Simulation study of cochlear implants stimulation protocols and its

application to surgical planning

Dejea i Velardo, Hèctor

Curs 2014-2015

Directors: Mario Ceresa, Miguel Angel González Ballester

GRAU EN ENGINYERIA BIOMÈDICA

Treball de Fi de Grau

GRAU EN ENGINYERIA EN

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Simulation study of cochlear implants stimulation protocols and its application to

surgical planning Final Degree Thesis

Hèctor Dejea i Velardo Bachelor’s Degree on Biomedical Engineering

2011 - 2015

Supervisors: Ing. Mario Ceresa, PhD

Prof. Miguel Angel Gonzalez Ballester, DPhil (Oxon.)

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Table of Contents

Summary .................................................................................................................................................... 3

1. Introduction ........................................................................................................................................... 4

1.1 Background ...................................................................................................................................... 4

1.1.1 The sense of hearing ................................................................................................................ 4

1.1.2 Cochlear Implants .................................................................................................................... 6

1.2 Motivation ....................................................................................................................................... 9

1.3 Structure of this document ............................................................................................................. 9

1.4 Dissemination ................................................................................................................................ 10

2. State-of-the-art .................................................................................................................................... 12

3. Methodology for electrical simulations ............................................................................................... 14

3.1 General pipeline ............................................................................................................................ 14

3.1.1 Computational mesh generation ........................................................................................... 14

3.1.2 Finite Elements Method definition ........................................................................................ 16

3.1.3 Automation of the simulations .............................................................................................. 17

3.2 Automatic creation of the nerves .................................................................................................. 19

4. Results .................................................................................................................................................. 23

4.1 Computational study of monopolar stimulation protocol ............................................................ 23

4.2 Computational study of bipolar stimulation protocol ................................................................... 27

4.3 Computational study of tripolar stimulation protocol .................................................................. 29

4.4 Qualitative comparison of the stimulation protocols ................................................................... 31

5. Validation of the results in monopolar protocol case .......................................................................... 33

6. Discussion and conclusions .................................................................................................................. 39

7. Bibliography ......................................................................................................................................... 40

8. Appendixes ........................................................................................................................................... 43

8.1 Figures ........................................................................................................................................... 43

8.2 Publications ................................................................................................................................... 47

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Summary

Hearing impairment is one of the most common causes of disability worldwide, present both in adults

and newborns. The treatments are costly and invasive, hence lot of effort in research is done towards

cost effectiveness and minimally invasive surgery. In the specific case of sensorineural hearing loss

(SHL), which is caused by deficiencies inside the cochlea, usually cochlear implantation is

recommended when the hearing loss is too severe even it implies invasive surgery. Even so, the

outcome of the cochlear implant performance highly varies between patients due to the wide range

of cochlear anatomies and the level of hearing impairment.

In this work we study the effects of cochlear implants through computational modelling and finite

element simulations. The use of a computational model allows to predict pre-operatively the

parameters that better adapt a specific patient case such as the insertion depth, the total current

emitted and the implant model. In order to do so, three different types of implant protocols are

studied: monopolar, bipolar and tripolar.

In this project the computational simulations have proven to be useful to better understand the

behavior of the implanted cochleas. In addition, a validation study has been carried out in order to

demonstrate the feasibility of this work and to compare the results obtained with the literature.

This work is in the context of the European Project HEAR-EU (FP7, 2007-2013) under grant agreement

304857, and the work presented hereby has been applied in it.

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1. Introduction

1.1 Background

1.1.1 The sense of hearing

The perception of sound arises from the transduction of external mechanical waves into electrical

impulses sent through the nerves to the brain, where they are interpreted as sounds. This

transduction process allows encoding both frequency and intensity information into the electrical

impulses thanks to the complex anatomical structure found in the human ear (Fig. 1).

Figure 1: Structure of the human ear. The external ear focuses and transmits sound to the tympanic membrane, where the

middle ear begins. The vibration produced is propagated through the ossicles and arrives to the oval window, the access to

the inner ear, where the sound stimulates the cochlea and signals are sent to the brain (from Encyclopedia Britannica, Inc.).

The cochlea is the organ that transforms sound waves into electrical impulses. It is a spiral shaped

structured coiled around a bone called modiolus with a length of approximately 30 mm and a section

diameter of 9 mm. This section is divided in three tubular sections that contain liquid. The upper

chamber is the scala vestibuli, the lower is the scala tympani and the middle one contains the basilar

membrane and organ of Corti, the sensory organ that transduces mechanical energy into electrical

(Fig. 2-3).

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Figure 2: Anatomical structure of the cochlea. Pressure

waves in scala vestibuli and scala tympani coming from the

oval window cause vibration within the scala media (image

adapted from [1]).

Figure 3: A cross section of the cochlear chambers. From up

to down: scala vestibuli, scala media and scala tympani

(image adapted from Encyclopedia Britannica, Inc.)

The process of sound hearing begins with the action of the above mentioned mechanical, or pressure,

waves, which make the tympanic membrane to vibrate. This vibration is then transmitted through the

ossicles (malleus, incus and stapes) to a membrane inside the cochlea, called oval window, whose

vibration produces pressure waves in the fluid contained in within, called perilymph.

The perilymph propagates the pressure waves making the basilar membrane to oscillate and thus

activating the mechanism of the Organ of Corti. Depolarization occurs and electrical pulses are

transmitted to the spiral ganglion cells, which are the intermediates to finally send the electrical

signals through the auditory nerve to the brain.

The basilar membrane produces complex oscillatory patterns due to its variation in mechanical

properties along its length, feature that allows to observe what is known as frequency tonotopic

mapping (Fig. 4). As a result, low frequencies are detected in the apex of the cochlea whereas the high

frequencies are sensed in the base.

Deficits in any of the steps of the hearing chain can produce hearing loss. However, the most common

types of impairment are the conductive (CHL) and sensorineural (SHL) hearing loss, defined regarding

the anatomic structure damaged or affected.

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Figure 4: The tonotopic mapping of the cochlea. The mechanical properties of the basilar membrane change along its

length, thus causing the decomposition of sound (Image adapted from Encyclopaedia Britannica, Inc.).

In total approximately 278 million people live with moderate to severe hearing loss [2]. However, it is

not exclusively an adult disease, but 2-4‰ of newborns in developed countries suffers from bilateral

hearing impairment. This rate is even higher in developing countries, where the number is over 6‰.

