Transcript Document

MR TRACKING METHODS
Dr. Dan Gamliel, Dept. of Medical Physics,
Ariel University Center in Samaria
Overview
• Nuclear Magnetic Resonance (NMR)
• Magnetic Resonance Imaging (MRI)
• Magnetic Resonance Motion Effects
• Magnetic Resonance Tracking Methods
The NMR method
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Nuclear Magnetism
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Macroscopic magnet:
collection of magnetic moments
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single magnetic moment:
electric current loop
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nuclear or electronic magnetic moment:
from (orbital + spin) angular momentum
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non-zero nuclear moment: with Pauli
principle - usually odd number of nucleons
1H
,
13C, 17O
, 23Na , 31P , …
(non-zero spin)
The NMR method
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magnetic moment in external field
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Classically:
Energy term of magnetic moment in
external magnetic field:
U     B  cos( )
Larmor Precession of magnetic moment
around direction of external field
d
   B
dt
The NMR method
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magnetic moment in external field
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Quantum mechanically:
Splitting of energy levels
For S = ½ (e.g., 1H nucleus):
E  
1
1
hn 0   hB0
2
2
Each type of nucleus has its  value
(n0 = w0 / 2p = Zeeman frequency)
Longitudinal projection of
spin angular momentum
“spin” = nuclear magnetic moment
The NMR method
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Effect of time dependent transversal field
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Static (constant) magnetic field:
B0 = B0 z
Generates net magnetization along Z - parallel to static field
(longitudinal direction)
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Time dependent magnetic field:
B1 = B1 cos(w t) x
(transversal = perpendicular to static field)
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Effect of time dependent field:
Excitation of transitions between energy levels of static
field – rotates some spins from Z direction to XY plane (or to
the –Z direction)
The NMR method
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The resonance phenomenon
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For static field, transition (or precession)
frequency is
w0    B0
(typical: 107 – 108 Hz)
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For time dependent field, strength (amplitude) is
equivalent to
w1    B1
(typical: 103 Hz)
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The excitation is effective only if
| w  w0 | < w1 (close to resonance)
d
M
M x  (w  w0 )  M y  x
dt
T2
Classical Bloch equations:
precession and decay
M
d
M y  w1  M z  (w  w0 )  M x  y
dt
T2
d
M  M0
M z  w1  M y  z
dt
T1
The NMR method
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The energies
Transition frequencies
for a single atom:
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Nuclear or electronic
processes ( rays, X rays)
~ 1018 - 1020 Hz
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Chemical processes –
electronic transitions (visible – UV): ~
1014 – 1017 Hz
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Nuclear magnetic transitions
(NMR): ~ 107 – 109 Hz
(RF - radio frequencies - range)
The NMR method
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The importance of resonance
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Net magnetization depends on population
difference between “parallel” and “anti-parallel”
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The population difference depends on the
Boltzmann factor for the energy difference
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At room temperature:
exp(- hn / kT) ~ 10-5
- very small net magnetization (paramagnetic) in
the strong static magnetic field
- For a sufficient signal: need
resonance effect
a large (macroscopic) sample
The NMR method
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Modes of operation
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CW (continuous wave) (frequency domain):
- Constant static field (constant resonance value)
- “sweep” over oscillation frequency of the time-dependent field
- Measure signal for each oscillation frequency :
resonance peak at w  w0
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Pulsed operation (time domain experiment):
- Constant static field (constant resonance value)
- Operating the time-dependent field for a short time, exactly
needed to rotate magnetization from the Z axis to the XY plane
- Measure the signal for many time values  do a Fourier
transform from t to w  get the same resonance graph !
NMR method
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Relaxation of magnetization
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After time dependent field stops operating:
spins return gradually to original state
Thermal equilibrium (final) relaxation –
for longitudinal magnetization
- T1 time constant
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Earlier change – signal decay:
Loss of coherence – for transversal magnetization
- T2 time constant (partial relaxation)
T2 with field inhomogeneity
– T2* time constant
The NMR method
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the change in magnetization due to relaxation
Transversal magnetization decays as MXY ~ exp(- t / T2 )
Longitudinal magnetization recovers as MZ ~ M0 (1 – exp(- t / T1 )
The NMR method
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The resonance graph (CW or pulsed method)
Time domain signal
(pulsed method):
Mx + iMy ~
exp{-i(w0  w) t – t / T2 }
The peak of the frequency
domain graph: at w  w0
The width at half
the peak height:
1
T2
NMR pulse sequences
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Typical experiments (pulsed method)
Overall structure of pulse sequence:
Preparation – e.g. inversion
Excitation – cause change of state
Evolution – e.g. refocusing or other pulses
Detection – measurement of signal (as a function of time)
Data processing (Fourier transform)
NMR pulse sequences
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Typical experiments (pulsed method)
Essential steps:
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Excitation (by an RF “90º pulse”– rotating magnetization)
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Measurement of signal as a function of time
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Fourier transform of signal from time to frequency
Some additional options (with many possible combinations):
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Refocus Mxy (by an RF “180º pulse”) – to undo T2* decay
- “spin echo” experiment
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Invert Mz (by an RF “180º pulse”)
