Threshold Predictions Based on an
Electro-anatomical Model of the Cochlear Implant
by
Darren M. Whiten
B.S., Biomedical Engineering
Boston University, 1999
Submitted to the Department of Electrical
Engineering and Computer Science
in partial fulfillment of the requirements for the degrees of
MASTER OF SCIENCE
IN ELECTRICAL ENGINEERING AND COMPUTER SCIENCE
and
ELECTRICAL ENGINEER
MASSACHUSETTS INSTITUTE
at the
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
February 2003
@ Darren M. Whiten, MMIII. All rights reserved.
OF TECHNOLOGY
MAY 12 2003
LIBRARIES
The author hereby grants to MIT permission to reproduce and
distribute publicly paper and electronic copies of this thesis documentBARKER
in whole or in part.
A u thor ..............................................................
Department of Electrical
Engineering and Computer Science
January 30, 2003
Certified by..
.....................
Donald K. Eddington,Ph.D.
4seagrch LabUrat9ry cf Electronics
xiTsSDunervisor
Accepted by ......
Arthur C. Smith,Ph.D.
Chairman, Department Committee on Graduate Students
-
2
-1
--.1-
Threshold Predictions Based on an Electro-anatomical
Model of the Cochlear Implant
by
Darren M. Whiten
Submitted to the Department of Electrical
Engineering and Computer Science
on January 30, 2003, in partial fulfillment of the
requirements for the degrees of
MASTER OF SCIENCE
IN ELECTRICAL ENGINEERING AND COMPUTER SCIENCE
and
ELECTRICAL ENGINEER
Abstract
The cochlear implant is an auditory prosthetic used to restore the sensation of hearing
by electrically stimulating auditory nerve-fibers via current injections delivered through an
intracochlear electrode-array. The detailed peripheral anatomy (e.g. the total number and
distribution of surviving spiral ganglion, the proliferation of new bone and soft tissue, and
the shape of the cochlear duct) as well as the characteristics of the implanted array are
likely to influence the pattern of neural excitation during electrical stimulation, but as of
yet the influence of these factors remains largely unknown.
We hypothesized that patient-specific models of the implanted cochlea that incorporate individualized anatomy might prove a useful tool in investigating how, and to what
extent, the peripheral anatomy influences electric hearing. To investigate the feasibility of
formulating such patient-specific models, the histologically processed temporal bone of one
implanted patient was used to construct a 3D electro-anatomical model incorporating that
patients unique anatomy. Using an iterative finite-difference algorithm, the electric field in
the model cochlea was solved in response to 20 different electrode configurations. Coupling
these field estimates to a single-neuron model allowed for the prediction of both the neural
activation pattern and perceptual threshold for each configuration.
To test the degree to which this model captures an influence of the peripheral anatomy,
model-derived perceptual thresholds were compared with those measured psychophysically
during the patient's last audiological exam. Several qualitative aspects of the patient's
pattern of psychophysical thresholds were captured by the model, although, quantitatively
the only significant correlations were observed for a subset of the more apical electrode
configurations.
Collectively, the results of this feasibility study suggest: (1) this preliminary model
captures some gross features of electric-stimulation that are influenced by the peripheral
3
anatomy, (2) the inclusion of new intracochlear bone and soft tissue is likely to be an important consideration in developing future patient-specific models, and (3) with additional
refinement, patient-specific models are likely to become a useful tool in explaining the influence the peripheral anatomy.
Thesis Supervisor: Donald K. Eddington,Ph.D.
Title: Research Laboratory of Electronics
4
Acknowledgments
Portions of this work were funded by:
NIH training grant DC00038 administered by the
Speech and Hearing Bioscience and Technology Program at the
Harvard-MIT Division of Health Sciences and Technology
and
NIH contract NO1-DC-2-1001
I would like to thank my advisor, Don Eddington, for his invaluable guidance,
encouragement, and tutelage as this work evolved from a summer research project
into a thesis. His door was always open and his willingness to invest time, regardless
of the hour, was always greatly appreciated. I would also like to thank the members of
the Cochlear Implant Research Laboratory - Vic Noel, Joe Tierney, Maggie Whearty,
and Meng Yu Zhu - for their eagerness to help, patience in answering questions, and
comic relief.
This project would not have been possible without the help of the Otolaryngology
Department at the Massachusetts Eye and Ear Infirmary. I am especially grateful to
Aayesha Khan for providing the histological cell counts, and Ridzu Mahamed for providing the segmented histological images. Additionally, I would like to acknowledge
Gary Girzon and Johannes Frijns, whose modelling studies contributed substantially
to portions of this work.
Last, but certainly not least, I wish to thank my family for encouraging me to
attend MIT, and my friends for encouraging me to avoid the perils of having a real
job for as long as possible by remaining in school.
5
6
Contents
1
2
13
Introduction
1.1
The Peripheral Auditory System . . . . . . . . . . . . . . . . . . . . .
15
1.2
Introduction to Cochlear Implants . . . . . . . . . . . . . . . . . . . .
19
1.3
Cochlear Implant Modelling . . . . . . . . . . . . . . . . . . . . . . .
24
1.4
Project Goals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
26
29
Methods
2.1
Three-Dimensional Model Formulation . . . . . . . . . . . . . . . . .
30
2.2
Potential Field Estimation . . . . . . . . . . . . . . . . . . . . . . . .
44
2.3
2.2.1
Governing Equations . . . . . . . . .
44
2.2.2
Numerical Implementation of Current Conservation
46
Single-Fiber Model . . . . . . . . . . . . . . . . . . . . . . . . . . . .
52
2.3.1
Nerve Fiber Modelling . . . . . . . . . . . . . . . . . . . . . .
53
2.3.2
Numerical Simulation . . . . . . . . . . . . . . . . . . . . . . .
57
61
3 Results
3.1
Model Component Results . . . . . . . . . . . . .
. . . . . . . . .
61
3.1.1
Potential Field Estimates
. . . . . . . . .
. . . . . . . . .
61
3.1.2
Single-Fiber Model Results . . . . . . . . .
. . . . . . . . .
64
3.2
Spatial Distribution of Excited Fibers . . . . . . .
. . . . . . . . .
69
3.3
Recruitment Behavior and Dynamic Range . . . .
. . . . . . . . .
82
3.4
Model Comparison to Psychophysical Thresholds
. . . . . . . . .
91
7
4 Discussion
101
4.1
Model Methods and Assumptions . . . . . . . . . . . . . . . . . . . .
101
4.2
Discussion of Model Trends
. . . . . . . . . . . . . . . . . . . . . . .
107
4.3
Recommendations for Future Work . . . . . . . . . . . . . . . . . . .
115
4.4
Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
Appendices
117
A Single Fiber Model
117
A .1 Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
A .2 Param eters
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
121
B Supplemental Data/Figures
123
C Recommendations for Future Work
131
8
List of Figures
. . . . . .
17
. . . . . .
18
. . . . . .
20
. . . . . .
28
Model generation . . . . . . . . .
. . . . . . . . . .
34
. . . . . . . . . .
. . . . . . . . . .
35
. . . . . . . . . .
36
Spiral ganglion voxel distribution
. . . . . . . . . .
39
2-5
Electrode array position.....
. . . . . . . . . .
40
2-6
Temporal bone x-ray . . . . . . .
. . . . . . . . . .
41
2-7
Implant x-ray with model overlay
. . . . . . . . . .
42
2-8
Discretized potential grid
. . . .
. . . . . . . . . .
49
2-9
Single-fiber model
. . . . . . . .
. . . . . . . . . .
55
3-1
Representative field solution.
. . . . . . . . . . . . . . . . . . . . . . .
62
3-2
Potential solution at unstimulated electrodes
3-3
Membrane voltage behavior for a typical 17 node fiber.
. . . . . . . . . .
65
3-4
Sensitivity of fiber threshold to At . . . . . . . . . . . . . . . . . . . . .
66
3-5
Sensitivity of threshold calculation to pulse duration
. . . . . . . . . . .
68
3-6
Convention for relative threshold polar plots
. . . . . . . . . . . . . . .
69
3-7
Excitation patterns: RENDITION 1: Electrodes 1-4 . . . . . . . . . . . .
70
3-8
Excitation patterns: RENDITION 1: Electrodes 5-8 . . . . . . . . . . . .
71
3-9
Excitation patterns: RENDITION 1: Electrodes 9-12
72
1-1
Peripheral auditory system.
1-2
Inner ear structures.
1-3
Cochlear implant schematic
1-4
Histological slice comparison.
2-1
2-2
Cochlear axis
2-3
Side view of the cochlear axis
2-4
. . .
. . . . . ..
. . .
. .
9
. . . . . . . . . . . . . . .
. . . . . . . . . . .
63
73
3-10 Excitation patterns: RENDITION 1: Electrodes 13-16
3-11 Excitation patterns: RENDITION 1: Electrodes 17-20
. . . . . . . .
74
3-12 Excitation patterns: RENDITION 2: Electrodes 1-4
. . . . . . . .
75
3-13 Excitation patterns: RENDITION 2: Electrodes 5-8
. . . . . . . .
76
3-14 Excitation patterns: RENDITION 2: Electrodes 9-12
. . . . . . . .
77
3-15 Excitation patterns: RENDITION 2: Electrodes 13-16
. . . . . . . .
78
3-16 Excitation patterns: RENDITION 2: Electrodes 17-20
. . . . . . . .
79
. . . . . . . . . . . . . . . . . . .
82
3-17 Histogram of relative fiber thresholds
3-18 Fiber recruitment: Electrodes 1-10
. . . . . . . . . . . .
. . . . . . . .
83
3-19 Fiber recruitment: Electrodes 11-20
. . . . . . . . . . . . . . . . . . . .
84
. . . . . . . . .
. . . . . . . .
86
. . . . . . . . . . . . . . . . . . .
. . . . . . . .
88
. . . . . . . . . . . . . . . . .
. . . . . . . .
90
. . . . . . . . . . . . . . . .
. . . . . . . .
92
3-24 Threshold profiles: Model rendition 1
. . . . . . . . . . . . . . . . . . .
94
3-25 Threshold profiles: Model rendition 2
. . . . . . . . . . .
. . . . . . . .
95
3-26 Correlation verses N . . . . . . . . . . . . . . . . . . . .
. . . . . . . .
99
4-1
Psychophysical thresholds with hypothetical error bars. . . . . . . . . . .
107
4-2
Distribution of weighted fibers across 6
. . . . . . . . . . . . . . . . . .
110
4-3
Rendition 2 (N = 450), Electrodes 5 and 8
. . . . . . . . . . . . . . . .
114
B-1
Histogram of relative fiber thresholds: Rendition 1
. . . . . . .
124
B-2
Histogram of relative fiber thresholds: Rendition 2
. . . . . . .
125
B-3
Basal Fiber-Tracks. . . . . . . . . . . . . . . . . . . . . . . . .
126
B-4
Truncated model: Correlation verses N : Electrodes 1-12
. . . .
127
B-5
Collective distribution of 0 for recruited fibers: Apical 12 subset
128
B-6
Correlation verses N : Electrodes 1-19
129
3-20 Fiber recruitment: Electrode 7 verses 10
3-21 Electrode 7 verses 10
3-22 Range of threshold values
3-23 Patient psychophysical data
10
. . . . . . . . . . . . .
List of Tables
. . . . . . . . . . . . . . . . . . .
43
. . . . . . . . . . . . . . . . . . . . . .
43
Model-fiber dimensions . . . . . . . . . . . . . . . . . . . . . . . . . .
54
2.1
Resistivity values for model tissues
2.2
Model rendition descriptions
2.3
11
This page intentionally left blank.
12
Chapter 1
Introduction
Possibly the most plaguing issue surrounding cochlear implant research is how to account for the overwhelming variability in implantee performance as measured by their
ability to comprehend speech. Implant users regularly post scores ranging from zero
to 100 percent on speech recognition tests designed to measure auditory performance
via the use of word or sentence lists [28]. While some factors such as subject age
and duration of deafness have been shown to correlate with performance [3], it is not
uncommon for two seemingly identical patients (with regard to audiological history,
etiology of deafness, age, etc.) to have extraordinarily different outcomes after being
implanted with the same device. Unfortunately, it is often the case that virtually no
explanation can be offered to those patients experiencing a poor outcome as to why
the implant procedure essentially failed to restore an ability to understand speech.
This unexplained variability motivates researchers to address the following questions:
what mechanisms limit performance, how do these interact, and to what extent can
these be reconciled with device design changes to afford the next generation of implant
users an improved ability to understand speech?
These questions are a difficult set to investigate, since the performance of each
implant patient represents the combined influence of many factors. These are typically
13
CHAPTER 1.
14
INTRODUCTION
categorized into two classes: (1) peripheral factors that govern the pattern of neural
excitation delivered to the auditory nerve by the implanted electrode-array, and (2)
central factors that govern how the patterns of neural activity propagate through the
auditory pathways and are interpreted by the central nervous system.
The focus of this work is on the periphery, specifically how the anatomy and
physiology of the implanted cochlea, along with the characteristics of the implanted
electrode array, influence neural activation. Issues associated with the sound processing strategy or stimulation waveform are not considered.
Many anatomical features of the implanted ear could potentially influence performance; for example, the precise position of the array, the ingrowth of new bone and
soft tissue, the distribution (and number) of the remaining auditory nerve-fibers, and
the complex anatomy of the temporal bone. These features vary extensively across
patients, although the effects of these anatomical differences remain unknown.
We hypothesize that a patient-specific model that captures the detailed peripheral
anatomy could prove to be a useful tool in understanding the intricacies of electric
stimulation on a patient-by-patient basis. A collection of these patient-specific models could ultimately: (1) address whether, and to what extent, differences in the
peripheral anatomy influence patient performance, and (2) identify desirable and undesirable anatomies. Because cochlear implants have been in use for over 20 years,
the histological data necessary to derive a meaningful set of such models is quickly
becoming available.
This project is primarily a feasibility study that generates the first such patientspecific model of an implanted cochlea. Using a single donor's histologically processed
temporal bone, a 3-dimensional electro-anatomical model is created that incorporates
many of the unique anatomical attributes mentioned above. This model predicts neural activation patterns in response to each of 20 electrode stimulation configurations.
To test whether the model is capturing an influence of the peripheral anatomy,
model-derived estimates of stimulation threshold (one for each individual electrode
1.1.
THE PERIPHERAL AUDITORY SYSTEM
15
along the implanted array) are compared with the psychophysical thresholds measured
during the patient's last audiological test. The advantage of this approach is that the
comparison of model estimates to actual patient data allows for a measure of how
well the modelling technique captures an influence of the observed anatomy. Since
it is the peripheral auditory system that is being modelled, a review of the normal
anatomy and physiology is presented first.
1.1
The Peripheral Auditory System
The mammalian auditory system is a remarkable sound-processing instrument capable
of detecting sound energies across a wide spectrum of frequencies and intensities. In
the functional human auditory system, the detection of sound is often described as
occurring in three steps: collection by the external ear, transmission across the middle
ear, and transduction into a neural code by the inner ear.
Sound propagating through air is collected by the external ear at the pinna and
guided toward the tympanic membrane, or eardrum, which marks the boundary to
the middle ear (figure 1-1).
Energy is transmitted across the middle ear into the
inner ear by the bones of the ossicular chain: the malius, incus and stapes. These
effectively counter the (acoustic) impedance mismatch between the air-filled external
ear and the fluid-filled inner ear. Accordingly, the middle ear overcomes the loss of
transmission that typically occurs when sound propagating through air meets a fluid
interface.
Transduction into a neural code occurs in the cochlea, a system of fluid-filled
compartments encased in the unusually dense temporal bone. The spiralling cochlear
duct is partitioned by two tissue membranes to form three parallel chambers called
the scala vestibuli, scala media, and scala tympani as shown in figure 1-2. The scala
media and scala vestibuli are separated from the scala tympani by a fibrous divide
called the basilar membrane. This serves as a basement membrane for the Organ of
CHAPTER 1.
16
INTRODUCTION
Corti, whose motion-sensitive hair cells perform transduction.
These compartments spiral around a common bony axis, the modiolus, that incases the auditory-nerve. Cell bodies of the nerve are aggregated into a spiralling
cluster (spiral ganglion), that sits in a cavity of the modiolus (Rosenthal's canal).
These neurons are bipolar. The peripheral process extends radially to exit the bony
modiolus at the habenula perforata and synapse on the base of an individual sensory
hair cell. The axonal process extends through the internal auditory canal to terminate
in the cochlear nucleus of the brainstem. In the normal human, approximately 30,000
myelinated afferent fibers innervate hair cells over roughly 2.5 turns of the cochlear
spiral [41]. Superficial fibers along the nerve trunk exterior peel off first to innervate
the base of the cochlear spiral whereas medial fibers travel further up toward the apex
before fanning out to innervate the apical turns.
Sound energy is injected into the scala vestibule through the round window by
the piston-like action of the stapes. Since the fluid of the scala vestibuli is essentially
incompressible, a travelling wave displacement of the basilar membrane is initiated
that propagates up the cochlear spiral. Local displacements of the basilar membrane
cause the attached sensory hair cells to release neurotransmitter, thus initiating neural
impulses on the synapsed afferent fibers. Accordingly, information about the local
membrane motion (e.g. its frequency and amplitude) is carried to the central nervous
system (CNS) by this corresponding subset of local auditory nerve-fibers.
The elastic properties of the basilar membrane systematically vary over the length
of the spiral such that the mechanical resonant frequency of the partition systematically varies from the base to the apex, allowing the structure to behave as a mechanical frequency analyzer. Disjoint frequency components of the incoming sound
preferentially excite disjoint frequency regions of the membrane: high frequency components excite basal regions while low frequency components excite apical regions.
Consequently, the power spectrum of the incoming sound is mirrored in both the
displacement profile along the basilar membrane and the corresponding discharge
1.1.
THE PERIPHERAL AUDITORY SYSTEM
17
Auricle
I
-
ma1ieus
Cochlear nerve
Cochlea
Round window
Tympanum
ternol
auditory
Frneatus
esEustachian
tube
cavity
Figure 1-1: Peripheral auditory system.
Shown are the structures of external ear, the middle ear (malius, incus, and stapes),
and the inner ear. From this vantage point, the axis of the cochlear spiral is nearly
perpendicular to the page. [Adapted from Noback, CR. 1967. The human nervous
system : basic principles of neurobiology. New York : McGraw-Hill. (Permission
granted)]
patterns of fibers spread along the membrane. Nerve fibers, and the hair cells on
which they synapse, are typically referenced by the sound frequency to which they
are most sensitive - the characteristic frequency (CF). The logarithmic map of characteristic frequencies along the basilar membrane's 2.5 spiraling turns is called the
cochlear frequency axis. Note in the following discussions, the terms frequency axis or
CF are used to describe positions along the (spiralling) basilar membrane, while the
term cochlear axis is used to describe the axis around which the basilar membrane
spirals.
INTRODUCTION
CHAPTER 1.
18
Anterior
vertical
Semicircular
Posterior
canals
vertical
Utricle
Saccule
Vestibular nerve
Modiolus
Horizontal
Cochlear nerve
Scala media
Ampulla
Oval window
Spiral ganglion
Round window
Helicotrema
Scala vestibuli
Scala media
SHair cells
Reissner's
membrane
Organ of Corti
Scala tympani
Spiral
ganglion
Basilar
membrane
Figure 1-2: Inner ear structures.
Sound energy injected at the round window travels up the cochlear spiral via a travelling
wave displacement of the basilar membrane. The elastic properties of the membrane
vary from base to apex allowing it to behave as a mechanical frequency analyzer.
[Adapted from from Noback, CR. 1967. The human nervous system : basic principles
of neurobiology. New York : McGraw-Hill. (Permission granted)]
1.2. INTRODUCTION TO COCHLEAR IMPLANTS
1.2
19
Introduction to Cochlear Implants
The cochlear implant is a neural prosthetic used to partially restore hearing in patients
with specific types of profound sensorineural hearing loss. The most common forms
of sensorineural deafness involve a loss of hair cell function or viability [19], thus
interfering with the transduction process even though a viable population of afferent
nerve-fibers may remain. The implant attempts to bypass the external ear, middle ear,
and transduction apparatus of the inner ear (hair cells) to directly stimulate afferent
fibers via a surgically-implanted electrode-array. Typically, arrays have up to 24
contacts spaced along an inert silastic carrier that is surgically inserted into the scala
tympani (figure 1-3). The electrode array parallels the frequency axis of the basilar
membrane, such that adjacent contacts along the array may focally stimulate adjacent
fiber populations that, in the normal ear, encode different frequencies of the incoming
sound. Accordingly, the distribution of stimulation across electrodes attempts to
mimic the excitation profile along the frequency axis of the basilar membrane present
in the normal ear.
