As mentioned earlier, the goal of field shaping strategies is to accurately and precisely specify the region of AN neurons activated at any moment. Analysis and design of these strategies begins with modeling to determine current levels for intracochlear electrodes that are needed to achieve desired patterns of AN stimulation. This modeling has three steps: the first is determination of the distribution of the potential field within the cochlear tissues, the second is prediction of the location of neurons activated by this potential, and the third is validation of the predictions. After validation, the model can be used to aid in the design of stimulation strategies that will appropriately activate the desired AN region.
2.1. Modeling methods
The distribution of electrical potentials within the cochlear tissues in response to arbitrary stimulation patterns can be predicted using simple parametric or network models (Jolly et al., 1996
; Kral et al., 1998
; O’Leary et al., 1985
; Rodenhiser and Spelman, 1995
; Suesserman and Spelman, 1993
; Townshend et al., 1987
; Van Compernolle, 1985
; van den Honert and Kelsall, 2007
) or by finite element modeling (Briaire and Frijns, 2000
; Frijns, 1995
; Frijns et al., 1996
; Hanekom, 2001
; Rattay et al., 2001a
; Whiten, 2007
). The simplest models assume that the conductivity of cochlear tissues is uniform, and that current sources (i.e., the stimulating electrodes) are point sources within this homogeneous medium [e.g. (Litvak et al., 2007a
)]. In response to stimulation from a single electrode, homogenous models predict iso-potential contours that are spherical in shape (). An example of a simple, homogeneous, finite element model is presented in .
Fig. 1 Computational model describing monopolar isolevel contours for potentials (A,C) and potential gradients (B,D), and effects of homogeneous (A,B) and nonhomogeneous (C,D) tissue resistivity. Left of each panel shows 3-dimensional representation of potential (more ...)
On the left in , a transparent rendition of the model is illustrated. The diagonal cylinder represents the scala tympani, the seven small spheres represent intrascalar electrode contacts placed in the center of the scala. The black spheres and lines to the lower right of the scala represent spiral ganglion cells and their peripheral and central processes. For the sake of simplicity, the peripheral and distal portions of the central processes are drawn orthogonal to the long axis of the scala and are parallel to the x-axis. The large sphere represents an isopotential contour surface generated by applying current to the active (light colored) contact for the simplest case where electrical resistivity is homogeneous throughout the modeled volume (e.g., the cochlear bone and the perilymph are equally conductive). The parallelogram represents one cross-sectional plane through the scala and spiral ganglion at the level of the activated electrode. In all panels, the level of the contour highlighted is chosen so that decreasing stimulus current by 6 dB would shrink the contour so that it just intersects the peripheral tip of the closest neuronal process; this is designated as the condition for threshold level of neuronal activation. Thus, the contour shown represents a stimulus level 6 dB above this minimum threshold.
On the right in are several isopotential contours calculated across the cross-sectional plane (parallelogram) shown on the left. The heavy black lined circle represents the isolevel contour shown in the transparent model. Additional potential contours are represented by the light black circles. The potential is indicated by shades of grey. The hatched annulus indicates the cross-section of the cochlear bone. The white circle (located at x & y = 0) represents the activated electrode. The small black circle (with the heavy black line through it) represents a spiral ganglion cell located at this cross-sectional level. The highest potential is located adjacent to the activated electrode, and potentials drop monotonically as distance from the electrode increases.
The second modeling step is determining AN activation patterns that result from the potentials induced by electrical stimulation. The simplest of these models assume that neuronal activation will occur when the intrascalar potential field exceeds a pre-defined threshold, while the most complex use compartmental models of SG neurons which incorporate ionic channels. Compartments are included that correspond to cell soma and spike initiation zones, as well as myelinated and unmyelinated processes. An intermediate approach has been proposed by Rattay (1990)
, who determined that the “activating function”, corresponding to the second derivative of the potential directed along the neuron, is appropriate for characterizing the effective stimulation of neural processes, and has been employed in many models (Bruce et al., 1999a
; Litvak et al., 2007a
). However, the first derivative of the potential directed along the neuronal process may be more appropriate for modeling activation either in the vicinity of the soma, which is the presumed site of activation with a cochlear implant (Whiten, 2007
), or of peripheral processes (Warman et al., 1992
). Examples of isolevel contours of the first derivative, directed along peripheral processes of model neurons, of the potential field in are shown in .
On the left in , an isolevel contour of the gradient of the potential field in is shown (gradient taken in the direction of the x-axis). The light-grey “knob” protruding from the cylindrical scala tympani shows the radial and axial extents of the gradient isolevel contour. In this figure for the sake of simplicity, the scala tympani and the isolevel contour are rendered opaque and the spiral ganglion cells are omitted. On the right in , the model elements are represented as shown A except that the cochlear bone cross-section is omitted and the shades of grey indicate gradient values. The highest gradients (both positive and negative) are adjacent to the activated electrode, and in the direction parallel to the x-axis, the gradients decrease monotonically as distance from the activated contact is increased. The potential gradient was computed along the radial trajectory of the peripheral processes (parallel to the x-axis) by taking centered differences in the x-dimension using the MATLAB (MathWorks, Natick, MA) gradient function. Note that these iso-gradient contours are typically sharper than the iso-potential contours.