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Add a changeable time interval before another pulse
NMR pulse sequences
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Typical results (spectrum: signal vs. frequency)
This is the spectrum of a
sample containing two
types of chemical groups –
in each group the hydrogen
nucleus has a different
resonance frequency.
In addition, interactions
between spins cause
splitting of each resonance
to several spectral lines
NMR
Experimental system
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Superconducting magnet
(cooling – liquid nitrogen,
liquid helium)
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Transmitter/ receiver
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Spectrometer
NMR
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Main applications
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Main nucleus: 1H (water, lipids, …)
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Study chemical structure by:
- chemical environment of atom
- interactions between atomic nuclei
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Study dynamic processes involving spins:
- diffusion processes
- exchange processes
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Study details of structure and processes by
special pulse sequences
The MR Imaging (MRI) method
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Transmission of NMR frequencies in body
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X-ray images of human body are possible because Xrays are (partly) transmitted through the human body
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Also RF waves are partly transmitted through the body !
- The following graph shows absorption of electromagnetic
radiation in the human body – as a function of wavelength
The MRI method
Background – other medical imaging
modalities
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Optical images (visible light): reflection and diffraction
good resolution in diffraction (short wavelength)
high contrast (absorption differences)
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X-ray images: transmission and diffraction
good resolution in CT (beam collimation)
contrast: absorption differences and contrast materials
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Nuclear medicine:  emission from radionuclide
low resolution, low contrast
very good functional information
The MRI method
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Problems for NMR imaging
Needed:
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spatial resolution
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contrast
Problem for resolution:
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In optical images: resolution ~ wavelength (very short)
– but NMR wavelength ~ 1 meter !
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In X-ray images: resolution ~ focusing of beam –
difficult for NMR wavelength
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Problem for contrast:
Water density in body – similar in different tissues
The MRI method
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Solution for spatial resolution
Spatial dependence of resonance frequency by modification of
“static” magnetic field:
w0 =  B0   Bz =  { B0 + Gz (t) z + Gy (t) y + Gx (t) x }
• During excitation pulse: slice selection
Gz  z-dependent excitation resonance
• During signal readout (sampling): frequency encoding
Gx  x-dependent readout resonance
(many time points for resolution)
• Between excitation and readout: phase encoding
Gy  y-dependent added phase
(many repetitions of sequence with different phase)
The MRI method
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Basic pulse sequence
• Excitation,
field gradients,
signal readout
with two time
parameters:
TE
TE, TR
• initial dephase
in view axis –
for (k-space)
symmetry
around echo
TR
The MRI method
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Solution for image contrast
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TE (Time to Echo) = time from excitation to
(refocusing moment of) readout
= time for decay of signal -
determines contrast by T2 differences between tissues
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TR (Time to Repeat) = time from excitation to
next excitation
= time for return of magnetization to equilibrium -
determines contrast by T1 differences between tissues
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Relative density of 1H (“proton density”) – minor
contrast factor, useful in some applications
The MRI method
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Solution for image contrast
Some typical values (times in ms):
Tissue
T1 (0.5 T) T1 (1.5 T)
T2
proton density
grey matter
680
1130100
10.6 %
white matter
450
720
90
10.6 %
skeletal muscle 560
1180
34
9.3 %
liver
360
720
60
9.7 %
Blood
200
1200
30(v)-250(a)
Fat
200
260
60
tumors
(longer)
(longer)
9.6 %
The MRI method
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Solution for image contrast
Signal amplitude vs. time
for two tissues with
different T2 values
Recovery of MZ
after excitation for
two tissues with
different T1 values
The MRI method
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Useful timing combinations for image contrast
1. short TE, long TR (TE << T2 and TR >> T1 ):
little decay, "full relaxation" - "proton density" contrast - signal
increases with spin density
2. long TE, long TR (TE ~ T2 and TR >> T1 ):
much decay, "full relaxation" - T2 contrast
signal increases with T2
3. short TE, short TR (TE << T2 and TR ~ T1 ):
little decay, little relaxation - T1 contrast
signal decreases when T1 increases
(Note: T2* replaces T2 where appropriate)
The MRI method
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Clinical utility
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Advantages:
- Non-ionizing radiation (unlike CT and NM)
- Many different contrasts available (various pulse
sequences - T1, T2, spin density, static tissue, blood
vessels, …)
- No limitation on imaging plane (same as in CT)
- Both anatomic and (more limited) functional information
The MRI method
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Clinical utility
• MRI system
Superconducting
magnet
Gradients
Transmit/receive
system + coils
The MRI method
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Clinical utility
• Some images:
• Top left:
T1 contrast
(useful to distinguish
tumors)
• Top right:
T2 contrast
(anatomic detail)
The MRI method
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Clinical utility
• Some images (Joseph Hornak – online course):
The MRI method
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Measured signal and image reconstruction
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Measured signal (in “k-space”) – without relaxation:
S (k x , k y )    (x, y )  e(i2p k x x )  e

