1. Magnetic Resonance Imaging: Physical Principles
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Magnetic Resonance Imaging: Physical Principles
Richard Watts, D.Phil.
Weill Medical College of Cornell University,
New York, USA

2. Physics of MRI, Lecture 1 Nuclear Magnetic Resonance Spatial Encoding
Nuclear spins
Spin precession and the Larmor equation
Static B0
RF excitation
RF detection
Spatial Encoding
Slice selective excitation
Frequency encoding
Phase encoding
Image reconstruction
Fourier Transforms
Continuous Fourier Transform
Discrete Fourier Transform
Fourier properties
k-space representation in MRI
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3. Physics of MRI, Lecture 2 2D Pulse Sequences Medical Applications
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2D Pulse Sequences
Spin echo
Gradient echo
Echo-Planar Imaging
Medical Applications
Contrast in MRI
Bloch equation
Tissue properties
T1 weighted imaging
T2 weighted imaging
Spin density imaging
Examples
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4. Physics of MRI, Lecture 3 3D Imaging Magnetization Preparation
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3D Imaging
Magnetization Preparation
Chemical Shift and FatSat
Water/Fat Separation
Inversion Recovery and T1 Measurement
Double Inversion Recovery
Imaging blood flow
Time-of-Flight
Phase Contrast
Fast Imaging
Spoiling
Spin Saturation
Ernst angle, signal and contrast levels
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5. Summary – So Far Spatial encoding Tissue contrast Scan Parameters
It’s all done with gradient fields
Spatially varying Larmor precession frequency
Slice select
Frequency encode
Phase encode
Tissue contrast
Different magnetic properties of tissues
Different relaxation times
T1 = Longitidunal relaxation constant
T2 = Transverse relaxation constant
Scan Parameters
TE = Echo time
TR = Repetition time
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6. Spatial Encoding – Slice SelectionRF Gz
Resonant
Frequency
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7. 2D Spatial Encoding – Frequency and Phase EncodingGx
Phase Shift
Frequency  X-Position
Phase  Y-Position
Phase encoding
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8. 3D Imaging
Instead of exciting a thin slice, excite a thick slab and phase encode along both ky and kz
Greater signal because more spins contribute to each acquisition
Easier to excite a uniform, thick slab than very thin slices
No gaps between slices
Motion during acquisition can be a problem
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9. 2D Sequence (Gradient Echo)ky
acq Gx Gy kx Gz b1 TE
Scan time = NyTR TR
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10. 3D Sequence (Gradient Echo)
acq kz Gx Gy Gz ky b1 kx
Scan time = NyNzTR
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11. 3D Imaging - example
Contrast-enhanced MRA of the carotid arteries. Acquisition time ~25s.
160x128x32 acquisition (kxkykz).
3D volume may be reformatted in post-processing. Volume-of-interest rendering allows a feature to be isolated.
More on contrast-enhanced MRA later
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12. Chemical Shift - Spectroscopy
Precession frequency depends on the chemical environment e.g. Hydrogen in water and hydrogen in fat have a f = fwater – ffat = 220 Hz
Single voxel spectroscopy excites a small (~cm3) volume and measures signal as f(t). Different frequencies (chemicals) can be separated using Fourier transform
Concentrations of chemicals other than water and fat tend to be very low, so signal strength is a problem
Creatine, lactate and NAA are useful indicators of tumor types
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13. Spectroscopy - Example
Intensity
(Concentration)
Frequency
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14. Chemical Shift - FatSat
Use a small bandwidth (long, ~20ms) 90º pulse to excite only protons within fat
Destroy the transverse magnetization by dephasing (spoiling)
Not spatially selective – no gradients
Useful for reducing the fat signal in abdominal and breast imaging
Cost – extra acquisition time
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15. Chemically Selective Saturation
Resolution Phantom
(water)
Bottle of Oil
(fat)
No saturation
Fat saturation
No saturation
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16. Water/Fat Separation
Proton spin in fat precesses at a frequency lower than in water (-220Hz at 1.5T).