Unfortunately, this is not the only difference. Children born in the developed world are more likely to

receive medical treatment and thus have possibilities to attend school and eventually live an

independent life. In a developing country, such opportunities are unusual and economic dependency

during whole life is very common. In the future, the availability of cost effective implant technologies,

as well as minimally invasive surgical techniques, would sufficiently reduce treatment costs to provide

treatment options for a larger number of the world population, many of them being children [3, 4].

Usually, a cochlear implant is recommended when external hearing aids are not enough to palliate

hearing loss and not as the first option since implantation implies invasive procedures.

1.1.2 Cochlear Implants

Cochlear implants are surgically placed devices able to reproduce and substitute the transduction

process that occurs in the pipeline of sound perception. In other words, cochlear implants convert

sound waves to electrical signals, which are emitted from an array of electrodes. Such signals bypass

the hair cells and directly produce stimulation in the spiral ganglion cells, thus stimulating directly the

nerves. See in Fig. 5 a brief description of its parts and how it works.

In order to better understand the work in this project, it is important to briefly introduce the three

types of stimulation that a cochlear implant can deliver (Fig. 6). In the monopolar protocol, an

electrode in the array acts as current source and another reference electrode in the temporal bone

acts as ground. The bipolar one uses an electrode as a source and another one in the array as ground.

Finally, in the tripolar case, again an electrode acts as a source and the two lateral ones act as ground.

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Figure 5: Cochlear implants are composed of a speech processor that digitalize sounds; an internal antenna that receives

the digital signal; an internal processor that converts such signal into electrical energy; and an array of electrodes, that

emit electrical energy in order to stimulate the spiral ganglion. From: http://www.bcfamilyhearing.com/my-child-has-a-

hearing-loss/hearing-and-amplification/cochlear-implants/. Online. Accessed: 4/03/2015.

Figure 6: Schematic diagram of the three stimulation protocols. From top to bottom: monopolar, bipolar ad tripolar. The

gray electrode represents the source while the striped ones represent the ground. The dashed arrows represent the current

path from source to ground electrode. From [5].

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The stimulation delivered by the array aims to be specific and excite the nerves corresponding to a

certain frequency, but the conductivity and shape of the cochlea make it difficult to obtain and

produce hearing discrepancy, which is the perception of sounds that do not correspond to the real

frequencies. Firstly, when stimulation is given there is a high spread of the voltage that excites the

contiguous nerves to the zone of interest thus producing a wrong perception of the sound. Secondly,

the organization in turns of the cochlea makes distant points in linear distance to be close, one just

above the other, in a way that when stimulation is given in one turn the voltage is able to arrive to the

consecutive turn and excite the nerves there, yielding again to perception of wrong frequencies. This

effect is the so called cross-talk, depicted in Fig. 7.

Figure 7: Radial cross section of an implanted cochlear anatomy. The cyan circles correspond to the electrode array, the

circular lines in cyan and orange to the electrical field induced by the electrodes and the lines in green, blue and red to

nerves of the first, second and third turn respectively. Due to the geometry of the cochlea, the current emitted by the

electrode array stimulates nerves from different turns (marked in black boxes) thus producing hearing discrepancy. These

black boxes are the so called crosstalk zones.

Cochlear implants were firstly thought to be an aid to speech intelligibility for profound hearing

impaired people. Nevertheless, more and more people with still some residual hearing have been

observed to benefit from cochlear implantation. Successful treatment results together with the

advances in performance allow expanding the indications for implantation so rapidly, almost year after

year. Even though, implantation also has contraindications, mainly identified using high-resolution CT

scans and related to anatomical aspects of the structure.

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1.2 Motivation

This project aims to study the effects of the electrical stimulation in the cochlear structures produced

by cochlear implants as well as to demonstrate that computational modeling and simulation are

powerful tools in order to obtain accurate patient-specific predictions (given that the population

presents a huge anatomical variability). These effects are the answer of questions regarding how the

potential spreads along the structure, which is the amount of fibers stimulated, which of them

produce action potentials or how the type of stimulation can be changed so that hearing discrepancy

is reduced the maximum possible.

This study is done in the context of the European project HEAR-EU1, which has four major objectives.

Firstly, to develop a novel high-resolution high-energy microCT device to obtain detailed images of the

middle and inner ear, even in the presence of metallic implants. Secondly, to build a model of the

shape variability of the middle and inner ear from high-resolution images, also incorporating

functional information. Thirdly, to build a computer-assisted patient-specific preoperative planning

system and, finally, to improve the design of cochlear implant electrode arrays and associated

insertion tools using a population-based optimization framework. Therefore, this work is mainly

related to the second and third objectives of HEAR-EU.

In the following, I present a computational framework to preoperatively predict the effects of cochlear

implantation as well as a comparison between the prediction in the three different configuration

protocols (monopolar, bipolar and tripolar).

In order to proceed with the aforementioned framework, it is necessary to obtain clinical CT images

from patient’s head. These images, once registered and segmented, allow us to create a Statistical

Shape Model. The integration of this process, including a proper visualization of the results and the

clinician feedback could give rise to a planning system highly useful for the clinician practice producing

at the same time a significant impact in the state-of-the-art procedures.

1.3 Structure of this document

The present document is structured in six main chapters and an annex.

Chapter 1, Introduction, describes the anatomical and physiology knowledge about hearing and its

impairment as well as some information about cochlear implants. In addition, it contains the

motivation to do this project and how it has been or is planned to be disseminated.

Chapter 2, State-of-the-art, discusses the last advances and research results in the literature related to

the work developed in this project.

1 www.hear-eu.com

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Chapter 3, Methodology for electrical simulations, explains the pipeline used in order to obtain

prediction on potential spread from CT images acquisition. In addition, it emphasizes on the

automation of some pipelines and the creation of the nerves, which are two of the main contributions

of this project.

Chapter 4, Results, presents the results obtained from the application of the pipeline in Chapter 2

under different conditions. Moreover, it analyzes these results and gives clues on which errors could

have been made or why some scenarios are observed.

Chapter 5, Validation of the results in monopolar protocol case, compares the results and analysis from

Chapter 4 and compares them to other found in bibliography in order to give credibility to the project.

Chapter 6, Discussion and conclusions, presents the principal issues that arise from the results in

Chapter 4 and 5 with respect to the literature and analyses the future work for the project.

The annex shows extended figures not included in the main manuscript of this project. In addition, the

first pages of the publications related to this work are presented.

1.4 Dissemination

Scientific discovering and improvement has no sense if it is retained within a research group or, even

worse, a single researcher. Research is a loop in which your studies may help someone get

improvements and discoveries, which in turn may come back and help you on new projects.

Therefore, the results of this project have been disseminated and published in related conferences and

journals.

