Neural Network Model of Vestibular Nuclei Reaction to Onset of Vestibular Prosthetic Stimulation

Abstract

The vestibular system incorporates multiple sensory pathways to provide crucial information about head and body motion. Damage to the semicircular canals, the peripheral vestibular organs that sense rotational velocities of the head, can severely degrade the ability to perform activities of daily life. Vestibular prosthetics address this problem by using stimulating electrodes that can trigger primary vestibular afferents to modulate their firing rates, thus encoding head movement. These prostheses have been demonstrated chronically in multiple animal models and acutely tested in short-duration trials within the clinic in humans. However, mainly, due to limited opportunities to fully characterize stimulation parameters, there is a lack of understanding of "optimal" stimulation configurations for humans. Here, we model possible adaptive plasticity in the vestibular pathway. Specifically, this model highlights the influence of adaptation of synaptic strengths and offsets in the vestibular nuclei to compensate for the initial activation of the prosthetic. By changing the synaptic strengths, the model is able to replicate the clinical observation that erroneous eye movements are attenuated within 30 minutes without any change to the prosthetic stimulation rate. Although our model was only built to match this time point, we further examined how it affected subsequent pulse rate modulation (PRM) and pulse amplitude modulation (PAM). PAM was more effective than PRM for nearly all stimulation configurations during these acute tests. Two non-intuitive relationships highlighted by our model explain this performance discrepancy. Specifically, the attenuation of synaptic strengths for afferents stimulated during baseline adaptation and the discontinuity between baseline and residual firing rates both disproportionally boost PAM. Comodulation of pulse rate and amplitude has been experimentally shown to induce both excitatory and inhibitory eye movements even at high baseline stimulation rates. We also modeled comodulation and found synergistic combinations of stimulation parameters to achieve equivalent output to only amplitude modulation. This may be an important strategy to reduce current spread and misalignment. The model outputs reflected observed trends in clinical testing and aspects of existing vestibular prosthetic literature. Importantly, the model provided insight to efficiently explore the stimulation parameter space, which was helpful, given limited available patient time.

Keywords: adaptation; electrical stimulation; functional models; physiological; synapses; vestibular ocular reflex; vestibular prosthesis.

Figures

Figure 1

Electrode–nerve interface. (A) Distributions of resting mean firing rates for the population. (B) The percentage of regular (67%) and irregular (33%) afferents is illustrated in the pie plot; the distribution of CVs for each afferent type is also shown. Each afferent will have a mean residual firing rate sampled from (A) and a variance sampled from (B). (C) Concept of stimulation from a monopolar electrode (black dot) in an environment with uniform conductance. The area stimulated depends on pulse amplitude, while the frequency of action potentials depends on pulse rate. A sinusoidal envelope modulates both modalities from baseline to ± maximum values. This modulation envelope is a 2-Hz sine wave. At baseline, there is no modulation (e.g., Am and/or PRm go to 0). Positive (negative) values of the modulation envelope correspond to delivering higher (lower) values of pulse amplitude and/or pulse rate than baseline (e.g., Am and/or PRm are non-zero). Pink arrows show that the first and last examples here are at baseline stimulation, while the middle example is a peak positive modulation. (D) Simulated vestibular afferent populations during baseline stimulation followed by PAM or PRM. In purple, we overlay the zoom into brief section of the applied stimulation pulses, including baseline, maximum, and minimum modulation values.

Figure 2

Nerve–nucleus interface. (A) Model of primary afferents in BVL without prosthetic stimulation. There is no eye movement despite residual afferent activity. (B,C) The onset of baseline stimulation introduces imbalances between the synaptic strengths, self-regulation, and induced firing rates within stimulated afferents. Any changes are color coded in orange. (D) Nystagmus occurs immediately after baseline stimulation onset, but attenuated in all tested patients within a maximum of 30 min. We model this as a change in synaptic strengths and/or self-regulation in (C).

Figure 3

Relationship between head rotation and afferent activity. (A) Approximate transfer function between head rotations along a single axis and afferent firing rates in healthy monkeys (Fernandez and Goldberg, 1971). (B) Imposed transfer function for each axis in a vestibular prosthetic using PRM. The width of the linear region can be set based on the observed patient-specific head rotations or the maximal range of possible rotations (Gong and Merfeld, ; Della Santina et al., 2007).