Stimulation of individual electrodes is typically accomplished via short biphasic
current pulses (20 to 400 ps per phase) delivered at a carrier rate of around 800 Hz.
Current pulses can be delivered to an individual electrode referenced to a far-field
ground (monopolar) or between adjacent electrodes (bipolar). An externally worn
sound processor employs a filter-bank to decompose the incoming sound spectrum into
bands, then uses the band-energy to modulate the pulse train amplitude applied to
each electrode. Accordingly, temporal changes in an electrode's pulse-train amplitude
reflect temporal changes in the corresponding sound spectrum band.'
In one popular stimulation strategy, continuous interleaved sampling (CIS), the
phase of the pulse-train delivered to each electrode is staggered such that no two electrodes are pulsed simultaneously. This helps to minimize field interactions between
'The effective stimulus strength can also be modulated by adjusting the the pulse phase duration.
As a first-order approximation, the stimulus strength can be specified as the charge delivered during
each pulse phase (i.e. the duration-amplitude product).
CHAPTER 1.
20
INTRODUCTION
scala vestibuli
scala media
scala tympani
electrode contact
electrode carrier
auditory-nerve
Figure 1-3: Cochlear implant schematic
Typical electrode carriers have up to 24 electrode contacts, each intended to stimulate
a different subpopulation of afferent nerve-fibers. [Figure courtesy of Cochlear Corp.]
electrodes, however the subpopulations of nerve-fibers excited by adjacent electrodes
are still likely to overlap extensively. This overlap has generally been considered a
cause for poor performance, as discussed below.
Several variants of the CIS scheme have been suggested and implemented using
different methodologies for transferring the rich spectral and temporal information
of speech to the auditory nerve. For example, some schemes only activate a subset
of the electrodes based on the analysis bands with the highest band-energies. Work
1.2. INTRODUCTION TO COCHLEAR IMPLANTS
21
aimed at improving the encoding strategy is an active area of research, but outside
the scope of this discussion since this thesis is primarily directed at anatomical factors
that influence electric stimulation of the peripheral neurons. It is likely that substantial improvements in implant performance will require advances in both the coding
schemes and the interface between the electrode-array and the auditory nerve.
Implants must be calibrated on a patient-by-patient basis. To fit individual patients, two psychophysically defined levels are recorded for each electrode in isolation:
threshold and maximum comfortable level.
These measures mark the lowest and
highest pulse train amplitudes used by the device. Audiologists routinely use these
to specify an electrode-specific function that maps a range of sound energies in the
analysis band across the dynamic range of pulse train amplitudes bounded by the
threshold and maximum comfortable levels.
Limitations
Ideally, each contact along the electrode array would excite small, disjoint populations of afferent fibers along the cochlear spiral. Theoretically, this would allow for a
detailed representation of the incoming sound spectrum to be encoded in the auditory
nerve while preserving the temporal information in each band. Unfortunately, this
is not the case. Focal stimulation is severely limited because of interference between
adjacent electrodes; the geometry, proximity, and viability of the target fibers; electrode placement; and a host of other implicated problems. Present estimates indicate
that while the number of disjoint frequency bands in a device can be as high as 22,
the maximum number of independent channels of information received by the implant
user is typically limited to about 8 [9, 11, 21]. In the limit that two adjacent electrode
pairs excite an identical fiber population, it is virtually impossible for the patient to
discriminate between these two unless temporal information can be utilized.2
Besides the limitations imposed by the inability of the electrode array to focally
2
For example, a patient might discriminate these two if the pulse train carrier frequencies differed.
CHAPTER 1. INTRODUCTION
22
stimulate narrow regions along the frequency axis of the cochlea, others are imposed
by the population of surviving cochlear neurons. Neuronal survival is typically accessed by the viability of the neuron cell body located in the spiral ganglion. It is
well documented that the hair cell is more susceptible to injury (ototoxic or noise
induced) than cochlear neurons or supporting cell structures. A staggering loss of
hair cells may be accompanied by almost no immediate loss of cochlear neurons or
supporting cells. However, the secondary loss of spiral ganglion cells following hair
cell degeneration typically occurs [31, 56, 30]. In histological studies of the deafened
ear, the survival of spiral ganglion cells has been reported to decrease with both age
and the duration of deafness, but is reportedly most influenced by the etiology of the
hearing loss. Data suggest that patients who experience aminoglycoside exposure or
idiopathic sudden sensorineural hearing loss have the highest survival of spiral ganglion cells, while patients who lost hearing to postnatal viral labyrinthitis, bacterial
meningitis, or congenital factors have the lowest survival rates [31]. Recently, this has
led researchers to search for, and find, neurotrophic factors that appear to prevent
the secondary degeneration of spiral ganglion cells after an experimentally-induced
sudden loss of hair cells. [54, 49, 46].
Intuitively, one might presuppose that implant users with higher spiral ganglion
survival would have better speech recognition scores. While it has been reported that
electric stimulation thresholds tend to be anti-correlated with spiral ganglion survival
[23], no positive correlation between spiral ganglion survival and speech scores has
been reported to date. In fact, Nadol et al. [30] reported a negative correlation on
the basis of eight cases.
Another variable across patients is the depth to which the electrode array can be
inserted into the scala tympani during surgery. This is often limited, theoretically
resulting in a mismatch between the frequency band a particular electrode is encoding,
and the frequency region of the cochlea it stimulates. Ketten et al. [26] used computer
aided tomography (CAT scanning) to image patients to assess where in the cochlea
1.2. INTRODUCTION TO COCHLEAR IMPLANTS
23
the electrodes were positioned. Out of 20 patients, it was found that the most apical
electrode was positioned on average near the 1 kHz region of the basilar membrane's
frequency axis. This is consistent with many patients' reports of speech sounding very
high-pitched when the implant processor was initially turned on. While one might
expect better performance with a deep electrode insertion where the placement of the
electrodes is closer to the "correct" place along the cochlea, to date there is only a
limited amount of evidence to supports this [47]. In fact, it is not unusual for patients
with limited insertion depths perform as well as, or even better than, patients with
deep electrode insertions [28].
Various other factors have been suggested to explain implantee performance, including the medial-lateral' position of the electrode array, insertion trauma, changes
in the tissue properties of the cochlea (e.g. ossification or granulation tissue formation), the status of neural pathways central to the auditory nerve, and a host of
cognitive and age-related factors.
For most of these factors, no direct method of
measuring an individual contribution to auditory performance has been identified.
Likewise, no method for estimating how factors interact has been found. Observable
statistics including the age at implantation, age at onset of deafness, duration of
deafness, duration of implant use, electrode insertion depth, and etiology of hearing
loss have been used in factor analysis studies designed to predict the influence of each
on speech recognition scores. While the aforementioned factors account for a portion
of the variance in speech recognition scores, a relatively large unexplained variance
remains [3]. Furthermore, observing that a factor such as age is anti-correlated with
performance reveals next to nothing about the physiological mechanisms responsible;
except, of course, to suggest that its likelihood increases with age. Consequently,
these factors are used mostly as prognosticators for counselling. Identifying the underlying peripheral physiologies that lead to a successful implant user is the ultimate
goal of this research.
3 Medial refers to a position closer to the cochlear axis in a radial coordinate scheme.
CHAPTER 1.
24
INTRODUCTION
Generally, three approaches are used in researching the mechanisms that limit
implantee performance: human psychophysical or physiological experiments, animal
models, and computer modelling. The question of how the peripheral anatomy influences the device performance lends itself to a computer modelling approach. A
disadvantage of most previous computer models is the lack of comparison between
model results and animal or patient data. For this reason we sought a model that
would allow for such a comparison.
1.3
Cochlear Implant Modelling
Several generations of electrical models have been developed to investigate the potential distributions and current flows that drive neural stimulation in the implanted
ear. The earliest models of current flow used lumped-parameter models to treat
the cochlear spiral as a transmission line [2, 25, 50, 32]. These models assumed the
cochlear spiral could effectively be "unrolled", implying that adjacent turns could
essentially be decoupled. These model predictions show the potential and current
density along the scala tympani to decay exponentially as a leaky transmission line,
nearly obeying the formula:
Vmp(r)
=
Ve
-Irn
e A
.
(1.1)
Here Vmp is the potential referenced to a far field ground, r is the distance from an
active monopolar electrode, V is the electrode potential, and A is a length constant.
While these models give insight into the gross current flow during electric stimulation,
they do not provide the enough data to make predictions of neural excitation.
More recent approaches have used volume conduction models to solve for the potential field in the cochlea in response to stimulation. Several methods have been applied, including the boundary-element method [13, 4], finite-element method [10, 39],
1.3. COCHLEAR IMPLANT MODELLING
25
and finite-difference method [16]. All of these methods treat the cochlear structure as
resistive based on the measurements of Spellman et al. [48], who reported impedance
measures to be dominated by the resistance component up to frequencies of 12.5 kHz.
Several investigators have coupled these calculated cochlear potential fields with
single nerve-fiber models to render a prediction of neural excitation. Finley et al. [10]
developed a 3-dimensional (3D) volume conduction model to infer excitation patterns
by utilizing a passive nerve-fiber model based on the activation functions described
by Rattay [38].
Citing differences between the human auditory-nerve and the cat auditory-nerve
used in previous models, Rattay et al. [40] developed a single fiber model based on
modified Hodgkin-Huxley kinetics [20]. This was later used to make neural excitation
predictions using potential distributions obtained from a volume conduction model
based on a single mid-modiolar image from a normal-hearing human [39].
Frijns et al. constructed a 3D, rotationally-symmetric model [13], and later a 3D,
spiralling model [4] of the cochlea which were used to calculate cochlear potentials.
Neural excitation was then estimated using an active, nonlinear nerve-fiber model
based on mammalian voltage-clamp data. Model predictions of neural activation were
compared with electrically-evoked auditory brainstem responses (EABRs) measured
in cats by Shepard et al. [44]. Frijns concluded that the use of an active nerve-fiber
model was superior in predictive capability as compared to a passive model and that
the use of an unrolled cochlear model would lead to erroneous estimates of neural
excitation.
Until this point, all models discussed have been derived from mid-modiolar histological images taken from unimplanted humans or animals. Models assume an
electrode array, implanted into an otherwise pristine scala tympani, with little or no
insertion trauma. All cochlear structures remain unaltered, which is not the case in
the implanted ear where, as pointed out by Nadol et al. [30], insertion of the electrode
array results in significant damage to the inner ear. Growth of new bone and soft tis-
CHAPTER 1.
26
INTRODUCTION
sue into areas unoccupied in the normal cochlea is typical in the implanted patient, as
is seen in the histological image from the implanted patient used in this model shown
in figure 1-4A. For comparison, the mid-modiolar image of the unimplanted cochlea
used by Rattay et al. [39] for the generation of their model is shown in figure 1-4B.
In the implanted patient, the electrode has penetrated the basilar membrane and sits
in the scala vestibuli. This, along with the growth of new bone and soft tissue leaves
the anatomy of the implanted cochlea unquestionably different from that seen in the
normal.
1.4
Project Goals
It is not clear how the altered anatomy, especially the ingrowth of new bone and
soft tissue, might affect electric stimulation and the results obtained from volume
conduction models derived from the normal anatomy. It is also not clear how the
electrode position, remaining population of auditory nerve-fibers, and shape of the
cochlear spiral influence the performance of the implant. Accordingly, the goals of
this research were to:
1. Generate a volume conduction model based directly on the anatomy of an implanted cochlea as it may have existed in situ. This patient-specific model
attempts to capture the precise position of the electrode array, the distribution
and number of surviving afferent fibers, and the new bone and soft tissue that
fill the cochlear duct.
2. Estimate neural activation patterns and fiber recruitment under simulation by
each electrode pair in the model. Given a suitable criterion for estimating
perceptual thresholds from these model activation patterns, a comparison can
be made between the psychophysical thresholds recorded from the patient and
those generated by the model. This comparison measures the extent to which
1.4. PROJECT GOALS
27
the model captures the influence of the peripheral anatomy assuming no limitations are imposed by the central nervous system.
3. Determine whether including the new bone and soft tissue necessarily changes
the modelling results.
This modelling approach has two prominent advantages. First, the comparison between the model-derived and actual psychophysical thresholds can gauge the model's
predictive capability as well as guide model revisions. Second, many free model parameters (e.g. spiral ganglion densities) can be measured directly from the histological
data set. Ultimately, a series of such individualized models of implant anatomy may
allow for the identification of peripheral pathologies that degrade the performance of
patients who are otherwise expected to do quite well.
28
CHAPTER 1. INTRODUCTION
Petrous Bone
Bone fluid interface
Area of scala vestibuli
Electrode contact
Electrode carrier
Soft tissue
Area of scala tympani
Spiral ganglion cells
(in modiolus)
-
Scala Vestibuli
-
Scala Media
___
Organ of Corti
(on Basilar Membrane)
-
Scala Tympani
-
Modiolus
Figure 1-4: Histological slice comparison.
(A[top]) Mid-modiolar histological image from the implanted cochlea used in this study.
(B[bottom]) Histological image from the normal unimplanted cochlea used by Rattay
et al. [39] to generate their model.
Chapter 2
Methods
Overview
The model presented is based on an anatomical reconstruction of postmortem tissue
specimens taken from the temporal bone of a single cochlear implant patient. Estimating neural activation patterns in the model cochlea was accomplished in essentially
three steps. First, digitized histological images were used to generate a 3-dimensional
model of the cochlea capturing the relevant anatomy. The model was represented as
a 3D matrix of volume elements (voxels), with each voxel assigned a resistivity value
based on the tissue or material it represented. The capacitance of all tissues was
ignored. Electrodes were modelled as simple point sources in the resistive volume.
Second, the resistive matrix and electrode positions were used to estimate the
potential field in the model during a unit current (100 mA) injection between each
of 20 bipolar electrode pairs for which behavioral thresholds had been measured.
Estimated nerve-fiber tracks were added to the model by an ad hoc automated tracing
of expected fiber paths given the location of spiral ganglion cells in Rosenthal's canal.
From each field estimate the potential along an individual model fiber-track was
extracted and treated as that fiber's extracellular potential during stimulation.
Finally, these extracellular potentials were passed to a single-fiber model of the
29
CHAPTER 2. METHODS
30
mammalian auditory nerve that computed an estimate of stimulation threshold (i.e.
the lowest current level required to initiate a propagating action potential) for each
electrode configuration. The end result is a data matrix containing the calculated
thresholds for 1,354 model fibers computed for each of the 20 electrode configurations.
Using these fiber thresholds, comparisons can be made between the relative sensitivity
across electrodes predicted by the model and the relative sensitivity measured during
the patient's most recent audiological evaluation.
2.1
Three-Dimensional Model Formulation
The cochlear model is based on 304 histological slices from the donated temporal
bone of one implant patient who successfully used the device for more than 9 years.
Histological processing included slicing at 20 pm, staining, and mounting for photographing. A gray-scaled 480x512 digital image was taken of every other slice (152
images) at a resolution of 12.5pm x 12.5pm. Image registration was preformed by
manually aligning each image prior to acquisition against a ghost image of the previous slice. A copy of each image was made, and imported into a bitmap editor to allow
key features to be segmented manually. Image areas representing spiral ganglion cells,
the electrode contacts, the electrode carrier, new bone growth, and new soft tissue
were labelled and the segmented images saved. The histological processing, photography, and segmentation were preformed by a research member of the Otolaryngology
Department at the Massachusetts Eye and Ear Infirmary. Features were verified by
comparing the digital images to the histological slides as viewed under a light microscope. Next, both the original and segmented images from each slice were imported
into MATLAB for further segmentation and analysis. The model cochlea was created by incorporating information from both the raw and segmented image sets. The
segmented image set could not be used directly since it contained slight registration
errors such that the segmented areas were not contiguous in 3-dimensional space.
2.1.
THREE-DIMENSIONAL MODEL FORMULATION
31
Bone/Fluid Interface
A mid-modiolar raw image is shown in figure 2-1A, which also illustrates the model
coordinate system. Here many structures of the normal anatomy ar' either missing entirely or indistinguishable; for example, a contiguous basilar membrane is not
present. As a result, the first in a series of segmentation steps performed on the raw
data set was to define a continuous bone-fluid interface in each raw image that would
eventually define the cochlear duct. This continuous interface was drawn in each image for each cochlear turn by fitting a spline curve to a number of user-defined points.
This is shown in figure 2-1B. Next the voxels inside the defined cochlear duct were
designated as fluid and the voxels outside designated as bone (figure 2-1C). This step
defined a two-tissue model, essentially a fluid-filled spiral encased in bone. Since the
overall data set at this point was 512 x 480 x 152 for both the raw and segmented image
sets, each image was cropped and downsampled by a factor of two, resulting in a more
manageable size of 206 x 225 x 152 with a spacial resolution of 25pm x 25pim x 40pm.
Since the base of the cochlea is cropped in several of the raw images, additional bone
and nerve tissue needed to be added to the base of the model.
Spiral Ganglion Cells
Spiral ganglion cells were next added to the modiolar bone of the two-tissue model by
sampling pixels labelled as ganglion tissue in the segmented image set. These ganglion
voxels are shown in figure 2-1C as gray points. Each was then used as a landmark to
render an ad hoc fiber track for a single model-fiber. All ganglion voxels were indexed
by their angular position (6) in cylindrical coordinates about an estimated cochlear
axis, with the most basal ganglion cell serving as the reference (6 = 0) as shown in
figure 2-2. Using this axis, the ganglion voxels were assigned angular indices from
0 to 720 degrees. This ad hoc cochlear axis was chosen as a visual best fit to the
cochlear spiral. However, given the lack of precise anatomical detail in the model, it
remains a subjective choice.
CHAPTER 2. METHODS
32
Defining this axis was deemed necessary in order to automate the tracing of fibertracks, although one ambiguity that remains is the orientation of fibers attached to
the ganglion cells at the spiral apex. The lack of precise anatomical detail (e.g.
the ability to see peripheral dendrites in the histological images) made it difficult to
assign angular indices to the most apical spiral ganglion cells (grayed cells in figure
2-2). Rosenthal's canal typically spirals approximately 1.5 turns, with ganglion cells
in its most apical half-turn innervating the apical 1.5 turns of the organ of Corti. A
review of the literature revealed no systematic method to relate the precise position
of these most apical ganglion cells to the position along the basilar membrane they
innervate. Conversely, toward the base the relationship between ganglion cell position
and basilar membrane innervation is rather well defined. Accordingly, the assignment
of an angular index to a ganglion voxel is likely to be appropriate near the base and
arbitrary near the apex.
Fiber Tracks
With the exception of the ganglion cell location, there is no other information about
individual fiber paths in either the raw or segmented images sets. As such, the angular
index assigned to each ganglion voxel in figure 2-2 was used to generate a relation
between ganglion voxel location and fiber track orientation. Beginning at the base
of the model, fiber-tracks run parallel to the cochlear axis, fan out radially at the
appropriate cochlear angle, and pass through the parent spiral ganglion voxel. The
dendritic section of the track extends from the ganglion voxel toward the habenula
perforata as shown in figure 2-1D. Since the existence of the peripheral dendrite was
not verified in every histological section, the model fibers extend a short distance
toward the habenula perforata, but do not extend out of the bony modiolus. A side
view of the model showing the cochlea axis with model fiber-tracks shaded gray is
shown in figure 2-3.
Fiber-tracks were added to the model using an automated procedure written in
2.1. THREE-DIMENSIONAL MODEL FORMULATION
33
MATLAB. The path of each track was designated initially by four points: two points
at the model base' (parallel the the cochlear axis) where the auditory nerve exits
into the internal auditory canal, a point at the ganglion cell voxel, and a point along
the habenula perforata where the peripheral process is expected to exit the osseous
spiral lamina. The remainder of the fiber track was defined by spline fit interpolation.
This was accomplished in cylindrical coordinates by fitting a spline curve though the
mentioned points. Spline curves were forced parallel with the cochlear axis near the
model base, with the apical fibers placed closer to the cochlear axis. As a result, the
most apical fibers, whose angular orientation is somewhat ambiguous, travel along a
path essentially parallel to the cochlear axis with only a short peripheral segment at
the apex that fans out toward the cochlear duct. For basal fibers, much less of the
the fiber-track is orientated parallel to the cochlear axis since these fibers peel off first
to pass through basal ganglion voxels.
The modiolar bone, spiral ganglion voxels, and areas surrounding model fibertracks were all designated as a single homogeneous tissue. For notational ease, we
refer to this as nerve tissue although it represents the porous bone of the modiolus,
neural tissue in the modiolus, and a short segment of the auditory nerve at model's
base. At this point, the model consisted of only three segmented tissues: bone, fluid,
and nerve tissue. This is referred to as the basic model.