This work has been involved in the following publications:

Ceresa, M., Mangado N., Dejea, H., Carranza, N., Mistrik, P., Kjer, H. M., Vera, S., Paulsen, R.,

González, M. A. Patient- Specific Simulation of Implant Placement and Function for Cochlear

Implantation Surgery Planning, Medical Image Computing and Computer-Assisted Intervention

- MICCAI 2014, 49-56, 2014, Springer International Publishing.

Dejea Velardo, H., González Flo, E., Claramunt Molet, M., Ceresa, M. and Gónzalez Ballester,

M.A. Distribución de potencial en los nervios auditivos debido a estimulación mediante

implante coclear. Congreso Anual de la Sociedad Española de Ingeniería Biomédica, CASEIB

2014. (Special Students Poster Session).

Mangado, N., Ceresa, M., Duchateau, N., Dejea, H., Kjer, H.M., Paulsen, R.R., Vera, S., Mistrik,

P., Herrero, J. and González, M.A. Automatic Generation of a Computational Model for

Monopolar Stimulation of Cochlear Implants. Computer Assisted Radiology and Surgery - CARS

2015. (Accepted)

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Mangado, N., Ceresa, M., Duchateau N., Kjier, H. M., Dejea Velardo, H., Mistrik, P., Fagertun, J.,

Paulsen, R., Piella, G. and Gonzalez Ballester, M. Automatic mesh generation framework for

computational model of cochlear implantation. PLOS ONE 2015. (Submitted)

Mangado, N., Ceresa, M., Dejea, H., Kjer, H.M., Vera, S., Mistrik, P. and González, M.A.

Functional outcomes of cochlear implantation surgery in a monopolar stimulation protocol: a

virtual population-based study. International Conference on Medical Image Computing and

Computed Assisted Interventions, Workshop on Clinical Image-based Procedures - MICCAI CLIP

2015. (Submitted)

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2. State-of-the-art

Cochlear implants give the patients with severe hearing loss the possibility to recover the capability of

sound perception. Even though, the performance of the implants varies highly along the population

due to patient-specific factors mainly related to the cochlear geometry. In addition, its current designs

produce discrepancies that make it difficult for the patients to perceive the sounds correctly.

These are the reasons why many studies have been done in order to better understand which are the

effects of electrical stimulation in the cochlea and which are the factors that contribute to produce

variation in this effects along the population.

Most of the aforementioned studies used synthetic geometrical models. Edom et al. [6] studied the

perylimph flow and basilar membrane vibration in a 2D box model of the cochlea. In addition, the

approach by Nogueira et al. [7, 8] focused on the interface between electrode and nerve in a 3D finite

element mesh coming from a single midmodiolar horizontal section of a cochlea. In another case, Dr.

Saba [9] used uncoiled and coiled 3D models constructed by geometrical building techniques.

On the contrary, other studies were animal based. Frijns et al. [10] used a rotationally symmetric

model of the second turn of a guinea pig cochlea whereas Dr. Malherbe [11] constructed a 3D mesh of

the whole cochlea using micro-CT images from the same animal model.

For the best of my knowledge, it was not until previous work to this project [12], also in the context of

HEAR-EU, that the combination of human high-resolution imaging techniques and finite element

methods was used in order to study this topic.

Ceresa et al. [12] presented a cochlear model constructed from the segmentation of high-resolution

μCT images of cadaveric samples. The model also included 49 nerve fibers, 12 cylindrical electrodes

isolated by silicon cylinders and the basilar membrane, which were all created manually. The resulting

mesh was used to perform 11 different electrical simulations of bipolar protocols, from BP12 to

BP1112, with the typical 1 mA stimulation current [10] and the voltage spread in the nerve fibers was

measured in order to observe the level of excitation.

The extraction of the results needed a parameterization of the nerve fibers and several steps of post-

processing that had to be manually performed. Finally, a set of spread curves showing how the

potential was distributed along the nerve fibers was obtained and it was able to show some relevant

features such as crosstalk zones and high voltage spread in consecutive fibers mentioned in the

literature [13, 14].

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Nevertheless, this work had some limitations:

Convergence: in most of the simulations the convergence values were oscillating and never

reached the desired convergence value of 1e-6 even they were run for a long time. This was

caused by degenerated elements in the mesh.

Manual procedures: a big part of the methodology used was manual, fact that makes the

process tedious and limits some features of the model such as the low number of nerve fibers.

Protocols: the presented model only allowed running simulations on bipolar protocol. Other

features needed to be added in order to run monopolar and tripolar.

Amount of stimulation: as mentioned above, 1 mA is within the range of common stimulation

given by cochlear implants. Even though, the geometry of the electrodes was not taken into

account even it was necessary, as the definition of the simulation requires current per unit area

and not total amount of current .

Most of the limitations have been solved by the people working on HEAR-EU [15, 16, 17, 18] and some

of these improvements are presented in the project.

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3. Methodology for electrical simulations

3.1 General pipeline

In order to carry out the framework and generate a computational model, some prior data had to be

obtained (first step in Fig. 8). High-resolution images of cadaveric samples of the inner ear were taken

using a Scanco µCT 100 system (Scanco Medical AG, Switzerland). After that, advanced image

processing tools allowed to obtain detailed cochlear surface models, which were used to construct a

Statistical Shape Model of the cochlea [12] (second step in Fig. 8). The SSM represents the mean

cochlea and provides the main types of variation throughout the population, thus allowing to generate

virtual cochleas by means of sampling methods, also called instances. Finally, a fitting procedure is

used to obtain a patient-specific cochlear surface from CT images of such patient [16].

At this point begins the definition of the general framework for mesh generation and electrical

simulations (steps 3 and 4 respectively in Fig. 8). This work is disseminated in [15].

Figure 8: Presentation of the general pipeline. First, the data is acquired and then processed to construct a Statistical Shape

Model (SSM), which can be used to create virtual patients or to fit real patient CT images and create a 3D instance. This

instance is meshed with all necessary components and is prepared for electrical simulations of cochlear implantation.

3.1.1 Computational mesh generation

The meshing framework (Fig. 9) begins with the cochlear 3D model as its main input and was

developed in Matlab using open-source toolboxes [20]. The first step in the figure is to create the rest

of components of the model, which are the electrode array, nerves and surrounding bone.

The electrode array geometry was provided by the manufacturer Med-EL based on the Flex28 design

with 12 contacts. This geometry is meshed and used to simulate the insertion into the cochlear model.

To this end, two different procedures were available: the centerline approach or the Simulation Open

Framework Architecture (SOFA) [21] approach. The first one allows a middle/inner placement of the

electrode array in the scala while the second allows an outer placement. Note it clearly in the radial

cross sections in Fig. 10.

