ULTRASOUND WAVE TRANSMISSION BETWEEN HUMAN TISSUES USING THE

BOUNDARY ELEMENT METHOD

TRANSMISIÓN DE ONDAS DE ULTRASONIDO ENTRE TEJIDOS HUMANOS

EMPLEANDO EL MÉTODO DE ELEMENTOS DE FRONTERA

JUAN DIEGO MORALES DEL CORRAL

UNIVERSIDAD DE SAN BUENAVENTURA SECCIONAL MEDELLÍN

FACULTAD DE INGENIERÍAS

INGENIERÍA DE SONIDO

MEDELLÍN

2016

ULTRASOUND WAVE TRANSMISSION BETWEEN HUMAN TISSUES USING THE

BOUNDARY ELEMENT METHOD

TRANSMISIÓN DE ONDAS DE ULTRASONIDO ENTRE TEJIDOS HUMANOS

EMPLEANDO EL MÉTODO DE ELEMENTOS DE FRONTERA

JUAN DIEGO MORALES DEL CORRAL

Proyecto presentado para optar al título de Ingeniero de Sonido

Asesor

Héctor García Mayén MSc. Sonido y Vibraciones

UNIVERSIDAD DE SAN BUENAVENTURA SECCIONAL MEDELLÍN

FACULTAD DE INGENIERÍAS

INGENIERÍA DE SONIDO

MEDELLÍN

2016

1. CONTENTS

1. JUSTIFICATION ................................................................................................ 5

2. THE PROBLEM ................................................................................................. 5

3. OBJECTIVES ..................................................................................................... 6

3.1 Main objective ............................................................................................. 6

3.2 Specific objectives ....................................................................................... 6

4. ABSTRACT ........................................................................................................ 7

5. RESUMEN ......................................................................................................... 7

6. KEY WORDS ..................................................................................................... 7

7. PALABRAS CLAVES ......................................................................................... 7

8. REFERENTIAL AND THEORETICAL FRAMEWORK ........................................ 8

8.1 Ultrasound ................................................................................................... 8

8.1.1 Background ............................................................................................. 8

8.1.2 Sonochemistry ......................................................................................... 8

8.1.3 Ultrasound in medicine ............................................................................ 8

8.2 Anatomical structure of the ear and cochlea ................................................ 9

8.2.1 Computed tomography and Magnetic resonance imaging ....................... 9

8.2.2 Anatomical planes ................................................................................... 9

8.2.3 The ear, structure and innervation ........................................................... 9

8.2.4 Cochlea ................................................................................................. 10

8.2.5 Structure and Function of the cochlea ................................................... 12

8.2.6 Acoustic, and mechanical properties, and dimensions of human tissues 14

8.3 Hearing loss .............................................................................................. 15

8.4 Hearing aids .............................................................................................. 15

8.4.1 Acoustic Hearing Aids ............................................................................ 16

8.4.2 Carbon hearing aids .............................................................................. 16

8.4.3 Vacuum tube hearing aids ..................................................................... 16

8.4.4 Transistor hearing aids .......................................................................... 17

8.4.5 Digital hearing aids ................................................................................ 17

8.4.6 Cochlear Implant ................................................................................... 17

8.5 Boundary Element Method (BEM) ............................................................. 18

8.5.1 Basic BEM theory .................................................................................. 18

8.5.2 OpenBEM approach .............................................................................. 20

8.5.3 Additional information on some BEM terms ........................................... 21

9. PROCEDURE .................................................................................................. 21

9.1 Materials and methods .............................................................................. 21

9.1.1 OpenBEM toolbox for MATLAB ............................................................. 21

9.1.2 Variables used and test cases ............................................................... 22

9.1.3 Method .................................................................................................. 23

10. RESULTS AND DISCUSSION...................................................................... 26

11. CONCLUSIONS ........................................................................................... 28

12. REFERENCES ............................................................................................. 28

5

1. JUSTIFICATION

This project seeks to simulate a model of a system which generates a sound pressure

maximum point in the space looking towards to produce a sono-stimulation of the

auditory nerve without the traditional acoustical to mechanical to chemi-electrical

transduction process generated by the physical movement of the stereocilia and

kinocilium. It is desired to improve the existing processes to recover the audition. The

main objective of this project is the simulation of the transmission between tissue layers

of the head to reach a certain point with maximum sound pressure using an ultrasonic

sound source and phase shifts between them.

To date the research has been concentrated on how to stimulate a neuron with an

electrical signal. Some authors have investigated the stimulation of various receptor

structures of humans and animals with focused ultrasound waves, researching even

the effects of such waves on the conduction properties of neural tissue with different

energy levels. This researches have established conditions for transcranial stimulation

for example, for the mouse somatomotor response [1, 2, 3].

My purpose was to generate a stimulation on the auditory nerve without a surgical

procedure, employing ultrasound waves. For this it is needed to investigate the

transmission between tissue layers, the frequency of the ultrasound wave and its

minimal and maximal power to produce a neural stimulation without damaging the

tissue. The project aim is to show the possibility of helping people with auditory

disability, avoiding a costly and traumatic surgical procedure.

2. THE PROBLEM

When the stereocilia and the kinocilium suffer some permanent damage because of

high sound pressure level exposure to noise or a birth disease, the ear starts loosing

sensibility or does not have the capability of transducing the arriving sound wave at all,

producing in a person hearing loss; without the stereocilia and kinocilium humans do

not possess the physical conditions to hear, because there is nothing there to make the

mechanical to chemi-electrical transduction to send a neural stimulation through the

auditory nerve. Cochlear implants were developed to solve this problem, stimulating

directly the auditory nerve with electrical discharges. The problem with cochlear

implants is that a surgical procedure is required to implant the electrodes into the

cochlea. This surgical procedure is costly, and furthermore the patients have to go

through an uncomfortable and tough trial. It is desired to send the information directly

to the hair cells with an ultrasound wave, producing this way the chemical stimuli

needed for generating the electrical signal that goes through the auditory nerve, to

avoid the downside of the surgical procedure this way.

