1. MR TRACKING METHODS Dr. Dan Gamliel, Dept. of Medical Physics,
Ariel University Center in Samaria

2. Overview Magnetic Resonance Imaging (MRI)
Nuclear Magnetic Resonance (NMR)
Magnetic Resonance Imaging (MRI)
Magnetic Resonance Motion Effects
Magnetic Resonance Tracking Methods

3. The NMR method Nuclear Magnetism
Macroscopic magnet: collection of magnetic moments
single magnetic moment: electric current loop
nuclear or electronic magnetic moment: from (orbital + spin) angular momentum
non-zero nuclear moment: with Pauli principle - usually odd number of nucleons
1H , 13C, 17O , 23Na , 31P , …
(non-zero spin)

4. The NMR method magnetic moment in external field Classically:
Energy term of magnetic moment in external magnetic field:
Larmor Precession of magnetic moment around direction of external field

5. The NMR method magnetic moment in external field Quantum mechanically:
Splitting of energy levels
For S = ½ (e.g., 1H nucleus):
Each type of nucleus has its g value
(n0 = w0 / 2p = Zeeman frequency)
Longitudinal projection of spin angular momentum
“spin” = nuclear magnetic moment

6. The NMR method Effect of time dependent transversal field
Static (constant) magnetic field:
B0 = B0 z
Generates net magnetization along Z - parallel to static field (longitudinal direction)
Time dependent magnetic field:
B1 = B1 cos(w t) x
(transversal = perpendicular to static field)
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)

7. The NMR method The resonance phenomenon
For static field, transition (or precession) frequency is w0 = - g B0 (typical: 107 – 108 Hz)
For time dependent field, strength (amplitude) is equivalent to w1 = - g B1 (typical: Hz)
The excitation is effective only if | w - w0 | < w1 (close to resonance)
Classical Bloch equations:
precession and decay

8. The NMR method The energies Transition frequencies for a single atom:
Nuclear or electronic processes (g rays, X rays)
~ Hz
Chemical processes – electronic transitions (visible – UV): ~ 1014 – 1017 Hz
Nuclear magnetic transitions (NMR): ~ 107 – 109 Hz
(RF - radio frequencies - range)

9. The NMR method The importance of resonance
Net magnetization depends on population difference between “parallel” and “anti-parallel”
The population difference depends on the Boltzmann factor for the energy difference
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

10. The NMR method Modes of operation
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
Pulsed operation (time domain experiment):
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 !

11. NMR method Relaxation of magnetization
After time dependent field stops operating:
spins return gradually to original state
Thermal equilibrium (final) relaxation –
for longitudinal magnetization
- T1 time constant
Earlier change – signal decay:
Loss of coherence – for transversal magnetization
- T2 time constant (partial relaxation)
T2 with field inhomogeneity
– T2* time constant

12. The NMR method 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 )

13. The NMR method 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:

14. NMR pulse sequences 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)

15. NMR pulse sequences Typical experiments (pulsed method)
Essential steps:
Excitation (by an RF “90º pulse”– rotating magnetization)
Measurement of signal as a function of time
Fourier transform of signal from time to frequency
Some additional options (with many possible combinations):
Refocus Mxy (by an RF “180º pulse”) – to undo T2* decay - “spin echo” experiment
Invert Mz (by an RF “180º pulse”)
Add a changeable time interval before another pulse

16. NMR pulse sequences 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

17. NMR Experimental system
Superconducting magnet
(cooling – liquid nitrogen, liquid helium)
Transmitter/ receiver
Spectrometer

18. NMR Main applications Main nucleus: 1H (water, lipids, …)
Study chemical structure by:
- chemical environment of atom
- interactions between atomic nuclei
Study dynamic processes involving spins:
- diffusion processes
- exchange processes
Study details of structure and processes by special pulse sequences

19. The MR Imaging (MRI) method
Transmission of NMR frequencies in body
X-ray images of human body are possible because X-rays are (partly) transmitted through the human body
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

