FEM simulations of an Acoustic Radiation Force Impulse applied to a Soft Tissue with a Tumor ...

166 Pages·2013·4.29 MB·English

by  Lars Edvard Dæhli

FEM simulations of an Acoustic Radiation
Force Impulse applied to a Soft Tissue
with a Tumor Inclusion
Lars Edvard Dæhli
Mechanical Engineering
Submission date: June 2013
Supervisor: Leif Rune Hellevik, KT
Norwegian University of Science and Technology
Department of Structural Engineering

Institutt for konstruksjonsteknikk TILGJENGELIGHET
Fakultet for ingeniørvitenskap og teknologi
Åpen
NTNU- Norges teknisk- naturvitenskapelige universitet

MASTEROPPGAVE 2013

FAGOMRÅDE: DATO: ANTALL SIDER: 164
Beregningsmekanikk 10.06.2013 17+90+57

TITTEL:
FEM-simuleringer av en svulst i et bløtt vev utsatt for bølgeindusert impulslast

UTFØRT AV:

Lars Edvard Bryhni Dæhli

SAMMENDRAG:

De elastiske egenskapene til bløtt vev kan estimeres ved å indusere lokale forskyvninger og
skjærbølger. Vi har laget en plan tøynings FEM-modell for å simulere en stiv elastisk svulst inne i
et bløtt vev. Det bløte vevet er påført en bølgeindusert impulslast. Vi har brukt et vev-
etterlignende materiale for å representere de viskoelastiske materialegenskapene til bløtt vev, og
kalibrert en Maxwell-modell ut i fra eksperimentelle data. Bølgelasten som genereres av en
fokusert ultralydprobe ble beregnet i en ultralydsimulering. En gaussisk funksjon ble tilpasset
lastfordelingen fra simuleringen og implementert i FEM-modellen som en impulslast.

Fra FEM-simuleringene kunne vi se at den påførte impulslasten induserte lokale aksielle
forskyvninger i fokalpunktet, som videre dannet en skjærbølge som forflyttet seg vekk fra
fokalpunktet. Basert på den tidsavhengige forskyvningen i fokalpunktet og
skjærbølgepropagasjonen gjennom det heterogene vevet, så har vi undersøkt tre forskjellige
metoder for å estimere den elastiske stivheten: (i) ved å bruke skjærbølgehastigheten; (ii) ved å
betrakte skjærbølgerefleksjonene fra svulsten; (iii) ved å måle tiden det tar før vi oppnår maksimal
forskyvning i fokalpunktet.

Skjærbølgehastigheten ble eksakt gjengitt i det bløte vevet, men skjærbølgehastigheten i svulsten
var avhengig av størrelsen og formen til svulsten, noe som resulterte i upålitelige estimater av
stivheten til svulsten. Skjærbølgerefleksjonene fra svulsten var kompliserte, og refleksjonsfaktoren
var avhengig av formen til svulsten. Vi må vite stivheten til det bløte vevet på forhånd, for å kunne
bestemme stivheten til svulsten. Ved å måle tiden før maksimal forskyvning inntraff, så vi at
denne tiden var relatert til stivheten. Vesentlige problemer ved denne metoden er at den var
avhengig av varigheten på impulslasten, at den bare kan brukes for en perfekt Gaussisk
ultralydbølge og at det kan være vanskelig å observere når maksimalforskyvningen inntreffer, på
grunn av begrensede målefrekvenser på ultralydproben.

FAGLÆRER: Professor Leif Rune Hellevik

VEILEDER(E): Professor Leif Rune Hellevik, Førsteamanuensis Victorien Prot,
Post.doc Abigail Swillens (Universitetet i Gent)

UTFØRT VED: Institutt for konstruksjonsteknikk

Department of Structural Engineering
Faculty of Engineering Science and Technology
NTNU - Norwegian University of Science and Technology
MASTER THESIS 2013
for
Lars Edvard Bryhni Dæhli
FEM simulations of an Acoustic Radiation Force Impulse applied
to a Soft Tissue with a Tumor Inclusion
FEM-simuleringer av en svulst i et bløtt vev utsatt for bølgeindusert
impulslast
Softtissuesconsistmainlyofwaterandtheremainingpartismadeupofcellularstructures.
The material properties of soft tissues are consequently quite similar to those of water, in
terms of mass density and volume elasticity. Water does not have any resistance to shear
deformations, but the cellular structure gives the soft tissue shear stiffness. Tumors have
higher stiffness than the surrounding soft tissue and they can be felt by manual palpation
of the tissue. However, this is not possible for tumors that are small in size or located
deep within the tissue.
Due to the relatively low shear stiffness, ultrasound induced shear waves travel at a much
lower speed than the ultrasound compression waves. The shear wave speed is therefore
easier to measure than the compression wave speed. Modern ultrasound techniques takes
advantage of this and measures the shear wave speed in the tissue to determine the elastic
stiffness. In this thesis the relation between measurements and material properties should
be assessed by means of FEM simulations. Suggested content for the thesis are:
(cid:136) A study of relevant theory, such as ultrasound and wave propagation.
(cid:136) Finite element simulations of wave propagation in a soft tissue.
The thesis should be organized according to existing guidelines.
Supervisors: Prof. Leif Rune Hellevik (NTNU), Ass.Prof. Victorien Emile Prot (NTNU),
Post.Doc. Abigail Swillens (UGhent)
The thesis should be delivered at the Department of Structural Engineering
within the 10th of June.
Leif Rune Hellevik
Main supervisor

