Ansys analysis o weakly magne ic ma e ials in MR omog aphy
15
ANSYS ANALYSIS OF WEAKLY MAGNETIC MATERIALS IN MR TOMOGRAPHY
Milosla S einbaue *, Ka el Ba usek **
*Facul y o Elec ical Enginee ing and Communica ion, B no Uni e si y o Technology,
Pu kyo a 464/118, 612 00 B no, Czech Republic, s einbau@ eec. u b .cz
**Ins i u e o Scien i ic Ins umen s, Academy o Sciences o he Czech Republic,
K alo opolská 147, 612 00 B no, Czech Republic, ba @isib no.cz
Summa y The pape deals wi h he impac o weakly magne ic ma e ials on magne ic ield in MR omog aphy. The esul s
ob ained by ini e elemen me hod modelling as well as da a measu ed by MR omog aphy a e in oduced. Me hod o
magne ic suscep ibili y de e mina ion using MRI is discussed.
1. INTRODUCTION
Basic ield homogenei y is one o he p incipal
equi emen s in MR omog aphy. P esence o magne ic
ma e ials in measu ed specimen b ings abou local
pe u ba ion o his ield, which esul s in de o ma ion
o cap u ed image. Because o high equi ed
homogenei y (10
-6
and be e ), al eady ma e ials wi h
e y low suscep ibili y ha e signi ican impac .
Because o possibili y o u u e elimina ion o
a e ac in MR images caused by such ma e ials,
knowledge o ma e ial suscep ibili y is e y impo an .
Fo example, p esence o den al illing, when an MR
image o head is made, b ings ou local loss o pic u e
in o ma ion.
Fig. 1 Impac o pa amagne ic specimen on MR ield
homogenei y
Measu emen o suscep ibili y can be ealized
by se e al me hods. One me hod based on low-
equency induc i e b idge wi h ield in ensi y abou
300 A/m was de eloped by AGICO Company [5], [6].
Achie ed sensi i i y o his me hod allows measu emen
o ma e ial wi h suscep ibili y o o de 10
-5
, mo eo e
magne ic aniso opy can be obse ed.
Magne ic esonance e ec b ings ano he
possibili y o suscep ibili y e alua ion. P inciple o
measu emen is elemen a y o ma e ials which gi es
signal in MR omog aphy. When sui able imaging
me hod is applied (usually g adien echo – GE),
in o ma ion abou local change o magne ic induc ion o
ield in sample is phase-coded in ob ained image. F om
known shape o induc ion, local alue o pe meabili y µ
o suscep ibili y χ can be de i ed using Laplace's
equa ion
m
0
ϕ
∆ =
(1)
One o me hods o suscep ibili y measu emen
o ma e ials, which gi es no MR signal, was desc ibed
in [1]. This me hod uses compa ison wi h e e ence
ma e ials o known χ (such as wa e , ace one, …).
Because no signal o m inside a ea is acqui ed and hus
change o magne ic induc ion inside i can’ be
enume a ed, he induc ion in specimen icini y is an
objec o in e es .
Below in his pape we will discuss measu ing
echnique, which is sui able o subs ances wi h no
signal in MR omog aphy. Fo illus a ion see Fig. 1,
whe e is shown slice o MR expe imen model wi h
specimen o suscep ibili y
4
S
1 10
χ
−
= ⋅ in basic ield
wi h magne ic induc ion
0
4.700 T
B
=. De o ma ion o
magne ic induc ion ield in specimen a i e, mo eo e
ield in specimen icini y is a ec ed. This igu e has
been ob ained om Ansys model Fig. 3 below.
2. PRINCIPLE OF THE METHOD
The me hod is based on cons an magne ic lux
in wo king space o supe conduc ing magne . Inse ing
o he specimen o hickness ∆x and wi h magne ic
suscep ibili y
χ
s causes local de o ma ion o
homogeneous magne ic ield (idealized case is in Fig. 2)
(
)
s 0 s
1
B B
χ
= ⋅ + . (2)
Assume cons an magne ic lux
Φ

h u no mal
a ea o c oss-sec ion
S
o he magne wo king space
.
S
B dS cons
φ
= ⋅ =

(3)
Suppose he specimen has enough la ge leng h
in
y
-axes di ec ion, so we can neglec bounda y e ec .
Fo
z-x
c oss-sec ion Fig. 2 in he middle o he
specimen we can w i e
( )
0
0
B x B dx
ε
ε
−
− ⋅ =
 