Some paths are simulated, in order to verify the transmission between tissues and to

propose a source array to stimulate the hair cells. The simulation is going to be

performed with the boundary element method for an axial and coronal cut of the

cochlear area on the temporal bone of the head including skin, bone, and other tissues

and layers.

6

3. OBJECTIVES

3.1 Main objective

Simulate tissue paths with an ultrasonic wave to reach the cochlea from the

skin tissue aiming for auditory nerve stimulation.

3.2 Specific objectives

Simulate an axial cut path of the head with the BEM for a single source.

Simulate a coronal cut path of the head with the BEM for a single source.

Propose a source array for a focal sound pressure point implementing the

paths.

7

4. ABSTRACT

The ultrasound wave transmission between human tissue layers was investigated in

this project, aiming for a focal stimulation of the auditory nerve on the cochlea. A

simulation of the transmission was implemented with the boundary element method in

order to visualize the behavior of the ultrasound wave. The ear and some basic

information about its function are presented. Some acoustic parameters for the

boundary conditions are written. The results obtained show transmission between

layers and a 30 dB attenuation on the cochlea caused by the transmission. It is

proposed a source array with multiple ultrasound sources, using phase differences

between the sources to focus this way the area desired for stimulation, because the

results with one acoustic piston source, producing a plane wave are not satisfactory for

a focused stimulation.

5. RESUMEN

En este proyecto se investigó la transmisión entre capas de tejidos humanos con

miras a la estimulación focal neuronal del nervio auditivo en la cóclea. Se implementó

una simulación de la transmisión mediante el método de fronteras para visualizar el

comportamiento de las ondas de ultrasonido. Se presentará información básica sobre

el oído su funcionamiento. Se escriben algunos parámetros acústicos para las

condiciones de frontera. Los resultados obtenidos muestran transmisión entre capas y

una atenuación de 30 dB en la cóclea causada por ésta transmisión. Se propone un

arreglo de fuentes con múltiples emisores de ultrasonido, empleando diferencias de

fases entre las fuentes para focalizar de esta manera el área de estimulación deseada,

debido a que los resultados con un pistón acústico como fuente producen ondas

planas, las cuales no son satisfactorias para una estimulación focal

6. KEY WORDS

Ear, Boundary Element Method, BEM, Ultrasound.

7. PALABRAS CLAVES

Oído, método de elementos de frontera, BEM, ultrasonido.

8

8. REFERENTIAL AND THEORETICAL FRAMEWORK

8.1 Ultrasound

8.1.1 Background

The discovery of the piezoelectric effect in 1880 was the basis for the generation of

ultrasound, established by Jacques and Pierre Curie. In 1883, Francis Galton

discovered the earliest form of an ultrasonic transducer, and this was developed to

investigate the frequency threshold of human hearing. The first commercial application

in 1917 was the "echo-sounder" a sonar (Sound navigation and ranging) invented and

developed by Paul Langévin. In later years ultrasound was used for imaging for

medical uses as a non-destructive procedure [4].

Applying a powerful ultrasound wave at a low frequency to a system, a phenomenon

called cavitation occurs which produces chemical changes. In 1895 Sir John

Thornycroft and Sidney Barnaby were the first to identify and report this phenomenon.

Around 1927 Robert Williams Wood and Alfred Lee Loomis were the pioneer scientists

to recognize the usefulness of ultrasound in chemistry; they observed that the chemical

reactions they were working on were not a consequence of the heat but of sonic

energy produced by cavitation [4, 5].

8.1.2 Sonochemistry

The process which uses the sonic energy with a certain power to introduce directly

into a mixture energy to produce a chemical reaction is called sonochemistry. Vinatoru

in his work used high power and high frequency waves to input energy in a liquid

reaction mixture. The liquid molecules in the mixture create voids, bubbles or

cavitation; they are pulled apart when the minimum power is exceeded, i.e. for water

this value is approximately 0.15 ∙ 109 𝑃𝑎 when no weak-spots are present (which lower

the liquid’s tensile strength), otherwise cavitation can occur at values less than 2.03 ∙

106 𝑃𝑎. A chemical reaction occurs when mechanical energy from the ultrasound

waves produces a collapse of the bubbles [4, 5].

8.1.3 Ultrasound in medicine

A well-known topic about ultrasound in medicine is the local destruction of tissue, as

in animals, as in humans. However its use for inducing reversible changes on the

activity of neural structures is less known. Investigations have shown that is possible,

with focused ultrasound pulses, to induce a significant modification in vitro, in nerve

excitability. Using short duration and high intensive focused ultrasound stimuli, it is

possible without any significant damage on the tissues to induce a variety of somatic

sensations, for example thermal, pain or tactile, as well as auditory responses. The

advantages of ultrasound stimuli are a locally stimulation, controlled and changed with

the resonant frequency, and the noninvasive technique, because it does not use a

surgical intervention [1].

9

8.2 Anatomical structure of the ear and cochlea

8.2.1 Computed tomography and Magnetic resonance imaging

CT scanners (computed tomography) were invented by Sir Godfrey Hounsfield in the

1970s, as mentioned in Drake, Vogl and Mitchell work. This scanners create images of

slices of the body in series [6]. Not as different as the Nuclear magnetic resonance

imaging, that is used to determine the structure of molecules, with the process of MRI

(magnetic resonance imaging) that uses the hydrogen proton which is present in

almost all biological tissues, and was first described in 1946. Both scanners divide the

body into different planes depending on the body position, called anatomical planes [6].