Although the homogenous model is desirable because it is mathematically tractable, introduction into the model of appropriate inhomogeneities corresponding to different impedances of various cochlear tissues improves accuracy of predictions (Whiten, 2007
). For example, introducing a tubular volume of lower conductivity to model () the bony wall that separates excitable neural elements of AN neurons from the intrascalar space increases the predicted spread of the potential field along the axis of the scala tympani and has been shown to be essential for accurate prediction of intra-scalar potentials recorded from cochlear implant users (Whiten, 2007
Effects of increasing the resistivity of the cochlear bone in the example model are illustrated by comparing panels 1A and 1B with panels 1C and 1D, in which the resistivity of the cochlear bone has been increased by a factor of 10. Comparison of the isopotential contour shown in the left of panel 1C with that in panel 1A shows that increasing the cochlear bone resistivity results in a greater spread of the potential in the axial direction. Comparison of the protruding “knob” of the gradient isolevel contour in panel 1D with that in 1B shows a similar increase along the axial dimension.
The cross-section showing isopotential contours on the right side of 1C demonstrates that the contours become “bunched” within the volume of the cochlear bone when the bone resistivity is 10 times larger than the resistivity of other fluids and tissues. This is reflected in the large gradients observed within the cochlear bone in the cross-section shown in panel 1D. The non-monotonic change in potential gradient along the x
-axis produces a local maximum of potential gradient within the volume of the cochlear bone. This suggests that response thresholds would be lower for neurons with peripheral processes traversing this bony wall. Further increasing the bone resistivity to 100 times that of perilymph (Whiten, 2007
) would further increase axial spread of the potential and also the gradient within the bone.
Addition of greater detail in cochlear tissue impedances and geometry, as well as impedances and geometry of the CI array, generates models of greater complexity, and presumably greater predictive accuracy. It is important to note that while the results of modeling studies are interesting and can provide valuable insight, validation of models, especially of the more complex models, remains an important step.
2.2. Full-array field shaping paradigms
In theory, the goal of the modeling effort as applied to field shaping has been to determine a stimulation configuration which will produce an arbitrary desired pattern of activation in the auditory nerve. Potentially, such a configuration could involve stimulation on all intra-cochlear electrodes. However, given the complexity of the neural activation models described above, and lack of knowledge as to the cochlea of individual subjects, such use of the computational models has been prohibitive. Consequently, various methods have been proposed for determining the optimal configuration for an individual subject.
One interesting approach was proposed by White and colleagues (Van Compernolle, 1985
; Townshend and White, 1987
). In this approach, psychophysical measurement of threshold shift is used to determine the degree of interaction between adjacent electrodes. Once this is determined, it is possible to determine the compensation currents necessary to cancel the interaction. Although in theory such stimulation should result in greater channel independence, compensation currents computed this way were unfortunately too great to be realizable in devices available at that time (Van Compernolle, 1985
Several investigators have proposed a method of shaping the intra-scalar potential profile based upon measurements of potentials made using intracochlear electrodes themselves. In this technique, potentials are recorded at one electrode while current is applied on each of the other electrodes. If every combination of stimulation and recording electrode is used, it is possible to invert the resulting matrix of transimpedance measurements to determine currents that result in a potential profile that is identically zero everywhere except at the stimulation electrode (Townshend and White, 1987
; Rodenhiser and Spelman, 1995
; Hartmann and Klinke, 1990
; Ross, 2006
; van den Honert and Kelsall, 2007
). Theoretical support for such field shaping strategies is predicated upon linear summation of field potentials, i.e., that the field resulting from simultaneous stimulation of two or more electrodes is simply the sum of the fields created when each electrode is stimulated individually. Accuracy of transimpedance measurements or estimates is critical to achieve accurate predictions (Van Compernolle, 1985
), and can be complicated by a number of factors including residual polarization of the stimulated electrode. Recently van den Honert and Kelsall (2007)
have described a method of estimating transimpedance elements that reduces the influence of residual polarization and appears to work well in practice. Empirical measurements of potential field spread in human subjects can be made only using intrascalar electrodes, and implementation of stimulation strategies are subject to safety and CI current and compliance voltage limitations. In animal studies, potential fields can be measured using additional electrodes that are introduced into the scala tympani or the modiolus, as well as on CI electrodes, and hardware limitations are less restrictive.
2.3. Simplified field shaping paradigms
Although full-array field shaping paradigms promise to be useful, they have a number of drawbacks. First, these paradigms require independent control of a large number of electrodes, which could result in increased complexity of implant electronics, and put increased demands on the rates of the data transfer between the external processor and the implant. Second, the full-array field shaping configuration that results in minimum potential spread within the scala tympani does not necessarily result in minimal spread of activation of auditory nerve fibers.
