MRT Systeme - Medizinische Fakultät Mannheim

Transcription

RUPRECHT-KARLSUNIVERSITY HEIDELBERG
Computerunterstützte Klin. Medizin
Dr. Friedrich Wetterling
11/24/2011 | Page 1/20
Hochschule Mannheim
Bildgebende Systeme in der Medizin
Magnet Resonanz Tomographie II:
MR-Systeme und Kodierverfahren
RF Methoden und Bildgebung
Lehrstuhl für Computerunterstützte Klinische Medizin
Medizinische Fakultät Mannheim, Universität Heidelberg
Theodor-Kutzer-Ufer 1-3
D-68167 Mannheim, Deutschland
[email protected]
www.ma.uni-heidelberg.de/inst/cbtm/ckm/
11/24/2011 | Page 2/20
Zusammenfassung MRT Ia
• Das MR Signal:
- magnetisches Moment des Kerns
- Drehimpuls des Kerns
• Anregung mit RF Puls
⇒
Präzession
• Blochsche Gleichungen
• Relaxation in Flüssigkeiten:
- Spin-Gitter Relaxation (T1)
- Spin-Spin Relaxation (T2)
• Grundlagen der MR Messung:
- Spin echo ⇒ T2
- Inversion Recovery ⇒ T1
- Repetitionszeit (TR)
- Echo Zeit (TE)
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Zusammenfassung MRT Ib
• Komponenten eines Spektrometers: - Polarisationsmagnet
- Shimspulen
- Hochfrequenzspule
- Breitbandverstärker zum Senden und
Empfangen
• Das MR Signal:
- magnetisches Moment des Kerns
- Drehimpuls des Kerns
- Magnetisierung bildet sich aus
• Anregung mit RF Puls
⇒
Präzession
• Detektion in Leiterschleife
⇒
Induktion
11/24/2011 | Page 4/20
Notation: NMR & MRI
(Nuclear)
(Kernspin)
Magnetic
Magnet
N
S
Resonance
Resonanz
(Imaging)
Tomographie
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Gradient Field: Slice Selection
magnetic field gradient, i.e. Gz
G
z
radiofrequency:
ω(z) = γ (B0 + Gzz)
gradient Gz
11/24/2011 | Page 6/20
Gradient Coil: Principle I
coil for static B0 field
typical value for G:
1 - 25 (40) mT/m
example:
x = 30 cm, B0 = 1 T, G = 10 mT/m
B = 0.9985 T .... 1.0015 T
y-gradient
x-gradient
z-gradient
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11/24/2011 | Page 7/20
Gradient Coil: Principle II
gradient
• paper clip design
• localization of MR signal
• current through coil design
• linear increasing magnetic field
technical data
• gradient strength
• rise time
• linearity
• active shielding
• cooling
• noise
10 - 40 mT/m
200 - 600 µs
35 - 40 cm
11/24/2011 | Page 8/20
Gradient Coil: Active Shielding
concept
• elimination of gradient fields outside
the gradient tube
• desired field inside the gradient tube
realization
• counter-windings on a second radius
• increased total currents
power
• 500 A at 2000 V → MW power for
short time
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Gradient Coil: Design
• current through the coil
pairs runs in opposite
directions
• B-field of the gradient coil
is added or subtracted to
B0, respectively
11/24/2011 | Page 10/20
Gradient Coil: Construction
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11/24/2011 | Page 11/20
Gradients: General
- total magnetic field:
r
r
B = (B 0 + B G , z )⋅ k
- three gradient coils simultaneously:
BG , z = G x ⋅ x + G y ⋅ y + G z ⋅ z
r
r
B = B0 + G x ⋅ x + G y ⋅ y + G z ⋅ z ⋅ k
(
- abbreviations:
- direction of
)
r
r
r
r
G = Gx ,G y ,Gz = Gx ⋅i + G y ⋅ j + Gz ⋅ k
(
)
r
r
r
G is defined as gradient orientation of B or B G
r
r
r r
B G , z = G ⋅ r in general: G = G (t )
11/24/2011 | Page 12/20
Gradient Homogeneity
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11/24/2011 | Page 13/20
Gradient Eddy Current Compensation
I(t)
problem
• time-varying gradient fields induce
eddy currents
• partial annihilation of gradient fields
t
compensation
• modified shaping of gradient-timesignal (gradient pre-emphasis)
• short and long eddy current time
constants
G(t)
11/24/2011 | Page 14/20
station:
I
Gradient Post-Processing: Cut & Glue
II
