular stimulation and recording in the pelvic nerve. The pelvic nerve is the primary source of autonomic innervation to the pelvic organs, and a prime target for electrical stimulation to treat a variety of voiding disorders. We simulated recordings of spontaneous and electrically-evoked activity using biophysical models for myelinated and unmyelinated axons. As expected, stimulus thresholds depended strongly on both fibre type and electrode-fibre distance. In conclusion, EIDORS can be used to accurately simulate extracellular recording in complex, heterogenous neural geometries.

Fig. 1.

Verification of simulation error against theory. A: cross-section through a 3-D spherical forward model mesh in EIDORS for a small mesh size. B: Model error relative to mesh size for different meshes and boundary conditions. Red arrowhead: relative size of the mesh shown in Fig. 2A.

Fig. 2.

Pelvic Nerve stimulation & recording model. A: Overall modeling domain, showing fascicles(blue), electrode array (yellow), and stimulating / recording electrodes (red). Scale: 1mm. B: pelvic nerve cross-section adapted from Hulsebosch [13] showing fascicles and simulated distribution of axons of each type. C: Sensitivity relationship $T_{\mathit{\text{elec}}}(\overrightarrow{x})$ as a function of length along the center of one fascicle for each electrode.

Fig. 3.

Simulations of electrical recordings using EIDORS. A: Simulation of ongoing activity, 2 imp/s/axon spike rate. Traces show the voltage observed by each bipolar measurement pair, and the contribution of each axon type to the potential observed between E3–E4. B: 20 imp/s/axon spike rate. C: Simulation of evoked activity, stimulated at E12, showing the propagating evoked compound action potential. D–F: frequency spectra for each of A–C, average of 10 simulations, showing the contribution of each axon type.

Fig. 4.

Electrical Stimulus Thresholds. A: Pelvic nerve cross-sections for myelinated (top) and unmyelinated (bottom) fibers; color corresponds to the threshold. Electrode located at the bottom of the cross-section. B: thresholds as a function of fiber diameter. C: Recruitment curves for each type of axon.