NMR imaging
Mikael JensenAssociate professor
Dept. Mathematics and Physics
Royal Veterinary and Agricultural University
April 2002
• Non-destructive • Dynamic• In-vivo
• or
• Destructive• Static• Once in a lifetime
Why imaging
Medical use
•Røntgen
•Ultralyd
•Termografi
Veterinary use
Penetrating radiation
• X-rays (20-200 keV)• Gamma (80-511 keV)• Radiofreqency 63
MHz• Light(near infra-red)• Ultrasound
X-ray
• 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)
• 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)
• 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 imagingFrequency= γ B
For protons γ= 42 MHz / Tesla
Wawelength at 1 Tesla ?Wawelength = c/f = 7 meter !
?
x
y
Bo
External magnetic field necessary for NMR
z
By convention we choose z axis along Bo
N
S
We need nuclei with magnetic moment for NMR
Could be Hydrogen in water (protons)
Nuclei
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
Larmor condition
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.
E = h B E = h f
f = B (Larmor condition)
(proton)= 42 MHz/ Tesla
Boltzman StatisticsAt 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
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 )
T1 relaxation
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”)
90o
Short RF pulse at Larmor frequency
Detected RF signal from nuclei
Fourier transform af FID
tid
frekvens(sted)
F
F-1
NMR in organic chemistry
CH3CH2OHAlso known asEthanol
Frequency alias ”chemical shift”
1951
1991
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
pw 2pw 3pw
90o 180o 270o
Spin echo
90o 180o
TE/2 TE/2
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
Gradient
FFT
time f
Imaging of one slice
Gzz
x
y
Slice selected echo
90o
180o
Gz
Only signal from slice
Normally chosen as z-direction
Read-out gradient90o
180o
Gz
Gx
Phase encoding gradient90o
180o
Gz
Gx
Gy
Repeat this, and you got the image
n repetitions
2D FFT
n
m data points
m
Another way to do imagingSelect 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. RoderickThe Radon Transform and Some of its Applications.Wilwy, New York1983
Slice selective MRI by back projection
Many values
Many values
Repeat formany angles
Multi slice imaging
Inversion recovery imaging
MRI hardware
Magnet
0.015 – 0.3 Tesla Resistive0.5 – 3 Tesla Superconducting
B0
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 MRINormal 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 CENTERMR IMAGES
http://www.newmri.com/humanbo2.htm
RADIOLOGIC ANATOMY BROWSER™
http://rad.usuhs.mil/rad/iong/homepage.html
End of lecture
Bloch Purcell Lauterbur