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Virtual Rhesus Labyrinth Model Predicts Responses to Electrical Stimulation Delivered by a Vestibular Prosthesis

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Abstract

To better understand the spread of prosthetic current in the inner ear and to facilitate design of electrode arrays and stimulation protocols for a vestibular implant system intended to restore sensation after loss of vestibular hair cell function, we created a model of the primate labyrinth. Because the geometry of the implanted ear is complex, accurately modeling effects of prosthetic stimuli on vestibular afferent activity required a detailed representation of labyrinthine anatomy. Model geometry was therefore generated from three-dimensional (3D) reconstructions of a normal rhesus temporal bone imaged using micro-MRI and micro-CT. For systematically varied combinations of active and return electrode location, the extracellular potential field during a biphasic current pulse was computed using finite element methods. Potential field values served as inputs to stochastic, nonlinear dynamic models for each of 2415 vestibular afferent axons, each with unique origin on the neuroepithelium and spiking dynamics based on a modified Smith and Goldberg model. We tested the model by comparing predicted and actual 3D vestibulo-ocular reflex (VOR) responses for eye rotation elicited by prosthetic stimuli. The model was individualized for each implanted animal by placing model electrodes in the standard labyrinth geometry based on CT localization of actual implanted electrodes. Eye rotation 3D axes were predicted from relative proportions of model axons excited within each of the three ampullary nerves, and predictions were compared to archival eye movement response data measured in three alert rhesus monkeys using 3D scleral coil oculography. Multiple empirically observed features emerged as properties of the model, including effects of changing active and return electrode position. The model predicts improved prosthesis performance when the reference electrode is in the labyrinth’s common crus (CC) rather than outside the temporal bone, especially if the reference electrode is inserted nearly to the junction of the CC with the vestibule. Extension of the model to human anatomy should facilitate optimal design of electrode arrays for clinical application.

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Acknowledgments

We thank Lani Swarthout and Kelly Lane for assistance with animal care.

Funding

This work was funded by NIH NIDCD (mainly R01DC009255 and partly by R01DC2390 and R0113536).

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Correspondence to Abderrahmane Hedjoudje.

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Conflict of Interest

CDS is CEO of and holds an equity interest in Labyrinth Devices LLC. The terms of these arrangements are being managed by the Johns Hopkins University in accordance with its conflict of interest policies.

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Appendix

Appendix

Model Geometry, Conductivities, and Boundary Conditions

Model geometry was generated through coregistration, segmentation, and 3D reconstruction of micro-CT and micro-MRI image stacks of a post-mortem rhesus temporal bone acquired using isotropic voxels of side lengths 70 μm without contrast and 48 μm with air contrast, respectively. Figure 1 shows representative images. We used Amira software (FEI Visualization Sciences Group, Burlington, MA) to segment and then mesh image stacks into tissue volume domains and tetrahedral elements of different conductivity including nerve, bone, brain, and inner ear fluid (Fig. 2a, b). To individualize the model for each live implanted monkey, CT scans were acquired with 0.4-mm isotropic voxels to determine actual electrode locations with respect to labyrinth landmarks. Virtual electrodes were represented in the model’s 3D geometry by 200-μm-diameter spheres at the same locations relative to landmarks in the reference anatomic data set. The 3D geometry was then meshed (divided into small, non-overlapping, tetrahedral volumes), with mesh density adaptively adjusted to be greatest where electrical potential gradients were likely to be steepest, such as immediately around an electrode.

Each of 1,142,609 tetrahedral elements was assigned a conductivity drawn from published data (Table 1) (Tasaki 1964; Geddes and Baker 1967; Kosterich et al. 1983; Suesserman and Spelman 1993; Hayden et al. 2011). Perilymph and endolymph fluid spaces were lumped into one contiguous volume-denoted vestibular lumen with a single isotropic conductivity. Neither the membranous labyrinth nor any other thin epithelial surface (e.g., osseous labyrinth endosteum, blood vessel endothelium) was explicitly included in the model, because (1) they are too thin to represent as a volume of different conductivities without compromising solvability of the finite element equations and (2) they present negligible impedance to biphasic current pulses of the 25–200 μs/phase durations typically used in a vestibular prosthesis or cochlear implant.