'Model base refers to the YZ boundary plane where the nerve exists the model, not to be confused
with the base of the cochlear spiral.
CHAPTER 2. METHODS
34
B
A
50
50
100
100
150
150
(D
(D
200
200
E 250
E 250
300
300
350
350
400
400
450
450
100
300
200
y-dim [pixels]
400
100
500
E
20
20
40
40
60
60
80
80
100
0E
120
X
120
140
160
160
180
180
200
50
150
100
y-dim [pixels]
500
100
140
200
400
D
C
x)
300
200
y-dim [pixels]
200
50
150
100
y-dim [pixels]
200
Figure 2-1: Model generation
for the X and Y dimensions, while the Z-dimension in
pixels
in
are
Note all axis units
the figures that follow refers to the histological slice number. (A) Raw digital image
of a near mid-modiolar slice. (B) Spline curves defining the fluid-bone interface are
added using user-defined marker points (C) The area inside the spline is filled as fluid
[black] while the area outside the spline is defined as bone [white]. The location of
spiral ganglion cells are determined from the segmented image set and added to the
modiolar bone as ganglion voxels [gray]. (D) The position of ganglion voxels are used as
landmarks to add individual fiber tracks to the model. The modiolar bone surrounding
the fiber tracks is then labelled as nerve tissue [dark gray].
2.1.
35
THREE-DIMENSIONAL MODEL FORMULATION
most basal
0=0
y-dim [pixels]
0
I
50
100-
150-
200-
120
100
80
204
140 z-slice
x-dim [pixels]
200
150
100
50
0
Figure 2-2: Cochlear axis
View looking down the estimated cochlear axis with spiral ganglion voxels as black dots.
The relative position of the electrode array is shown by connected circles. In cylindrical
coordinates, an angular index is assigned to each ganglion voxel as theta increases
clockwise from 0 to 720 degrees and the axial height increases accordingly. The angular
index is used as a metric for relating ganglion cell position to fiber orientation. Note
that the angular index of the fibers attached to the apical most cells is somewhat
arbitrary since it is sensitive to the choice of this cochlear axis. However, these fibers
essentially travel parallel to the axis with minimal fanning out.
CHAPTER 2. METHODS
36
p~.
* ...
Figure 2-3: Side view of the cochlear axis
View from a vantage point perpendicular to the cochlear axis. Here only the axonal
portions of the fiber-tracks [gray] are shown as they enter the base of the model parallel
to the axis before fanning out radially to innervate individual spiral ganglion voxels
[black].
2.1.
THREE-DIMENSIONAL MODEL FORMULATION
37
Fiber Count Calibration
The number of fibers added to the model was dependant on the number of pixels
labelled as ganglion tissue in the segmented image set. Since the density of actual
ganglion cells in a segmented area of ganglion tissue can vary, we sought a method to
calibrate the number of ganglion voxels in the model to the actual number of ganglion
cells present in the histological sections.
Ganglion cell counts taken under a light microscope were available from previous
research done by the Otology Department on the temporal bone in question. These
provided a ganglion cell count at every tenth histological section, or equivalently
every fifth histological image (since every other section was photographed). In midmodiolar sections there are typically several separate clusters of spiral ganglion cells,
as in figure 2-1C where the spiral crosses the section plane in three distinct areas. For
each of these clusters, a separate visual cell count was performed.
Using microscope cell counts, a relation between the number of ganglion voxels in
the model and the number of counted ganglion cells was established. Every fifth z-slice
in the model (corresponding to the section planes where cell counts was performed)
was designated as the center of a 3D bin in the model. For example, cells counted on
section 80 were associated with ganglion voxels on model slices 78 through 82, while
cell counts from section 85 were paired with model slices 83 through 87. For the 3D
bins toward the model center, a distinct cluster of ganglion voxels are present for each
turn of the spiral ganglion represented. In these bins, clusters of ganglion voxels from
separate cochlear turns are treated separately.
The voxels in each cluster in each model bin were assigned a weight such that the
sum of the voxel weights equalled the number of cells counted from the the associated
histological section. For example, in the model bin centered on slice 80, three separate
clusters were identified, with a group of 49 ganglion voxels populating the cluster from
the basal-most turn. A total of 22 ganglion cells were counted under the microscope
on section 80 for the associated basal-most turn of the spiral ganglion. Accordingly,
38
CHAPTER 2. METHODS
each of these model (ganglion) voxels was assigned a weight of (22/49) such that when
the 49 model fibers associated with this cluster are excited, the weight ascribed to
this group corresponds to 22 counted neurons.
Viewed from above, the distribution of ganglion voxels is displayed in figure 2-4
looking down on the Y-Z plane of the model base. The vertical grid lines denote bin
edges. The distribution of ganglion voxels in the model is depicted as the voxel count
per 25pm x 40pm rectangle after projecting each ganglion voxel's position onto this
Y-Z model plane.2 Note that for some areas in this 2D rendering, separate clusters
from distinct turns of the ganglionic spiral overlay each other.
For the remainder of this discussion, fiber recruitment is taken to mean the collective sum of fiber weights from all fibers that produce a propagating action potential.
Since the sum total of spiral ganglion cells counted was 1,138, fiber recruitment varies
from 0 to 1138 as a function of the model stimulus level.
Electrode Array
The next feature imported into the basic model was the center of the electrode array as
estimated from the raw image set. The electrode being modelled is part of a Nucleus22
® device. 3
This electrode array consists of 32 platinum bands spaced 0.75 mm
apart along a silastic carrier. The most apical 22 bands are active electrodes, while
the remaining bands serve as stiffening rings. There are 23 bands present in the
histological sections used, which were indexed 1 to 23 from apex to base. Note that
this numbering scheme is opposite to the convention used by the Nucleus corporation.
Since the electrode carrier passes through many image planes, its center conveniently served as a fiducial marker allowing slight adjustments in slice registration in
both image sets. These adjustments were made to insure the continuity of the bony
2
1n other words, if the X-dimension is simply removed from the model, the 2D representation of
ganglion density in figure 2-4 results.
3
Nucleus is a registered trademark of the Cochlear Corporation, 400 Inverness Drive South Suite
400, Englewood, Colorado 80112
2.1.
THREE-DIMENSIONAL MODEL FORMULATION
39
15
50
10
100
150
5
200
20
40
60
80
100
120
140
160
0
z- slice
Figure 2-4: Spiral ganglion voxel distribution
Projecting all spiral ganglion voxels onto the Y-Z plane of the model base shows the
distribution of voxels in the cochlear spiral. Note the Y-dimension is in pixels while
the Z-dimension is the section number. The colorbar indicates the number of ganglion
voxels per 25pm x 40pm rectangle in this plane. Notice the 2nd turn overlays the
first from this vantage point. To relate the number of voxels to the actual number of
ganglion cells, visual cell counts were performed on the slides centered between vertical
grid lines. Weighting factors were then assigned to each model fiber to reconcile the
number of voxels with the number of counted neurons.
duct such that misregistrations did not result in a fluid connection between adjacent
turns. Bone was intentionally added in some areas where thin bone separated cochlea
turns to insure against a breach in duct continuity. Additional bone was also added as
a buffer to the cochlear base and walls in order to further isolate the model boundaries
from the simulating electrodes. This pushed the final model size to 215 x 240 x 152
total voxels. The center of the electrode array was used to define a spline onto which
CHAPTER 2. METHODS
40
100
50.
-50-
-100
50
100
15 0
200
50
0,,0
15
200
x-dimension
y-dimension
Figure 2-5: Electrode array position
The electrodes [circles] are specified as point sources located along the spline travelling
through the electrode carrier center [line]. Both the x-dimension and y-dimension are
given in pixels.
the electrodes were placed as point sources during model simulations, as shown in
figure 2-5.
The confirmation of the electrode positions was important since the platinum
electrode contacts are often displaced during histological preparation. The position
of the electrodes along the center spline was confirmed by comparison to an x-ray film
taken before the specimen was sliced (figure 2-6). Since one electrode was missing
from the image sets, the comparison to the x-ray film was also used to estimate this
electrode's position. To compare the x-ray film with the 3D segmented image set, the
voxel positions in the model corresponding to electrode contacts were projected onto
a user-defined plane, then rotated and translated to overlay an appropriately scaled,
digitized image of the x-ray film. This was done by hand tuning the orientation of
the x-ray plane relative to the model coordinate axis, then adjusting the rotation
and translation of the projected model points so the two images could be overlayed.
2.1. THREE-DIMENSIONAL MODEL FORMULATION
41
Figure 2-6: Temporal bone x-ray
film taken before slicing shows the position of the platinum
x-ray
(A [top]) Digitized
bands spaced along the inert silastic carrier. The length of the white calibration bar
(upper left) is 1 mm.
This projection of the segmented electrodes onto the digitized x-ray is shown in figure
2-7A. The center spline of the model carrier along with its electrode points was also
projected onto the digitized x-ray as shown in figure 2-7B.
42
CHAPTER 2. METHODS
Figure 2-7: Implant x-ray with model overlay
(A [top]) Digitized x-ray film with segmented electrodes overlayed in black. Notice
the 7th electrode is missing from the segmented image set. (B [bottom]) Model center
spline with electrodes as points projected onto the same plane as in (A).
2.1.
THREE-DIMENSIONAL MODEL FORMULATION
43
Model Renditions
The resistivity of each voxel in the model was specified according to the values in
table 2.1. Two renditions of the model were constructed as detailed in table 2.2. The
second incorporated additional tissues in the cochlea duct including new bone and
soft tissue deposits. Here a 3-dimensional lowpass filter was applied to the soft tissue
of the segmented data set to fill in small fluid gaps. This effectively filled in small
pockets of fluid with a resistivity value proportional to the density of the surrounding
soft tissue. Filtering was necessary since small (a few voxels) pockets of fluid inside the
soft tissue often caused convergence problems in the potential estimation algorithm.
Table 2.1: Resistivity values for model tissues
Tissue
bone
modiolus with nervous tissue
fluid
soft tissue
new bone growth
resistivity (Qcm)
ref
5000
[15]
300
[15]
50
[33]
300
5000
[15]
[15]
Table 2.2: Model rendition descriptions
Rendition
Description
1
Basic three-tissue model (bone, fluid, nerve tissue)
with the entire cochlear duct filled with fluid
2
New bone and soft tissue added to the cochlear duct
of the basic model as extracted from the segmented image set.
Since soft tissue typically surrounds the array, the electrode
carrier resistivity was changed to that of soft tissue to remove
the tunnel of low conductivity fluid that would otherwise result.
Each rendition of the model was run separately, such that 20 potential distributions were calculated for each.
44
2.2
CHAPTER 2. METHODS
Potential Field Estimation
The 3D matrix of resistivity values and electrode positions are passed from MATLAB to a routine written in C [16] that computes an estimate of the potential field in
response to the first phase of a 100 mA biphasic pulse. The field during the second
phase is obtained by inverting the solution polarity. Twenty electrode configurations
are specified as bipolar+1 electrode pairs with the most basal electrode becoming cathodic during the first half of the biphasic pulse. For convenience, bipolar stimulation
between apical electrodes 1 and 3 is referred to simply as electrode 1 or configuration
1. Likewise, stimulation between the 20-22 electrode pair is referenced as electrode 20.
Note that this convention (electrode number increasing in the apical-to-basal direction) is opposite to the convention used by the Cochlear Corporation, but consistent
with the convention used by other implant systems. Before discussing the numerical implementation of the potential field estimation, a brief review of the governing
equations is given.
2.2.1
Governing Equations
The field estimate is formulated as a quasi-static formulation of Maxwell's equations
with the electric field, E(x,y,z), expressed in terms of the potential field,
<b(x,
y, z),
as
E = -V(D.
For time-varying (sinusoidal oscillating) fields, the current density J[
(2.1)
] is
related
to the electric field by the complex conductivity tensor as
J = (a + jwF0Fr)E,
where - is the material conductivity
[-], w
(2.2)
is the angular frequency of the sinusoid,
2.2. POTENTIAL FIELD ESTIMATION
45
,o is the dielectric constant of free space [1], and E, is the dimensionless material
For the biological tissues and stimulus durations
permittivity relative to &o [43].
being modelled, equation 2.2 is dominated by the conductive term such that the
material can be modelled as an ohmic isotropic medium [35]. By analogy to ohms
law we have the relation
J =o-E.
(2.3)
The rate of free charge (p) entering or exiting any enclosed surface is found by the
surface integral
j - ds = -
Pencoseda
dv = jI
(2.4)
where I,[6] is an enclosed current source. Comparing this to the divergence theorem,
J
- ds = IV - J dv
(2.5)
one obtains the result known as the conservation of charge [43],
dp
dt
(2.6)
which is used here as a numerical scheme. For direct currents, equation 2.6 will equal
zero, thus reducing to Laplace's equation,
V -J
=
-
V
- (-UVI)
(2.7)
0.
The task of estimating the potential field in the electrically stimulated cochlea es-
CHAPTER 2. METHODS
46
sentially reduces to solving Laplace's equation on a 3-dimensional discretized grid
at all positions not containing a current source. The two electrodes are inserted as
hypothetical point-sources that make equation 2.6 nonzero at two positions in the
model.
2.2.2
Numerical Implementation of Current Conservation
A nonconservative method for solving the potential field @(x,y,z) involves writing
difference equations derived from a Talyor series expansion of the second-order partial
differential equation in 2.7. An alternative, although similar, technique employed here
is to use current conservation to formulate a numerical scheme. The surface integral of
equation 2.4 is used as a basis for this scheme, where current is conserved across media
of different resistivities. This scheme is typically referred to as the finite-difference
approach.
To estimate the potential field (4D(x, y, z)), all that is required is a 3D matrix of
conductivities and the location of the current sources. The elements of the resistive
matrix are inverted so that resistivities [Qcm] become conductivities [A]. A potential
node is placed in each corner of every conductive voxel such that the 215x 240 x 152
set of conductive voxels fits inside a 216 x 241 x 153 lattice grid of potential nodes
as in figure 2-8B. Here each internal node sits at the interface of eight conductive
cubes that influence its potential. The potential grid F(Xi, Yj,
Zk)
is referenced by the
shorthand 4Dk. Since the conductive cubes fall between consecutive nodes on the
grid they are indexed at the half-step (e.g. i +
,j + 1, k + }).
To implement current conservation, we use a cubic control surface (physical dimensions Ax=25ptm, Ay=25pm, Az=40pm) centered on each individual node as in
figure 2-8A. Here the cubic control surfaces and conductive volumes are interdigitated
such that each control surface encloses a corner of the eight neighboring conductive
cubes, as in figure 2-8. If the control volume is sufficiently small relative to the second
spacial derivative of the electric field, then the surface integral of equation 2.4 can
2.2. POTENTIAL FIELD ESTIMATION
47
be expressed as the sum of six current vectors, each orientated normal to a control
surface face as in figure 2-8A. Current conservation requires
ix- - IX+ + IY~ - I+ + IZ--
where I, in an enclosed internal source.
IZ+ = Is,
(2.8)
The calculation of each normal current
requires an estimate of both the electric field and conductivity at the control face
center. The electric field is estimated from the difference in potential between the
center node and its neighbor, while the conductivity is taken as the average of the four
conductive cubes the control face lies in. For example, the current (Ix+) is calculated
at a position half way between the center node (
positive x-direction
(Pi+1,j,k)
ij,k)
and the adjacent node in the
using the following as estimates for the electric field and
conductivity respectively.
E lD
I
4i+l,j,k
-
ijk
To get the current Jz+ we simply multiply these by the control surface area. Accordingly, the six surface normal currents for a control volume centered on node
are
2
[IX
i+Ij-
4
'i,j,k
CHAPTER 2. METHODS
48
,k
ilA
' '
x
2'
K2 2' 2 -2'
±.
1i~
x
'j+,k
-
Ay
+ . i ,j ,k
.+1
Ay
(i-Ij-I~
i+.,j+.,k+}
A
i~J1,k
-4
-
AYAZ
(2.11)
+Ji+,j+,k-
Izliajk+ 1=
(2.10)
-!k+l
±1
2'
2
Ui
(07-.~j-I~ +
--
-
k+ i
+
i
Ij
1
7i+-J ,k
(2.12)
+
(2.13)
.Ik !
(2.14)
Notice the computation of these six currents uses only the conductivities of the
eight adjacent cubes, the potential of the center node, and the potentials of the six
adjacent nodes. Consequently, the potential at each node is coupled only to that of
its six principle neighbors. Equations 2.9 - 2.14 can be consolidated and written as
[i-,j,k
=
[Ixi+,j,k
=
-,k
i,j+ ,k
[Izi,j,k+
=
(i,j,k
i-1,j,k)
(2.15)
Dij,k)
(2.16)
4 i,j-1,k)
(2.17)
-
1
i+,j,k (' i+1,j,k -
-i,j-I,k
[Yli~j+.k
1Iz ij,k-l
-,J,k
('i,j,k -
(
1
1
i,j,k-! ( i,j,k
iJ,k+1 (
4
'Ii,j,k)
(2.18)
4i,j,k-1)
(2.19)
I~ij,k)
(2.20)
i j+1,k -
i,j,k+1 -
2.2. POTENTIAL FIELD ESTIMATION
49
(A) CONTROL SURFACE
+Y, k00
t
'
0
so
ijk
,k
k+%2
AY
'Z
2jk
S-i+,
i
i, j,
Az
k..i'/k
(B) CONDUCTIVE MESH
i-M j+%
k-%
kio0
0,
Figure 2-8: Discretized potential grid
(A) Cubic control surface used for conservation of current around node <bi,j,k located at
its center. Normal currents are calculated by estimating the electric field and conductivity at each face center, then multiplying by the face area. (B) Potential grid used in
current calculation. Each conductive cube is defined at its corners by eight potential
nodes. Here the upper right conductive cube is left out to view the orientation of the
control surface about the center node. The dotted line added to the control surface in
(A) shows how this surface is orientated in (B).
CHAPTER 2. METHODS
50
where the 3's are formed from the (known) conductance values and the physical
dimensions. Substituting equations 2.15-2.20 into the current conservation relation,
one obtains
[xI]
Ilyi,j+! ,k + [Izj
,k -
[xli+I,j,k + ['"]iYj
-
.
-
i,j,k+
[
=
i,j,k
(2.21)
where I, is only nonzero at the two nodes modelling the electrodes. In this manner a
complete nodal equation can be written for each potential node that does not lie on
the model exterior. For example, the nodal equation for node
/31!,2,2('D2,2,2 -
'D1,2,2) -
021,2,2(03,2,2 -
4CD2,2,2)
+
/32,11,2('b2,2,2 -
4)2,1,2)
02,21,2()2,3,2 -
(D2,2,2)
+
2,2,1
(1)2,2,2 -
-
'12,2,1) -
02,2,21 (4D2,2,3 -
4D2,2,2)
)2,2,2
=
becomes
12,2,2
Here Dirichlet boundary conditions specify the potential as zero for each boundary
node. In this formulation, an approximation to Neumann boundary conditions 4 is
accomplished by setting the conductivity of voxels at the model boundary close to
zero, thus confining current flow to the model interior.
The complete set of nodal equations form a system of coupled equations that can
be recast in matrix form as B
=
I where
1,1,1
4)
=
'11,1,2
41)216,241,153
4Neumann boundary condition require the derivative normal to the boundary
surface to be zero.
For example,
1 =
dx
0 at the Z-Y boundary surface.
2.2. POTENTIAL FIELD ESTIMATION
51
1,1,1
I=
1,1,2
I216,241,153
and B is a banded, sparse matrix containing only seven nonzero diagonals filled with
the entries of 3. All the entries of I are zero except for the two points in the model
where a current source and sink are specified. Estimating the potential field now
conveniently reduces to performing a matrix inversion of B to solve for <1. Since B is
a (7 x 10) - by - (7 x 107) sparse matrix, iterative methods must be employed. The
estimated solution to di was obtained using the PreConditionedConjugate Gradient
algorithm ' (PCCG) as implemented by Girzon [16]. The solution vector <b is simply
reshaped into a 3D matrix to yield a (216 x 241 x 153) estimate of the potential field.
'For a discussion of the PreConditioned Conjugate Gradient algorithm see Axelson and Barker
[1]
CHAPTER 2. METHODS
52
2.3
Single-Fiber Model
The single-fiber model used in this work is based on the modified spatially extended
nonlinear node (SENN) model as described by Prijns [13]. The model provides an
estimate of stimulation threshold in response to a transient extracellular stimulus.