III
IV
Seite
V
VI
11/24/2011 | Page 15/20
station:
Gradient Post-Processing: Cut & Glue
I
II
III
IV
V
VI
11/24/2011 | Page 16/20
Gradient’s “3D Piano”
magnetic field gradient G
“3D piano”
Gz
Gy
_
b
#
Gx
Gx
precession frequency
ω=γ•B
Gy
with B = B0 + Gx + Gy + Gz
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NMR History: Imaging I
Downstate
Medical
Center
Brooklyn
Raymond V. Damadian
• the first scanner for clinical purposes
1972
United States Patent 3,789,832
The method envisioned scanning with a focused “sweet spot” similar to the scanning raster
on a television.
Either the “sweet spot” would move, or the patient would move across the “sweet spot”,
thereby collecting one tissue data point at a time.
© Yves De Deene. University of Gent, Belgium
11/24/2011 | Page 18/20
Magnetic Resonance Imaging: Principle
interaction of spins
with static magnetic
field
B0 → M0
ω = γ.B0
interaction of protons with
resonant magnetic
radiofrequency field
B1 → FID signal
∆E = hω
linear magnetic field
gradient
across the object
G → spatial encoding
ω(x) = γ.B0(x)
B = B0 + Gx·x
B0
x
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11/24/2011 | Page 19/20
radiofrequency RF
MRI Components: Physical Parameters
gradients Gxyz
shim coils
static field B0
transmitter
shim
receiver
350 MHz
control
panel
computer
350 MHz
image
processor
gradient
technical
component
static field B0
physical
parameter
M0
radiofreq. RF signal
gradients Gxyz image
11/24/2011 | Page 20/20
MRI Components
• strong magnet producing a homogeneous static magnetic field
(0,1 - 8,0 Tesla)
(for comparison: earth magnetic field 30 µT - 60 µT)
• radiofrequency unit creating a periodical magnetic field used
for spin excitation and signal detection
• gradient coils producing a linear magnetic field gradient for
spatial encoding
• receiver coils for signal detection
• computer for controlling the MRI scanner
• input/ouput panel for data-flow and -evaluation
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11/24/2011 | Page 21/20
NMR History: Scanner
The first MR scanners ...
normal MRI unit
interventional MRI unit
open MRI unit
mobile MRI unit
… and the most recent
© Yves De Deene. University of Gent, Belgium
11/24/2011 | Page 22/20
Slice Selective Excitation
frequency spectra
of RF pulse
ω
ω
ω = γ (B0+Gzz)
ω (z2)
ω (z1)
ω( z ) = γ ⋅ ( B0 + Gz ⋅ z )
d =
ω0
I(ω)
z1z2
z
d
∆ω
2π ∆ f
=
z
γ ⋅G
γ ⋅Gz
1. slice thickness d = z2 - z1 can be varied by RF bandwidth (frequency width) or
gradient strength Gz.
2. slice position can be changed by shifting the frequency spectra with constant RF
bandwidth
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Slice Selective Excitation: Sinc-Pulse
- RF excitation with a sin(x) / x amplitude function (sinc-pulse) creates a
rectangular frequency distribution
- sinc-pulse at different gradient strength leads to slices with different
positions and thickness
- problem: Larmor frequency is different within slice thickness
source: Liang and Lauterbur. “Principles of Magnetic Resonance Imaging” 2000
11/24/2011 | Page 24/20
Gradient Compensation
excited
slice
“dephasing” of transversal
magnetization after unipolar
gradient pulse
z-gradient with compensation and RF
sinc-pulse for creating a homogeneous
transversal magnetization
source: Dössel. “Bildgebende Verfahren in der Medizin” 2000
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11/24/2011 | Page 25/20
Gradient Compensation: Magnetization
RF
Gslice
slice
thickness
vector sum of
transversal
magnetization
11/24/2011 | Page 26/20
Other Slice Selective RF-Pulses
 τ 
− a ⋅ t − 
A⋅e  2
2
• Gauss-pulse
B1e ( t ) =
• Secans hyperbolicus-pulse
B1e ( t ) = B1 ⋅ sech( β ⋅ t )1+ i µ
2