The 7th and 8th cranial nerves were meshed into elements that each had a long axis approximately parallel to the nerve’s axis in that region. Each element was assigned anisotropic conductivity (axial 23-fold greater than transverse) to reflect that fact that current runs along axons more readily than across them. Brainstem and cerebellum were modeled as isotropic, homogenous conductors, using the average value of conductivity between white and gray matter. Solid bone was modeled using 7200 Ω cm, an average value determined from empiric data for multiple species and a sensitivity analysis for finite element modeling in the chinchilla (Hayden 2007). A “body” domain lined the model volume’s outer edges to represent paths for flow of current from within the labyrinth to a reference electrode outside of the temporal bone. The facial nerve’s extratemporal aspect was considered to be at “body” potential. Few if any bony septae remain in the mastoid after mastoidectomy for vestibular prosthesis electrode implantation, so the middle ear and mastoid air spaces were modeled as a perfect insulator. We did not include middle ear bones (other than the stapes footplate) or spiking models of fibers in the cochlear, facial, or chorda tympani nerves in the model.

Calculation of Extracellular Potential Field

Finite element analysis (FEA) was performed using the DC Conductive Media Module in COMSOL Multiphysics (COMSOL Inc., Burlington, MA) using the conjugate gradient method. We assumed quasistatic conditions (i.e., that all tissues are purely conductive without any reactance). This is a common and well-justified assumption for models of this type (Malmivuo and Plonsey 1995; Spelman et al. 1995), because dielectric relaxation times of biological tissues are much shorter than stimulus pulses used in MVPs. For any given constellation of active electrodes passing current, the 3D potential field and current density vector field were computed for each mesh vertex for a unit stimulus current (Fig. 2c). To determine the potential at any point in the volume, one can then interpolate between mesh vertices. To determine the potential at that point in space as a function of time during a train of stimulus pulses, one can multiply the unit-current potential by the stimulus current as a function of time. Using this approach does not mean that the overall model lacks realistic temporal dynamics or stochastic behavior, because extracellular potential outputs from the FEA serve as inputs to the stochastic, dynamic neuronal models described below.

Models of Vestibular Afferent Neurons

Each of the three ampullary nerves was represented by 505 model afferent neurons, and each of the two macular nerves (i.e., the utricular and saccular nerves) comprised 450 model neurons. We randomly chose the starting location of fibers in each of three concentric zones (central, intermediate, and peripheral) on each neuroepithelial surface, using a distribution for each zone that was uniform over most of that zone but then tapered to zero near the zone’s border with an adjacent zone. Figure 3a shows 100 such starting points in each zone for a flattened map of the posterior semicircular canal’s crista surface. For each model neuron, fiber diameter was randomly chosen from a Gaussian distribution for which the mean and variance were determined by the zone of fiber origin using previously published data for rhesus monkey vestibular nerve (Gacek and Rasmussen 1961).

Modified versions of the Smith-Goldberg model for vestibular primary afferent neuron spike discharge timing (Smith and Goldberg 1986) and the spatially extended nonlinear node (SENN) axon model (Frijns et al. 1994; Frijns and ten Kate 1994; McIntyre et al. 2002; Hayden et al. 2011) were used to simulate the subthreshold and spiking dynamics of each model afferent fiber’s heminode and axon respectively. The Smith-Goldberg model allowed simulation of fibers with different degrees of spontaneous discharge regularity, examples of which are shown in Fig. 3b. Apart from model geometry, the only parameters requiring a change from the fiber model used in the chinchilla model were the mean and variance of the fiber diameter distribution. All other parameters, including channel conductances and membrane-specific capacitance, were unchanged from those defined previously in a similar model of the chinchilla vestibular nerve (Hayden et al. 2011).

The extracellular potential field produced by the FEA was sampled at many points along each fiber to obtain inputs for an individualized model of that fiber’s activity. Each afferent fiber’s trajectory through the FEA model’s nerve domain was defined by a series of piecewise-linear segments that “grew” medially through the internal auditory canal model volume under control of a semi-automatic, stochastic algorithm that maintained relative positions of neighboring fibers as nerve branches merge (Fig. 3b). All fibers were modeled as having a 2-μm nonmyelinated distal heminode spike-initiator zone at the model’s crista surface and then a series of 300 μm internodes and 1 μm nodes of Ranvier (Fig. 3c).