Under each bipolar configuration, the 3D potential field estimate, <P, is calculated for
a biphasic (30 pus per phase) 100 mA current pulse as discussed in section 2.2. From <P
the potential along each individual fiber is extracted by sampling the potential along
the fiber track as it courses through the model. By interpolation, the potential at the
model fiber's nodes of Ranvier are specified along both the peripheral dendrite and
axon. These are packaged as a vector of external potentials, V1, that the single-fiber
model iteratively scales to find a threshold Ve that generates an action potential.
Since we are modelling the cochlea as a collection of resistive media, scaling V' is
equivalent to scaling the current source used to excite the electrode pair.
Alternatively, the fixed-amplitude V. can be used and the stimulus intensity modulated by adjusting the duration of the biphasic current pulse. In fact, this is the
intensity-modulation scheme used in the Nucleus device over the range of psychophysical thresholds recorded from the patient. Here the stimulus intensity is modulated by
using pulse durations ranging between 22.26 ps and 32.85 ps; however, simply converting these measures to charge delivered per phase [nC] allows for easy comparison
with the model results.
Since the electrodes are modelled as point sources, instead of bands separated by
highly resistive silastic, the threshold charge [nC] returned by the single fiber model
is not expected to match precisely with what was measured psychophysically. This
is not a serious problem, since we are primarily interested in the relative sensitivity
across fibers and across the 20 bipolar electrode configurations. For the purposes of
this investigation, each fiber threshold is reported as the relative threshold (T,) in
reference to a 100 mA biphasic pulse of 30ps per phase.
53
2.3. SINGLE-FIBER MODEL
2.3.1
Nerve Fiber Modelling
The mathematical formulation for the time-varying membrane voltage, Vm(x, t), is
derived as a modified form of the cable equation. The passive cable equation for a
cylindrical fiber with a linear membrane conductance takes the form,
A2
a92Vm
Ox 2
~
-Vm
at
=
0
(2.22)
where A and r are space and time constants respectively. Equation 2.22 is a second
order partial differential equation (PDE) of the parabolic type where Vm is a continuous function of both space (x) and time (t). Incorporating the nonlinear membrane
conductances described by Schwarz and Eikhof [42] adds significant complexity to the
membrane behavior, essentially necessitating a simulated solution.
A typical method for dealing with a nonlinear PDE of this form involves a technique called the method of lines, where the spatial variable (x) is discretized into N
spacial regions, with the spatial derivative
(')
set to zero within each region. This
technique transforms the nonlinear version of equation 2.22 into a system of N coupled
ordinary differential equations (ODEs) where time is the only remaining independent
variable. Subsequently discretizing time leaves a set of coupled, nonlinear algebraic
equations [27]. In this model of the myelinated afferent auditory fiber, the spacial
discretion corresponds to specifying Vm at adjacent nodes of Ranvier, again resulting
in a system of coupled ODEs which can then be simulated by temporal discretization
and numerical integration.
A section of the modified SENN model-fiber employed here is shown in figure 2-9.
It is composed of N nodes of Ranvier, indexed by (i), and N-1 internodal segments,
indexed by (k). The membrane current at each node is composed of a capacitive current (Ic), a linear leak current (IL), a nonlinear sodium current (INa), and a nonlinear
potassium current (IK). The myelinated internodal segments of the membrane are
CHAPTER 2. METHODS
54
treated as perfect insulators, allowing only an axial current to flow between adjacent
nodes. The nodal capacitance and axonal conductance are determined by the fiber
dimensions (Appendix A).
The number of total nodes (N) varies between 14 and 23 depending on the fibers
orientation in the electro-anatomical model. Most fibers have 6 dendritic internodal
segments. The fiber dimensions and relation to the cell body are given in table 2.3.
Table 2.3: Model-fiber dimensions
node (i)
1
2
3
4
internode
(k)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
node length
f(i) [pm]
node diameter
d(i) [pm]
3
1
1
1
3
3
3
3
internode length
L(k) [pm]
internode diameter
D(k) [pm]
175
175
175
175
175
175
40
150
200
250
300
350
350
350
3
3
3
3
3
3
5.5
3
3
3
3
3
3
3
label
II
|
dendrite
|
[CELL BODY]
I
|
axon
I
II
55
2.3. SINGLE-FIBER MODEL
e(i-1)
*
n(i)
L
)
I.
ion
CI
L
(i-1)
L(i+1)
GNt
GK
GL
(H-i)
(1+1)
VNU
VK
+Cc+
+W
CI
On( +1)
Coi+1)
GNt
GK+
(0-1)
(0-1)
VNa
K
GL
_j
Cm(7
(-)
L
GNt
GK+
(i)
(i)
Node
( i-1i)
(i)
VN8VK
VL
+
+
+
+
GL
CI
(0+1)
(+1)
VL
+
Node
(I)
Intemode (k-1)
D(kL)
Intemode (k)
Node
(i)
L(k)
(i)
(I+1)
Figure 2-9: Single-fiber model
Three nodes of Ranvier are shown with transmembrane currents at each node composed
nonof a capacitive current (I,), a leak current (IL), and an ionic current (Io,). The
linear, voltage-dependant kinetics of the sodium conductance (GNa) and the potassium
internconductance (GK) are adapted from Schwarz and Eikhof [42]. The myelinated
are
(Ve(,))
node
each
at
odes are treated as perfect insulators. The external potentials
determined by the field estimate as in section 2.2. See table 2.3 for fiber dimensions.
See equation 2.23 or appendix A.2 for parameter conventions.
CHAPTER 2. METHODS
56
The deviation of the membrane voltage from its resting state at the ith node (V(j))
is given by
dV( )
-
[Ga(V(l
-
-GL(V(i)
-
2V(j) + V(±i+))] + [Ga(V
VL)
-
- 2Ve_ e + Vege)]
Iion(
(2.23)
using the conventions
Vi,
the internal potential referenced to a far field ground
Vm(i)
e ,M
the external potential referenced to a far field ground
Vmm
= [Vim - Ve()] the transmembrane potential
[Vm(1 ) - Vrest] the deviation of the membrane voltage from rest
V(i)
Vrest
the resting membrane voltage as calculated using the Goldman Equation
the membrane capacitance at node i
Ga( k)
the axial conductance at internode k
(note in equation 2.23 that Ga was treated as uniform)
GL
VL
the membrane leak conductance
the leak current equilibrium potential chosen such that
IL + Ii,, = 0 in the resting state
Equation 2.23 can be derived by balancing current at the internal node labelled Vi) in
figure 2-9. The values of the external potential V,
are taken from the scaled vector
V' as extracted from the estimated potential field. A subtle point worth mentioning
is that in this formulation the extracellular potential is completely dictated by Vo as
computed in the electro-anatomical model; consequently, the model fiber kinetics do
not influence the extracellular potential.
The model's nonlinear behavior is governed by the voltage-depentant sodium
(GNa)
and potassium (GK) conductances.
described by Frijns [13] are:
The sodium and potassium currents as
2.3. SINGLE-FIBER MODEL
INa%)
[PNah()mh)
57
(Vm(0
7
-(
cK]exp)
1-j
(V
(VF
= S K n j)
2
) [cs+] - [c%+] exp
R
S- exp
Vm
F\
(V
)
F
V
7dJ fj)
RT
.) F\~
-T
(2.25)
R
where
PK
potassium permeability
n(s),
potassium activating factor
PNa
sodium permeability
h(j)
sodium inactivating factor
d(j)
node diameter
R
gas constant
node length
T
absolute temperature
sodium activating factor
F
Faraday's constant
M(i),
Here the activating factors m(i), n(i), and h(j) are nonlinear, time-varying, and voltagedependant with each obeying a first order differential equation of the form
dm()
=
1M. +(OM()
+m
dt(
+! 3O
)m W
(2.26)
(2.27)
The voltage dependance of amn() and +)3m()
described in appendix A. Similar equa-
tions govern n(s) and h(j) as detailed below.
2.3.2
Numerical Simulation
We seek a solution to the membrane voltage deviation at each node (V()) as a function
of time to determine if a propagating action potential is observed in the numerics.
To accomplish this, only V(), m(i), n(j) and h(j) need to be simulated as a function
of time, since all other model variables can be formulated from these four and the
58
CHAPTER 2. METHODS
fiber dimensions. To simply our exposition, we form column vectors from each (e.g.
V
, V(N)]T) allowing this entire system to be concisely described with the
= [V),...
following four coupled equations ( from [13] ):
dV
d
dt
dm
dm
AV+BVe + C (Iact + IL)
(Oam( +
)
dt
dt
=
dn
0
/ ma))
+
m
am(N)
dh
-=+
dt
3
(2.28)
(am(N) +
0
(ah(1)
ah(1 )
+
3
1m(N))
0
h(j))
'-h
ah(N)
0
an(,)
(anl) + On())
(2.30)
(ah(N)
+
1h(N))
0
n
+
dt
an(N)
0
(2.29)
(an(N)
+
(2.31)
/3f(N))
Calculation of the vectors Iact and IL requires V, m, n, and h. Likewise, the
calculation of the a's and O's to find m, n, and _h requires V. Here A, and B are
tridiagonal matrices that describe the resistive coupling between nodes, and C is a
diagonal matrix containing the nodal capacitances. The entries of A, B, C, and the
voltage dependency of the a's and /'s can be found in appendix A.
Equation 2.28 implements a sealed-end (spatial) boundary condition requiring
zero axial current to the left of node 1 or to the right of node N in figure 2-9. This
2.3. SINGLE-FIBER MODEL
can be conceptualized as setting
59
GA(.)
and
GA(,,)
to zero, forcing any axial current
to flow only between nodes 1 through N.
To obtain a simulated V(t), equations 2.28 - 2.31 are discretized by replacing all
time derivatives with finite-difference approximations, then numerically integrated on
a uniform time grid of spacing At. The fiber is initialized in its resting state with
the membrane potential equal to the resting potential at all fiber nodes (e.g. V
=
0).
Likewise, all elements of the vectors _m, n, and h are initialed in their respective
resting states as m, no, and ho (given in appendix A). The time derivatives of V, m,
n, and h are also initialized as zero.
This system is driven by a time-varying vector of extracellular potentials, Ve(t),
that takes the form of a biphasic pulse with 30 pus per phase. During the stimulus
phase, Ve(t) is set to a scaled version of Vo as
Ve(t)
0
0 < t < 5ps
+ Cscale -Ve
5ps < t < 35pas
-
0
Cscale
e
(2.32)
35ps < t < 65pas
t> 65ps
where Cscale is a scale factor applied to vary the stimulus intensity across different
runs.
The choice of (temporal) integration technique is a tradeoff between the accuracy
and stability of the solution and the ease and speed of the implementation. Explicit
and implicit methods form two broad classes of integration methods used on coupled
60
CHAPTER 2. METHODS
ODEs of this type.6 For explicit methods, such as Euler's method or Runge-Kutta
methods, the technique boils down to evaluating the right side of equations 2.28 2.31 at known values of V(tn), _M(tn), n(tn), and h(tn) to obtain V(tn+1 ), _M(tn+1 ),
n(t,+ 1 ), and _h(tn+l) [27].
Implicit methods such as backward Euler and Crank-
Nicholson involve solving a linear system (i.e. a matrix equation) for the values of
V(tn+1 ), M(tn+1), _(tn+ 1 ), and h(tn+ 1).
Since 1,354 model fibers were included in this preliminary model, a simple first
order Euler method was implemented with a sufficiently small time step to obtain a
stable solution. This allowed for the simultaneous calculation of V(t) for upwards of
200 fibers with the same number of nodes by forming a 3D data structure in MATLAB
(node number x time iteration x fiber number ). A subset of fiber thresholds were
calculated using a smaller time step to evaluate the sensitivity of the model results
to the choice of time increment.
After integrating, the existence of a propagating action potential is determined by
thresholding V(i, t), the Ccaie factor changed, and another run initiated. The value
of Ccaie is iteratively scaled and the time evolution of V(i, t) checked for an action
potential until a threshold
Cscae
is found. Threshold is defined as finding two values
for Ccale that differ by less than 1 percent, one of which initiates an action potential,
while the other does not. The fiber's relative threshold (T,) is taken as the larger of
these values. In addition to providing threshold estimates, the single-fiber model also
returns an estimate of the spike initiation node.
6
The issue of primary interest in choosing between explicit and implicit methods is one of stiffness.
Stiffness measures the difficulty of solving an ODE or PDE as the ratio of the longest time scale
to the shortest time scale. This is analogous to the ratio of the largest to smallest eigenvalue (i.e.
condition number) in describing the difficulty of performing a matrix inversion. Explicit methods
usually suffice for non-stiff problems, while implicit methods have more desirable numerical behavior
for stiff problems, but are more difficult to implement. The stiffness of a compartmental neuron
model, such as this one, increases with both the number of compartments and the degree of resistive
coupling between compartments. For example, if the axial conductance G, on both sides of a node
is much smaller than the combined nodal membrane conductances (GL +GK +GNa), then the nodal
voltage is essentially decoupled from its neighbors, thus decreasing the stillness [27].
Chapter 3
Results
3.1
3.1.1
Model Component Results
Potential Field Estimates
Field estimates for the 20 electrode configurations typically required 8-10 hours to
compute using a Pentium IV, 1.4 GHz workstation. On average, 250-300 iterations
of the PCCG algorithm were required for convergence to a solution. A representative
contour-plot taken along a Y-Z plane' for the
12 th
electrode configuration is shown in
figure 3-1. As expected, in the regions close to the electrodes the potential solution is
nearly the same as that of an electrostatic dipole. 2 From figure 3-1 one notices that
the potential near the model center, where the excitable tissues of the modiolus are
located, deviates substantially from that predicted by a simple dipole solution. This
supports the use of an iteratively computed solution over an analytical approximation
to the potential field during electric stimulation.
The potential predicted at inactive electrodes shows an exponential decay toward
zero as the distance from the active pair is increased as shown in figure 3-2. The
'This plane is nearly perpendicular to the cochlear axis, see figure 2-5 for orientation.
The analogy between the electrostatic dipole problem and the direct-current problem being
modelled here is that if the electrodes are replaced with appropriate point charges, and the resistive
media replaced with free space, then the potential field solutions would be the same [43].
2
61
CHAPTER 3. RESULTS
62
20
40
60
80
C
0
E
100
120
140
160
180
200
220
240
20
40
60
80
100
z-slice
120
140
160
Figure 3-1: Representative field solution.
Contour plot of an estimated potential distribution on a mid-model Y-Z plane during
the first half of a 100 mA biphasic pulse delivered to electrode pair 12. The electrode
array is projected onto this plane with the most basal electrode located at the upper
right. During this phase the more apical electrode (0) is anodic first.
potential at the inactive electrode between the active pair is near zero, as expected
from the electric dipole analogy.
3.1. MODEL COMPONENT RESULTS
63
15
10
5
I-l
0
0
CL
-5.
-10
-15
2
4
6
8
12
14
10
Electrode Contact
16
18
20
22
Figure 3-2: Potential solution at unstimulated electrodes
Potential along the unstimulated electrodes for configuration 6 during the first half of
the biphasic pulse using model rendition 1.
CHAPTER 3. RESULTS
64
3.1.2
Single-Fiber Model Results
Computing threshold estimates for the 1,354 model fibers for the 20 electrode configurations required approximately 36 hours per model rendition. A typical 300 psec
simulation is shown in figure 3-3. Shown is the time progression for the external potential Ve(i, t) in 3-3A, the membrane voltage deviation V(i, t) due to a supra-threshold
pulse in 3-3B, and the deviation V(i,t) due to a sub-threshold pulse in 3-3C. Since it
is only the relative sensitivity of fibers across different electrode configurations that
is of interest, the fiber thresholds are presented as relative thresholds (re 100 mA, 30
psec per phase pulse). The relative threshold (T,) assigned to this fiber is 0.3313,
corresponding to a biphasic pulse delivering 993.9 nC of charge per phase. The psychophysical threshold (Tp) for this electrode was recorded using a pulse delivering
23.2 nC per phase (966 pA biphasic pulse with 23.98 ps phase duration).
Scaling
The magnitude of the threshold stimuli predicted by the single-fiber model does not
match the level of the biphasic pulses used by the device. This discrepancy is not
entirely unexpected since: (1) the electrodes were modelled as point sources that were
not separated by resistive silastic, meaning that current flow directly between them
was not impeded, (2) the impedance associated with the material interface between
the electrode and the surrounding fluid was ignored, and (3) the biphasic pulse used
in the model did not incorporate a short delay between pulse phases, as occurs in the
actual device.
Other potential sources of this scaling discrepancy are the assumed tissue resistivities and the model-fiber dimensions. Neither of these parameters have been well
studied. In this preliminary model, the fiber dimensions are based on measures in
guinea pig. Consequently, the peripheral dendrites are shortened such that they do
not exit the modiolus.
65
3.1. MODEL COMPONENT RESULTS
S-0
> -2,
-4
20
150
100
time [usec]
50
0
0
fiber node i
200
250
300
200
250
300
20
25
30
150
-...-.
--.....
S 100
50
--
-
-50.
20
E
10
0
0
~~.
.............
0
fibernode(i)
-
.
50
100
150
time [usec]
-.
-...
-...-...
E15O N
-...- ..- ..-
- 100
-501
20
10-
fiber node (i)
0
0
50
100
150
time [usec]
Figure 3-3: Membrane voltage behavior for a typical 17 node fiber.
(A-top) The time varying extracellular potential Ve(t) for a stimulus level of 33.0 mA
per phase (i.e. Cscaie = 0.33). The extracellular potential is positive first since this fiber
is closer to the anode in this configuration. In this figure, node index (i) 17 is the most
peripheral dendritic node. (B-middle) The membrane voltage deviation V(t) during
the initiation of an action potential by a super-threshold biphasic pulse with 33.1 mA
per phase. (C-bottom) The membrane deviation due to a sub-threshold pulse with 33.0
mA per phase.
CHAPTER 3. RESULTS
66
I
i
I change
160
~-748 fibers: % change = 0
140
120
100
E2,
(D
80
60
40
20
0
0
0.5
I
I
1
1.5
I
I
I
3
2
2.5
3.5
change in threshold [percent]
I
I
4
4.5
5
Figure 3-4: Sensitivity of fiber threshold to At
Histogram of change in fiber threshold (percent) by changing from a 0.2 ps to a 0.05
ps time-step.
Simulation Time-Step (At)
Stable threshold estimates were obtained using a time-step of 0.2 Ps even though a
transient ringing was present in the membrane-voltage solution following the stimulus
onset and offset. The amplitude of this instability typically decayed to zero within
5 ps, and the solution was otherwise well behaved.
Thresholds were obtained for
a series of 1,354 fibers using a 0.05 ps time-step to evaluate the sensitivity of the
threshold measurement to changes in time-step. As expected, the transient ringing
is not present in the 0.05 ps solutions, but the threshold estimates are remarkably
consistent with those computed using a 0.2 ps time-step. Of the 1,354 fibers recalculated at a smaller time step, 748 showed virtually no change in threshold. The
remaining fibers typically showed a slight increase (<2 percent) in threshold as shown
in figure 3-4.
3.1. MODEL COMPONENT RESULTS
67
Pulse Phase Duration
In the device being modelled, the biphasic pulse intensity is modulated by changing
both the pulse amplitude and phase duration.
Over the range of psychophysical
threshold measurements taken on the patient, the phase duration is varied between 22
ps and 32 As while the amplitude is held constant at 966 pA. In the single-fiber model,
thresholds were calculated by varying the pulse amplitude using a fixed, 30 As phase
duration. Consequently, the comparison of model thresholds (T,) to psychophysical
thresholds (T,) relies on the approximation that the stimulus intensity is simply a
linear function of charge delivered per phase of the stimulus pulse.
To the extent that an action potential is generated when a criterion membrane depolarization occurs, this charge equivalence-approximation should hold for sufficiently
short phase durations. The reasoning being that as the phase duration is shorted such
that the stimulus waveform approaches a series of Dirac delta functions, the nonlinear
voltage dependencies of the ionic currents can be ignored, and the circuit in figure
2-9 treated as a linear transmission line.
To verify this approximation, a subset of relative thresholds were recalculated
using a 23 ps phase duration. Converting these two threshold estimates to charge
delivered per phase allows the pairwise comparison shown in figure 3-5. Here the
threshold estimates obtained using 23 As/phase stimuli are plotted verses the estimates obtained using 30 ps/phase stimuli. Since the model deviation from this
equal-charge approximation was considered negligible, fiber thresholds were not recalculated by adjusting phase durations.
68
CHAPTER 3. RESULTS
-1.MRJi
a
.5
0.