8.2.2 Anatomical planes

The anatomical planes divide the body into anterior and posterior parts, right and left

parts, and superior and inferior parts, anatomical planes are the coronal planes, the

sagittal planes and the axial planes (also transverse or horizontal) respectively [6]. The

different planes are shown in Fig. 1.

Fig. 1. (A) Sagittal plane, (B) Coronal plane and (C) Axial plane [7].

8.2.3 The ear, structure and innervation

The external ear, the middle ear, and the internal ear are the three parts that

compose the ear, Fig. 2.(A) is a representation of it. The external ear consists in the

canal leading inward, called the external acoustic meatus, and in the auricula (the

pinna). The middle ear is filled with a mucous membrane and air inside the temporal

bone, between the tympanic membrane and the internal ear. The internal ear is

composed by the bony labyrinth (a series of bony cavities) and the membranous

labyrinth (membranous ducts and sacs within the cavities). The internal ear is the

structure that conveys information about hearing and balance to the brain [6]. Fig. 2.(B)

is a CT scan showing the cochlea pointed out by the axis (purple), temporal bone

where the cochlea resides (read) and the external auditory canal which goes from the

cochlea to the exterior of the head (blue) in an axial, coronal and sagittal cut.

10

Fig. 2.(A) Components of the ear [6], (B) axial, coronal and sagittal cut CT scan showing the position of the

cochlea in the head [8].

8.2.4 Cochlea

The cochlea is a cone-shaped bony structure that twists on itself around the

modiolus, Fig. 3 shows a cross section of the cochlea [6]. A thin lamina of bone called

the lamina of modiolus or spiral lamina attaches the cochlear duct, which is a

component of the membranous labyrinth. The cochlear duct is attached to the outer

wall of the cochlea, creating two canals, called the scala- vestibuli and -tympani,

continuous with each other at the apex through the helicoterma [6].

The organ which allow hearing is the cochlear duct and the nerve responsible is the

vestibulocochlear nerve. This nerve carries afferent fibers for hearing and balance. The

vestibulocochlear nerve enters the brainstem between the pons and medulla, it goes

out of the temporal bone through the internal acoustic meatus and crosses the

posterior cranial fossa. Inside the temporal bone, the vestibulocochlear nerve divides in

11

the cochlear nerve and the vestibular nerve. The cochlear nerve enters through the

base of the cochlea and passes upward through the modiolus. Through the lamina of

modiolus passes branches of the cochlear nerve to innervate the receptors [6].

Fig. 3. The structure of the cochlea [6].

To illustrate better the position of the cochlea on the head, Fig. 4.(A) shows a CT

scan of the temporal bone (yellow) with the basal turn of the cochlea (blue) and the

external auditory canal (cyan), and fig. 4.(B) shows a CT scan of the temporal bone

(yellow) with the basal turn of the cochlea (blue), the external auditory canal (cyan), the

mesotympanum (sea green) and the tympanic membrane (orange)

Fig. 4.(A) Axial, coronal and sagittal cut CT scan of the temporal bone with the basal turn of the cochlea,

(B) Axial and coronal cut CT scan of the temporal bone with the basal turn of the cochlea [8].

12

8.2.5 Structure and Function of the cochlea

8.2.5.1 Structure of the Cochlea

On the basilar membrane (BM) a propagation of a hydrodynamic surface wave

stimulates the main organ responsible for the transduction on the cochlea, called the

organ of Corti. Inside the petrous temporal bone of the skull is a long, tapered tubular

cavity, divided into three chambers called: scala vestibuli, scala media and scala

tympani, shown in Fig. 5.(A). The scala vestibuli is the uppermost chamber,

communicated mechanically with the stimulus-induced displacements of the middle

ear, filled with a liquid called perilymph or perilymphatic fluid, which possesses a high

concentration in sodium (𝑁𝑎+) ions and low concentration in potassium (𝐾+) ions. The

scala media is the chamber in the middle, mechanically bounded with the scala

vestibuli but chemically and electrically isolated by the Reissner's membrane. The

scala media is filled with a fluid containing a high concentration in potassium (𝐾+) ions

and low concentration in sodium (𝑁𝑎+) ions called endolymph. The scala tympani is the

lower chamber joined at the apical end by the helicoterma (a small hole), separeted by

the basilar membrane from the scala media and scala tympani. On the basilar

membrane in the scala media lies the organ of Corti, shown in Fig. 5.(B) [9].

Fig. 5.(A) Section through the cochlea, (B) section through the organ of corti [9].

Acoustical stimulation causes small fluctuations in the volume of the scala vestibuli,

causing both vertical and longitudinal displacement of the basilar membrane and the

perilymph respectively. The vertical displacement of the basilar membrane causes

vertical vibration of the organ of Corti. The organ of Corti is composed by two types of

receptor cells, the inner hair cells (IHC) and the outer hair cells (OHC). The IHC

modulates their standing current in sympathy with the mechanical displacements, and

sends this information through the afferent fibers. The cochlea separates into

frequency components the complex acoustic signals like a short-term Fourier analyzer,

generating this way sharply tuned receptor potentials. This is possible because of the

also sharply tuned mechanical vibrations of the cochlea. The driving force of the

receptor potentials release neurotransmitters at the base of the hair cells, generating

this way, potentials in the fibers of the auditory nerve, called action potentials [9]. A

detailed cross section of the organ of Corti is shown in Fig. 6.(A), and Fig. 6.(B) shows

an electron micrograph scanning of a fractured cross section of the human organ of

Corti.

13

Fig. 6.(A) Cross section of the organ of Corti, (B) Scanning electron micrograph of a fractured cross

section of the human organ of Corti [10].