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Figure 9: Blocks diagram describing the meshing framework. Once the cochlear mode is obtained, the first step is to create

the rest of components of the model in order to mesh them and merge them in a second step to obtain the full model

surface mesh. In the third step, the volumetric mesh is created after quality assessment of the surface mesh. Finally, the

output is the mesh file ready to be introduced in the simulation procedures. Adapted from [15].

Figure 10: Radial cross sections of two cochlear models with centerline and SOFA insertion approaches. The inserted

implants are marked in red. Left: the centerline approach allows inner / middle placement (the array is close to the center).

Right: the SOFA approach allow outer placement (the array is close to the outer wall of the scala).

As its name suggests, for the centerline approach the centerline of the cochlear model is computed. It

is located at the center of the scala tympani, were the electrode array will be further inserted. The

virtual electrode insertion algorithm reorients the electrode mesh along the cochlear centerline using

the parallel transport frame approach [22]. This is a fast and robust algorithm which allows the control

of the most relevant insertion parameters, such as the percentage of insertion.

The SOFA approach is based on the mechanical simulation of the electrode array being inserted inside

the cochlea [23]. It allows to obtainmore realistic results as the clinicians actually push the implants

into the cochlea in the surgical procedures. It also allows controlling the percentage of insertion and

other relevant parameters.

Another component of the model is the nerve fibers, which are needed to observe the level of

stimulation received by the patient. Specifically, this part is fully detailed in the section 3.2 Automatic

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creation of the nerves.

The last component is the surrounding bone, which is modeled as a cube that encloses the rest of the

model. It is an important component because it highly affects the conductivity of the model and the

electrodes of reference are placed in it when monopolar protocols are used.

In the second step of Fig. 9, once the surface meshes of all components of the model are created, they

are merged to form the full model surface mesh. Then, the third step ensures the convergence of the

finite element electrical simulation assessing the mesh quality using the aspect ratio, which is 0 when

the elements are highly degenerated and 1 when they are perfect tetrahedron.

Finally, in the fourth step the mesh is converted to a proper format in order to carry out the electrical

simulations. This mesh file is the output of the meshing framework.

3.1.2 Finite Elements Method definition

Once all components of the mesh are assembled and the volumetric mesh is built, electrical

simulations can be run. In order to execute the electrical simulations the tool used is Elmer [24], in

which the Static Current Conduction module is employed. The mentioned module is based on quasi-

static approximation of Maxwell equations (1, 2, 3),

which are combined in order to obtain the equation (4).

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Furthermore, if Ohm’s Law (5) is added and the electric field is rewritten (6) following the expressions

Poisson’s equation (7), which allows the computation of the electric potential p, and volume density

current’s J equation (8) are finally obtained.

where - is electric field and σ is electric conductivity [25]. For electric potential either Dirichlet or

Neumann boundary conditions can be used. The Dirichlet boundary condition gives the value of the

potential on specified boundaries. The Neumann boundary condition is used to set a current on

specified boundaries.

3.1.3 Automation of the simulations

The script that contains all parameters needed for the simulation, such as the number of iterations or

convergence tolerance, is a “.sif” file. This file also contains the components of the mesh, the materials

they are made of and the boundary conditions, which together define the physical problem wanted to

be solved.

When a certain number of simulations under different conditions have to be applied on several

meshes, a manual procedure for sif generation is tedious and time-wasting. This is the reason why all

the process, from sif generation to execution of the simulations, was automated using a combination

of Python and Linux Bash programming for all meshes and all simulations. See Fig. 11 for a visual

description.

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In the first major step, the code repeats the same procedure for each different mesh. A mesh folder is

created in addition to a subfolder for each simulation, where the mesh files are copied. Then, the

correspondent sif is created using a template, which is rewritten for each simulation depending on the

boundary conditions that have to applied, and copied together with other dependencies into the

simulation folder.

Once all simulation folders are ready, the second major step begins. The code goes into each mesh

folders and runs the corresponding simulation for each subfolder inside. The results of the simulation

are saved in each subfolder in the way that all results are clearly classified. See Fig. 12 for a visual

description.

Figure 11: Process followed in order to run the electrical simulations. For all different meshes, creates folders and subfolders

where all necessary files for each simulation are copied, specially the sif file, which is different for each simulation and is

created one at a time depending on the boundary conditions (BCs).

Figure 12: Organization in folders and subfolders for simulation execution and classification of the results. Each different

mesh is called instance and protocols can be monopolar, bipolar or tripolar. BPxy stands for bipolar-source-ground.

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Once all simulations arrive to convergence and are finished, another code automatically extracts data

of interest from these results. Thanks to the point nature of the nerves, which is further explained in

section 3.2 Automatic creation of the nerves, the code is able to read and extract which is the final

potential in each of these points for all simulations and save it in a CSV file for later analysis.

3.2 Automatic creation of the nerves

Nerve fibers are one of the most important components of the mesh since their response to

stimulation is the principal object of study of the project.

Human cochleas contain approximately 30.000 nerves [26] so it is important to include as many nerves

as possible in the mesh in order to get the closest to real conditions, but at the same time, not to

compromise the computational cost of the simulations. Previous synthetic studies contained up to 299

fibers [10] while computational studies manually meshed up to 49 fibers [12], which is a time-wasting

and very tedious process, but the aim of this section is to get an automatic method that rapidly

creates the desired number of nerves with much less limitation in its quantity and much more nerve

resolution in the analysis of the results.

In order to automate the creation of the nerves, the tools chosen were Matlab and its toolbox

iso2mesh [20], which allowed the modeling of the nerves as cylinders defined by multiple 3D

coordinates and its transformation from surface to mesh.

As mentioned, the cylinders were defined by multiple 3D points (Fig. 13):

Initial point: the nerves start at each point coming from the centerline extraction.

Middle point: defined between the initial point and the center of mass of the cochlea, in this

case at 50% distance.

End point: defined between the middle point and an auxiliary point, in this case at 70%

distance. The auxiliary point corresponds to the symmetric one to the most apical with respect

to the center of mass.

Once all points are computed, the nerve surface is created by building the curve joined by the points

and setting a radius and the number of divisions for the cross section circle [27]. The process was

repeated until the desired number of nerves was reached. Due to the fact that the origin of the nerves

comes from the centerline, the method was limited in the way that it allowed to introduce only as

many nerves as points the centerline contains. See two examples in Fig. 14.