*0
0
02
1000
0
E
C,,
c'J
5,
.5
a
500
a
.5
0
500
1000
relative threshold [nC] using 30 micro second pulse
1500
Figure 3-5: Sensitivity of threshold calculation to pulse duration
The charge-equivalence approximation predicts these points to fall on a line of slope
1.0 passing through the origin.
69
3.2. SPATIAL DISTRIBUTION OF EXCITED FIBERS
Spatial Distribution of Excited Fibers
3.2
The spatial distributions of relative fiber thresholds are shown in figures 3-7 to 3-11
and 3-12 to 3-16 for model renditions 1 and 2 respectively. As explained in figure
3-6, thresholds are displayed in polar coordinates using the angular indexing scheme
of figure 2-2 where the radial distance represents a fiber's relative threshold .
Electrode 1
ELECTRODE 8
270
anode first
0
0.5
1.0
30
15
60
120
90
660
marker
line
30
210
630
cathode first
300
240
1 0r
361-720 degrees
Electrode 1
0-360 degrees
Relative
Threshold
90
540 --
1.5
51
360
~-90
420
480
450
Figure 3-6: Convention for relative threshold polar plots
Each fiber's relative threshold is displayed in polar coordinates using the angular index
of figure 2-2. Since most relative thresholds fall between 0.02 and 1.0, the data are
displayed as points along a linear radius between the 0.0 and 1.0 circular contours.
The angular index begins at the most basal model fiber (0 = 0) and sweeps clockwise
through 720 degrees to index fibers at the model apex. Fibers in the basal turn (0-360
degrees) are shown on the left, and the apical fibers (361-720 degrees) on the right.
Note that fibers indexed at 1 and 360 degrees are not adjacent along the spiral. The
apical neighbors for a 360 degree fiber on the left are located in the right plot starting
at 361 degrees. The angular position of the electrodes in this radial coordinate system
are shown with symbols (0,O) on the 1.0 threshold contour of the basal turn (left plot).
During the initial pulse phase the more apical electrode (0) is anodic and the more
basal electrode (0) is cathodic. The lowest 50 fiber thresholds are highlighted with a
marker-line drawn inside the 0.0 contour circle. For illustrative purposes, only a single
fiber's threshold is shown on the left, while multiple fiber thresholds are shown on the
right.
CHAPTER 3. RESULTS
70
240
600
90
57
30
21
361-720 degrees
630
660
Electrode 1
0-360 degrees
270
300
Electrode 1
0
180
30
15
57
60
120
450
90
Electrode 2
240
Electrode 2
0-360 degrees
270
300
361-720 degrees
630
5190
30
21
600
0
180
15
a
.
60
54
30
60
120
450
90
Electrode 3
240
660
420
480
Electrode 4
0-360 degrees
270
300
600
0
180
90
57
30
21
361-720 degrees
630
660
540
Electrode 4
60
361-720 degrees
630
660
600
51
30
.
*
15
90
'
90
57
450
906
Electrode 4
240
420
480
60
120
54
0-360 degrees
270
300
360
-'90
51
0
21
420
480
450
-0
180
.'30
15
120
-60
90
Figure 3-7: Excitation patterns: RENDITION 1: Electrodes 1-4
71
3.2. SPATIAL DISTRIBUTION OF EXCITED FIBERS
Electrode 5
24
Electrode 5
0-360 degrees
270
300
600
30
21
57
0
180
90
Electrode 6
240
21
600
30
120
540
450
Electrode 7
-
120
0-360
450
Electrode 8
degrees
0
120
90 ''
660
57
0
180""
-
361-720 degrees
630
600
30
21
420
480
300
*
*."...90
.
270
15
6
51
30
90
i*
540
0
.
.
660
57
0
180
15
361-720 degrees
630
600
30
240
420
480
..
Electrode 8
90
.
0-360 degrees
270
300
90
60
-
5.
60
24
f.-90
57
30
-
361-720 degrees
630
660
Electrode 6
0
Electrode 7
420
450
0-360 degrees
270
300
90
*90
480
180
15
60
-
-
21
540
60
120
*90
51
30
-
15
361-720 degrees
630
660
30
90
540
360
51
90
480
420
450
Figure 3-8: Excitation patterns: RENDITION 1: Electrodes 5-8
CHAPTER 3. RESULTS
72
361-720 degrees
630
Electrode 9
0-360 degrees
Electrode 9
270
660
600
300
240
57
30
21
90
0
540
y
180
15
.
;
0
30
..
420
480
60
120
90
51
450
90
Electrode 10
240
-
240
90
60
540
30
..-
60
120
Electrode 11
660
57
0
'
15
361-720 degrees
630
600
30
21
18
Electrode 10
0-360 degrees
270
300
90
450
0-360 degrees
270
300
630
51
.
s. :
90
*.v
**
30
21
420
480
450
0
.
18
degrees
361-720 degrees
361-720
630
12
Electrode 12
Electrode
30
15
60
120
90
Electrode 12
0-360
degrees
270
660
600
300
240
90
57
21
180
30
360
540
0
30
15
51
90
-.
420
480
12060
90
450
Figure 3-9: Excitation patterns: RENDITION 1: Electrodes 9-12
73
3.2. SPATIAL DISTRIBUTION OF EXCITED FIBERS
Electrode 13
240
Electrode 13
0-360 degrees
270
300
600
0
180
60
90
51
450
90
Electrode 14
240
Electrode 14
0-360 degrees
270
300
660
90
57
0
180
540
60
51
30
15
361-720 degrees
630
600
30
21
90
600
12
0
450
90
Electrode 15
240
420
480
60
120
90
540
30
15
660
57
30
21
361-720 degrees
630
Electrode 15
0-360 degrees
270
300
660
600
57
30
21
361-720 degrees
630
90
60
54
1800
450
90
Electrode 16
240
Electrode 16
0-360 degrees
270
300
600
600
0
18
30
15
60
90
361-720 degrees
630
660
660
90
57
30
21
12
420
480
60
120
90
51
30
15
360
540
90
51
420
480
450
Figure 3-10: Excitation patterns: RENDITION 1: Electrodes 13-16
CHAPTER 3. RESULTS
74
Electrode 17
240
Electrode 17
0-360 degrees
270
300
600
0
180
15
57
30
21
23
90
54
60
51
30
480
240
Electrode 18
0-360 degrees
270
300
21
90
54
60
90
(51
30
60
480
240
Electrode 19
0-360 degrees
270
300
600
0
180
90
540,
60
51
30
15.
60
90
480
0-360 degrees
Electrode 20 361-720 degrees
270
600
300
240
420
450
90
Electrode 20
0
180
630
660
90
57
30
21
540-
60
-30
15
9
361-720 degrees
630
660
57
30
21
120
420
450
90
Electrode 19
660
57
0
180
15
361-720 degrees
630
600
30
120
420
450
90
Electrode 18
90
45
60
120
361-720 degrees
630
660
-90
1
60
120
90
9
480L420
450
Figure 3-11: Excitation patterns: RENDITION 1: Electrodes 17-20
75
3.2. SPATIAL DISTRIBUTION OF EXCITED FIBERS
Electrode 1
0-360 degrees
Electrode 1
270
600
300
240
57
30
21
0
180
30
15
90
0
54
90
51
420
480
60
120
450
90
Electrode 2
240
Electrode 2
0-360 degrees
270
300
600
0
180
90
54
9
420
480
60
120
60
-::
51
30
15
450
90
240
Electrode 3
0-360 degrees
270
300
600
361-720 degrees
630
660
90
.-
57
540
30
1
21
361-720 degrees
630
660
57
30
21
Electrode 3
361-720 degrees
630
660
..
a.
60
0
180
51*
30
15
240
420
450
90
Electrode 4
90
.
480
60
120
*.
Electrode 4
0-360 degrees
270
300
600
90
57
300
21
361-720 degrees
630
660
360
54
189
30
--
15
60
120
90
420
450
Figure 3-12: Excitation patterns: RENDITION 2: Electrodes 1-4
CHAPTER 3. RESULTS
76
54
..
...
24.
60
90
56
30
.480 .
*.'.
450-
Electrode
0-360 degrees
270
300
6
.
.26
361-720 degrees
630
600
57
30
--
21
90
3-
90
Electrode 6
.,
-
60
120
s.'
57
180
15
660
600
30
21
361-720 degrees
630
Electrode 5
Electrode 5 0-360 degrees
270
300
24
660
90
.
-*.
.
(
180
30
15
80..
120
450
90
Electrode 7
24
0-360 degrees
270
300
51
90
'-
30
21
54
180
87
Electrode
i60
361-720 degrees
degrees
630
600
15
51
30
-
5757
240
. I..'. .'.
90
90
420
40
90
Electrode 8
90
*-
480
60
120
.7. s
660
54
0-360 degrees
270
300
360
51
'90
30
21
420
480
450
C
18
30
15
60
120
90
Figure 3-13: Excitation patterns: RENDITION 2: Electrodes 5-8
77
3.2. SPATIAL DISTRIBUTION OF EXCITED FIBERS
Electrode 9
240
Electrode 9
0-360 degrees
270
300
57
0
18f
60
51
60
120
90
54
30
(15
9
240
21
40
450
Electrode 10
0-360 degrees
270
300
00
43
600
0
180
90
5
51
30
15
240
450
Electrode 11
0-360 degrees
270
300
600
30
21
0
18
30
15
90
51
90
54
480
Electrode 12
Electrode 12 0-360 degrees
270
600
300
0
180
30
1(5
60
120
90
361-720 degrees
630
660
90
57
30
21
40
450
90
240
361-720 degrees
630
660
57
60
120:0
0
480
60
90
Electrode 11
361-720 degrees
630
660
57
30
120
420
480
90
Electrode 10
660
600
30
21
361-720 degrees
630
360
540....
90
51
420
480
450
Figure 3-14: Excitation patterns: RENDITION 2: Electrodes 9-12
CHAPTER 3. RESULTS
78
Electrode 13
240
Electrode 13
0-360 degrees
270
300
600
30
21
361-720 degrees
630
90
57
0
180
660
54040W
60
-
30
15
480
60
120
Electrode 14
240
Electrode 14
0-360 degrees
270
300
0
.
540"
51
30
15
240
60
--
-.
420
361-720 degrees
630
660
90
57
30
60
I4L
51
30
15
.90
420
480
60
450
90
0-360 degrees
Electrode 16
361-720 degrees
630
270
600
300
0
180
30
15
60
660
90
57
30
21
90
90
.-
-
600
0
12
60
60
..
Electrode 15
180
240
9
450
21
Electrode 16
,
480
0-360 degrees
270
300
120
660
..
90
Electrode 15
361-720 degrees
600
5754066
12
3
630
21
180
420
450
90
540
360
90
51
420
480
450
Figure 3-15: Excitation patterns: RENDITION 2: Electrodes 13-16
79
3.2. SPATIAL DISTRIBUTION OF EXCITED FIBERS
Electrode 17
240
Electrode 17
0-360 degrees
270
300
600
361-720 degrees
630
660
..
57
-'30
21
0
180
0
540
51
30
15
90
480
60
120
90
420
450
90
240
21
Electrode 18
0-360 degrees
270
300
Electrode 18
600
57
30
*
0
180
15
0
51
90
480
60
420
450
90
Electrode 19
240
90
w,
54
30
120
361-720 degrees
,45630
660
Electrode 19
0-360 degrees
270
fuI 300
660
600
30
21
361-720 degrees
630
90
..
57
0
54
0
180-\
51
30
15
480420
60
120
*90
450
90
Electrode 20
0-360 degrees
Electrode 20
240
-.
0
15
60
90
90
--
-
540
360
Su90
51
-30
120
-
57
0
180-
660
600
300
21
361-720 degrees
630
270
420
480
450
Figure 3-16: Excitation patterns: RENDITION 2: Electrodes 17-20
80
CHAPTER 3. RESULTS
Possibly the most salient feature present in these spatial distributions is the eleva-
tion in threshold for fibers positioned at angular indices (0) between those of the active
electrodes. This result is seen in varying degrees for all electrode configurations in the
left (basal) panels of figures 3-7 to 3-16. A similar result has been reported by Frijns
et al. [13, 4] and Hanekom [18]. The explanation for this lies in an analogy to the
electric dipole, where the plane defining points equidistant from the two electrodes 3
is an equipotential plane. Since the excitation of a model fiber is proportional to the
second spatial derivative of the potential along the fiber's length [36], fibers lying in,
or nearby and parallel to, this plane are unlikely to be excited. Interestingly, in many
simulations a secondary collection of fibers with elevated thresholds was observed at
an angular index approximately 180 degrees basal to the active electrode pair. For
example, electrode 1 of rendition 2 shows this pattern in the basal turn. It is likely
that this results from the same equipotential effect as describe above. Fibers in the
apical turn (right panel) did not show a great deal of spatial selectivity, essentially
because action potentials were most often initiated in the axonal sections of these
fibers.
As shown by the marker-line in the polar plots, the 50 lowest threshold fibers were
typically located at 6 just basal and apical to the active electrodes. Accordingly, as
the stimulus level in the model is increased the first fibers recruited typically form
a bimodal distribution over 0 centered on the active electrode pair. This result is
also consistent with the model described by Frijns [13]. Qualitatively these patterns
support the hypothesis that the neural elements closest to the electrode pair are not
necessarily the most sensitive to electric stimulation.
A subtle trend in figures 3-7 to 3-16 is the similarity in thresholds between basal
fibers located near 0-5 degrees and mid-spiral fibers located at 355-360 degrees for
several electrode configurations. These fibers innervate different cochlear turns, yet
the thresholds calculated are often nearly identical as in the first 4 electrodes of
3
This plane is orthogonal to the line connecting the active pair and passes through a point midway
between the electrodes.
3.2. SPATIAL DISTRIBUTION OF EXCITED FIBERS
81
both renditions. This emphasizes the contribution of the fiber's angular position in
determining its threshold in the model. However, the threshold values for the mostbasal fibers may be inaccurate since the orientation of fibers around a single cochlear
axis is not a good anatomical approximation for the most basal fibers in the hook
region.
Analysis of the spatial results are somewhat limited by the fact that no psychophysical data are available for comparison. For example, if the patient's ability to
discriminate individual electrode pairs (e.g. d' measures) were known, these distributions might be used to derive a model-estimate of which electrode pairs the patient
could most easily discriminate.
Overall, the spatial distribution of relative thresholds were quite similar between
renditions 1 and 2.
While difference are apparent, these are most easily seen by
comparing the recruitment of fibers across electrodes.
CHAPTER 3. RESULTS
82
Recruitment Behavior and Dynamic Range
3.3
Histograms of the entire set of relative fiber thresholds across all 20 stimulus configurations are shown in figure 3-17 for both model renditions. Histograms for each
individual electrode are shown in appendix B. By ordering the fiber thresholds in
4
ascending order, the ability of each electrode pair to recruit fibers can be displayed.
The recruitment behavior for model renditions 1 and 2 are shown in figures 3-18 and
3-19.
Rendition 1
ca
2000
2000
1800
1800
1600
1600
1400
1400
Rendition 2
nI
1200
1200
E)
1000
1000
800
800
600
600
400
400
200
200
n I,.
0
1
0.5
Relative threshold
1.5
0
0
0.5
1
Relative threshold
1.5
Figure 3-17: Histogram of relative fiber thresholds
Note recruitment is taken to mean the collective sum of fiber weights from all spiking model
fibers. Since the sum total of spiral ganglion cells counted was 1138, fiber recruitment varies between
0 and 1138 as a function of the stimulus level (Cscaie) for each electrode configuration.
4
83
3.3. RECRUITMENT BEHAVIOR AND DYNAMIC RANGE
Electrode 2
Electrode 1
1200
-
1200
. ./
1000
1000
/
800
600
/-
/-
400
-30
-10
-15
-20
Electrode 3
-25
-5
600
v
400
0 -35
0
V
U)
1200
0
1000
U)
II
/
800
(0
U)
I
600
n
ii:
/
400
V
U)
I-
200
0)
U)
-30
-25
.
.
-10
-20
-15
Electrode 5
.
-5
C
.
800
600
/
400
/
-30
-5
-20 -15
-10
Electrode 7
-25
0-35
800
-o
U)
600
V
400
-30
-25
-5
0
.-
-20
-15
-10
Electrode 6
/
/
/
/
200
0-35
0
0
400
CO
0)
-5
200
1000
U)
-20
-15
-10
Electrode 4
600
1200 -
-c
200
-25
0
0
U)
/
-30
800
V
U)
-I
1000
0-35
.
200
1000
1200
800
'
1200
0-35
a
V)
/-
200
0-35
-
-30
-25
-10
-20 -15
Electrode 8
-5
0
-30
-25
-20 -15
-10
Electrode 10
-5
0
-5
0
1200
1200
1000
U)
1000
800
800
/
600
'0
a)
/-
600
400
400
I-
200
200
0 -35
-30
-10
-20 -15
Electrode 9
-25
-5
0-35
0
1200
V
U)
1200
1000
0
1000
U)
800
CO
U)
.0
600
ii:
-4
800
600
400
V
U)
400
200
-C
0)
200
01
-35
-
-30
-25
-20 -15
-10
Relative Threshold [dB]
-5
0
0
-35
-30
-10
-20 -15
-25
Relative Threshold [dB]
Figure 3-18: Fiber recruitment: Electrodes 1-10
Cumulative weighted fiber recruitment for model rendition 1 (dotted) and rendition 2
(solid). Threshold values are in dB re 100 mA, 30 ps per phase pulse.
84
CHAPTER 3. RESULTS
Electrode 11
Electrode 12
1200
1200
'
1000
cc)
..
800
U-
600
400
a)
V
al)
-30
-25
-20
-15
-10
Electrode 13
-5
0
ai)
1000
a)
200
0
-3 5
800
600
ai)
200
C-)
ci)
0
-25
-20
-15
-10
Electrode 15
-5
0
a)
Cl)
U-
1200
a)
1000
-25
-20
-15
-10
Electrode 16
-5
0
200
0
-3 5
1200
-
600
/-
400
200
Cc)
M
0
ai)
5
-30
-25
-20
-15
-10
Electrode 17
-5
0
'a
0)
I-
1000
/
I
400
800
ai)
a:
600
ai)
.5
U
-25
-20
-15
-10
Electrode 19
-5
0
1200
'0
ai)
Ci,
0
-3 5
800
800
'
/
-30
-25
-20
-15
-10
Electrode 20
-5
0
/
400
200
200
0-3
-35
0
600
/,-
'
-5
1200
-ii: 1000
' "~
-20
-15
-10
Electrode 18
200
1000
'
-25
400
200
-30
-30
1200
a-
/
5
0
-3 5
1000
/
I
800
600
200
Cl)
19AA
600
-30
400
800
ai)
400
400
-5
0)
600
_0
-15
-20
-10
Electrode 14
2M1000
800
Q
-25
1000
600
400
0
-30
1200
800
-30
-
-
1200
5
-
800
400
5
3:
1000
600
200
-I
-30
-25 -20
-15
-10
Relative Threshold [dB]
-5
0
0
-3 5
-30
-20
-15
-25
-10
Relative Threshold [dB]
-5
0
Figure 3-19: Fiber recruitment: Electrodes 11-20
Cumulative weighted fiber recruitment for model rendition 1 (dotted) and rendition 2
(solid). Threshold values are in dB re 100 mA, 30 pus per phase pulse.
3.3. RECRUITMENT BEHAVIOR AND DYNAMIC RANGE
85
The overall shape of these recruitment curves are qualitatively consistent with the
single fiber recordings from cats made by van den Honert and Stypulkowski [52] using
monopolar stimulation. For many electrode configurations, especially the apical-most,
the effect of adding the new bone and soft tissue (as identified in the patient's cochlear
duct) to model rendition 2 was to increase the range of fiber thresholds, making the
recruitment curves in figures 3-18 and 3-19 less steep for the second model rendition.
Overall, adding the tissues unique to rendition 2 had differential effects on recruitment; in some figures the recruitment curve is shifted to the left (i.e. fibers are
recruited at a lower stimulus level), while in others portions of the curve are shifted
to the right, meaning recruitment occurs at a higher stimulus level. Additionally, the
shape of the recruitment curve is often different for the two renditions (e.g. electrode
14).
One striking difference between model renditions is the relationship between the
recruitment curves of electrodes 7 and 10 as shown in figure 3-20. In the first rendition,
the recruitment behavior is very similar such that the recruitment curves in figure
3-20 nearly overlap. In the second rendition, the recruitment by electrode 7 typically
occurs at higher stimulus levels while recruitment by electrode 10 is shifted to lower
stimulus levels. This indicates that adding the additional tissues to the second model
rendition had a substantial impact on the potential field, enough to differentially
impact fiber recruitment even though these two electrode pairs are relatively close to
one another along the array.