8.2.5.2 Hair Cells, stereocilia, and mechanical-to-electrical transduction

The human have on each cochlea about 12000 outer hair cells and 3500 inner hair

cells approximately. A Hair cell is a mechanical sensor placed in the cochlea composed

of two types of ciliary processes, a kinocilium and three rows of several stereocilia

arranged in a W-shaped pattern on the OHC and a wide 'U' or 'W' shape on the IHC.

Moore writes that the stereocilia are mechanical sensitivity sensors, this stereocilia

work as follows: the tip of the stereocilia have mechanical sensitive ion channels, and

with the deflection towards or away from the basal body, a standing current from the

ion channels modulates, resulting then in an electrical current through the receptor [9,

11]. Fig. 7 shows the process that occurs when a mechanical stimulation is perceived

by the hair cells. The structure of the hair cell along with the electro-chemical properties

Fig 7.(A), and the process of excitation and inhibition Fig. 7.(B).

As Moore (1995) mentions in his work, the fluctuations in the atmospheric baseline

pressure are transduced by the cochlea into a neural code on the auditory nerve [9].

This is done by the hair cells that generate a differential electrical potential to stimulate

Corti's nerve which is in charge of sending the information to the auditory nerve

through the afferent fibers. Two fluids generate the differential electrical potential on the

scala media and tympanic. Hair cells have an intracellular potential with respect to the

scala tympanic, called cochlear potential [12].

Palmer mentions in his work, that inside the IHCs tuned voltages are generated as

the basilar membrane vibrates; these voltages are in charge of initiating action

potentials in the afferent neurons. The auditory nerve fiber has a rate of spontaneous

activity while there are no sounds, and its activity is increased by sound stimulation of

appropriate frequency and level. The whole hearing range on the auditory nerve is

equivalent to a bank of band pass filters that overlap each other. This narrow filters

responses are as sharply tuned as the basilar membrane vibration pattern and their

activity voltages are dependent on the frequency and level of stimulation [13].

14

Fig. 7.(A) Model of a Hair cell. (B) The model for the mechanical transduction [10].

8.2.5.3 Neural stimulation with ultrasound

The neural stimuli produced by a focused ultrasound wave is a mechanical aspect,

that produces a potential change on the membrane, which results in a neural stimuli for

the physiological activation of the somatomotor system and the auditory perception [1].

Previous researches show that depending on the intensity and the pulse of an

ultrasound wave one can interfere on basic cellular processes [14, 15, 16]. For

example, to stimulate the nervous system of mice, prior investigations determined that

a continuous stimuli is as effective as, or even more so than a pulsed stimuli. Moreover

the intensity and duration with a 50 ms to 150 ms interval increases the success of the

stimuli [3]. Also the stimuli of the sciatic nerve of a bullfrog with a 3.5 MHz ultrasound

wave at 1, 2 and 3 Watt for 5 minutes showed that the compound action potential and

the conduction velocity increase [2].

8.2.6 Acoustic, and mechanical properties, and dimensions of human tissues

To find the acoustic parameters needed for the simulation Eq. 1 were implemented

with the use of some acoustic properties like Young's modulus and density to find the

sound speed:

𝑐 = √𝑌𝑜𝑢𝑛𝑔′𝑠 𝑚𝑜𝑑𝑢𝑙𝑢𝑠

𝑑𝑒𝑛𝑠𝑖𝑡𝑦 (1)

and, the impedance (z) in Eq. 2, which is equals to density times sound speed:

𝑧 = 𝛿 ∙ 𝑐 (2)

The parameters in Table. 1 are taken and verified for different ultrasonic frequencies

for skin [17, 18, 19, 20, 21], for skull [22, 23], and for tympanic membrane [24, 25, 26,

27]. For the cochlea, the length is between 8.8 and 13.5 mm, the depth between 6.9

and 7.2 mm, and the high is 4.3 mm [28, 29].

15

Table 1. Skin, skull, tympanic membrane and cochlea acoustic characteristics and dimensions.

Tissue/Parameter Velocity

[𝒎

𝒔]

Density

[𝒌𝒈

𝒎𝟐]

Impedance

[∙ 𝟏𝟎𝟔𝒌𝒈

𝒎𝟐 ∙ 𝒔]

Thickness [𝒎𝒎]

Skin

1490 1200 1.78 1.7 1610 1200 1.93 1.7 1500 1060 1.56 1.7 1720 1060 1.82 1.7

Skull

2448 1412 3.46 - 2516 1412 3.55 - 2140 1904 4.07 - 2300 1904 4.38 -

Tympanic membrane

42 1200 0.05 0.030 – 0.110 60 1200 0.07 0.030 – 0.110 96 1200 0.11 0.030 – 0.110

129 1200 0.15 0.030 – 0.110 167 1200 0.2 0.030 – 0.110 183 1200 0.22 0.030 – 0.110

8.3 Hearing loss

Audition can be damaged slight, severe or profound either by conductive losses

which consist in abnormalities in the middle ear or in the outer ear, or neurosensorial

damages which consist in traumas in the auditory nerve or hair cells. Conductive

losses are due mainly to mechanoacoustic problems such as: an impaired transfer of

pressure to the round and oval windows, a damage in the tympanic membrane, an

obstruction on the outer ear, or the immobilization of the middle ear parts. Those

disabilities can be taken care of by hearing aids, because of the simple attenuation of

frequencies. On the other hand, neurosensorial loss arise generally within the cochlea

due to acoustic trauma, infections, drugs, presbyacusis (due to aging) or congenital.

Benign tumors can also produce impaired hearing [10].

8.4 Hearing aids

Hearing aids have evolved from acoustical devices that do not use electricity, to

Digital devices. The transition in the timeline was from Acoustical tools, to carbon

devices, and then came the vacuum tubes; those open the path to transistor apparatus

to finally reach the Digital components, shown in Fig. 8. acoustical hearing aids were

used around 1640 to 1990; ear trumpets fabricated of animal horns, systems called

conversation tubes and bone conduction devices were used to improve the hearing for

people with hearing disabilities [30].