20. The MRI method Background – other medical imaging modalities
Optical images (visible light): reflection and diffraction
good resolution in diffraction (short wavelength)
high contrast (absorption differences)
X-ray images: transmission and diffraction
good resolution in CT (beam collimation)
contrast: absorption differences and contrast materials
Nuclear medicine: g emission from radionuclide
low resolution, low contrast
very good functional information

21. The MRI method Problems for NMR imaging Needed: spatial resolution
contrast
Problem for resolution:
In optical images: resolution ~ wavelength (very short) – but NMR wavelength ~ 1 meter !
In X-ray images: resolution ~ focusing of beam – difficult for NMR wavelength
Problem for contrast:
Water density in body – similar in different tissues

22. The MRI method Solution for spatial resolution
Spatial dependence of resonance frequency by modification of “static” magnetic field:
w0 = g B0  g Bz = g { 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)

23. The MRI method Basic pulse sequence
Excitation, field gradients, signal readout with two time parameters:
TE, TR
initial dephase in view axis – for (k-space) symmetry around echo TE TR

24. The MRI method Solution for image contrast
TE (Time to Echo) = time from excitation to (refocusing moment of) readout
= time for decay of signal -
determines contrast by T2 differences between tissues
TR (Time to Repeat) = time from excitation to next excitation
= time for return of magnetization to equilibrium -
determines contrast by T1 differences between tissues
Relative density of 1H (“proton density”) – minor contrast factor, useful in some applications

25. The MRI method Solution for image contrast
Some typical values (times in ms):
Tissue T1 (0.5 T) T1 (1.5 T) T2 proton density
grey matter %
white matter %
skeletal muscle %
liver %
Blood (v)-250(a)
Fat %
tumors (longer) (longer)

26. The MRI method 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

27. The MRI method Useful timing combinations for image contrast
short TE, long TR (TE << T2 and TR >> T1 ):
little decay, "full relaxation" - "proton density" contrast - signal increases with spin density
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)

28. The MRI method Clinical utility 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

29. The MRI method Clinical utility MRI system Superconducting magnet
Gradients
Transmit/receive system + coils

30. The MRI method Clinical utility Some images: Top left: T1 contrast
(useful to distinguish tumors)
Top right:
T2 contrast
(anatomic detail)

31. The MRI method Clinical utility
Some images (Joseph Hornak – online course):

32. The MRI method Measured signal and image reconstruction
Measured signal (in “k-space”) – without relaxation:
Reconstructed image (spin density) – without relaxation:

33. The MRI method Time scales in imaging and in internal motion
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
Internal motion in body (examples):
Respiratory cycle ~ 2 – 4 s
Cardiac cycle ~ 1 s
Gastro peristaltic motion cycle ~ s
blood velocity ~ m/s

34. MR Motion Effects Phase change due to motion Some motion effects:
Some spins feel only early part of “imaging sequence”
Some spins feel only late part of “imaging sequence”
Some spins acquire a time dependent phase, reconstructed as a “change in position“. Example:
x(t) = x0 + v t  (time dependent phase)

35. MR Motion Effects Avoiding motion artifacts
Some ways of avoiding motion artifacts:
Change gradient pattern in pulse sequence to compensate for common motion effects (blood motion)
Cardiac/peripheral (ECG) gating
Respiratory gating (bellows)
Breathholding
Fast pulse sequence
Tagging (e.g. cardiac)
Dynamic correction using “navigator”
Spatial “suppression” of moving region in image

36. MR Tracking Methods The need for tracking a position
Compare stages in time change in anatomic structure
Interventional procedure:
- imaging while operation is being carried out
- follow position of instrument (e.g. needle)
- follow changes in anatomic region

37. MR Tracking Methods Using 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

38. MR Tracking Methods Using External Markers
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

39. MR Tracking Methods Using External Markers
A possible way to monitor (with MRI) temperature of ablated region:
Chemical shift (change in resonance frequency) depends on temperature
temperature difference  off-resonance difference
 phase difference:
Df = g DB t
 temperature mapping

40. MR Tracking Methods Using Navigator Pulse Sequence
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)

41. MR Tracking Methods Using Navigator Pulse Sequence
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

42. MR Tracking Methods Using Navigator Pulse Sequence
(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.