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Figure 13: Representation of a single nerve and the points that define it. The nerve begins in the initial point and goes to

the middle point (50% distance between initial point and center of mass CoM). Then, it changes its direction and goes to

the end point (70% distance between middle point and auxiliary point, which is the symmetric of the apical point with

respect to CoM). Note that the nerve is inverted.

a) b)

Figure 14: Two examples of nerve generation within the mesh of the cochlea. a) Generation of 100 nerves. b) Generation of

1000 nerves.

The meshing procedure by iso2mesh needs as input the nodes and faces of the surface of the object,

so they were computed manually as simple as possible to be later optimized and improved by

automatic techniques. In order to do so, the bases circles contained as many triangles as the number

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of divisions set so that each triangle was formed by two consecutive nodes of the perimeter and the

central node of the circle. As for the creation of the lateral surface, each triangular element was

created from adjacent points of the base and then joined them into a rectangle. When all nodes and

faces had been set, iso2mesh was used in order to transform them to a tetrahedral mesh.

Unfortunately, the described procedure produced a large number of intersections between the

cochlea mesh and nerves, mainly the most apical ones where the inner cochlea becomes narrower.

Intersections are caused by finite elements that cross each other and do not allow the FEM solver to

properly solve the equations that describe the system. That is the reason why they have to be

completely avoided when generating a model to be simulated. Therefore, it was decided to try to

improve the model by firstly, changing the centerline defining the source points for the nerves to an

inner position and, secondly, giving them a smoother shape.

Regarding the new centerline creation, the following process was repeated for each cochlear turn. All

points belonging to a given turn are characterized by its covariance matrix, which is analyzed using a

principal component analysis. That analysis allows obtaining the main directions of variance in the

data, which are used to make a 2D projection of the points to the given main directions. Then, a scale

factor is applied to reduce the radius of the turn and the new points are projected back to its original

3D space. The new placement avoids all intersections produced due to having the source points inside

the cochlea itself, so from now on the nerves will begin outside the cochlea but as close as possible to

the basilar membrane position.

In the case of the smoothing of the shape of the nerves, the sharp model described above is modified

with several interpolations. That is, new intermediate points between the three initial descriptors are

computed and interpolation is applied, thus smoothing the nerves. Finally, it results on nerves

characterized by 20 points instead of the initial three, which gives a much smooth shape that avoids

the intersection with the inner parts of the cochlear structure. See Fig. 15 for an example.

Figure 15: Representation within the mesh of the cochlea of 100 nerves characterized by 20 points. Note its smoother and

curved shape that tries to avoid intersection with other parts of the cochlea.

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Nevertheless, even after all features of the nerves were highly improved and all possible combinations

of parameters have been tried, some of the resulting nerves still intersected with the mesh of the

cochlea. Furthermore, most of the simulation trials were affected by convergence problems, probably

due to the large amount of elements and degeneration of some of them. Therefore, it was decided not

to mesh the new nerves and move on to a different approach.

At this point of the project, the cochlear models evolved from meshed segmentations to samples from

the Statistical Shape Model enclosed into a cube that allows to simulate monopolar protocols, as if it is

set to ground can be a simple representation of the reference electrode placed in the temporal bone

when theses protocols are used. Moreover, the cube also acts as the constituent of the volumetric

mesh that allows measurements all over its volume and not only on the surfaces.

Therefore, this last feature of the cube gives us the possibility to move on to the mentioned different

approach, which consists on modeling the nerves as a list of points instead of trying to mesh them,

thus having a simpler mesh to work on. These lists of points come from the last model in which the

shape of the nerves was described by 20 points, thus taking benefit from the previous work.

Therefore, if the lists contain points located within the volume of the cube, it will be possible to

measure the potential spread in them with no need of a mesh.

Since this work is in the context of the European project HEAR-EU, the approaches used have evolved

thanks to the effort of the entire consortium. That is why, for example, profit was taken from the

improvement of the cochlear models during the course of this project.

23

4. Results

4.1 Computational study of monopolar stimulation protocol

As previously explained, monopolar protocols consist of a source in the electrode array and a

reference in the temporal bone. In this case, the approach used for the reference electrode was a cube

surrounding the cochlea (Fig. 16), which was always set to ground. Each stimulation will be named

MPx, where x stands for the source electrode.

Figure 16: Pictures of the new model. Note in the left the enclosing cube representing the temporal bone and, in the right,

the implant inserted in the cochlea.

The results of the monopolar protocols for a given instance are shown in the spread curve in Fig. 17

below, which shows the resulting potential in the spiral ganglion of each nerve for a given stimulation

protocol. The potential is color coded, the horizontal axis contains the stimulating electrode and the

vertical axis the number of nerves. The convergence problems observed in past studies [12] have been

solved and the right amount of current for stimulation has been applied.

In Fig. 17 the higher voltage is concentrated on a principal diagonal (in warm color) that represents the

high stimulation received by the closest nerves to the source electrode. Looking deeper at every

protocol note that so many nerves are highly excited, thus agreeing with the high spread results

observed in literature [12, 13, 14].

In addition to the principal diagonal, there are also two more upper and lower diagonals that

represent high voltage areas in nerve fibers far from the source electrode. In fact, these zones show

the effect mentioned as cross-talk, since a wrong stimulation of the nerves. This is caused due to the

cochlear anatomy. In the apical part the cochlea becomes narrower and the nerves are closer to each

other and, consequently, to the electrode activated. The upper diagonal shows cross-talk from the first

24

turn to the second while the lower diagonal shows cross-talk the other way around. Again, it agrees

with results observed in literature [12, 13, 14].

Finally, notice that the most apical part is highly stimulated when the electrodes placed there act as

source. This fact could be explained by the anatomy of the cochlea, which becomes narrower in the

apical part increasing the voltage spread in the surrounding area.

Figure 17: Spread curve resulting from the simulation of 12 different monopolar protocols. It shows the potential spread in

the spiral ganglion for all 100 nerves in each of the 12 protocols. The horizontal axis represents the protocol number (which

electrode act as source), the vertical axis the number of the nerve (100 is the most apical) and the color, the potential level.

Moreover, find in Fig. 18 a single spread curve for each protocol resulting from the split up of Fig. 17.

Therefore, some observations made in Fig. 17 can be found in each of the components of Fig. 18:

1. The principal diagonal is translated to the uniform advance of high stimulation along the

nerves from MP1 to MP12. Note that the shape and amount of stimulation is almost equal

in all protocols except for its position.

2. Crosstalk can be observed in several samples, for instance MP5 or MP11, where in addition

to the main stimulation, high voltages appear lots of nerves after (MP5) or lots of nerves

before (MP11). These stimulations are the representation of the upper and lower diagonals

found in Fig. 18.