16

Fig 8.(A) Animal Horn, (B) Bone conduction, (C) Carbon Table-Top, (D) Carbon Body-Worn, (E) Vacuum

tube Table-Top, (F) Vacuum tube Body-Worn, (G) Transistor Body-Worn, (H)Transistor BTE, (I) Transistor

ITE, (J) Transistor Eyeglass, (K) Digital BTE [30].

8.4.1 Acoustic Hearing Aids

The acoustic or non-electric hearing aids were the first approach to solve a hearing

disability before the advent of electricity. It was mentioned around 1521, by Girolamo

Cardano, an Italian physician who wrote about the use of bone conduction to improve

the hearing, Fig. 8.(B). A later approach and first mentioned device was written by

Francis Bacon in 1627 who proposed an ear trumpet. Those were first made from

natural materials such as ram and cow horns, and snail-shaped seashells, shown in

Fig. 8.(A), later in the 18th century the ear trumpets were manufactured. The factory-

made devices were ear trumpets, conversation tubes, auricles, ear inserts and cone-

conduction devices. A conversation tubes could only pick up sound directly from the

speaker's mouth. Auricles were developed as hand free ear trumpets being the first

binaural hearing aid. Ear inserts were a hearing device that did nothing to help the

hearing. Bone-conduction devices were held against the teeth that transmitted sounds

to the inner ear via bone conduction [30].

8.4.2 Carbon hearing aids

This hearing aids were used from 1898 to 1939, and some examples of the carbon

hearing aids were: the table-top from Fig. 8.(C), which were placed on the table

because it was the size of a lunch-box, with a microphone facing the speaker, and the

body-worn that worked as the table-top, but could be worn, shown in Fig. 8.(D) [30].

8.4.3 Vacuum tube hearing aids

From 1921 to 1953 the vacuum tube devices were used. The first commercially-

available was the table-top from Fig 8.(E), then came the body-worn two piece, and the

17

body-worn one piece. The first table-top was manufactured by the Globe Ear-Phone

Company of Boston. The body-worn two-piece was named this way because the

hearing aids had shrunk to a wearable size, but the batteries were still too big to fit into

the hearing aid case and just floated around Fig 8.(F). The body-worn one-piece have

internal batteries and could be hidden [30].

8.4.4 Transistor hearing aids

Hearing aids with transistors were used from 1952 to 2005. At the beginning the

hearing aids were hybrid, using transistors and vacuum tubes. The transistor

technology came in different presentations, the body-worn, behind-the-ear (BTE), in-

the-ear (ITE) an eyeglass. The body-worn was used before the transistor hearing aids

had shrunk in size, shown in Fig. 8.(G). The BTE came out three years later and could

be worn behind the ear, Fig. 8.(H). ITEs were used in the ear presented in Fig. 8.(I).

Eyeglass hearing aids were BTE looking like glasses, the first device came out in 1954,

the eyeglass was the first contralateral routing of signal device in the industry, because

the microphone was on one side and the receiver on the other side, Fig. 8.(J) [30].

8.4.5 Digital hearing aids

Digital hearing aids are used from 1996 to date, after discrete components were

replaced with integrated circuits. This technology allowed the power and functionality of

the devices to increase, allowing them to evolve from a digitally programmable hearing

aid with analog parts, to a fully digital hearing aid, such as the Senso manufactured by

Widex, and DigiFocus-Compact produced by Oticon, the last shown in Fig. 8.(K) [30].

8.4.6 Cochlear Implant

The first researchers that wrote about cochlear implants were the Doctors André

Djourno and Charles Eyriès. André Djourno developed a prosthesis for the cochlea in

1953 which was an inductor implanted that were excited electromagnetically through

the skin, generating an electrical current on the implanted inductor (producing this way

a cochlear stimuli). In 1957 with the support of Charles Eyriès the first cochlear implant

was made [31].

A cochlear implant consists of both externally worn speech processor and surgical

implanted components, which are designed to bypass the damages of a severe to

profound sensori-neural hearing loss from the structures in the inner ear. The implant

stimulates the hearing nerve fibers directly with electrical discharges. As shown in Fig.

9 cochlear implant electrodes are placed in the scala tympani duct of the cochlea to

stimulate the nerve [32].

18

Fig. 9. Cochlear implant diagram [33].

8.5 Boundary Element Method (BEM)

8.5.1 Basic BEM theory

For a detailed reading on the BEM see [34, 35, 36, 37, 38, 39, 40, 41].

The basis of the BEM (boundary element method) consist in discretize with an

integral equation a mathematically equivalent PDE (partial differential equation). Just

the boundary of the domain of the PDE is calculated with this method. In cases where

the domain is exterior to the boundary, the infinite domain is calculated with an

equation representing the finite boundary. This implementation is expected to be more

computationally efficient than competing methods such as the Finite Element Method

(FEM) i.e. [34, 40].

In other words, the objective of the BEM is to replace the partial differential equation

of the domain for an equation on the boundary alone [34]. This is done by simplifying

the solution of the integral equations with a linear system of equations, this is achieved

by replacing the integrals by a quadrature formula of a weighted residual technique.

Often the method of collocation is used to replace the integral equations, this method

represents the boundary equations with panels and approximates the boundary

functions on each panel by a constant at the center of the panel, and this

representation is defined as an element in the BEM [34, 37].

In order to discretize the integral equation, the use of integral operators is required;

this integral operators demonstrates the relation between the integral equations and

the linear system of equations, the integral operators are like the matrices and the

boundary functions are like vectors [34].