Not only is the direction of this effect different for electrodes 7 and 10, but it is
likely the mechanism may be different as well. Histograms of theta for fibers recruited
by electrode 7 (recruitment=400) and electrode 10 (recruitment=200) are shown in
panels A and C of figure 3-21, respectively. These recruitment values are chosen from
figure 3-20 because they reflect where the recruitment curves of renditions 1 and 2
differ.
For both electrode pairs, the pattern of recruited fibers is bimodal across theta,
86
CHAPTER 3. RESULTS
1200endition 1
-
Rendition 2.-
1000 -
800-
Renndition
()
E2
Q(D
2
100
600
(D
~, 400
Rendition 2
,
-
200
0
-35
-30
-25
-20
-15
-10
-5
0
5
10
Relative Threshold [dB]
Figure 3-20: Fiber recruitment: Electrode 7 verses 10
Recruitment by electrodes 7 (solid) and 10 (dashed) in both model renditions.
with a distinct mode of stimulated fibers both above and below the angular position
of the electrodes (marked by X's). While the null separating the two modes5 is shifted
toward the base (lower theta) for electrode 10 compared with 7, the histograms for
rendition 1 (gray) and rendition 2 (black) are remarkably similar for each electrode
individually. This suggests that the difference between renditions 1 and 2 is not the
spatial distribution of fibers recruited. This is confirmed in panels B-C (electrode 7)
and E-F (electrode 10) which show scatter-plots of relative threshold verse theta6 for
the model fibers contributing to the bimodal recruitment patterns displayed in panels
A and C.
For electrode 7 in panels B and C, the difference in single-fiber thresholds between
rendition 1 (gray) and 2 (black) is not very prominent near the position (0) of the
electrodes, but steadily increases for 0 < 175 and 0 > 300.
Accordingly, electrode
7's rendition 1 and 2 recruitment curves do not diverge from each other until the
recruitment value is above around 175 weighted model fibers.
5
1n this region of theta fibers are relatively unlikely to be stimulated given the analogy to the
electric dipole discussed in section 3.2.
6
Note these plots are essentially the respective polar plots of section 3.2 re-plotted on cartesian
coordinates and focused on the most sensitive fibers.
3.3. RECRUITMENT BEHAVIOR AND DYNAMIC RANGE
87
For electrode 10 in panels E and F, the difference in single-fiber thresholds between
rendition 1 and 2 is both in the opposite direction and relatively uniform across
0. Accordingly, electrode 10's rendition 2 recruitment curve is translated to lower
stimulus levels for all recruitment values. In the sense that it impacts fibers at nearly
all 6, the mechanism causing this decrease in single-fiber threshold for electrode 10
seems more "systemic" than, and thus likely to be different from, the mechanism(s)
causing the threshold increases observed for electrode 7.
CHAPTER 3. RESULTS
88
I
r
0.35
60
0.6
I
Sd.
0.3
50
-D
0
-o
0
0
a)
.0
(C) ELECTRODE 7: Upper Mode
(B) ELECTRODE 7: Lower Mode
0.4
x
(A) ELECTRODE 7
70
a)
40
Ia)
30
IU L
0.25
0.4
0.2
W)
I-
.I.-
0.1
10
%h
0.1
0.05
0
,
100
.
200
300
Theta
0 '
100
i
40 0
5C
0
200
150
Theta
(E) ELECTRODE 10: Lower Mode
(D) ELECTRODE 10
.
AA
.
x
x x
0.35 -
4f
250
350
300
Theta
40 0
(F) ELECTRODE 10: Upper Mode
0.
0.3
0.3.
4C
35
0
> 30
25
'a
0
0.25
a)
2!
0.2
CC
0.05
200
S
..
400
100
0
120
140
Theta
160
cps-
0.05
0
300
Theta
1
0.1
0.1
10
5
0.2
*
-
15
0.25
0.15
0.15 F
20
0100
V
Z
0. 15
20
0.5
180
200
250
Theta
300
Figure 3-21: Electrode 7 verses 10
(A) Histograms of theta for fibers recruited by electrode 7 for rendition 1 (gray) and
rendition 2 (black). The position (0) of each contact of the electrode pair is shown by
an "x". (B-C) Scatter-plots of relative threshold verse theta for fibers contributing the
the lower/upper modes of the bimodal distribution present in panel A. Here rendition
1 is in gray and rendition 2 in black. (D) Histograms of theta for fibers recruited
of
by electrode 10 for rendition 1 (gray) and rendition 2 (black). (E-F) Scatter-plots
relative threshold verse theta for fibers contributing the the lower/upper modes of the
bimodal distribution present in panel C.
3.3. RECRUITMENT BEHAVIOR AND DYNAMIC RANGE
89
Range Estimates
The recruitment curves show that, for each electrode, a range of model stimulus
levels can be defined where fibers are actively being recruited (i.e. the sigmoidal
region of the recruitment curve). All the weighted fibers are recruited for levels above
this range, while no fibers are recruited for stimulus levels below this range. This
dynamic range can be estimated for each electrode individually using the stimulus
levels (relative thresholds) required to recruit 99% and 1% of the model fibers. 7 Here
the model range (in dB) can be calculated using the ratio of these two measures,
respectively.
Psychophysically, the maximum-comfortable and threshold levels measured from
the patient also define a range of stimulus levels that result in different sensations for
each electrode. A psychophysical range (in dB) can be calculated using the ratio of
these two measures, respectively.
To the extent that the psychophysical range estimate is substantially larger than
the model range estimate for any particular electrode, one can argue that the modelling results are inconsistent with the patient data. For example, if the patient's
maximum-comfortable and threshold levels [nC] for a particular electrode differ by a
factor of 100 (40 dB), but the model's highest and lowest single-fiber thresholds for
the same electrode vary by only a factor of 10, then an inconsistency in range exists.
To see this, assume threshold occurs in the model by recruiting the single most
sensitive fiber with a stimulus level of Mt. If the patients psychophysical range is
a factor of 100, then one expects that at 100 Mt the model fibers are still actively
being recruited, i.e., 100 Mt is in the model's dynamic range.8 If the dynamic range
of the model ends at 10 Mt then the model does not explain how the patient could
still report different sensations at levels of 100 Mt.
7Note the
9 9 th and 1 st percentiles are arbitrarily chosen instead of the highest and lowest fiber
avoid the influence of outliers.
thresholds
to
8
This argument subtly assumes that the model stimulus levels differ from the device levels only
in scale, without any offset term.
90
CHAPTER 3. RESULTS
Inconsistency in range was not found to be problem, as shown in figure 3-22
where the psychophysical range estimates (x) are plotted along with the model range
estimates from rendition 1 (<>) and rendition 2 (o). Especially for rendition 2, the
model range values are well above the psychophysical ranges, indicating the model is
consistent in this regard.
30-35
4
25 -
0a,) 2
*X ' ' X- -x-
10
x. -x.
-
5 -0'
2
4
6
8
10
12
Electrode
14
16
18
20
Figure 3-22: Range of threshold values
Model range estimates for each individual electrode are calculated using the ratio of
fiber thresholds marking the 1 " and 9 9th percentiles for rendition 1 (0) and rendition 2
(o). The patient's psychophysical range (x) was calculated using the ratio of maximum
comfort level to threshold for each electrode.
3.4. MODEL COMPARISON TO PSYCHOPHYSICAL THRESHOLDS
3.4
91
Model Comparison to Psychophysical
Thresholds
To the extent that behavioral thresholds are determined by the peripheral anatomy
and physiology, the patient-specific model should predict a pattern of relative thresholds across electrodes similar to the pattern of psychophysical thresholds measured
from the patient. In order to make such a comparison, all that is needed is a suitable
metric for deriving a perceptual threshold estimate from the model's collection of
single-fiber thresholds for each individual electrode.
Possibly the simplest metric to generate this estimate is to assume that perceptual threshold occurs in the model when a requisite number (N
) fibers are
recruited.
Accordingly, for any choice of N a (model-derived) perceptual threshold can be assigned to each electrode as the relative threshold of the last fiber needed to meet the
N weighted fiber recruitment criterion. For any choice of N between 1 and 1138, a
model threshold profile can be drawn showing the stimulus intensity needed to recruit
the N fibers for each of the 20 electrode configurations. Electrodes requiring a higher
stimulus intensity to recruit N fibers will show up as peaks in these model threshold
profiles. For the remainer of this discussion, the term thresholdprofile is used to make
the distinction that these are model-derived estimates of psychophysical threshold as
opposed to those actually recorded from the patient (Tn).
Correlating the Tp values with a threshold profile captured at a given N provides
an estimate of whether, and to what extent, the model is capturing an influence
of the peripheral anatomy on psychophysical threshold. The subject's most recent
psychophysical measures are displayed in figure 3-23. Threshold profiles for a subset
of N are shown in figures 3-24 and 3-25 for model renditions 1 and 2, respectively.
The patient's behavioral threshold pattern is reproduced in gray in each plot for
convenience. Both the product-moment correlation-coefficient (r) and the Spearman
rank-order correlation coefficient (rs) are displayed above each plot.
CHAPTER 3. RESULTS
92
Psychophysical Threshold
32[
0 28
Q.
S26 I
c 24
o2
22
2
120
UC
0O
4
6
8
10
12
Electrode
14
16
18
20
Maximum Comfort Level
.
110 100 90 801
)
60
0
2
4
6
8
10
Electrode
12
14
16
18
20
Figure 3-23: Patient psychophysical data
Psychophysical data are presented as the charge [nC] delivered per phase of the biphasic
stimulating pulse.
3.4. MODEL COMPARISON TO PSYCHOPHYSICAL THRESHOLDS
93
Figures 3-24 and 3-25 on pages 94 and 95
Figure 3-24: Threshold Profiles: Model Rendition 1
Threshold profiles (black line/right ordinate) and psychophysical thresholds (gray
line/left ordinate) across the 20 electrode pairs. The model-derived threshold is the
relative threshold value of the last fiber needed to meet the N-fiber criterion. N
ranges from 5 (upper left) to 800 (lower right).
Figure 3-25: Threshold Profiles: Model Rendition 2
Threshold profiles (black line/right ordinate) and psychophysical thresholds (gray
line/left ordinate) across the 20 electrode pairs. The model-derived threshold is the
relative threshold value of the last fiber needed to meet the N-fiber criterion.
ranges from 5 (upper left) to 800 (lower right).
N
CHAPTER 3. RESULTS
94
10 .2
0.11 40
R=0.122
N=15
R=0.101 R =0.124
N=10
R=0.14 R= 0.175
N=5
40
R =0.0465 R =0.0444
N=25
40i
Rs=0.188
0.2
40
0.2
.5
0.15
0.15 35 1
0.15 35 }
35
I-.
0
F-
0.1
0. 05 30
30
0
0.05
0.05 25
0.05 25
25
0
0.1
30
0. 1
30
-v
(L
20
201
0
0
5
0
20
15
10
35
0.3
30
0.22
30
02 301
0.2
0.1
0.1
30 }
0.1
25
0.05 25
10
5
0
15
0.11 25
0
20
'0
20
10
5
0
20
15
10
5
0
15
0
201
0
20
15
10
5
R=-0.0225
N =400
R =-0.0609 R= -0.0644
0. 5 40
N =350
40
0
0.3
35
251
'0
20
20
R=-0.057 Rs=-0.121
0.4
N =300
0. 4 40
R=-0.0855 Rs=-0.101
N =250
40
=-0.174
0.4
R=-0.158
N =200
10.4 40
s=-0.167
0.3
0.15
0.
R=-0.17
N =150
1
20
15
10
5
0
20
15
10
5
0
0
20
0
20
35
35
Z.
0
40
N =100
401
R =-0.0407 R= -0.0356
20
15
R=-0.156 Rs=-0.17
10.4
0.2
N =50
40
10
5
20
s=0.0197
0.5
-
0.3
35
0. 3 35
30
0. 2 30
0.2
25
0. 1 25
0.1
0
0
0
20
10
5
0
15
R=-0.00242 Rs = 0.113
0.5
N =450
40
20
0
20
0
5
10
15
R =0.00637 R= 0.17
N =500
0. 5
40
20 0
0
20
5
10
15
0
20
0
20
10
5
0
20
R =0.0809 R= 0.293
N =600
R =0.0408 R= 0.231
0.5 40
N =550
40
15
1
I50
0.
30
0,
0
20
0
5
10
15
0
1'
40
5
10
15
5
10
15
0
20
10
5
0
15
20
R=0.185 Rs=0.379
N =800
1
40
0
20
R=0.166 Rs=0.338
N =750
i1
i
40
0
20
R=0.141 Rs=0.366
N =700
R=0.113 Rs=0.361
N =650
20
20
20
1
40
0
0.5
30 1
0.5
30
0.5
30
0.
30
0'
0
'
20
0
5
10
Electrode
15
20
0
20
0
5
10
Electrode
15
0
20
o
20
0
5
10
Electrode
15
20
20
0
-
-
5
10
Electrode
Figure 3-24: Threshold profiles: Model rendition 1
15
20
95
3.4. MODEL COMPARISON TO PSYCHOPHYSICAL THRESHOLDS
10.1
40
0.1
R =0.275
N= 15
R =0.266 R=0.254
N=10
R =0.223 R=0.304
N=5
40
R =0.288 R=0.272
N =25
Rs =0.279
10.1
40
0.1
.
40
0
F0.
0.05 30
30
}
0.05
0.05 30
0.05 30
0
20
5
0
'
'
10
15
R=0.193
N =50
40i
20
201
0
10.2
0
20
15
10
5
'0
20
R =-0.00082
0
20
s=
20
15
10
5
0
20
15
10
5
0
N =150
R=0.0248 Rs =0.127
0.2 40
N =100
40
Rs=0.229
35
0
0
0. 2 40
R =0.0228 R, =0.05
0.4
N =200
0.0641
0.15 35
0.1 5 35
0.15 35
0.3
0. 1
0.2
0. 05 25
F-
30
0.113
0
0.1 30
25
0. 05 2 5
0.0 5 25
0.
0
20
15
10
5
0
R=0.0774
N =250
10
5
0
15
5
10
0
15
40
0.10
20
0.
20
10
5
0
R =0.239 Rs =0.224
0.5
N =350
10.4
0, 4 40
0
20
R=0.147 Rs=0.196
N =300
Rs =0.15
40
20
0
20
20
30
R =0.317
N =400
15
20
R= 0.3
0.5
40
~0
.5
II,
0.3
35
0. 3 351}
Fa
30
0. 2 30
0.2
0
25
01
0.1
25
020
0
5
10
15
0
20
R =0.368 R, =0.282
0.5
N =450
40
20
10
5
0
R =0.341
N =500
40
15
I-.
0
20
0
0
20
0
'
10
5
0
15
20
201
0
0.5
15
10
20
R=0.277 Rs =0.176
0.5
N =600
R=0.303 Rs=0.15
N =550
As =0.268
10.5 40
10
5
40
.5
I-.
0
0
3
0
5
0
10
15
0
20
5
1
10
15
40
20
0
20
R=0.227 Rs =0.164
1
N =700
R =0.257 R =0.2
N =650
40
0
'
20
'0
20
5
10
R=0.192
N =750
15
0
20
Rs=0.161
1
40
20
0
'
'
'
5
10
15
0
20
R=0.14 Rs =0.0853
11
N =800
40,
B
C.
.5-
0.
30
5 30
0. 5
0.5
0. 5 301
30
0
0.
0
20
0
5
10
Electrode
15
20
20 L
0
'0
5
10
Electrode
15
20
0
20
0
5
10
Electrode
15
20
0
20
0
10
5
Electrode
Figure 3-25: Threshold profiles: Model rendition 2
15
20
CHAPTER 3. RESULTS
96
The threshold profiles of figures 3-24 and 3-25 show a few notable qualitative similarities with the psychophysical thresholds. The Tp measures are essentially bimodal,
with elevated thresholds at electrodes 7-9 and 17-19. Other smaller fluctuations in
the Tp values are present, but since the magnitude of these fluctuations is close to the
step size used by the device to modulate intensity (5 nC per phase of the stimulating
pulse), they may not be significant (see discussion sections 4.1-4.2).
For both model renditions, there are several threshold profiles where a similar
bimodal pattern is present. For example, N = 5 in rendition 1; and N = 15 and N
= 450 in rendition 2 show this pattern. Possibly the strongest similarity between the
model and patient data is the prominent peak in the rendition 2 threshold profiles
near electrode 7 for values of N ~ 25 and N> 200. The strongest dissimilarity tends
to occur at electrode 20, which is typically elevated only in the model results.
Since N is a free parameter, the product-moment and Spearman correlation coefficients for every possible choice of N were calculated and are shown in figures 3-26A
and 3-26B for renditions 1 and 2. While the product-moment correlation coefficient
(r) is a widely used, and intuitive measure of linear correlation, it is a relatively poor
statistic for evaluating significance unless it is fairly certain that the data are from
a bivariate normal distribution [37]. Since no such certainty exists for this data set,
the Spearman rank-order correlation coefficient (rs) is relied on as the primary test
of significance. 9
The value of r, that denotes statistical significance is shown in the panels of figure
3-26 with a horizontal dotted line. A statistically insignificant positive correlation
9
Statistical significance is taken as p <0.05 (two-tailed) using the relation
t = r,
1r 2
(3.1)
where r, is the Spearman coefficient, n is the number of items in the data set, and t distributes as a
Student's t with n-2 degrees of freedom. This nonparametric measure of correlation is more robust
since it does not rely on the distributions from which Tp and the threshold profile values were drawn
[14, 45]. However, there is a loss in statistical power since all magnitude information is lost in the
rank-ordering process.
3.4. MODEL COMPARISON TO PSYCHOPHYSICAL THRESHOLDS
97
exists for many values of N for both model renditions (figures 3-26A and 3-26B).
However, it is interesting to note that the second rendition posts mostly positive
correlations over a range of N between 1 and 800. Since the elevated apical T, values
near electrode 7 seemed to be represented in the threshold profiles of model rendition
2 over a range of N (see N 250-750 in figure 3-25), the data were split to examine the
correlation in the basal and apical sections of the model individually. Accordingly,
the correlation plots across N are repeated using the apical 12 subset and basal 12
subset of electrodes in figures 3-26 C-D and figures 3-26 E-F respectively.
For the basal 12, no values of N yielded a significant correlation. Reasons why
the model may be more likely to capture the influence of the anatomy for the apical
electrodes as opposed to those near the base are discussed in the next chapter.
For the correlations calculated using the apical subset of electrodes (figures 326C and 3-26D), two distinct regions warrant further discussion: the insignificant
correlations occurring for N e-z 1-60 in both renditions and the significant correlation
over N - 350-700 in rendition 2.10 While the evidence for a correlation is strongest
for N ~ 350-700 in rendition 2, the weaker correlations near N - 1-60 better fit with
the intuition that perceptual threshold likely occurs after stimulating only a relatively
small population of neurons.
This intuition follows from a host of examples in the auditory system where remarkable efficiently is a recurring theme that allows for the encoding of an enormous
range of sound frequencies and intensities. A system where perceptual threshold is
reached only after stimulating a large percentage of the neural population is expected
to be much less efficient than one where perceptual threshold occurs after stimulating
only a few fibers. Further support for this intuition comes by analogy to research done
on tactile perception where researchers have found perceptual threshold to occur after
stimulating only a single tactile afferent fiber [51].
Bearing in mind that the normal human is expected to have an afferent fiber popu'This result was not sensitive to choosing 12 as the number of points in the subset. For example,
splitting the data into to apical/basil 11 or 13 yields the same result.
CHAPTER 3. RESULTS
98
lation of nearly 30,000 fibers [41], we might estimate this subject to have had a total of
approximately 8,000 fibers remaining." Accordingly,threshold profiles captured from
the model with N ~ 450 correspond to stimulating about 3,150 neurons; a number
that seems too high to fit with our notion of efficiency. However, it is not impossible that the connections of these 8,000 afferent fibers to the central nervous system
may be compromised such that only a small percentage of afferent spikes successfully
propagate through the normal auditory pathways to contribute to perceptual threshold. Regardless, none of these arguments satisfactorily address the problem of which
value(s) of N should be selected as a criteria for estimating perceptual threshold.
Only future research can answer that question.
Collectively, these observations are consistent with a weak correlation occurring
mainly in the apical electrodes of rendition 2. The strongest support for this comes
from the fact that, with a few exceptions, the correlation was always positive and
reached statistical significance over a range of N between 400-700.