kx 
 Gx  t
2p
•
ky 
(i2p k y  y )
 dx  dy

 G y 
2p
Reconstructed image (spin density) – without relaxation:
 (x, y )   S (k x , k y ) e
(i2p k x  x )
e
(i2p k y  y )
 dkx  dky
The MRI method
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Time scales in imaging and in internal motion
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MRI techniques (examples):
Standard (grad. echo, spin echo):
~ 100 – 1000 s
Fast (fast spin echo, FLASH, etc.): ~ 50 s
Very fast (EPI, single shot FSE etc.) ~ 0.1 s – 0.5 s
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Internal motion in body (examples):
Respiratory cycle
Cardiac cycle
Gastro peristaltic motion cycle
blood velocity
~2–4s
~1s
~ 10 - 20 s
~ 0.1 - 1 m/s
MR Motion Effects
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Phase change due to motion
Some motion effects:
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Some spins feel only early part of “imaging sequence”
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Some spins acquire a time dependent phase,
reconstructed as a “change in position“. Example:
Some spins feel only late part of “imaging sequence”
x(t) = x0 + v t

(time dependent phase)



  x  Gx  dt 
  x0  Gx  dt 
 v   t  Gx  dt
2p
2p
2p
MR Motion Effects
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Avoiding motion artifacts
Some ways of avoiding motion artifacts:
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Change gradient pattern in pulse sequence to compensate
for common motion effects (blood motion)
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Cardiac/peripheral (ECG) gating
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Spatial “suppression” of moving region in image
Respiratory gating (bellows)
Breathholding
Fast pulse sequence
Tagging (e.g. cardiac)
Dynamic correction using “navigator”
MR Tracking Methods
The need for tracking a position
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Compare stages in time change in anatomic structure
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Interventional procedure:
imaging while operation is being carried out
follow position of instrument (e.g. needle)
follow changes in anatomic region
MR Tracking Methods
Using External Markers
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External Markers:
markers seen in MR image, placed in known positions
reference points for position of special object (e.g. needle)
reference points for position of relevant anatomic region
employs simple and accurate calculations
enables directing treatment to desired location
requires: “static” region
MR Tracking Methods
Using External Markers
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Scan for locating external markers:
Fast, short TE (gradient echo type)
geometrical information used for operation
example:
locating ultrasound transducer during
Focused UltraSound ablation of tissue
MR Tracking Methods
Using External Markers
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A possible way to monitor (with MRI) temperature of ablated
region:
Chemical shift (change in resonance frequency) depends on
temperature
temperature difference 
 phase difference:
f   B t
 temperature mapping
off-resonance difference
MR Tracking Methods
Using Navigator Pulse Sequence
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For a “dynamic” region (large motion – mainly breathing):
must follow region dynamically
Navigator Pulse Sequence:
Sequence generates partial image data (e.g. a straight line)
– to mark a specific anatomic structure (e.g. diaphragm)
reference for position of relevant region (e.g. liver)
MR Tracking Methods
Using Navigator Pulse Sequence
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Using reference image:
Take a reference image(s)
Check correlation of specific image with a reference image
Check cross- correlation between images
Using a navigator sequence:
Run a reference navigator
Run navigators between some of the repetitions of the main
pulse sequence
Check correlation between reference navigator and a current
navigator, correct current image
MR Tracking Methods
Using Navigator Pulse Sequence
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(Commercial sequence)
The Cardiac Navigator feature
combines a cardiac gated, 3D
Fast GRE or 3D FIESTA
sequence with a navigator
pulse that tracks the motion of
the diaphragm. By placing the
navigator tracker pulse over
the right hemi-diaphragm, the
acquisition is synchronized to
the end-expiration respiratory
phase of the patient thus
minimizing respiratory
ghosting artifacts.