19

There are two methods to derive an integral equation formulation of a PDE: The direct

method, where Green's second theorem is used, and the indirect method, that uses a

source density function defined on the boundary to express the solution [34, 41].

According to Messner and Kirkup, the acoustic field is governed by the linear wave

equation,

∇2ψ(p, t) =1

c2

∂2

∂t2 ψ(p, t) (3)

where: ψ(p, t) is the scalar time-dependent velocity potential [34, 39].

Kaiser and Kirkup coincide that the solution to an interior or exterior boundary value

problem is determined by the boundary conditions and the shape of the boundary. The

boundary conditions are either the velocity potential 𝜑 called the Dirichlet boundary,

normal velocity 𝑣, called Neumann boundary, which is the derivative of 𝜑 with respect

to the normal to the boundary, or a Robin boundary, which is a relationship between

the velocity potential and the normal velocity [34, 41]. The boundary condition is of the

form:

𝛼(p)φ(p) + β(p)𝑣(p) = 𝑓(p) (4)

with (p ∈ S), where: 𝛼, β and 𝑓 are complex-valued functions defined on S.

To solve the linear wave equation with the BEM (the boundary condition from Eq. (4)),

the use of the integral operators 𝐿𝑘, 𝑀𝑘, 𝑀𝑘𝑡 and 𝑁𝑘 from Eq. (5), (6), (7) and (8) are

required. This operators are the integral equation formulations of the Helmholtz

equations, and are the expressions derived by the boundary panels with the

approximation of the boundary functions by a constant on each of this panels [34, 38].

The Helmholtz integral operators are:

{𝐿𝑘𝜁}Γ(p) ≡ ∫ Gk(p, q)𝜁(q)dSq

Γ (5)

{𝑀𝑘𝜁}Γ(p) ≡ ∫∂Gk

∂nq(p, q)𝜁(q)dSq

Γ (6)

{𝑀𝑘𝑡 𝜁}Γ(p; up) ≡

∂

∂up∫ Gk(p, q)𝜁(q)dSq

Γ (7)

{𝑁𝑘𝜁}Γ(p; up) ≡∂

∂up∫

∂Gk

∂nq(p, q)𝜁(q)dSq

Γ (8)

where: Γ is a boundary or partial boundary,

nq, up are unit vectors with nq the unique normal to Γ at q,

𝜁(q) is a function defined for q ∈ Γ,

𝜕∗

𝜕𝑛𝑞 represents the partial derivative of the function * with respect to the unit outward

normal at the point q on the boundary.

Gk(p, q) is the free-space Green's function for the Helmholtz equation (𝐺(𝑝, 𝑞)

represents the effect observed at a point p of a unit source at the point q).

20

8.5.2 OpenBEM approach

OpenBEM uses the method of direct collocation, dealing with the sound pressure (p),

particle velocity (v), and boundary conditions, this being the acoustic variables. To deal

with thin objects, an indirect variation of the BEM is used, called the indirect variation

method, where the acoustic variables are replaced by quantities, which represent the

variation across the boundary [42].

To obtain a solution over the domain, two phases are required, first: getting pressure

and normal velocity on the surface through the BEM system, second: selecting and

calculating points in the domain with the previous results [42].

With Eq. (9), omitting the harmonic time dependence (𝑒𝑗𝜔𝑡) one can relate the

pressure p(Q) and the normal velocity v(Q) on the surface of any shape of a body with

the pressure at any point p(P) and the pressure of an incoming wave p'(P) [42].

𝐶(𝑃)𝑝(𝑃) = ∫ (𝜕𝐺

𝜕𝑛𝑝(𝑄) + 𝑗𝑘𝑧0𝑣(𝑄)𝐺) 𝑑𝑠

𝑆+ 4𝜋𝑝𝐼(𝑃) (9)

where S is the surface of the body, Q a point on that surface and P any exterior or

interior point. The normal vector n is directed into the computational domain. The factor

C(P) is the geometrical constant and represents the exterior solid angle at P. G is the

Green's function from Eq. (13) [42].

To obtain a matrix of the form from Eq. (8) one need to discretized the surface S into

elements [48].

𝐂𝐩 = 𝐀𝐩 + 𝑗𝑘𝑧0𝐁𝐯 + 4𝜋𝐩𝐼 (10)

From Henríquez and Juhl's work: "Eq. (10) is the result of the collocation point P on

every one of the discrete Q points, the nodes of the surface mesh" [42]. The pressure

and normal velocities at the nodes are here p and v, the matrices containing the

integrals of the kernel function of Eq. (9) and Eq. (13) are matrices A and B. The left-

hand side can be subtracted from the diagonal of the first term in the right-hand side of

Eq. (10), given the fact that point P has been placed at the surface [42].

By solving the system of equations, the pressure on the nodes can be expressed, for

radiation problems, as a function of the normal velocity on the surface, or the incident

pressure on the surface for scattering problems. From the surface values of pressure

and normal velocity by integrating Eq. (10) again, the sound pressure on any point of

the domain can be obtained [42].

One can solve the system of equations of the BEM, depending on the boundary

conditions, Eq. (10) can be reformulated with Eq. (11) when the left-hand side (of Eq.

(10)) is already subtracted from the first term of the right-hand side [42]. Eq. (11) is

expressed as follows:

0 = 𝐀𝐩 + 𝑗𝑘𝑧0𝐁𝐯 + 4𝜋𝐩𝐼 (11)

In radiation problems is possible to combine a velocity 𝐯0 and an impedance

boundary condition through the velocity term in Eq. (12) with the Y𝒊 as the

21

admittances on the nodes, and the 𝐯0𝑖 as the fixed normal velocities on the nodes

[42].