10
"This estimates comes from multiplying the 1,138 counted ganglion cells by 10 (since only every
th section was counted) and then multiplying by a correction factor.
99
3.4. MODEL COMPARISON TO PSYCHOPHYSICAL THRESHOLDS
(A) Rendition 1: Electrodes 1-20
1
. . . . . . .. . . .. . . .
0.5
(B) Rendition 2: Electrodes 1-20
1
0.5_
C
U)
.5
U)
-..
8
C
0
0
0
0
ii
cc3
0
0
-0.5
-0.5 l-
-1
-1
400
200
0
600
800
200
0
1000
400
600
800
1000
(D) Rendition 2: Electrodes 1-12
(C) Rendition 1: Electrodes 1-12
0.5
0.5
0
0
0
0
0
C)
0
-0.5 [
-0.5 F
-1
0
200
400
600
800
-1
-1
1000
0
200
400
600
800
1000
(F) Rendition 2: Electrodes 9-20
(E) Rendition 1: Electrodes 9-20
1
0.5
0.5 I
0
.2
0
0
0
0
CU
0
-0.5 -
-0.5 .
-1
-1
0
200
800
600
400
fiber recruitment (N)
1000
0
200
800
600
400
fiber recruitment (N)
1000
Figure 3-26: Correlation verses N
coeffiShown are product-moment (black line) and Spearman (gray line) correlation
significance
cients for all values of N. The horizontal line (dotted) indicates statistical
(p<0.05).
100
CHAPTER 3. RESULTS
Chapter 4
Discussion
4.1
Model Methods and Assumptions
Fiber-tracks
As with any model, some anatomical features were captured while others neglected.
While the nonuniform distribution of ganglion cells is probably captured due to its
calibration against visually counted cells, the fiber trajectory may not be.
As pointed out by Plonsey [36], the excitation strength of an extracellularly applied field on a nerve fiber is proportional to the second spatial derivative of the potential along the fiber's length. Accordingly, the excitation of the single-fiber model
depends on the second spatial derivative as in equation 2.23. In the model this spatial
derivative is governed by: (1) the potential field solution, (2) the spatial fiber-track
trajectory through the model, and (3) the interpolation method used to estimate the
potential at the model fiber's nodes of Ranvier that fall between potential nodes of the
field estimation grid. Consequently, the ad hoc methods used to add fiber-tracks to
the model undoubtedly influenced the threshold calculations. Since the subjectively
chosen cochlear-axis and ad hoc tracing schemes were not systematically varied and
thresholds recalculated, the sensitivity to these parameters is not known, and should
be the focus of future work.
101
CHAPTER 4. DISCUSSION
102
Fiber-tracks were added to the model using the approximation that all fibers are
oriented around a single cochlear axis. Consequently, the most-apical fibers are less
likely to be accurately represented given the ambiguity in assigning 0 discussed in
section 2.1. Likely of more concern are the model-fibers near the base. For these
basal-most fibers this approximation is essentially a gross misrepresentation of the
anatomy, since in the human cochlea these afferent neurons do not converge toward
the same axis as fibers from higher cochlea turns (i.e. there is no single central-axis
these fibers converge toward, as in figure B-3 of appendix B). Given the anatomical
inaccuracies of these basal fiber-tracks, which are typically recruited first by basal
electrode pairs, it is not surprising that the threshold correlations tended to occur
mostly for the more apical electrodes pairs.
One question certainly worth addressing is whether these "anatomically-inaccurate"
fibers contribute substantially to the correlations observed for the apical 12 subset of
electrodes in figure 3-26 C-D. If these unreliable fibers (e.g. those closest to the base
with 0 < 30 and the most apical with 0 > 480) are removed from the model, similar
positive correlations are observed for both model renditions (figure B-4 of appendix
B).1 This suggests the contribution of these fibers to the correlations observed for the
apical 12 subset is small. The reason for this is that the fiber recruitment underlying
the observed apical correlations is mostly localized to values of 0 toward the middle
of the spiral (figure B-5 of appendix B).
Recruit-N Criterion for Estimating Model-Derived Perceptual
Threshold
The comparison between model and psychophysical data relies on the assumption
that perceptual threshold occurs in the model cochlea when a requisite N fibers
are recruited. While this assumption has several weaknesses discussed below, there is
some indirect evidence that this approximation may be an appropriate starting point.
1
Curiously, a region of anti-correlation appears in this truncated model for rendition 1 (N between
100 and 400), although the patterns of positive correlation remain similar.
4.1. MODEL METHODS AND ASSUMPTIONS
103
Recent advances in implant technology have afforded researchers the ability to
record the electrically-evoked compound action potential (ECAP) from inactive electrodes during electric stimulation. Previously these measure were only available intraoperatively [14] or with patients using the Ineraid implant system [5], which utilizes a
percutaneous plug to connect the sound processor to the electrode array. The ECAP
can be interpreted as the collective sum of electric activity as the action potentials
from the stimulated fiber population travel down the auditory nerve toward the brainstem [34]. For fibers with action potentials originating along the axonal process, the
antidromic component also theoretically contributes to this gross potential. Accordingly, the ECAP as recorded from an intracochlear electrode can vary depending on
the synchrony and location of the generated action potentials.
Several researchers have reported correlations (e.g., r a 0.7-0.85) between the
threshold stimulus level required to detect an ECAP and the psychophysical threshold level [6, 7, 55, 12, 22].
Under the assumption that the ECAP amplitude is a
monotonically increasing function of only the number of spiking fibers, 2 then psychophysical threshold should be be correlated with the stimulus level required to
excite some requisite number of fibers, which then give rise to an ECAP of some
requisite (detectible) amplitude.
Two lines of evidence support the notion that ECAP amplitude may be a near
linear function of the number of spiking fibers. First, and certainly more convincing,
Hall [17] reported a strong correlation (r= 0.75-0.92) between the maximum elicited
ECAP amplitude (all viable fibers stimulated) and the number of remaining spiral
ganglion cells in animals with graded cochlear lesions. 3 The second argument stems
from the work of Wang [53], who estimated single-unit contributions to the CAP
in hearing cats. These were successfully used to synthesize a model-predicted CAP
whose N1 (first negative wave) amplitude was consistent with that of the experimen2
This essentially assumes that all fibers contribute equally, regardless of differences in fiber position or size.
3
Note in this study the amplitude of the ECAP was measured at the brainstem, not intracranially.
CHAPTER 4. DISCUSSION
104
tally measured gross potential. Given (1) the lack of a systematic change in unit
response amplitude verses CF reported by Wang, (2) the expected synchrony of spike
initiation during electric stimulation, and (3) the presumably negligible differences in
spike latency for a reasonably small cluster of fibers, one might predict the threshold
ECAP amplitude to reflect the nmmber of spiking fibers. In fact, modelling work
by Miller et al. [29] similar in methodology to that of Wang, but using data from
electrically-stimulated nerve fibers, concluded that variable fiber latency has only a
small effect on the ECAP growth function, and therefore there are likely only small
differences between the growth functions of the ECAP amplitude and the simple
count of spiking fibers.
However, there are a few arguments against assuming that perceptual threshold
occurs with the recruitment of some fixed number of fibers. For example, this can
only be the case if the spatial distribution of recruited fibers is irrelevant to the
perceptual detection task, a concept that is known to be false in the normal ear. With
hearing subjects, psychophysical threshold and loudness percepts are often explained
in the framework of an auditory filter-bank. Near threshold, sound energy within an
auditory filter can be integrated, while sound energy within adjacent filters can not.
Consequently, the threshold level for detecting a narrowly spaced tone-complex falling
in a single auditory filter will be lower than that of a similar tone-complex with widely
spaced frequency components falling in adjacent auditory filters. If the concept of
an auditory filter is applied to the psychophysics of electric hearing, then we expect
the recruitment of N closely spaced model-fibers to induce a different psychophysical
percept than the recruitment of N model-fibers dispersed over a wide range of angular
indices.
Additionally, given the potential for changes that may differentially occur in more
central portions of the auditory pathway in the hearing impaired, the possibility exists
that exciting two similar populations of fibers will not result in the same perceptual
threshold, even if the populations are nearly identical with regard to the total number
4.1.
MODEL METHODS AND ASSUMPTIONS
105
and distribution of excited fibers. This is especially a concern given the variety of
congenital and non-congenital etiologies that may bring about hearing loss at various
ages. However, it is unlikely that in the near future such centrally mediated influences
will be well characterized.
Psychophysical Measurement Error
One issue that limits the correlation between model-derived and measured behavioral
thresholds is the a priori accuracy of the psychophysically measured thresholds, which
range between 71 and 92 clinical units (21.5 -31.7 nC/phase).
These values contain measurement error due to: (1) quantization, since the stimulus level is varied in discrete increments of ~ 5 nC/phase, and (2) the test-retest
variability associated with all psychophysical measures. Consequently, the measured
threshold levels can be considered as the sum of the actual psychophysical thresholds
and the, presumably zero-mean, measurement error. 4
To the extent that perceptual thresholds are determined by peripheral mechanisms, we might expect the model to capture some percentage of the variation in
threshold 5 across electrodes. However, even in the hypothetical context that (1) the
variation in psychophysical threshold across electrodes is completely determined at
the periphery and (2) the model is perfect, the measurement error places an upward
4
Here we consider the actual threshold measures as stationary, and describe the test-retest variability, attention-related variability, and quantization noise in this single error term. This error is
presumably uncorrelated across electrodes, and uncorrelated with the true threshold value.
5The square of the measured correlation coefficient (r 2 ) is referred to as the coefficient of determination, which is interpreted as the proportion of variance in one measure that can be accounted
for by the other [45].
CHAPTER 4. DISCUSSION
106
bound on the percentage of the threshold variance that can be predicted by the
model.6
Given that we have only one set of psychophysical observations, we can not quantify the measurement error except to use approximations based on the observations
of other Nucleus implant users. Here we rather arbitrarily estimate the measurement
error (95% confidence interval) to be ± 2 nC, or equivocally ± 4 clinical units. 7 Casual observations by members of the Audiology Department at the Massachusetts Eye
and Infirmary suggest that the test-retest error is likely to be much less than this for
a user of the Nucleus device; nevertheless, we choose ± 4 clinical units as a conservative upper bound for our discussion. Using this error estimate, and the variance
observed in behavioral threshold measures across electrodes(var(T,)), the theoretical
maximum percentage of variance the model can predict is ~ 88% (i.e. r=.94). 8
For this reason, patients selected for deriving future models should show large
differences in threshold across electrodes, at least as large as those observed here.
Even better would be a patient with multiple sets of psychophysical data so that the
measurement error and stationarity of the threshold measures could be examined.
Additionally, the next patient selected should have a pattern of threshold measures
dissimilar to the bimodal pattern seen in this patient in order to test whether the
model can predict a wide range of psychophysical threshold patterns.
'More precisely, the coefficient of determination (p2 ) is limited by the ratio of the measurement
error variance (ut) to the true threshold variance (a2 ) as:
2
2
at
+
m(4.1)
02
M
Conceptually the variance in behavioral threshold across electrodes at might be further partitioned
into the variance that results from independent peripheral (-2)
and central (k) factors such that
02 = 0 2 +0 2 . Here we simply assumed that o2 =0.
'Here the measurement error is assumed to distribute as a zero-mean gaussian (o = 1.125)
quantized into 0.5 nC steps such that ~ 95% of the error values are between -2 nC and 2 nC
inclusive.
8
Variability due to central factors (at) only decreases this percentage.
4.2. DISCUSSION OF MODEL TRENDS
4.2
107
Discussion of Model Trends
For convenience, the patient's psychophysical threshold measures are reproduced below in figure 4-1 with hypothetical error bars representing + 4 clinical units (see
previous section). Figure 4-1 shows that after including this ad hoc expectation of
measurement variability, there are, arguably, three salient trends in the patient's
behavioral thresholds:
Trend #1
-
a peak centered on electrodes 7-9
Trend #2
-
a steady increase from electrode 14 to 19
Trend #3
-
a decrease from 19 to 20
34
-
32-
0. 30-
.C
co
70
c
0
282624-
C)
IL
222018
-
0
5
10
Electrode pair
15
20
Figure 4-1: Psychophysical thresholds with hypothetical error bars.
The error bars (± 4 clinical units) represent the 95% confidence interval
for the ad hoc measurement noise described in the previous section.
Careful examination of the threshold profiles in figures 3-24 and 3-25 shows that
the first two of these trends are present in varying degrees for selected N in both
renditions.
CHAPTER 4. DISCUSSION
108
Trend #1
Possibly the strongest similarity between the model-derived and behavioral thresholds
is the distinctive decrease in model threshold moving from electrode 7 to 10, consistent
with the right half of the peak in behavioral thresholds at electrodes 7-9. This decrease
in the threshold profile is present for nearly every choice of N in rendition 2 (fig. 325), where for values of N above ~ 200 it represents half of a peak in the model
profile centered on electrodes 7-8 that is consistent with the the peak in behavioral
thresholds.
However, in the model-derived estimates, electrode 9 is typically not
included in this peak of elevated thresholds, whereas in the behavioral estimates it
is. For rendition 1, this peak is also weakly present only for very low N (see N = 5
of fig 3-24).
A major difference between renditions 1 and 2 is that only in rendition 2 is there a
substantial peak in predicted thresholds near electrode 7 for N > 200. The difference
in model-derived thresholds between electrodes 7 and 10 is the result of adding new
bone and soft tissue to the model as discussed in section 3.3. A detailed analysis of
the influence of the new bone and soft tissue on the potential field is beyond the scope
of this thesis, but should be the focus of future work. However, it is certainly the case
that the impact of new bone and soft tissue can be both substantial and complex,
and thus unlikely to be captured with a transmission line or 2D modelling approach.
Trend #2
Also present to varying degrees in the threshold profiles of rendition 1 and 2 is the
steady increase in thresholds from electrode 14 to 19. Variation across electrodes
in the model-derived thresholds is a result of: (1) the nonuniform distribution of
weighted fibers along the length of the cochlear spiral (theta), and (2) differences in
single-fiber thresholds across theta resulting from the complex model geometry, new
bone and soft tissue, and the position of the active electrode pair. The nonuniform
distribution of weighted fibers is shown in the histogram of figure 4-2A. Centered on
4.2. DISCUSSION OF MODEL TRENDS
109
O ~ 100 is a gap region almost completely devoid of model fibers. For many values of
N this gap partially explains why the model-derived thresholds increase for electrode
pairs from 13 to 20. As the stimulated electrode pair moves from 13 toward the
base, the area being excited by the electrodes is increasingly likely to include this gap
region. The impact of this is shown in panels B-I of figure 4-2, where the angular
distribution of excited fibers for an N = 50 criterion is displayed for odd electrode
pairs between 5 and 19.' For electrode pairs 5-13 in panels B-F the stimulated subset
of fibers form a bimodal distribution that translates across 0 as the position of the
electrode pair (X's in figure ) moves toward the base. For model electrode pairs 15-19
(panels G-I), a portion of the expected bimodal region of excitation falls in the gap
where very few fibers are present; consequently, higher stimulus levels are needed to
recruit more distant fibers (i.e the model-derived thresholds are elevated). While this
provides a partial explanation of why the patient might have elevated thresholds for
electrodes toward the base (trend #2), it does not explain why the patient's threshold
for electrode pair 20 was relatively low (trend #3).
Nevertheless, these observations
show that the distribution of remaining nerve-fibers is likely an important factor in
determining perceptual threshold.
In order to evaluate the relative influences of the nonuniform fiber distribution
verses the variation in fiber threshold imposed by the model geometry, future work
should include a model repopulated with fibers spread uniformly across 0. Comparisons between these two models would help differentiate the influences of fiber density
from the influences of the model geometry.
9
Data from rendition 2
CHAPTER 4. DISCUSSION
110
(A) Weighted fiber density verse theta
50
C) 40
30
20
-C
.9 10
0
0
100
200 300 400 500
(B) Electrode Pair 5
600
70
(F) Electrode Pair 13
30
15
.x
x x
10
20
0
(
0
U)
10
0
)
100
200 300 400 500
(C) Electrode Pair 7
30
600
0
0
70
100
20
200 300 400 500
(H) Electrode Pair 17
600
70 0
200 300 400 500
(1) Electrode Pair 19
600
70 0
200
600
70 0
nL...
30
o
30
20
10
10
40
70 0
x x
40
100
600
50
xx
0
200 300 400 500
(G) Electrode Pair 15
200 300 400 500
(D) Electrode Pair 9
600
00
7C0
25
xx
100
-
x x
020
30
o
20
15
0I
.05
10
5
0
0
100
200
300
400
500
600
0
0
7C0
100
(E) Electrode Pair 11
30
25
xx
x x
20
0 20
15-
(
10
10
5
A
0
100
200 300 400 500
Theta [degrees]
600
7C0
0
0
100
300 400 500
Theta [degrees]
Figure 4-2: Distribution of weighted fibers across 6
(A) Histogram of weighted fibers across 0 (B-I) Histogram of recruited fibers under the
N = 50 criterion for odd numbered electrode configurations 5-19. The angular position
of each electrode of the stimulatus pair is marked with an "x". The 0 bin width is 10
degrees. Data from rendition 2.
4.2. DISCUSSION OF MODEL TRENDS
ill
Trend #3
One glaring discrepancy between the model-derived and behavioral threshold patterns
occurs at electrode 20. While the patient's psychophysical threshold is among the
lowest for electrode 20, the model predicts an elevated threshold for electrode 20 for
many choice of N (see figures 3-24 and 3-25). Since this is the most basal electrode
pair, to some degree, it may be considered the least reliable given the anatomical
inaccuracy of fiber-tracks toward the base discussed in section 4.1. Furthermore, the
more basal point-source of electrode pair 20 is relatively close to the X-Z boundary
plane of the model, raising the suspicion that the potential field solution for this
particular electrode pair may contain artifacts from the boundary condition.
In fact, plotting the correlation verse N with only electrode pair 20 removed yields
two regions of significant correlation in rendition 2, as shown in figure B-6 of appendix
B. Future model renditions using more anatomically accurate fiber-tracks at the base
and more isolation from the influence of the model boundary may provide a better
correlation for the basal electrode pairs.
Correlation Results
The degree to which similarities were present between the model-predicted threshold
patterns and those measured psychophysically were quantified by measuring the correlation coefficient between the two sets of measures. Regardless of the the model's simplifying assumptions (e.g. only three physiological tissues represented, point-source
electrodes) anatomical inaccuracies, (e.g. basal fiber-tracks, guinea pig nerve-fiber dimensions) and subtle methodological weaknesses (e.g. forward-euler method), there is
still moderate evidence for a correlation between the model-predicted and behavioral
thresholds for the apical set of electrodes. The strongest support for this correlation
comes from rendition 2, where the observed correlations in the apical subset (figure
3-26D) were always positive below N = 1000 and had peaks as high as r=0.57 (@N
=20) and r=0.82 (LN =417), indicating that for these particular choices of N the
CHAPTER 4. DISCUSSION
112
model predicts 32% and 67% of the variance in the behavioral measures (for the apical
12 subset). By measuring the correlation for a subset of electrodes toward the apex,
the correlation required to achieve statistical significance increases. Accordingly, only
the second of these peaks is significant, even though the first may be of more interest given our expectation that a relatively small N be used in estimating behavioral
thresholds. Admittedly, our interpretation of these results is certainly limited by the
choice of N, however under the hypothesis that no correlation exists (i.e. p=O), we
might certainly expect to measure a negative correlation for some values of N less
than 1000.
It should be noted that this treatment makes three crucial assumptions: (1) variation in the measured psychophysical thresholds across electrodes (o2 ) results from
the influences of the peripheral anatomy, centrally-mediated factors, and measurement error; (2) these three influences are treated as independent such that we can
simply partition the observed variance (o 2)
as the sum of the individual variances,10
and (3) the variation in behavioral thresholds due to an influence of the peripheral
anatomy is on the order of, or larger than, the variation imposed by central influences. Admittedly, it is possible the influence associated with central mechanisms
could be much larger than that of the periphery. In such cases, this modelling approach would not be expected to predict a substantial portion of the variation in
behavioral threshold across electrodes. However, this scenario seems unlikely given
the reported correlations between behavioral thresholds and ECAP-predicted thresholds.
It is not the focus of this work, nor can this work address the question of the
extent to which peripheral mechanisms are primarily responsible for the variation in
"In other words, the variation imposed by the periphery, by central mechanisms, and by measurement error are unrelated such that knowledge of one does not change the expectation of another.