fwater = ffat + 2p.Df.TE
@ TE1 = 1/Df = 4.55 msec,
I1 = Iwater + Ifat
@ TE2 = 3/(2Df) = 6.82 msec,
I2 = Iwater  Ifat
Then, Iwater = (I1+I2)/2, Ifat = (I1  I2)/2
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17. Inversion Recovery (IR)
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Inversion Recovery (IR)
After 180 inversion pulse the longitudinal relaxation Mz grows back towards its equilibrium value, M0
Mz = 0 when e-t/T1 = ½
T= T1.ln2
Select the inversion time, TI to null out the required signal
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18. Inversion Recovery (IR)
1800 RF
Rest of Sequence
TI (inversion time)
T1=260 Mz
T1=1000
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19. Inversion Recovery - Example
No Inversion Recovery
Inversion Recovery, TI = 150ms
Oil (fat)
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20. Measurement of T1
Image using different inversion times (TI) until the signal is minimized
Signal  |Mz(TI) |
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21. Measurement of T2 Measure signal as a function of echo time, TE
Spin echo sequence gives T2 (irreversible)
Gradient echo sequence gives T2* (reversible and irreversible)
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22. Double Inversion Recovery
With two inversion pulses at appropriate times, two tissue types can be nulled out
e.g. CSF and fat in the brain
1800
1800 Mz
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23. Blood Flow – Time of Flight Effect
Fast imaging TR<T1, T2
Spins do not fully recover after each repetition
Magnetization producing MR signal decreases with the number of pulses until equilibrium reached
Spins flowing into the slice have not “seen” previous excitations, so have greater signal a RF Mz
fresh inflow spin
inplane stationary spin
More on spin saturation later
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24. Time of Flight - Example
Renal arteries
Aorta
Inflow from vein
Inversion recovery (TI 300 ms)
FatSat
Inversion recovery (TI 300 ms)
FatSat
IR Volume extends more inferior so
that vein signal is also saturated
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25. Time of Flight – Brain MRA
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26. Blood Flow – Phase Contrast
With a given gradient field, stationary spins precess at a constant rate
Moving spins experience a change in precession frequency, depending on their velocity v, and the gradient strength, G.
This causes a velocity-dependent phase shift, f
For constant flow velocity,
With an x-Gradient Gx, the field strength is
The phase shift is linear with velocity
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27. Blood Flow – Phase Contrast
Add bipolar gradient in the flow direction after RF excitation
Stationary spins are not dephased
Repeat acquisition with reversed gradients
Complex subtraction of images gives flow image
Acquisition 1: Gx
Acquisition 2: Gx Gz RF
Gx1: fflow = gvM1, fstationary = 0
Gx2: fflow = -gvM1, fstationary = 0
|I1-I2| ~ rflowsin gvM1
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28. Phase Contrast - Example
Kidney Transplant
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29. Fast Imaging Fast imaging = TR<T1,T2
Spins do not have time to relax between one RF pulse and the next
Transverse magnetization: Spin memory produces artifacts in images. Many RF pulses contribute to each acquisition
Longitudinal magnetization: Spins get “beaten down” so that after each pulse there is less magnetization available.
Equilibrium between pulses and relaxation
Optimum angle to maximize steady-state signal – Ernst angle
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30. Spoiling
Destroy transverse magnetization so it doesn’t contribute to later echoes
Dephase the spins with large spoiling gradients after each acquisition
Assume perfect spoiling
Readout
Phase encoding
Slice encoding
Spoiler
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31. Spin Saturation At equilibrium full magnetization is available
Each pulse and spoiling reduces the magnetization
Some signal regrowth due to T1 decay
1. Equilibrium
M=M0
3. Spoiling
M=M0cos 
5. RF Excitation
Flip Angle 
2. RF Excitation
Flip Angle 
4. T1 Regrowth
6. Spoiling
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32. Ernst Angle
Maximize the equilibrium transverse magnetization available  signal
Calculate the optimum flip angle for a required TR
Immediately after nth TR
After RF Flip of  and spoiling
After T1 recovery
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33. Ernst Angle In equilibrium, Mz(n+1)=Mz(n)=Mz
Equilibrium Transverse Magnetization, M=Mzsin
Show that Maximum Transverse Magnetization (signal) when
E = Ernst Angle
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34. Tissue Contrast
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35. Ernst Angle
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