𝐯 = 𝐘𝐩 + 𝐯0 (12)

8.5.3 Additional information on some BEM terms

8.5.3.1 About Sommerfeld condition

For computational purposes many engineering problems that deal with waves and

involve infinite domains are truncated, so that the wave problem can be solved in a

finite domain. The Sommerfeld boundary condition, or Sommerfeld radiation condition

is an artificial boundary that absorbs impinging waves, this is called a Non-Reflecting

Boundary Condition (NRBC). The Sommerfeld condition relates the normal and

temporal derivatives of the unknown for a source far away from the boundaries and

normal to the propagation wave. For a non-perpendicular wave incidence and

boundaries that are close to the source, this condition is inexact, because it avoids

wave reflection with an approximation in those cases [43].

8.5.3.2 About Green's function

The Green's function is defined as:

Gk(p, q) =i

4H0

(1)(k𝑟) (13)

with 𝑘 ∈ ℂ\{0} in a two dimensional space, where: 𝑟 = |𝐫|, 𝐫 = p − q, ℂ is the set of

complex numbers and i is the unit imaginary number, H0(1)

is the spherical Hankel

function of the first kind of order zero [34, 35, 38, 41].

To solve differential equations, such as ordinary or PDEs, an integral kernel called

Green's function is used. This kernel uses initial or boundary value conditions [44, 45].

9. PROCEDURE

9.1 Materials and methods

9.1.1 OpenBEM toolbox for MATLAB

The software used in this work was an open source toolbox coded by Peter Juhl and

Vicente Cutanda Henriquez, called OpenBEM [46], for MATLAB. The version used in

this work was 02/2015. The toolbox implements the conventional 2D-BEM for external

or internal problems. The main steps of the BEM used are [41]:

Mesh generation.

Import and validation of mesh.

Definition of boundary conditions.

Solution for surface variables.

Solution for field variables.

Display and evaluation of results.

22

For the mesh generation, the use of CAD programs are normally used to create

computer models of objects which mostly can be exported into a mesh format. The

kernel 'nodegen' where used to create the rectangular bodies used in the simulation,

and the kernel 'nodummy', which reduces the input matrix by eliminating dummy

elements [41]. To import and validate the mesh, usually CAD programs are employed

to generate the mesh.

To declare boundary conditions, where the boundary conditions are defined for every

node. Dirichlet, Neumann or impedance (Robin) boundary conditions can be defined. In

case of impedance boundaries the force or prescribed velocity and the admittance had

to be defined [41].

To solve surface variables, first the incident pressure was calculated with the kernel

'greendef' which calculates the 2D Green's function for free field, rigid planes, or

impedance planes. Then the coefficient matrix was calculated with the kernel 'bem2d',

to solve the system 𝐴𝑥 = 𝑏, where matrix A and vector b contains the knowns and

vector x contains the unknowns [41].

To solve field variables, first the coefficients for a set of field points were calculated

with the kernel 'fieldpoints'. The incident pressure was calculated in the previous step

with the kernel 'greendef', to produce a new system 𝐴𝑥 = 𝑏, that was later solved [41].

Display and evaluation of results; the surface variables could be plotted over the

radiating objects, encoded in color by the kernel 'plotpoints' and 'SPL'.

9.1.2 Variables used and test cases

The frequency chosen for the simulations was 0.27 MHz based on previous studies

[22], with a wavelength in the cochlea 𝜆 =𝑠𝑜𝑢𝑛𝑑 𝑠𝑝𝑒𝑒𝑑 𝑜𝑓 𝑡ℎ𝑒 𝑐𝑜𝑐ℎ𝑙𝑒𝑎

𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦= 5.7 𝑚𝑚. The Table

2 shows the parameters of each tissue used in the simulations for this frequency,

parameters as velocity, density, impedance, high and length of each layer from Table.

1 either extrapolated or taken.

Table 2. Tissue parameters used in the simulation.

Tissue/Parameter Velocity

[𝒎

𝒔]

Density

[𝒌𝒈

𝒎𝟐]

Impedance

[∙ 𝟏𝟎𝟔𝒌𝒈

𝒎𝟐 ∙ 𝒔]

Length [𝒎𝒎]

High [𝒎𝒎]

Skin 1540 1200 1.8 1.7 4.3 Skull thin 2291 1904 4.3 1.4 - 2.7 4.3 Skull thick 2291 1904 4.3 11.5 - 42.6 4.3 Tympanic

membrane 96 1200 0.1 0.1 4.3

Cochlea 1540 1200 1.8 8.8 4.3

In Fig. 10 all paths for the wave propagation are shown, these paths were simulated

separately to verify the transmission of an ultrasound wave through them. A source

array called a phased array [47], using at least tree of this paths with acoustic pistons

simultaneously could be employed to focus a desired area on the cochlea to stimulate

the hair cells or the specific bandwidth with different delays on this sources.

23

Fig. 10. (D) Direct path for both coronal and axial cut. (1A) Alternative path 1 for the axial cut, (1C)

Alternative path 1 for the coronal cut, (2A) Alternative path 2 for the axial cut, (2C) Alternative path 2 for

the coronal cut [6].

9.1.3 Method

A simulation for each path was done, for each of the simplified cases, to verify the

transmission between layers to observe the attenuation from the transmission. With

these results we could propose a source array to focus the ultrasound wave, in order to

stimulate the desired area.

9.1.3.1 Direct path

The path to reach the cochlea with the shortest distance, shown in Fig. 11, was the

path from the external auditory canal, passing through the tympanic membrane, to

reach the mesotympanum (which is a cavity of air), then passing through the thin layer

of the temporal bone that surrounds the cochlea, to reach at the end the cochlea itself.

Fig. 11. Direct path of wave propagation for the coronal and axial cut [8].