= B1 ⋅  β ⋅t

− β ⋅t
e +e

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1+ i µ
11/24/2011 | Page 27/20
Frequency Encoding
- iso-frequency-lines are perpendicular
to G
- oscillation frequency of an activated
MR-signal is linearly dependent on
spatial coordinate, since
ω(x) = γ (B0+ Gx·x)
11/24/2011 | Page 28/20
Frequency Encoding: Gradient Schema
RF
signal
acquisition
t
- superposition of a gradient field
Bx= Gx·x during the acquisition
phase results in:
ω(x) = γ (B0+ Gx·x)
Gz
t
where the Lamor frequency is
linked with the spatial
information x
- spatial information is encoded
in the precision frequency of the
transversal magnetization
Gx
t
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Principle of Frequency Encoding
11/24/2011 | Page 29/20
y
Gx
- all nuclei in a stripe perpendicular to the
gradient direction are contributing to the
NMR signal at Lamor frequency ω(x)
x
⇒ direct one-dimensional diagram of
the spatial distribution of excited nuclei
in the slice
z
x1 x2
frequency spectrum
- Fourier-transformation of the FID-signal
yields the amount of different frequency
components
I(ω)
- I(ω) ~ number of nuclei at frequency ω
ω(x1) ω(x2)
x =
ω(x)~x
projection of spin density in direction of gradient
ω − γ B0
γG x
11/24/2011 | Page 30/20
Frequency Encoding: Spatial Resolution
- FID-signal S(t) is digitalized by using an “analog to digital converter” ADC and
a discrete timing interval ∆t in a total acquisition window taq
- for the Fourier-analysis of the FID-signal there are in total N = taq/∆t measured
data points:
S(∆t), S(2∆t), S(3∆t), … , S(N∆t)
- spatial resolution in x-direction ∆x is given by the sampling theorem:
∆x = X / N = 2π / γ Gx N ∆t
with X: the maximum object diameter (FOV), N: number of sampling points,
Gx: gradient strength, ∆t: sampling interval (= bandwidth BW in Hz/pixel)
- example: with N = 256, ∆t = 30 µs, Gx = 1.566 mT/m the spatial resolution
in x-direction (pixel resolution in x) is:
∆x = 1.953 mm and X = N ∆x = 50 cm (= field-of-view FOV)
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11/24/2011 | Page 31/20
in-vivo
Problem: Chemical Shift Artifact
1H-spectrum
of human thigh at 1.5 T
BW = 220 Hz/pixel BW = 20 Hz/pixel
BW = 20 Hz/pixel
BW = 20 Hz/pixel
+ fat suppression
- chemical shift between protons of water H2O and fatty tissue CH2
is about 3.5 ppm or 220 Hz at 1.5 T
- frequency encoding of fat and water leads to a spatial shift between fat and water
structures in the image, e.g. a frequency encoding interval of 110 Hz
(bandwidth BW) results in a shift of 2 pixels in the image
- to avoid chemical shift artifact a frequency encoding interval of about 200 Hz
has to be used at 1.5 T
11/24/2011 | Page 32/20
Phase Encoding
- phase encoding is performed by
stamping an initial phase angle onto
the spins of an excited slice
- iso-phase-lines are perpendicular
to G
- after switching off the phase
encoding gradient the magnetization
is continuing to precede at the same
frequency ω0 but with different phase
- phase information of an activated
MR-signal is linearly dependent on
spatial coordinate, since
φ(x) = - γ · Gx · x · Tpe
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11/24/2011 | Page 33/20
Gz
Phase Encoding: Gradient Schema
slice selection
gradient
Gy
phase encoding
gradient
Ty
y
- phase encoding is performed before signal
acquisition
- gradient field is switched on for a constant
time Ty
- gradient strength is increased stepwise by
∆Gy after every sequence passage
11/24/2011 | Page 34/20
Zusammenfassung
• Komponenten eines MRTs:
- Polarisationsmagnet
- Shimspulen
- Hochfrequenzspule
- Breitbandverstärker zum Senden und
Empfangen
- Gradienten
• Möglichkeiten der Bildkodierung:
- Frequenzkodierung
- Phasenkodierung
Seite

MRT Systeme - Medizinische Fakultät Mannheim

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