Abstract
Theelasticstiffnesspropertiesofsofttissuescanbeestimatedbytheuseoflocallyinduced
displacementsandshearwaves. Inthiswork,wehavemadeatwo-dimensionalplanestrain
finiteelementmodeltosimulateasofttissuewithastifferelasticinclusion. Thesofttissue
was subjected to an acoustic radiation force impulse. The elastic inclusion represents
a potential tumor within the healthy tissue. We have used a tissue-mimicking gel-agar
phantom to represent the viscoelastic material properties of soft tissue and calibrated a
three-element Maxwell model based on stress relaxation data from an experiment carried
outonthegel-agarphantom. ThecalibratedMaxwellmodelwasverifiedinafiniteelement
simulationofthestressrelaxationtest. Theacousticradiationforcegeneratedbyafocused
linear array transducer was determined from an ultrasound pressure field simulation. A
three-element Gaussian function was fitted to the resulting acoustic radiation force field
and implemented as a body force in the finite element model.
From the finite element analyses of the soft tissue with an inclusion, we found that the
applied body force induced a local axial displacement in the focal region, which gave
rise to a shear wave propagating away from the region of excitation. Based on the time
dependent axial displacement profile in the focal region and the shear wave propagation
through the heterogeneous tissue, we have examined three different ways of estimating the
elastic stiffness: (i) using the shear wave speeds; (ii) using shear wave reflection factor
values; (iii) using the time to peak displacement in the focal region.
We found that the shear wave speed was accurately (<0.15 % deviance) represented in
the soft tissue and could be used to estimate the elastic stiffness in this region. However,
the shear wave speed in the tumor was dependent upon the size and shape of the tumor,
which resulted in unreliable stiffness estimates. The shear wave reflections from the tumor
were rather complex and the reflection factor was highly dependent upon the shape of the
tumor. Also,wemustknowtheelasticstiffnessvalueofthehealthytissueinadvance,since
the shear wave reflection only provides information about the relative stiffness difference
between the healthy tissue and the tumor. Thus, this method may be used to locate an
inclusion, but cannot be used to quantify the stiffness of neither the surrounding tissue
nor the inclusion. The time to peak displacement was inversely related to the stiffness and
independent of the load magnitude, which is favorable for medical imaging application.
However, the time to peak displacement was dependent upon the impulse time of the
appliedloadandcanonlybedirectlyrelatedtotheelasticstiffnessforaperfectlyGaussian
ultrasound beam. Also, limitations of the pulse repetition frequency can make it difficult
to detect the peak displacement.
The results in this thesis indicate that stiffness estimation methods based on shear wave
speed measurements are most reliable.

Preface
This work is conducted as my master thesis concluding my M.Sc degree in Mechanical
Engineering at Norwegian University of Science and Technology (NTNU). The thesis was
written in the period between 14th of January and 10th of June 2013 at the Department
of Structural Engineering.
Cancer, referred to as malignant tumors, is the cause of about 13 % of all human deaths
worldwide [1]. If these malignant tumors are detected at an early stage, the number of
deaths may be reduced. Today, different imaging techniques have been developed in order
to detect tumors within healthy tissue. In regard to this, the Finite Element Method
(FEM) may be used to examine the reliability of such imaging techniques. I was intrigued
by this application of FEM and decided to dedicate my master thesis to this topic.
Acknowledgments
First, I would like to thank my main supervisor Professor Leif Rune Hellevik at the
DepartmentofStructuralEngineeringforhisvaluableguidancethroughoutthesemester. I
wouldalsoliketothankco-supervisorAssociateProfessorVictorienEmileProtforsharing
his thoughts and knowledge. I would like to express my appreciation to co-supervisor
Post-Doctoral Researcher Abigail Swillens at Ghent University for answering an enormous
amount of questions and showing interest in my work. Also, I would like to thank Annette
Caenan for providing experimental data.
In addition, I think it is in order to thank my peers Arne, Erik, Johan and Knut for all
the fruitful discussions and the great atmosphere in the office.
Lastly, thanks to my partner in crime, Caroline, for letting me spend most of the time at
the university writing this thesis.
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