Prediction of 3D VOR Eye Movement Responses from Model Afferent Activity

Like humans, monkeys exhibit VOR-mediated eye movements in darkness that are partly compensatory for head rotations over ~ 0.1–10 Hz and conjugate in 3D. When considered in head coordinates, the monkey VOR is not perfectly isotropic (i.e., gains for roll and pitch head rotations are ~ 50 % and ~ 90 %, respectively, of the gain for yaw head movements (Migliaccio et al. 2004, 2010) but it does approximately obey linear vector superposition for prosthetic stimuli delivered to combinations of ampullary nerves (Cohen et al. 1964; Cremer et al. 2000; Davidovics et al. 2013). To account for gain anisotropy, we first assumed isotropic gain to estimate the 3D axis of VOR eye rotation responses for any stimulus as a three-valued vector defined in a canal-axis coordinate system by the relative fraction of model afferents excited each ampullary nerve, then we remapped the resulting axis of rotation by decomposing it into roll, pitch, and yaw components; scaling those components by 0.5, 0.9, and 1.0, respectively, and then recombining and transforming the eye velocity vector prediction back to canal-based coordinates.

We neglected the effects of macular nerve activity when predicting 3D eye movement axes from the pattern of vestibular nerve activity reported by the model, because (1) existing evidence suggests that eye movement responses to natural stimulation of macular nerves are modest compared to VOR responses to SCC input during natural head rotation in the spectral range of interest for a vestibular implant targeting semicircular canals (Angelaki 1998; Angelaki et al. 2000) and (2) lack of published data on the VOR eye movement responses that would be elicited by selective electrical excitation of different patches on the utricular and saccular maculae.

Simplifications

Like the chinchilla labyrinth model from which it was adapted (Hayden et al. 2011), the Virtual Rhesus Labyrinth includes several simplifying assumptions regarding anatomy, biophysics and physiology.

Anatomic Simplifications

We neglected the membranous labyrinth and instead treated endolymph and perilymph as a single contiguous space with uniform isotropic conductivity. This is well justified for the brief current pulses typically used in a vestibular implant, because capacitive currents readily cross the membranous labyrinth walls; however, this assumption would lead to errors if applied to DC or low-frequency current stimuli. We neglected dura and endosteum for analogous reasons.

Rather than individualize all aspects of labyrinth anatomy when modeling a given implanted animal, we relied on a standardized labyrinth geometry created from micro-CT and micro-MRI images of a single normal rhesus temporal bone, then placed virtual electrodes in the model mesh after coregistration of an implanted animal’s micro-CT with the standard model’s geometry. Although labyrinthine anatomy is highly conserved between individual animals of a given species, there is still variation in the shape of individual structures and the orientation of the labyrinth with respect to the skull landmarks upon which we base the coordinate system for oculographic measurements of eye rotation axes, so this approximation contributes some error to model predictions of fiber activity and eye movement responses.

We did not model the diversity of post-synaptic specializations such as calyces or bouton arbors, although they are consistent features in nonhuman primates and other species and likely play important roles in determining afferent responses to natural stimuli (Baird et al. 1988; Goldberg et al. 1990). We justified this simplification because including such features would render the modeling intractable without greater computing power and because electrophysiologic measurements in squirrel monkey vestibular nerve prosthetic currents predominantly act at directly at the spike initiator zone of a primary afferent (Goldberg et al. 1984). We also ignored afferent fiber somata and efferent fibers in the vestibular nerve, and we did not model the thin cribriform bone through which nerve fascicles transit between the inner ear and the internal auditory canal.

Each of the 2415 fibers in the model is simulated as though it is alone in a conductive volume that is homogeneous apart from anisotropic conductivity that varies in direction such that the least conductive direction is perpendicular to the axis of the nerve. We did not account for changes in membrane excitability that could occur due to ephaptic transmission between adjacent axons or changes in extracellular ionic environment immediately adjacent to each node of Ranvier. The model does not yet estimate or account for the effects of vestibular efferent stimulation.

In its current form, the model does not include physiologic models of cochlear or facial nerve axons. However, those nerves are segmented as separate volumes in the model geometry, and the model does provide estimates of extracellular potential throughout the temporal bone, including the cochlea, cochlear nerve, and intratemporal course of the facial nerve, so neuromorphic models of axons in those nerves could be added to allow estimation of tinnitus, facial muscle activation, or dysgeusia as side effects of electrical stimulation intended only for the vestibular nerve.

