Download NMR imaging

NMR imaging
Mikael Jensen
Associate professor
Dept. Mathematics and Physics
Royal Veterinary and Agricultural
University
April 2002
Why imaging
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Non-destructive
Dynamic
In-vivo
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or
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Destructive
Static
Once in a lifetime
Medical use
Veterinary use
•Røntgen
•Ultralyd
•Termografi
Penetrating radiation
• X-rays (20-200 keV)
• Gamma (80-511 keV)
• Radiofreqency 63
MHz
• Light(near infra-red)
• Ultrasound
X-ray
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Show differences in electron density
Small inherent contrast in soft tissue
Many photons means good S/N ratio
Good geometric resolution
Planar ( projections )
Can be used for tomography ( CT-scan)
Uses ionizing radiation
Radio-isotopes (gamma radiation)
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Function more than anatomy
Totally dependent on nature of tracer
Few photons, high contrast
Poor gometric resolution
Uses ionizing radiation
Ultrasound
• Shows differences in sound velocity and
density*
• Tissue borderlines
• Air-filled cavities creates shadows
• Real-time
• Cheap and safe
• Interactive
* Egentlig: Forskel i akustisk impedans !
NMR – imaging (MRI)
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No ionising radiation
Large inherent contrast in soft tissue
Can demonstrate both anatomy and function
Good geometrical resolution
Expensive
Restricted acces to patient during exam
Very good web introduction to
MRI
http://www.cis.rit.edu/htbooks/mri/inside.htm
Go and read it !
NMR imaging
Frequency= γ B
For protons γ= 42 MHz / Tesla
Wawelength at 1 Tesla ?
Wawelength = c/f = 7 meter !
?
External magnetic field necessary for NMR
S
z
Bo
y
N
By convention we choose z axis along Bo
x
We need nuclei with magnetic
moment for NMR
Unpaired
Protons
Unpaired
Neutrons
Net
Spin
(MHz/T)
1H
1
0
1/2
42.58
2H
1
1
1
6.54
31P
0
1
1/2
17.25
23Na
0
1
3/2
11.27
14N
1
1
1
3.08
13C
0
1
1/2
10.71
19F
0
1
1/2
40.08
Nuclei
Could be Hydrogen in water (protons)
Larmor condition
E=h B
E=h f
f= B
(Larmor condition)
(proton)= 42 MHz/ Tesla
When the energy of the photon matches the energy difference between the two spin states an
absorption of energy occurs.
In the NMR experiment, the frequency of the photon is in the radio frequency (RF) range. In
NMR spectroscopy, is between 60 and 800 MHz for hydrogen nuclei. In clinical MRI, is
typically between 15 and 80 MHz for hydrogen imaging.
Boltzman Statistics
At room temperature, the number of spins in the lower energy
level, N+, slightly outnumbers the number in the upper level,
N-. Boltzmann statistics tells us that
N-/N+ = e-E/kT.
E is the energy difference between the spin states; k is
Boltzmann's constant, 1.3805x10-23 J/Kelvin; and T is the
temperature in Kelvin.
1.000.000
1.000.001
T1 relaxation
The time constant which
describes how MZ returns to its
equilibrium value is called the
spin lattice relaxation time (T1).
The equation governing this
behavior as a function of the
time t after its displacement is:
Mz = Mo ( 1 - e-t/T1 )
T2 relaksation
The time constant which describes the return to equilibrium of
the transverse magnetization, MXY, is called the spin-spin
relaxation time, T2.
MXY =MXYo e-t/T2
Bloch equations
Free induction decay (“FID”)
Short RF pulse at Larmor frequency
90o
Detected RF signal from nuclei
Fourier transform af FID
F
tid
F-1
frekvens
(sted)
NMR in organic chemistry
CH3CH2OH
Also known as
Ethanol
1951
1991
Frequency alias ”chemical shift” 
MRI imaging is ”broadband”
•In chemical NMR typical resolution (linewidth) is 0.1 ppm
•Chemical shifts are of the order of 1- 10 ppm
•In imaging we have inhogeneous magnetic fields
•In imaging we use frequncy to encode spatial position
•Typical space coding 100 Hz/mm or 500 ppm/mm
f
f
Pulsewidth and flipangle
90o
pw
180o
2pw
270o
3pw
Spin echo
TE/2
90o
TE/2
180o
Gradient in magnetic field
B = Bo + Gx x
Bo = 1,5 T
Gx = 25 mT /cm
Frequency coding df/dx = Gx γ =
1 kHz /cm = 100 Hz/mm
FFT 
Gradient
time
f
Imaging of one slice
y
x
z
Gz
Slice selected echo
90o
180o
Only signal from slice
Gz
Normally chosen as z-direction
Read-out gradient
90o
180o
Gz
Gx
Phase encoding gradient
90o
180o
Gz
Gy
Gx
Repeat this, and you got the image
m data points
2D FFT
n
n repetitions
m
Another way to do imaging
Select one slice !
Do many experiments with different directions of readout gradient
Back projection
Filtered back projection
Radon transformation ( MRI, CT, PET, Spect ….)
S.R. Deans, S. Roderick
The Radon Transform and Some of its Applications.
Wilwy, New York
1983
Slice selective MRI by back
projection
Many values
Repeat
for
many
angles
Many values
Multi slice imaging
Inversion recovery imaging
MRI hardware
Magnet
B0
0.015 – 0.3 Tesla Resistive
0.5 – 3 Tesla Superconducting
Gradients
Safety
•Static magnetic field
•No metal objects
•Shielding
•B < 3 Tesla
•RF power deposition
•Deposited power < 4 W / Kg
•No hot spots
•B < 3 Tesla (f < 130 MHz )
Images!
Lumbar spine MRI
Normal
Prolaps
Malignancy ?
Liver
Arrows point to multiple lesions in the liver demonstrating metastases.
Tværsnit af rygmarv hos rotte
Hjernen af en stær (in vivo)
Good image archives:
NORTHEAST WISCONSIN MRI CENTER
MR IMAGES
http://www.newmri.com/humanbo2.htm
RADIOLOGIC ANATOMY BROWSER™
http://rad.usuhs.mil/rad/iong/homepage.html
End of lecture
Bloch
Purcell
Lauterbur