Vanpoucke et al. (2004)
showed that the intra-cochlear spread observed in human subjects can be very closely approximated by a “leaky tube” model. If this is the case, then current spread in the cochlea can be limited by using only electrodes adjacent to the center electrode. In this paper, we will therefore focus on configurations that use four or fewer intracochlear electrodes, in combination with external ground (). We will refer to configurations using three electrodes as partial tripolar configurations. In general, we define a partial tripolar configuration as one in which current I
is placed on the center electrode, while currents σ(1 - α) I
are simultaneously applied in opposite polarity to the apical and basal electrodes respectively. The coefficient σ is referred to as the tripolar
[as in Litvak et al. (2007a)
] and controls the “degree” of focusing, while α is the steering coefficient
. The configuration of σ =1, α = 0.5 will be referred to as the full tripolar configuration
. Note that the term “quadrupolar” has also been used to describe the full tripolar configuration, while the term “tripolar” has also been used to describe the partial tripolar configuration (e.g. Jolly et al., 1996
Fig. 3 Spatial response profiles showing response in the inferior colliculus to virtual channel stimuli. Successive panels show IC response rate (color) to increasingly larger total applied cathodic current. Variation along abscissa corresponds to variation (more ...)
shows the predictions of the potential and gradient amplitudes in the vicinity of the nerve fibers in response to various partial tripolar stimulation configurations. Potentials and gradients were computed using the finite element model described in . Stimulus current levels are shown in the left column: In
indicate currents on intracochlear electrodes 2-4, and IX
indicates current on the extracochlear (return) electrode. The gradients (right column) are of particular interest because they are believed to describe effective stimuli to the neural tissue (Whiten, 2007
). Monopolar configuration (panel A) corresponds to the tripolar compensation coefficient of σ = 0. In this configuration, applying stimulus current equal to twice the minimum threshold current results in potential or gradient levels that exceed the threshold potential (θ) over a broad region of the simulated cochlea. For example, in the panel showing the gradient strength for monopolar stimulation, neurons that lie within the region where the strength curve lies to the right of θ would experience a supra-threshold gradient, and therefore be activated.
Fig. 2 Strength of electrical potential (center column) and potential gradient (right column) predicted by the model of . Configurations were: monopolar (A), focused (partial) tripolar (B), tripolar (C), virtual channel using asymmetric tripole (D), bipole (more ...)
Neural spread can be decreased if tripolar compensation coefficient σ is increased to 0.5 (panel B). However, the current level needed to reach threshold must be increased (in this case, by a factor of 1.3). Greater narrowing in activation will result if compensation coefficient σ is increased to 1 (full tripolar configuration, panel C). However, with this configuration, one also sees the presence of negative side-lobes in the gradient function. Since cochlear implant systems typically use stimulation pulses which have both cathodic and anodic phases of equal amplitude, these side lobes can be of perceptual significance (Litvak et al., 2007).
By adjusting the steering coefficient α, it is possible to “steer” the peak of the gradient function (e.g. α = 0.75, σ = 1, panel D). Presumably, such “steering” could be used to provide increased spectral information to the CI user.
Two other field shaping configurations will be considered in this paper. The first is the bipolar configuration (panel E). This configuration is predicted to be less focused than the tripolar and some partial tripolar configurations, and also has a large side lobe in the vicinity of the compensation electrode. However, the bipolar configuration is of interest because it is readily available in most common cochlear implant systems, and has been studied extensively. Note that in our model, if the side lobes are considered, the bipolar configuration does not
result in narrower excitation patterns compared to monopolar stimulation (panel A); however, other models do indicate an advantage for bipolar stimulation (e.g. Whiten, 2007
). Finally, a monopolar steering configuration (panel F) allows for shifting of the peak of excitation, but does not attempt to sharpen the excitation pattern. Because this configuration has maximum current requirement that is similar to the monopolar, it can be readily implemented using contemporary cochlear implants.
One question that has been of theoretical interest with regards to field shaping has been whether configurations that produce more constrained fields will also produce narrower neuronal activation patterns once the current has been adjusted to be of equal loudness (Pfingst et al., 1997
). In principle, the answer to this question will require knowledge of what aspects of neural excitation account for loudness. Litvak and colleagues (2007a)
used the assumption that loudness is related to the total number of spikes on all active neurons. They showed that if one assumes the intrasite variance in single-fiber thresholds of humans to be similar to that recorded in cats (van den Honert and Stypulkowski, 1987
), the neural activation patterns resulting from constrained configurations should be somewhat narrower than monopolar stimulation, so long as the side-lobes associated with the focused configuration remain below neural thresholds.
In summary, theoretical and physical modeling studies indicate that field shaping strategies should be effective in stimulating narrow regions of the auditory nerve, and should also be effective in stimulating regions that are not “centered” on intracochlear electrodes. To determine whether the responses to stimuli created by current steering and shaping strategies differ from one another, we turn to studies of central auditory system responses and studies of perceptual differences. Recent advances in these areas are described in the following sections.