24

9.1.3.2 Alternative paths

One could reach the cochlea in a different way than the direct path, this other ways

have a longer distance than the direct path. In Fig. 12 the line 1 (in green) shows an

alternative path to reach the cochlea, and the line 2 (in blue) shows a second way to

reach the cochlea. Both ways pass through the skin, part of the temporal bone, the

mesotympanum, a thin layer of the temporal bone to get to the cochlea at the end. The

difference in these paths is the thickness of the layers to reach the cochlea, especially

the temporal bone layers, as shown in Fig. 12.

Fig. 12. Alternative paths for the wave propagation for a coronal and an axial cut [8].

9.1.3.3 Simplified test case

The bodies used for the paths were simulated as a model of rectangles with the

properties of each tissue. All the paths contained 5 bodies with different characteristics,

shown in Table 2. The direct ways are composed by a layer of air, a layer for the

tympanic membrane, a layer of air, a bone layer, and the cochlea layer as shown in

Fig. 13.(A) The indirect ways are all composed by a skin layer, a bone layer, an air

layer, another bone layer, and the cochlea layer, shown in Fig. 13.(B) [6, 8, [48].

Fig. 13.(A) Direct path construction, and (B) Alternative path construction for the axial and coronal planes.

Fig. 14, 15, and 16 show the meshes used for the simulations. Each figure shows a

path with its respective layer dimensions. Each mesh is composed of five bodies. Fig.

25

14.(A), 15.(A), and 16.(A). show the boundary points for an axial cut in the direct path,

the alternative path 1 and alternative path 2 respectively. Fig. 14.(B), 15.(B), and

16.(B). show the boundary points for a coronal cut in the direct path, the alternative

path 1 and alternative path 2 respectively.

Fig. 14.(A) Boundary points for the direct path for an axial cut, and (B) for a coronal cut, abscissa and

ordinate in meters.

Fig. 15.(A) Boundary points for the alternative path 1 for an axial cut, and (B) for a coronal cut, abscissa

and ordinate in meters.

26

Fig. 16.(A) Boundary points for the alternative path 2 for an axial cut, and (B) for a coronal cut, abscissa

and ordinate in meters.

10. RESULTS AND DISCUSSION

In Fig. 17 to Fig. 19, it is presented the sound pressure level (SPL) obtained for each

path shown in Fig. 14 to Fig. 16, with an acoustic piston source for each stimulation.

Transmission through layers is present for the 3 paths for an axial and coronal cut, and

in the cochlear region a plane wave was visible, with a pressure reference of 20 µPa. In

Fig. 17.(A), 18.(A), and 19.(A) are presented the results of wave propagation for each

path way for an axial cut. And in Fig. 17.(B), 18.(B), and 19.(B) are presented the

results of wave propagation for each path way for a coronal cut.

Fig. 17.(A) SPL for the direct path for an axial cut, and (B) for a coronal cut.

In the cochlear area in Fig. 17.(A), and 18.(A) the maximal SPL had a value of around

50 dB to 60 dB, the source had an SPL of 80 dB approximately. Similar to the results in

the cochlear area in Fig. 17.(B), and Fig. 18.(B) with maximal SPL value of around 50

dB to 60 dB, the source had an SPL of 80 dB approximately, as well.

27

Fig. 18. (A) SPL for the alternative path 1 for an axial cut, and (B) for a coronal cut.

In the cochlear area in Fig. 19.(A) the maximal SPL had a value of around 50 dB to

55 dB, the source had an SPL of 80 dB approximately, like in the cochlear area in Fig.

19.(B) with maximal SPL value of around 50 dB to 55 dB, the source had an SPL of 80

dB approximately.

In Fig. 17, 18, and 19 one can see the sound transmission and the sound pressure

level, with a maximum around 50 dB to 60 dB on the area of the cochlea. Each path

suffered a transmission loss between layers of about 30 dB from the source with an 80

dB SPL. In the cochlear layer a plane wave behavior was present.

Fig. 19. (A) SPL for the alternative path 2 for an axial cut, and (B) for a coronal cut.

Despite the loss in sound pressure level for each path, propagation through the tissue

layers existed. SPL at the cochlea could be increased or decreased for the hair cells to

react chemically and produce a neuro-electrical stimuli without exceeding the minimum

level for cavitation which is 220 dB approximately for a 20 µPa reference pressure [4].

For reaching a focal region with less powerful transducers with more sound pressure,

it is to be design a source array to focalize the stimulation region, dividing the energy

needed in each transducer and the possible negative effects from the wave energy on

28

the non-focal areas. A source array with five transducers (for each path shown in Fig.

10) could be implemented in further investigations to obtain a maximum sound

pressure level in a specific region of the hair cells with a source placed for every path

presented in this work with different phases between sources.

11. CONCLUSIONS

The existence of transmission between layers with an ultrasound wave was

demonstrated. This results show plausible hair cell stimulation, regardless of

transmission loss between layers. With the sound source simulated, the SPL does not

reach the minimum level for cavitation, avoiding this way possible damages on the

tissues caused by this phenomenon. This results show that one could increases the

SPL for compensating the transmission loss between layers.

With a piston-like ultrasound source, focused hair cell stimulation as the results

shown in this work, was not possible, because of the arriving plane waves. For a focal

stimulation is recommended a source array, for example a five source array that uses

the five paths shown in Fig. 10 with the desired cochlear area as the focused point,

which would guarantee a focal stimulation, or at least a different behaviors of the

arriving ultrasound wave.

In order to assure that the desired area would be stimulated, a different ultrasound

source or a source array with at least three or more sources, could reduce the focal

area to generate a stimuli in the desired frequency bandwidth on the cochlea.

Another way of stepping into the research would be to start simulating a source array

using a combination of the paths shown in Fig. 10 from the ear to the desired cochlear

area, in order to visualize the behavior of the ultrasound waves, and the changes

produced with variations in the phases between the sources.

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