3. Finally, when going to the apical part the main stimulation becomes wider due to the

variations in section of the scalae. It is the representation of the high stimulation area

produced from MP9 to MP12 observed in Figure 21.

25

26

Figure 18: Spread curves resulting from the monopolar stimulation protocols simulated. Subfigures are ordered left to right

and up to down, from MP1 to MP12. The horizontal axis stands for the number of nerve, the vertical axis for the point of

the nerve and the color for the potential level.

27

4.2 Computational study of bipolar stimulation protocol

We will discuss in the following the bipolar protocol. As previously explained, in this configuration an

electrode is acting as source and another as ground. The model used for the study is the same one

shown in Fig. 16. Each stimulation will be named BPxy, where x stands for the source electrode

applying a current of 1 mA and y for the ground one, which is set to 0 V.

We simulated the results of a full bipolar stimulation for a given instance and plot the results in the

Fig. 19, where you can appreciate the resulting potential in the spiral ganglion of each nerve for a

given stimulation protocol. The potential is color coded, the horizontal axis contains the stimulating

electrode and the vertical axis the number of the nerve receiving the stimulation.

Before obtaining these spread curves, bipolar protocols gave problems of convergence that took a long

time to be solved. The mesh quality, boundary conditions and many other parameters were checked

as source of the errors but finally, the high electric conductivity of the electrodes was the cause of the

non-convergence in the simulations.

The results deviate quite significantly from the ones shown in the previous sections. There is a high

difference in the mean stimulation values of the 11 different protocols that complicates the

interpretation of this spread curve. Even though the mean values of the stimulation vary with each

protocol, we can still observe a principal diagonal with high voltage values for each of the stimulations.

The most probable cause for these results is a problem in the definition of the simulation case. We are

currently investigating how to fix it.

Figure 19: Spread curve resulting from the simulation of 11 different bipolar protocols. It shows the potential spread in the spiral ganglion for all 100 nerves in each of the 11 protocols. The horizontal axis represents the protocol number (which

electrode act as source), the vertical axis the number of the nerve (100 is the most apical) and the color, the potential level. Note the bias in the mean stimulation levels that may be caused by an error in the definition of the simulation parameters.

28

We present in Fig. 20 the plots of the spread curves from single protocols for further analysis.

Comparing those results to those of the monopolar case, we can conclude that:

1. Although the level of stimulation is incorrect, the observed shape seems in agreement with

bipolar behavior. The voltage spread is blocked by the ground electrode, thus avoiding the

stimulation to be transmitted to the lower frequencies. Therefore, less hearing discrepancy

is produced regarding these frequencies.

2. Crosstalk can be observed in some samples, for instance BP910 or BP1112, where in

addition to the main stimulation, high voltages appear in distal nerves.

Figure 20: Spread curves resulting from the bipolar stimulation protocols simulated. Subfigures are ordered left to right and

up to down: BP34, BP67, BP910 and BP1112. The horizontal axis stands for the number of nerve, the vertical axis for the

point of the nerve and the color for the potential level.

Bipolar stimulation protocols are still being studied and checked in order to find which problems give

rise to these erroneous results.

29

4.3 Computational study of tripolar stimulation protocol

In this section, we present the results of the study of the tripolar stimulation protocol. As previously

explained, in tripolar configuration we consider three electrodes. The one in the center acts as source

and the two lateral as ground. The model used for this study is the same presented in Fig. 16. Each

stimulation will be named TPxyz, where y stands for the source electrode applying a current of 1 mA

and xz for the ground ones, which are set to 0 V.

The results of the tripolar protocols for a given instance are shown in the spread curve in the Fig. 21

below, which shows the resulting potential in the spiral ganglion of each nerve for a given stimulation

protocol. The potential is color coded, the horizontal axis contains the stimulating electrode and the

vertical axis the number of nerves.

Before obtaining these spread curves, tripolar protocols gave the same problems of convergence as

bipolar protocols and the cause was the same, the high electric conductivity of the electrodes’

material.

The results suffer from the same problems seen in the bipolar case. Namely, the interpretation is less

straightforward because there is a high variability in the mean stimulation values of each different

protocol. However, the principal diagonal of stimulation can be observed more clearly than in the

bipolar case.

Figure 21: Spread curve resulting from the simulation of 10 different tripolar protocols. It shows the potential spread in the spiral ganglion for all 100 nerves in each of the 10 protocols. The horizontal axis represents the protocol number (which

electrode act as source), the vertical axis the number of the nerve (100 is the most apical) and the color, the potential level. Note the bias in the mean stimulation levels that may be caused by an error in the definition of the simulation parameters.

30

We present in Fig. 22 the electrical results for each protocol separately. We can observe that:

1. Although the mean level of stimulation is incorrect, the shape observed seems to be in

agreement with tripolar behavior. The ground electrodes block the potential spread and

restrict it to the closest surrounding of the source of current. Hence, the hearing

discrepancy is even lower as the stimulation cannot be transmitted to higher nor lower

frequencies.

2. Crosstalk can be observed in some samples, for instance TP789 or TP101112, where in

addition to the main stimulation high voltages appear in distal nerves in higher and lower

frequencies respectively.

Figure 22: Spread curves resulting from the tripolar stimulation protocols simulated. Subfigures are ordered left to right and

up to down: TP123, TP456, TP789 and TP101112. The horizontal axis stands for the number of nerve, the vertical axis for

the point of the nerve and the color for the potential level.

31

Like in the bipolar case, tripolar stimulation protocols are still being studied and checked in order to

find which problems give rise to these erroneous results. The type of error (the high levels of voltage)

is the same, so the hypothesis is that the error is the same for both protocols and due to problems in

the definition of the simulation.

4.4 Qualitative comparison of the stimulation protocols

Although it is difficult to make a comparison between the different protocols due to the errors in the

levels of stimulation occurred in bipolar and tripolar cases, some features of the different results can

be qualitatively contrasted between them and against literature [5]. Find in Fig. 23 a sample of each of

the three different protocols for a better visual comparison.

a) b) c)

Figure 23: spread curve samples of monopolar (a), bipolar (b) and tripolar (c) protocols (MP6, BP67 and TP567

respectively). The voltage ranges are: a) 0 – 0.25 V, b) 1.35 – 1.6 and c) 0.8 – 1 V. Note in monopolar case (a) that the

voltage spreads to all directions while in bipolar (b) it is transmitted only to lower nerves and in tripolar (c) is confined to

the closest surrounding of the source. In addition, the crosstalk zone around nerve 80 is stronger in monopolar (a) than

tripolar (c) protocols.

Regarding the shapes of the zones of high stimulation it is observed that in the monopolar case (Fig.