 

, (4)
wha means ha sum o ha ched a eas bounded by cu e
in Fig. 2 wi h espec o he base alue o induc ion
B
0 is
Ad ances in Elec ical and Elec onic Enginee ing
16
ze o, whe e
ε
is su icien dis ance om specimen wi h
espec o i s impac on induc ion change.
Fig. 2 Change o magne ic induc ion ield in pa amagne ic
specimen and i s icini y – idealized case
I we can de e mine he cou se o
(
)
B x
(using
sui able MRI echnique and e e ence subs ance gi ing
MR signal in su oundings o ma e ial), we can also
enume a e
B
s and χs alues o he in es iga ed specimen
ma e ial. F om p incipal case in Fig. 2 we can de i e:
( ) ( )
x
0 S 0
/2
2
x
B x B dx B B
ε
∆
− ⋅ ≅ ∆ −
 
 

, (5)
and using (2)
( )
x
0
/2
S
0
2
x
B x B dx
B
ε
χ
∆
− ⋅
 
 
≅∆ ⋅

. (6)
Desc ibed me hod was nume ically modelled
in Ansys and checked on 200 MHz MR omog aph in
Ins i u e o Scien i ic Ins umen s, Academy o
Sciences.
3. NUMERICAL MODELING
a) b)
Fig. 3 Geome ical and meshed model (cylind ical
a angemen )
One o used Ansys 3D models is on Fig. 3
(a - geome ical model, b - meshed model). Volumes
wi h di e en magne ic p ope ies ha e di e en colou .
Nume ical modelling was p o ided using
Ansys 6.1 so wa e. Using FEM he scala magne ic
po en ial
Φ
m was compu ed by sol ing o Laplace’s
equa ion (1).
One o used model is in Fi . 4. The model was
meshed wi h Solid96 elemen ype. Bounda y
condi ions we e se up o achie e induc ion
B
0 = 4,700 T in
z
-axes di ec ion:
•
.
m
cons
Φ = on he su aces Γ1, Γ2,
•
0
m
n
∂Φ
=
∂ on he shell su ace Γ3.
Fig. 4 Simple Ansys model, dimensions a e in mm
The module o magne ic induc ion
B
along he
“pa h” ma ked in Fig. 4, ob ained by sol ing o
men ioned model, is depic ed in Fig. 5.
Fig. 5 Cou se o magne ic induc ion in sec ion o model
in ig. 4
Ano he model, used o e i ica ion o
suscep ibili y measu emen is in Fig. 6. He e weakly
pa amagne ic specimen is su ounded by diamagne ic
χs
160
160
pa h
Γ1
Γ2
Γ3
z
B(x)
B
0
∆x
B
s
2
x
∆
x
ε
Ansys analysis o weakly magne ic ma e ials in MR omog aphy
17
e e ence subs ance. Ob ained cou se o B in sec ion is
in Fig. 7.
In eal expe imen he e e ence ma e ial and
he specimen a e sepa a ed wi h hin laye , e.g. cu e e
wall. In model (Fig. 6) we conside ed 1 mm hick
cu e e made om PE. Because polye hylene is
pa amagne ic, li le peak occu s in g aph Fig. 7.
Fig. 6 Magne ic induc ion ield p ojec ed on meshed model
Fig. 7 Cou se o magne ic induc ion in sec ion o model
in Fig. 6. Peak is caused due o PE cu e e
4. EXPERIMENTAL MEASUREMENT
P esen ed me hod was expe imen ally e i ied
wi h numbe o specimens on 200 MHz MR omog aph
in ISI AS B no. Re e ence subs ance was wa e
(χ
H2O
= -9.04·10
-6
) illed in o cu e e. The me hod o
G adien echo [3] was used o acqui e MR image wi h
con as co esponding o he magne ic induc ion
changes in measu ed olume o specimen icini y. Used
measu ing sequence o GE is on Fig. 8.
Exci a ion o hyd ogen nucleus p o ides HF
pulse 90°, which d ops ec o o magne iza ion spin M
0
om di ec ion z (pa allel o B
0
) o ans e sal plane x-y.
Ene gy o his pulse causes phase-ma ching o nucleus
spins. Du ing exci a ion, slice g adien G
S
alloca es
measu ed specimen laye . Only his laye is exci ed and
only om his laye he MR image is consequen ly
acqui ed.
Read-ou g adien G
R
causes coding o x-