More precisely, we are treating each behavioral threshold value as the sum of three independent random variables that describe: the threshold due the peripheral influence (X 1 ), the central influence
(X 2), and measurement error (X 3 ). Accordingly, the variance imposed by these three collectively is
simply the sum of the individual variances, i.e., var(X 1 + X 2 + X 3 ) = var(Xi)+var(X 2)+var(X 3 )
[8].
4.2. DISCUSSION OF MODEL TRENDS
113
psychophysical thresholds. Only a series of such models might be able to approach
answering this question. It is simply taken as an underlying assumption of this work
that a peripheral influence is likely a substantial one that can be captured by a
patient-specific model.
Spatial Excitation Patterns
One interesting question that arises is the extent to which the spatial distribution
of the fibers stimulated by one electrode is distinct from other electrodes, especially
for higher values of N. If the collection of excited fibers is essentially the same for
each electrode, then one can argue that the model results are not consistent with the
patient's ability to discriminate speech sounds."-" In general, the results show that
the pattern of excitation is different between electrodes even for relatively large N.
For example, two representative polar plots of the fibers recruited at N
=
450 are
shown in figure 4-3.
Also illustrated in figure 4-3 is the tendency at higher values of N for fibers to
be recruited from adjacent turns of the cochlea (e.g. those with 6 ~ 675). Should
this "cross-turn" recruitment actually occur in the implanted ear, it would essentially
deliver afferent spikes to the CNS from cochlear regions not intended to be stimulated.
Besides highlighting the complexities of electric stimulation of the auditory nerve,
this model makes several predictions that can be investigated further with psychophysical experiments. One example is the tendency for the recruited fibers to
form a bimodal distribution along the cochlear length (e.g. figure 4-2 B). This occurs
since the fibers positioned between the electrodes typically have elevated thresholds;1 3
a result that has also been reported by Frijns et al. [13, 4] and Hanekom [18].
"This argument considers only the spatial or frequency cues used for speech perception without
considering temporal cues.
12
The patient's most recent speech scores were:
92% CID Everyday Sentences Test
71% Iowa Medial Consonant Recognition Test
28% Monosyllabic Word Test
13
See spatial distributions in figures of section 3.2
CHAPTER 4. DISCUSSION
114
Given the complex interaction between the computed potential fields and the nonuniform distribution of surviving nerve-fibers observed in this patient, to some degree
it is not surprising that simple measures such as the total number of surviving ganglion
cells have not been found to correlate with speech perception scores. Finding an single
anatomical attribute that correlates with speech reception is likely to be much more
complicated that counting the total number of remaining ganglion cells.
Electrode 5
Electrode 5 0-360 degrees
270
300
24
600
0
180
30
15
90
54
60
90
51
60
120
450
Electrode 8
Electrode 8 0-360 degrees
270
300
240
30
60
660
57
0
180
15
361-720 degrees
630
600
30
21
90
420
480
90
120
660
57
30
21
361-720 degrees
630
90
0
6060
540
90
51
420
480
9
450
Figure 4-3: Rendition 2 (N = 450), Electrodes 5 and 8
See figure 3-6 for conventions. Polar plots for N = 450 show that the recruited populations are not completely overlapping and may contain fibers from adjacent cochlear
turns, as it the case here where fibers at 0 ~ 675 have been recruited.
4.3. RECOMMENDATIONS FOR FUTURE WORK
4.3
115
Recommendations for Future Work
Given the results reported here, future work should focus on three issues: (1) increasing the anatomical accuracy of the most apical and, more importantly, the most basal
fiber-tracks, (2) increasing the accuracy with which ganglion cells are segmented and
the frequency with which they are calibrated against visual cell counts, and (3) estimating a suitable value of N by comparing a series of models. Additionally, many
changes could be made to each individual part of the modelling technique as listed
in appendix C. One serious weakness of the modelling technique presented here is
that formulating the model is very time consuming (> 1.5 months), a problem that
may be alleviated by automating portions of the segmentation process, or possibly
by switching to the finite-element approach.
4.4
Conclusions
The purpose of this thesis was to investigate the feasibility of generating a patientspecific model with sufficient detail to address two questions:
1. Can such a patient-specific model of the implanted cochlea be used to capture
the influence of the peripheral anatomy on psychophysical thresholds?
2. To what extant does the inclusion of new bone and soft tissue, which typically
invade the implanted cochlea, influence the neural recruitment observed in these
models?
While the results presented do not answer either of these questions unequivocally,
they do suggest that a patient-specific model used to predict psychophysical thresholds is probably feasible, and worth pursuing. The observed similarities between
the model-derived and measured perceptual thresholds suggest this simple model is
at least beginning to incorporate some of the relevant anatomical features necessary to capture the intricacies of electric stimulation at a patient-specific level. This
CHAPTER 4. DISCUSSION
116
conclusion is tempered by the observation that, as of yet, many of the subjective
parameter choices in the model (e.g. cochlear axis, dendrite representation) have not
been systematically varied to test their influence on the results. Of course, the extent to which this modelling technique truly captures the influence of the peripheral
anatomy on psychophysical thresholds will only be clear after several other models
derived from different patients are tested for their ability to predict different patterns
of psychophysical threshold. A collection of models will also likely provide evidence
of whether there is a suitable choice for N that maximizes the correlation across all
models.
Based on the results reported here, a critical part of future models will likely be
the inclusion of the new bone and soft tissue that infiltrate portions of the implanted
cochlear duct. These modelling results support the importance of these tissues for
primarily two reasons: (1) the inclusion of these tissues substantially changed the
shape of the recruitment functions and (2) for many values of N one effect of including
these tissues was to increase the correlation between model-predicted and behavioral
thresholds. While it may be the case that new bone and soft tissue deposits influenced
thresholds measures in this patient more than most, the results certainly argue that
including these tissues makes a difference and should not be neglected.
Incorporating changes to this preliminary approach may eventually yield a collection of patient-specific models that fairly accurately predict psychophysical thresholds. Because cochlear implants have been in use for well over twenty years, donated
temporal bones representing a wide range of anatomies (e.g. different distributions
of spiral ganglion cells and patterns of new tissue formation) are an increasingly
more available resource that can be used to refine such patient-specific models. It
is hoped that a collection of these histologically-derived models will eventually help
reveal anatomical differences, patterns of electrode position, and other peripheral
features that account for the differences in both psychophysical and speech-reception
performance.
Appendix A
Single Fiber Model
117
APPENDIX A. SINGLE FIBER MODEL
118
A.1
Equations
As described by Frijns [13], the vector form of equation 2.23 is
dV
dV
dt
=
AV + BVe + C (Iact + IL)
(A.1)
where
(A.2)
V
=
[(Vm(l)- Vrest), ...
Ve
=
, V(N) T
[Ve ) ....
(A.3)
Iact
-
[Iact(l)
(A.4)
IL
, (Vm(N)
-
I...lact(N)]T
[-GLl)VL,...
,-GL(N)
L T.
Vrest)] T
(A.5)
(A.6)
The nodal conductances and capacitances are calculated using the fiber geometry
as:
7r(0.5D(K))2
Ga(k)
(A.7)
PaL(k)
GL )
=
gL7rd(i)l(i)
(A.8)
Cm(
=
cmlrd() l(i).
(A.9)
The resistive coupling between nodes along with the sealed end (spatial) boundary
condition are incorporated in A,B, and C as
A.1.
119
EQUATIONS
-(GA(
1
GA
) +GL(j))
0
Cm)
Cm1 )
-(GA()
GA()
Cm(2
+GA(
2)
+GL(
2
GA( 2 )
))
Cm( )
2
C,(2)
-(GA(Kl)
0
C.(
GA
-(GA(
GA(K)
Cm(N)
Cm(N)
2)
0
1)
+GA(
1
GA(K)
Cm(N-1)
-(GA(K) +GL(N))
GA(j)
-(Gl)
C.(
+GA(K) +GL(N-1))
Cm(N-1)
Cm(N-1)
GA( 2 )
2 ))
Cm(2)
C1(
2
)
GA(K- )
1
Cm(N-1)
-(GA(Kl) +GA(K))
GA(K)
Cm(N-1)
GA(K)
Cm(N-1)
-(GA(K))
Cm(N)
Cm(N)
0
1
0
Cm1
1
Cm( )
2
1
Cm(N-1)
1
Cm1,(N)
0
The voltage-dependant a's and O's that determine the activation factors m(i), n(i),
and h(j) are given by:
[Aam(V()
1exp
-
3am)
amV)W)a/-
( T-T")]
Q10am
(A.10)
APPENDIX A. SINGLE FIBER MODEL
120
Aa (ax - V(i))
exp V
")
(Ccth
Aen (V(i) - Oan)
afn()
.1-exp
Oa-)
1-xp(
(A.12)
(-TO)
(A.13)
C)3h
A,3n(0,3-V)
1
-
exp
io-To
on
- Qi
V(i) -0"
Acem(V(i) - oam)
Ach(!ah - V(i))
.(
exp V(i)-3h)
-eP Cah
Aan(V(i)
an(.)
1
-
-
I
exp
)om
1-exp 00 (
AQf -
i
(A.17)
[Q1Oan I
(A.18)
V
(Tio-To
Q10/3m
I
(A.19)
(A.20)
io
Q10h
(T-T)
Aon (Oon - V())
1-exp
10ah
I
pos-vte '
3
(T)-To
V(i)
1-exp ((
/ f(j)
(A. 15)
(A.16)
/an)
Am(/3m - V()))
=
.-
(-To
Q10am
,3.-ve
ah()
(A. 14)
ioa
-
44,,_79
=
-Q10an
[om
-exp (V-oom
h(i)
(A.11)
I
Aom(oom - V())
3
[0Qah]
Q T[Qo)]
a
4i " -00
.-
Toa)
IQ 3
(A.21)
I
A.2. PARAMETERS
A.2
symbol
121
Parameters
value
units
description
V,
V
the internal potential referenced to a far field ground
Ve M
V
the external potential referenced to a far field ground
Vm(.
V
V(i)
V
-[Vi,
- Ve()] the transmembrane potential
=[Vm(1 ) - Vrest] the deviation of the membrane voltage
from its resting potential
Vrest
-0.0846
V
the resting membrane voltage as calculated using the
Goldman Equation
CmM
F
the membrane capacitance at node i
Ga(k)
Q-1
the axial conductance at internode k
GL
Q-1
the membrane leak conductance at node i
VL
V
the leak reversal potential
e(i)
ym
node length
d(j)
pm
node diameter
L(k)
um
internode length
D(k)
um
internode diameter
PK
2.04e- 6
m X s-1
potassium permeability
PNa
51.5e-6
m x s1
sodium permeability
Pa
0.70
9L
728
Q-1 x mn-2
unit area leak conductance
Cm
0.02
F x m-2
unit area leak membrane capacitance
T
301.16
K
corrected absolute temperature
TO
293.15
K
absolute temperature
F
96485
C x mo1-1
Faraday's constant
R
8.314
mol-1 x K- 1
gas constant
[C±
[Na+
142.0
mol x m-3
Na concentration outside
10.0
mol x m-3
Na concentration inside
[cs.]
4.2
mol x m-3
K concentration outside
[cN<+]
141.0
mol x m-3
K concentration inside
[Nas]
[COa+
axoplasmic resistivity
Sx m
0.0077
initialization value
no
0.0267
initialization value
no
0.76
initialization value
122
APPENDIX A. SINGLE FIBER MODEL
symbol
value
units
description
qlOm
2.2
temperature dependant parameter
q103m
2.2
temperature dependant parameter
q10ah
2.9
temperature dependant parameter
q10h
2.9
temperature dependant parameter
q10an
3.0
temperature dependant parameter
q10p3
3.0
temperature dependant parameter
A am
0.49
am constant
Barm
25.41
am constant
Cam
6.06
am constant
Aom
1.04
am constant
Bom
21.0
am constant
COM
9.41
am constant
Aah
0.9
-
ah constant
Bah
27.74
-
ah constant
Cah
9.06
.
ah constant
A)h
3.7
Bflh
56.0
-
ah constant
COh
12.5
-
ah constant
Aan
0.02
-
an constant
Ban
35.0
-
an constant
Can
10
-
an constant
A3n
0.05
-
an constant
B)3
10.0
-
an constant
Can
10.0
-
an constant
ah constant
Appendix B
Supplemental Data/Figures
123
APPENDIX B. SUPPLEMENTAL DATA/FIGURES
124
300
250
250
250
200
200
200
200
150
150
150
100
100
100
100
50
50
50
50
2
150
L
0.5
0
200
250
200
200
150
e
1
E8
~Ia
200
150
150
150
.
100
100
50
50
100
100
50
50
"
,
0
0
0.5
n
0
0.5
0
1
0
0
0.5
0
1
3001
250
250
200
2001
150
1
r
AMM
0.5
0
1
E 12
Ell
E10
E9
150
100
150
100
100
50
1001
50
50
50
0
0
0.5
0
0
1
0.5
0.5
1
0.5
0
1
300
250
250
200
1
E 16
E 15
E 14
E 13
200
150
150
200
8
0.5
0
1
E7
E6
0
250
0.5
1
0.5
1
E5
300
250
0
0
0
.
E4
E3
E2
E1
150
100
150
100
100
100
50
0 """"."""
0
0
0
0.5
50
50
50
0.5
1
0
0
1
0
1
150
150
100
rn
100
u> 100
La
50
50
1
n
120
150
0.5
E 20
E 19
E 18
E 17
0.5
120
100
40
50
20
0
U""**""
0
0.5
Relative Threshold
0
0
0
1
0
0.5
Relative Threshold
1
0
0.5
Relative Threshold
1
0
0.5
Relative Threshold
Figure B-1: Histogram of relative fiber thresholds: Rendition 1
1
125
250
200
200
150
E4
E3
E2
E1
200
150
150
150
100
100
100
100
50
50
50
0
0
0
0
0.5
IltTIUUL
0.5
E5
50
0
1
0
150
150 1
100
100
1
E8
150
100
100
ii
50
50
50
50
0 mu*"*"*"MuA
0
0
0
0
0.5
0
0.5
250
150
0
1
0.5
EI 2
250
300
200
0.5
Ell
E10
E9
a
200
L
200
150
150
100
150
100
100
50
50
50
50
0
0
0
0.5
0
0.5
0
11
100
80
100
80
860
0.5
E 16
150
120
100
150
100
0
0.5
E 15
E 14
E 13
A
0.5
200
150
8
0
1
E7
E6
200
0.5
60
50
40
50
20
01
0
-0.5
20
flIllIlIUIfIIIIIIhJII~la
0
UllMlllliuJ
0
0
1
dl
150
120
100
100
100
880
0.5
E 20
150
[I
150
0.5
E 19
E 18
E 17
140
0
0.5
1
A
60
50
40
50
50
20
0
0
0
0.5
Relative Threshold
0
0
' "*"""1"IM"""'
0
0.5
Relative Threshold
0
0.5
Relative Threshold
1
0
0.5
Relative Threshold
Figure B-2: Histogram of relative fiber thresholds: Rendition 2
1
APPENDIX B. SUPPLEMENTAL DATA/FIGURES
126
(A
(B)
Cochlear Neurons of
of Lower Basal Turn
Basa
Cochear
erv*
Cochlear Neurons of
of Lower Basal Turn
FRber-Tracks
Model Cochlear Axis
Figure B-3: Basal Fiber-Tracks.
(A) Schematic of the basal cochlear neurons as they join the nerve trunk.
Note these neurons do not converge toward a single cochlear axis, but
rather course downward toward the internal auditory canal. (B) In the
model, these basal fibers converge toward the model cochlear axis. Also
note the change in direction of the nerve trunk as it enters the internal
auditory canal is not included in the model. [Adapted from Schuknecht
[41]]
127
(A) Rendition 1: Electrodes 1-12
1-
0.8 -
0.6
.
0.4
0.2
0
C
0
0
-0.2
-0.4
-0.6
-0.8
0
100
200
300
500
400
fiber recruitment (N)
600
700
800
900
(B) Rendition 2: Electrodes 1-12
0.8 -
....... .
. ... .......
. .. ....
...
...
. .. . . ..
. ..
. ..
... .. . .....
0 .6 ...
. .. ..
..
0.4
:C
0.2
0
-0.2
-0.4
-0.6-0.80
100
200
300
600
500
400
fiber recruitment (N)
700
800
900
Figure B-4: Truncated model: Correlation verses N : Electrodes 1-12
Here the most basilar (0 < 30) and the most apical (0 > 480) fibers have been removed
from the model. Shown are product-moment (black line) and Spearman (gray line) correlation coefficients for all values of N . The horizontal line (dotted) indicates statistical
significance (P<0.05).
APPENDIX B. SUPPLEMENTAL DATA/FIGURES
128
1200
C,>
U)
1000 V
800-
U)
6001a>)
400
200
0
~-rrF1Th
-
0
100
200
300
400
500
600
700
Theta [degrees]
Figure B-5: Collective distribution of 0 for recruited fibers: Apical 12 subset
Pooling the 700 lowest threshold fibers under stimulation by each of electrodes 1-12
are located in
(rendition 2) shows that the overwhelming majority of recruited fibers
the middle of the model spiral.
129
(A) Rendition 1: Electrodes 1-19
0.5 - . ...................
0
0
0
0
o -0.5-
-1
0
200
800
600
400
1000
fiber recruitment (N)
(B) Rendition 2: Electrodes 1-19
1
. . . . . ..
.5
(
- - -
,..
-- -
- ..
- -.- . -..- .- .-+
0
0
0
CO -0.5 -
-1
0
200
400
600
800
1000
fiber recruitment (N)
Figure B-6: Correlation verses N : Electrodes 1-19
correlation coeffiShown are product-moment (black line) and Spearman (gray line)
significance
statistical
cients for all values of N . The horizontal line (dotted) indicates
(P<0.05).
130
APPENDIX B. SUPPLEMENTAL DATA/FIGURES
Appendix C
Recommendations for Future Work
131
APPENDIX C. RECOMMENDATIONS FOR FUTURE WORK
132
There remain many issues that could be further investigated, and changes that
could be made to the modelling approach that would potentially improve its ability
to capture an influence of the peripheral anatomy:
1. The resolution and accuracy with which anatomical structures are segmented
and labelled could be increased, possibly by photographing every section. This
might help to avoid the ambiguities encountered here, such as the orientation of
the apical fibers and the slight registration errors between consecutive images.
2. The problem of estimating the potential field in the modiolus may be better approached using the finite-element or boundary-element method. Future models
might use these methods to increase the model resolution in the modiolus while
simultaneously decreasing the model resolution near the model boundaries since
these formulations do not require a uniform mesh [24].
3. Visual ganglion cell counts should be obtained at a spacing closer than every
10
th
section. This will allow for a better calibration of the model fiber distribution.
4. The model could be extended at the base to include regions of the internal
auditory canal. This would allow for longer fiber-tracks with more nodes of
Ranvier.
5. The fiber trajectory should include the change in direction that fibers undergo
near the base of the cochlea as they exit into the internal auditory canal.
6. The trajectory of the most basal fiber-tracks should be adjusted such that the
dentritic section is nearly perpendicular to the osseous spiral lamina, as opposed
to the approach used here where these fiber tracks orient towards a common
cochlear axis.
7. Future models should incorporate regional measures of whether the peripheral
dendrite was present or degenerated.
Additionally, the peripheral dendrites
133
added to the model should extend to their anatomically correct position, instead
of simply orientating the toward habenula perforata as was done here.
8. The sensitivity of the potential field estimate and the single-fiber thresholds to
the resistivity values used might be investigated.
9. The effect of changing the electrode geometry to bands separated by silastic
should be investigated.
10. In this initial model the dimensions of the single fiber were adapted from Frijns
[13] as an initial approximation. The dimensions of the model fiber should
be changed to reflect those of a human auditory nerve fiber, including varying
internodal distances and axonal diameters. Additionally, Rattay et al. [40] have
provided evidence that morphological differences in human fibers may cause
changes in spike propagation not accounted for in this model (for example, the
inability of a peripherally initiated spike to successfully cross the cell body due to
a lack of myelination around the cell body). These morphological considerations
should be incorporated in future models.
11. The estimation of the potential along a given model-fiber's nodes of Ranvier
were calculated by linear interpolation of the potential field grid. Changing to
a quadratic interpolation scheme may allow for a more accurate estimate.
12. The scheme used to integrate the coupled nonlinear difference equations in the
single-fiber model should utilize higher order implicit methods where the error
scales as At 2 [O(At 2 )] instead of the O(At) obtained with forward Euler. Either
a backward Euler or Crank-Nicolson scheme would accomplish this [27].
13. A delay between pulse phases, consistent with the device specifications, should
be added to the biphasic pulse used in the single-fiber model.
134
APPENDIX C. RECOMMENDATIONS FOR FUTURE WORK
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