Download MRI

MRI
Magnetic Resonance
1. Principle first observed in 1946
2. Used for spectroscopy and imaging
3. Imaging techniques are a form of tomography, where
slices are ’cut’ and depict
4. MRI utilizes signals from the body
5. MRI is non-ionizing, operating in radiofrequency range,
unlike CT, PET, SPECT
6. Resolution is not limited to radio wave lengths
7. MRI is pricy
2
Nuclear spin
A nucleui possesses a spin angular momentum, (p)
Can be view as a rotation of the nuclei
p 
I I  1
I is the quantum number of the spin.
The spin gives raise to a magnetic moment:
μ  p
Where  is the gyromagnetic ratio
3
Nuclear spin
I can be an intenger, half an intenger, or
0
If I is 0 there is no spin and no magnetic
moment
The natural isotope 12C has quantum
spin of 0 whereas 13C has ½.
p 
I I  1
4
Nuclei in a magnetic field – The classics
Torque on the nuclei
L  µ  B0
Torque makes the muclei precess chancing p
dp
 L  µ  B0
dt
dµ
 L  µ  B 0  B 0  µ  0  µ
dt
ω 0  B 0
ω0 is the Larmor frequency, the frequency that
the nuclei precesses with
5
Nuclei in a magnetic field – Quantum mechanics
p is quantified allowed 2I +1 states
Eg a proton 1H is allowed two states or directions
parallel to the field (spin up)
antiparallel to the field (spin down)
E  B 0
6
Many nuclei in a magnetic field
An equlibrium between spin up and spin down will emearge
A small excess of nuclei in the low energy state, N
N  N 0
E
2kT
7
Back to the Larmor Frequency
ω0  B0  0  B0
, the gyromagnetic konstant ‘material’
constant
, Can be affected by chemical bounds
The magnetic field may be
inhomogeneous
8
The Chemical shift effect
Shielding electrons reduces the magnetic field
’seen’ by the nucleus
Bˆ0  B0 1   
The resonance frequency is also reduced
ˆ 0  0 1   
 is the shielding constant
 ~5e-6
 depends on local chemical envionment
Used for gaining knowledge about chemical
structure; Spectroscopy
9
Bulk / Macroscopic / Sum magnetization
Ns
M   i
i 1
Ns is the number of atoms in a sample
i is the magnetic moment of the i-th atom
M is always aligned to B in equilibrium
M can be pertubed and will precess
dµ
 0  µ
dt
dM
 ω 0  M  M  B 0
dt
10
Excitation
Adding a field B1 perpendicular to B0 at Lamor
frequency will excite the system
An ocillating magentic field at 1 – 500 MHz is a Radio
frequency wave
B1 ~ 50 mT & B0 ~ 1-5T
 is the flip angle
A pertubation pulse is often named after the flip angle
90° pulse
180 ° pulse
11
Excitation
B1 (t )  B1 (t ) exp i0t   
B1 is the envelope function
The duration of the pulse  affects the flip angle
 = B1
or if different amplitudes are allowed

    B1 (t )dt
0
12
Induced current
In Eqlibrium
Mz = M0
Mx = My = 0 ~ Mxy
After perturbation
V  M xy sin(  )
13
Free Indusction Decay (FID)
The Mxy component decays to 0
The frequency is the peak
The decay rate T2 is proportional to the width at half max
Area under the envolope is the hight of the spectral amplitude
14
Relaxation
Mxy  0 : Spin-spin relaxation
M xy (t )  M 0 sin   exp i 0t    exp t T 2 
T2 time to 36.7% of M0
Mz  M0 : Spin-lattice relaxation
M z (t )  M 0 1  1  cos  exp t T 1
T1 time 63.2% of M0
Important for contrast in images
15
Inversion recovery
180-TI-90-FID
M z (t )  M 0 1  2 exp TI T 1
16
Invertion recovery
17
Spin Echo
M y (t )  M 0 exp TE T 2 
18
Magnetic Field Gradients
G is the gradient of a magnetic field
Bz ( x)  B0  xGx
 ( x)   B0  xGx 
19
Slice selection
•
•
By applying a gradient G the resonance frequency
becomes dependent on direction
The bandwidth of the pulse determines the thickness of
the slice
20