posi ion in o equency and a he same ime phase
g adien G
P
causes coding o y-posi ion in o phase o
esul MR signal.
Spin-spin incidence and g adien ields induce
lapse o phase-ma ching o magne iza ion ec o s, so e-
ma ching o spins by ead-ou g adien in e sion is
used. Signal acquisi ion is pe o med in echo ime TE
a e exci a ion.
Fig. 8 P inciple o g adien echo measu ing sequence
One o GE me hod p ope y is i s sensi i i y on
basic ield inhomogenei y and inhomogenei y induced
by magne ic ma e ial in he specimen. GE MR image is
phase-modula ed by magne ic induc ion change [2], [3]
and on condi ion o p ope expe imen a angemen we
can ob ain image o magne ic ield dis ibu ion in
specimen icini y and inally enume a e specimen
suscep ibili y (6).
Fig. 9 Unw apped cu e o signal phase change in specimen
icini y
Using desc ibed GE me hod we ob ained MR
image wi h phase-con as – Fig. 10 uppe , which was
u he p ocessed in Ma lab. A e de-noising by he
limi a ion o signal he spa ial de o ma ion e oked by
magne ic ield inhomogenei y in specimen icini y was
elimina ed. Acqui ed phase images we e consequen ly
sub ac ed o elimina e inhomogenei y o he basic ield
and unw apped ( his means discon inui ies in phase
Ad ances in Elec ical and Elec onic Enginee ing
18
change be ween –π and π we e emo ed) – esul is on
Fig. 10 lowe . By p ope ly selec ed slice o his image
we ge he cu e o phase change Θ(x) o he wa e MR
signal in he specimen icini y, see Fig. 9.
Fig. 10 Images ob ained om expe imen al e i ica ion o he
me hod, p ocessed in Ma lab
Fo he used MR echnique he phase change
Θ(x) esponse o he magne ic induc ion change
( )
(
)
0
E
x
B x B
T
γ
Θ
= +
⋅, (7)
whe e
γ
is gy omagne ic a io o wa e and T
E
= 5.56 ms
was used echo- ime. In his way we can iden i y he
cou se o magne ic induc ion change in wa e nea by he
specimen. F om known hickness ∆
x
o he specimen
wi h use o (6) he suscep ibili y o specimens can be
inally calcula ed.
5. CONCLUSION
The me hod designed o magne ic
suscep ibili y measu emen based on MR omog aphy
echniques is simple and enables o de e mine he
magne ic suscep ibili y o such ma e ials, which gi e no
MR signal. P inciple o he me hod was designed using
Ansys modelling and expe imen ally e i ied in
labo a o y. A e an op imiza ion his me hod can be
used o in es iga ion o he ma e ials used in MR
omog aphy as well as o biological issues a ec ing
quali y o MR images.
ACKNOWLEDGEMENT
This wo k has been pa ially unded by a g an
GA

R 103/03/7048 and g an GAAV IAA2065201.
LITERATURE
[1]
ZEMAN, V. M

ení magne ické suscep ibili y
pomocí NMR. Tesla B no, in e ní zp á a, 1981
[2]
BLUMLICH, B. NMR Imaging o Ma e ials.
Cla en on P ess, Ox o d, 2000, ISBN 0 19 850683
X
[3]
ERNST, R. R. – BODENHAUSEN, G. –
WOKAUN, A. P inciples o NMR in One and Two
Dimensions. Ox o d Science Publ. 1987, ISBN 0-
198-55647-0
[4]
LEVITT, M. H. Spin Dynamics: Basics o Nuclea
Magne ic Resonance. John Wiley & Sons, 2001,
ISBN: 0-471-48921-2
[5]
HROUDA, F. A de e mina ion o he symme y o
he e omagne ic mine al ab ic in ocks on he
basis o he magne ic suscep ibili y aniso opy
measu emen s. Ge l. Bei . Geophys., 82,1973,
pp.390-396
[6]
HROUDA, F. Magne oc ys alline aniso opy o
ocks and massi e o es: a ma hema ical model
s udy and i s ab ic implica ions. J. S uc . Geol., 2,
1980, pp.459-462