Biophysical Simplifications

When using finite element analysis to compute the extracellular potential at each point in the model volume, we assume quasistatic conditions, meaning that temporal dynamics of the extracellular potential field can be ignored. To compute the potential for a given point in the model volume as a function of time, we then need only scale the stimulus current waveform by the extracellular potential computed for a unit stimulus current pulse. This approximation is standard for finite element modeling and is well justified in our case, because dielectric relaxation times for biological tissues are much shorter than the stimulus pulses we typically use. Spelman et al. found that quasistatic assumptions hold for stimuli up to 12.5 kHz in the cochlea (Spelman et al. 1982). For the stimuli we typically use in vestibular stimulation (symmetric 200 μS/phase biphasic pulses with 25 μS interphase gap), 95 % of the spectral energy lies below 10 kHz, and the quasistatic assumption probably incurs negligible errors. However, errors due to the quasistatic assumption would be greater when this model is applied to pulses < 50 μS/phase.

In general, tissue conductivity is frequency dependent. Fortunately, conductivities have been described for several species and tissue types; however, many tissues have only been characterized for frequencies outside of our region of interest (Geddes and Baker 1967). In such cases, we used values measured at lower frequency. Nerve and bone conductivities were chosen based on the results of a parameter sensitivity analysis described by Hayden et al. (2011)).

Physiological Simplifications

The model estimates the proportion of fibers in each vestibular nerve branch that propagate an action potential to the brainstem end of the simulated fiber within the first 2 ms after the onset of a single biphasic stimulus pulse. This duration was chosen because it is short enough to model efficiently but long enough to encompass all stimulus-driven activity in the model fibers. To model the responses of some or all simulated axons for the entire duration of a long train of stimulus pulses or any other prosthetic current waveform, one could simply run the neuromorphic models for a larger number of time steps while assigning each mesh vertex’s extracellular potential over time to equal the unit-stimulus potential multiplied by the stimulus current waveform. However, the time required to complete the simulation would scale linearly with the duration of the simulated pulse train.

Although fiber spiking dynamics were varied according to starting location on each crista or macula to reflect morphophysiologic correlations described by Goldberg et al. (1990) (Baird et al. 1988; Lysakowski et al. 1995), the neuromorphic models do not otherwise reflect variation in synapse type (i.e., calyceal versus bouton), or differential effects of prosthetic current on different branches of fibers with broadly distributed dendritic trees. Effects due to spurious activation of vestibular efferent fibers were not modeled.

Hair cells in the rhesus utricle and saccule are relatively unaffected by gentamicin at doses sufficient to severely diminish canal-ocular reflexes (Sun et al. 2015); however, absent clear guidance from the literature regarding the relationship between utricular and saccular nerve excitation patterns and the 3D axis of VOR responses, we assumed that macula-mediated responses were negligible.

Even after gentamicin treatment sufficient to ablate VOR responses to head rotation, destroy type I hair cells in rhesus canal cristae, and destroy the stereocilia of canal type II hair cells, those surviving type II hair cell bodies are still present and can probably modulate neurotransmitter release in response to prosthetic currents (Sun et al. 2015). Hair cells were not included in the present model. Errors due to excluding them were probably small for suprathreshold stimuli, given that available evidence suggests that currents delivered by stimulating electrodes in perilymph mainly act at the vestibular afferent heminode (Goldberg et al. 1984).

Apart from scaling roll, pitch, and yaw components of the predicted VOR responses by 0.7, 0.9, and 1.0, respectively, to correct for the VOR gain anisotropy observed in normal rhesus monkeys and humans (Migliaccio et al. 2006), we assumed a direct mapping from relative activation levels of one labyrinth’s three ampullary nerves to the 3D VOR components about the axes of the corresponding SCCs. Prior studies suggest that this is a reasonable approximation for the acute stimulation paradigms we used to acquire data against which the model was tested (Davidovics et al. 2011, 2013), but it ignores contributions of otolith inputs and central nervous system circuits that may remap the 3D VOR response in a space-fixed rather than canal-fixed coordinate frame (Angelaki et al. 1995; Shao et al. 2009), and it does not model effects due to habituation, long-term depression (Mitchell et al. 2016, 2017), directional plasticity (Dai et al. 2013), or changes in VOR gain due to vestibular compensation.

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Hedjoudje, A., Hayden, R., Dai, C. et al. Virtual Rhesus Labyrinth Model Predicts Responses to Electrical Stimulation Delivered by a Vestibular Prosthesis. JARO 20, 313–339 (2019). https://doi.org/10.1007/s10162-019-00725-3

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