Figure 4

Model outputs and patient measurements. Models were trained using clinical settings of 200-pps baseline stimulation and then ±25% modulation depth was applied. (A) PAM generated relatively large positive eye velocities with muted negative eye velocities. Applying a sinusoidal fit shows a peak positive eye velocity of 2.5 in arbitrary units. (B) Applying PRM to the same model generates much smaller eye velocities, but without any imbalance in positive and negative outputs. There is complete overlap of the model outputs on the sinusoidal fit. (C) The peak eye velocities for each modality are shown. (D) Representative PAM recording from a single patient during stimulation of the lateral ampullary nerve (which should elicit purely horizontal eye velocities) shows a 2-Hz modulation of eye position (dots) in the horizontal (red) and vertical (blue) dimensions. Traces are generated with a 5-Hz low-pass filter. (E) Differentiating these traces estimates eye velocity. (F) Compiling all cycles of modulation reveals a broad and uneven positive velocity peak followed by a more sinusoidal shaped and larger magnitude negative velocity peak. (G) Alternatively, each cycle of the position signal in (D) is fitted with a sinusoid, then differentiated. This dramatically cleans up the velocity outputs but obscures any imbalance in positive and negative outputs or modulation shapes.

Figure 5

Ensemble and residual firing rates. (A) Given changes in pulse rate or pulse amplitude, there is a larger modulation in firing rate for PAM. Here, the baseline recruitment (Ab) is fixed to 40% of afferents, modulation (pulse rate or pulse amplitude) is fixed to 25%, and we scan over all residual firing rates and baseline pulse rates. (B) There is higher peak eye velocity for PAM (red) over a large region of this space. However, PRM does generate higher peak eye velocities (blue) for low baseline pulse rates, especially if the residual firing rate is also low.

Figure 6

Synaptic strengths and learning rate ratios. (A) Modeled healthy afferent strength values connecting to the vestibular nuclei. Increased firing rates from left SCC afferents cause positive eye movement (move to right); decreased firing rates from right SCC afferents have the same effect as they are multiplied by a negative strength (B) During baseline adaptation to left SCC stimulation by a vestibular implant, there is a population (shown in gray) of afferents entrained to 200-pps activity. This excess activity causes nystagmus (error). To correct this error, the network increases the bias term and adapts the other strengths. Here, the bias strength was 2 × 103. Now, there are strengths in the incorrect region of space (inverted synapses are colored yellow), and increasing firing rates in these afferents would yield negative eye movement. Additionally, the mean strength value is lower in the gray area compared to the rest of the population (mean values shown as white overlay lines for each region). This creates an advantage for PAM, which interacts with a subpopulation of afferents (shown in purple) with larger strengths during the positive phase of modulation. (C) The ratio of learning rates between the bias term and neurons is adapted to simulate heterosynaptic (bias rate very high) vs. homosynaptic (synapse rate very high) LTD. The ratio of learning rates affects the magnitude of PRM and the symmetry of PAM. Relatively faster bias term adaptation increases both the factors. (D) Simulation of different bias rates showing the increase in PEV for PRM, as bias learning rate increased above 3 × 104. The increase in symmetry (PEV/|NEV| goes toward 1.0) for PAM occurs around the same learning rate.

Figure 7

Modulation efficacy. (A) Peak eye velocity over different modulation strengths for PAM and PRM at 100- and 200-pps baseline stimulation. There is a clear attenuation of PAM at lower baseline stimulation while PRM remains unaffected. (B) Normalizing to the change in output at 10% modulation, we see both PAM and PRM increase PEV about 100% per 10% change in modulation.

Figure 8

Comodulation. An alternative stimulation strategy to PAM and PRM is to modulate both the pulse amplitude and rate of stimulation. (A) The orange and purple dots represent pure PAM and PRM, respectively, as previously presented. Combining these modulation methods further increases the possible PEV output. (B) Similarly, there are multiple combinations of stimulation methods which are equivalent to 25% PAM. For example, the white dashed line shows that the same output can be achieved with 12.5% PAM combined with 55% PRM.