23a), where the reference is set in the temporal bone, the current spreads around the cochlea with no

limitation except for the conductivities of the materials used to model the organ. In the bipolar case

(Fig. 23b), it is observed that the voltage spread is more confined around the source electrode. Finally,

in the tripolar case (Fig. 23c), this tendency to voltage confinement is even stronger between the

ground electrodes that surround the source one in the way that there is a low voltage spread.

Furthermore, although the difference in the mean levels of stimulation is high all range values in the

single spread curves are of 0.2-0.25 V amplitude, which is similar to the monopolar case. It is difficult

to see in the bipolar protocol due to the high stimulation in the background, but if monopolar and

tripolar stimulations are compared it can be observed that the voltage range amplitude of the former

is 0.25 V while in the case of the latter is 0.2 V, so it can be concluded that tripolar protocols show a

lower spread and a lower crosstalk effect around nerves 80-90. This observation is in agreement with

32

literature [5].

Moreover, in [5] it is stated that in order to get the same voltage level than in monopolar cases,

bipolar and tripolar protocols need higher level of currents. The voltage range for bipolar case is 1.35 –

1.6 V, which is higher than the tripolar range of 0.8 – 1 V thus in agreement with [5]. We are

investigating whether this high difference of 0.5 V is realistic or an artifact of the simulation problems.

Future work will be focused on solving the problems observed in order to get further and more

accurate comparisons in order to better understand the differences between the different protocols.

33

5. Validation of the results in monopolar protocol case

In order to validate the results obtained in this work, we wanted to prove the feasibility of the model

to reproduce similar results that the ones from other studies.

To this end, it was decided to validate the monopolar stimulation results by comparing them to the

ones obtained by Dr. Rami Saba in his PhD thesis [9], who works in the hearing solutions company

MED-EL2, part of the consortium of HEAR-EU. Dr. Saba measured the impedance along the spiral

ganglion path produced by the stimulation of 22 electrodes activated separately in a synthetic model

(Fig. 24).

Figure 24: Model used by Dr. Rami Saba in his simulations. All cochlear structures are represented together with the spiral

ganglion pathway, where potential spread is measured [9].

Dr. Saba results in Fig. 25a of results show some important features to take into account for the

validation:

1. The impedance increases when going to the apical part due to the narrowing of the scalae that

reduces the distance between the electrodes and the path of interest, thus producing this

increase.

2. The impedances resulting from electrode activation are composed of two peaks, one much

higher than the other. The higher one corresponds to the potential spread in the closer spiral

ganglion section while the lower is the result of the so called cross-talk between turns in the

2 www.medel.com

34

cochlea. That is, although both peaks are far away in Euclidean distance they are actually one

above the other in the real anatomy, so when an electrode activates in the first turn the

potential spreads to the upper turn and produces excitation.

3. The impedance ranges from 0 to 0.2 kΩ approximately.

In order to compare our results to [9] the same kind of diagram was extracted and analyzed, looking

for the presence of the same important features. Nevertheless, it was also expected to obtain a

different envelope shape and not exactly the same impedance values, as the geometry of the cochlea

used is different and the amount of electrodes is reduced to 12.

The results of our simulations in Fig. 25b of results show the following features:

1. Some variation in the impedance levels along the whole path. The geometry used also

presents a narrowing of the scalae that indeed reduces the distance between the electrodes

and the path of interest, thus producing said variations.

2. The impedance results for each electrode are composed of two peaks, one much higher than

the other. Therefore, the cross-talk scenario mentioned above is repeated demonstrating the

potential spread between turns that could activate nerves not involved in the hearing of

certain frequencies.

3. The impedance ranges from 0 to 0.15 kΩ approximately, showing lower values. That could be

explained by differences in the geometry or placement of the electrode array. That is, if the

model used has the electrode array in a more outer position than [9], the amount of voltage

that arrives to the spiral ganglion is lower.

Note that some irregularities affect the smoothness of the curves obtained. This is result of the

sampling method and the fact that the nerves are formed by discrete points.

Therefore, it can be stated that, compared to [9], our simulations give good and credible results, as the

main important features are reproduced and shown in the diagram (Fig. 28).

35

a) b)

Figure 25: Comparison of the results obtained by Dr. Saba and our results. The horizontal axis show the distance along the

spiral ganglion and the vertical axis the impedance measured. Each line correspond to a different monopolar protocol. a)

Figure with the results from [9]. b) Figure with our results.

Furthermore, Dr. Saba presents a sensitivity analysis for resistivity changes in the materials of his

model, which are bone, platinum, perilymph, silicone isolator and basilar membrane. Hence, he

changed the resistivity of the materials in a factor of 2, simulated a single monopolar stimulation in

the middle of the array and observed which were the effects. This is a good opportunity to observe if

the simulations run in our study behave the same way as others in the literature when some of the

parameters vary. Therefore, the same sensitivity analysis was carried on the results of this project.

In this case, the parameter used is the conductivity and not resistivity as in Dr. Saba’s work.

Nevertheless, resistivity is the inverse of conductivity, so when multiplying by a factor of 2 the

conductivity of a material it is expected to obtain the same results as in the case of dividing the

resistivity by a factor of 2. In addition, the analysis was carried on the protocol MP6 (the electrode

source in the middle of the array of 12) and on the same materials except for basilar membrane,

which is not present in our model.

Find the results of this sensitivity analysis together with Dr. Saba’s ones in Fig. 26-29.

36

a) b)

Figure 26: Sensitivity analysis for bone. a) Dr. Saba’s results b) Results of this project.

a) b)

Figure 27: Sensitivity analysis for electrodes. a) Dr. Saba’s results b) Results of this project

37

a)

b)

Figure 28: Sensitivity analysis for perilymph. a) Dr. Saba’s results b) Results of this project

a) b)

Figure 29: Sensitivity analysis for silicone. a) Dr. Saba’s results b) Results of this project

Note in the figures above that not all materials have the same effect on the voltage spread. The

principal factor is the position of the object in the cochlea, that is, if it is placed in the pathway

between the source electrode and the spiral ganglion its effect will be higher than being outside that

pathway. Furthermore, note that the range of values is lower in the case of this work in comparison to

[9]. The reason for that is the placement of the electrode array. In the presented case, the electrode

array is outer placed while in the sensitivity analysis in [9] it is inner placed. Consequently, the

electrodes are further from the nerves and the level of stimulation received is lower.

The explanation for the effects of each material is the following:

38

Bone: it is the material that has the greatest effect on the voltage spread. That effect in the

impedance is produced by the large quantity of bone present in the model, which interferes in

the path between source and spiral ganglion.

Platinum: changes in platinum conductivity have no effects as it continues to be very

conductive and the electrode does not interfere in the pathway source – spiral ganglion, it just

sends the electrical signal.

Perilymph: this material mainly affects the amplitude of the peaks of stimulation. When the

conductivity is reduced, the potential is not spread throughout the liquid and goes directly to

the nerves, thus rising the excitation in the place.

Silicone insulator: changes cannot be observed in the spiral ganglion when silicone

conductivity is changed. The function of the silicone is to hold the electrodes and increase the

resistivity between them, so there is a variation in the closest surrounding of the bone that is

not transmitted to the spiral ganglion as it is not placed in the pathway of interest.

Therefore, this sensitivity analysis demonstrates that changes in conductivity of silicone and platinum

have negligible effects on the excitation spread. On the other hand, perilymph conductivity modulates

the amount of stimulation in the site of excitation while bone conductivity changes produce the

highest effects. The model is highly sensitive to bone conductivity and robust to electrode metal and

silicone, the same results presented in [9].

39

6. Discussion and conclusions

The results of this work have proven that computational models and simulations provide such a

valuable tool to assess and predict the electrical effects of cochlear implants.

On one hand, the results of the monopolar protocol are promising since they have been proved to

follow a proper behavior. In addition, they have been validated in front of the work presented by Dr.

Saba [9] regarding the voltage spread and conductivity effects of the materials. On the other hand,

bipolar and tripolar protocols show a bias in the mean level of stimulation that cause complications in

the analysis and comparison between the three protocol configurations. Therefore, only a qualitative

comparison has been done. Even qualitatively, this comparison shows that the type and amount of

voltage spread as well as the difference in the stimulation values, is in agreement with the literature

[5].

Moreover, the methodology and framework presented could potentially be integrated in a planner

system that pre-operatively computes patient-specific electrical effects of cochlear implantation.

Hence, the clinicians could be informed in advance of which parameters, such as depth of insertion or

implant model, are the best for a particular case.

Although the results are very promising, there is still work that has to be done in order to improve the

results obtained from this study.

Firstly, the voltage spread does not provide a whole picture of the effect of cochlear implantation. It is

not known whether the stimulation received by the nerve fibers is enough to depolarize, and thus

send action potentials to the auditory cortex or not. Therefore, a Generalized Schwarz-Eikhof-Frijns

(GSEF) model [10] for the nerve fibers is planned to be coupled to the voltage spread results in the

near future. This new model will allow to evaluate the actual amount of nerve fibers stimulated as

well as the extension of hearing discrepancy along the cochlea due to the different stimulation

protocols.

Secondly, the approach to locate the spiral ganglion needs to be reviewed as the currently implied

gives non-desired irregularities in the voltage distribution. To this end, the research group is working

towards a continuous function that describes the position of the spiral ganglion.

Thirdly, the errors observed in bipolar and tripolar stimulation protocols need to be fixed. Our main

purpose now is to solve these differences in the mean stimulation value, which we hypothesize that

comes from a wrong definition of the physical problem in the parameters of the simulations.

Afterwards, a quantitative comparison of the three stimulation protocols would give deeper clues on

which are the differences between them. In order to do so, we believe that principal component

analysis and power computation are the best approaches to assess this comparison.

40

7. Bibliography

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McGraw Hill; 2000, p. 602.

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stimulated cochlea. In: DAGA Proceeding. (2014)

9. Saba, R.: Cochlear Implant Modelling: Stimulation and power consumption. University of

Southampton, Faculty of Engineering and the Environment & Insitute of Sound and Vibration

Research. PhD Thesis. (2012)

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patterns in a rotationally symmetric model of the electrically stimulated cochlea. Hearing

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physics 35(7) (2013) 926-936

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González, M. A.: Patient-Specific Simulation of Implant Placement and Function for Cochlear

41

Implantation Surgery Planning,Medical Image Computing and Computer-Assisted Intervention

-MICCAI 2014, 49-56, Springer International Publishing

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14. Gani, M., Valentini, G., Sigrist, A., Kós, M.I., Boex, C.: Implications of deep electrode insertion

on cochlear implant fitting. Journal of the Association for Research in Otolaryngology 8(1)

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Paulsen, R., Piella, G. and Gonzalez Ballester, M. Automatic mesh generation framework for

computational model of cochlear implantation. PLOS ONE 2015. (Submitted)

18. Mangado, N., Ceresa, M., Dejea, H., Kjer, H.M., Vera, S., Mistrik, P. and González, M.A.

Functional outcomes of cochlear implantation surgery in a monopolar stimulation protocol: a

virtual population-based study. International Conference on Medical Image Computing and

Computed Assisted Interventions, Workshop on Clinical Image-based Procedures - MICCAI CLIP

2015. (Submitted)

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Danasingh, A., Barazzetti, L., Reyes, M., Ceresa, M. and González Ballester, M.A.: Cochlear

Implant Planning, Selection And Simulation With Patient Specific Data. Computer Assisted

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43

8. Appendixes

8.1 Figures

Fig. 20 and Fig. 22 show representative samples of the single spread curves of bipolar and tripolar

protocols, respectively. In this section, the complete figures are shown. Fig. 30 contains the 11

stimulations of the bipolar protocol while the 10 stimulations of the tripolar one are shown in Fig. 31.

The potential is color coded, the horizontal axis corresponds to the number of nerves and the vertical

axis to the section of these nerves.

44

45

Figure 30: Spread curves resulting from the bipolar stimulation protocols simulated. Subfigures are ordered left to right and up to down, from BP12 to BP1112. The horizontal axis stands for the number of nerve, the vertical axis for the point of the

nerve and the color for the potential level.

46

Figure 31: Spread curves resulting from the tripolar stimulation protocols simulated. Subfigures are ordered left to right and up to down, from TP123 to TP101112. The horizontal axis stands for the number of nerve, the vertical axis for the point of

the nerve and the color for the potential level.

47

8.2 Publications

Here follows the list of publications that aroused from all work done in this thesis with the conference

or journal, the date and a picture of the first page.

International Conference on Medical Image Computing and Computed Assisted Interventions

(MICCAI), October 2014.

48

Congreso Annual de la Sociedad Española de Ingeniería Biomédica (CASEIB), November 2014.

49

Computer Assisted Radiology and Surgery (CARS), June 2015. (Accepted)

50

PLOS ONE. (Submitted)

51

International Conference on Medical Image Computing and Computed Assisted Interventions

(MICCAI), Workshop on Clinical Image-based Procedures: Translational Research in Medical Imaging,

October 2015. (Submitted)