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Medical Imaging and Pattern
Recognition
Lecture 8
Magnetic Resonance Imaging
Oleh Tretiak
Medical Imaging Modalities:
History
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1895: X-ray†
~1950: Ultrasound
~1955: Radionuclide
1972: CT†
~1980: MRI†
†Nobel
Prize
MIPR Lecture 8
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MRI Procedures
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Magnetic Resonance Angiography (MRA)
Body MRI
Cardiac MRI
Chest MRI
Head MRI
Musculoskeletal MRI
Spine MRI
Functional MRI of the Brain (fMRI)
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Full Carotid Artery MRI
• There are four carotid arteries, two on
each side of the neck: right and left
internal carotid arteries, and right and
left external carotid arteries.
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Cardiac MRI: Akinetic Wall
Animated clip and contrast image
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Cardiac MRI: Valvular Reflux
Reduced heart function due to aortic valve dysfunction.
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Chest MRI
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Head MRI
Cerebral Aneurism - Schematic
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Aneurysm
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Musculoskeletal MRI
QuickTime™ and a
TIFF (Uncompressed) decompressor
are needed to see this picture.
• Left: normal knee. Right: torn anterior
cruciate ligament
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Spine MRI
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Functional MRI of the Brain
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Strengths of MRI
• Images of soft-tissue structures of the body, such as
the heart, lungs, liver, are clearer and more detailed
• MRI can help evaluate the function as well as the
structure
• Invaluable tool in early evaluation of tumors
• MRI contrast materials are less harmful than those
used in X-ray or CT
• Fast, non-invasive angiography
• Exposure to radiation is minimal (non-ionizing)
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Risks and Weaknesses
• Metal implants may cause problems
• Problems with claustrophobia
• MRI is to be avoided during the first 12
weeks of pregnancy
• Bone is usually better imaged with Xrays
• MRI typically costs more than CT
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Magnetic Materials
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Nuclear Magnetism
No magnetic field
Strong magnetic field
Atomic nuclei have intrinsic quantized magnetic
moments
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Nuclear Magnetic Resonance
• A transverse RF field at the appropriate frequency causes the
moments to tilt from the magnetizing field axis
B0
H
HB0
B0
H
Ht = Acost
 = H0
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Copyright Oleh Tretiak, 2004
H
B0
Ht = Acost
 ≠ H0
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Excitation of Spins
In a static field, the spins line up with the magnetic field. There is
no external magnetic signal.
If a magnetic nucleus is in field strength H0 (Larmour frequency
0), and a RF field normal to H0 and at frequency 0 is applied, the
magnetic moments move away (tip away) from the direction of Ho.
Tip angle is proportional to the magnitude and duration of the
exciting field (RF field).
This is a resonance phenomenon. If , the RF field frequency, is
different from 0, the tip angle is equal to 0.
The motion of the magnetization is described by the Bloch
equation.
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Excitation of Spins
H0
  AT / 
H1  Acos 0 t
0tT
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Nuclear Magnetic Resonance
0


0  H0
When a nuclear magnet is tilted
away from the external magnetic
field it rotates (precesses) at the
Larmour frequency. For hydrogen,
the Larmour frequency is 42.6 MHz
per Tesla.
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Slice Selection
• If the external field is equal to Hz(x, y, z) = H0 + zGz,
and an exciting field at frequency w0 is applied, the
slice z=0 is selected. That is, spins in that plane are
tipped, while other planes are not affected.
• Slice profile is proportional to the Fourier transform of
the RF field envelope. Short, strong pulse — thick
plane. Weak, long pulse — thin plane.
• The plane can be selected by field gradients.
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Slice Selection Examples
Gradient
x
y
z
x-y-z
Plane
y-z
x-z
x-y
oblique
Hx  Acos 0 t
Hz
Hz
Hz  H0  xGx
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External Signal from Resonance
H0
0
s(t)
Spinning magnetization induces a voltage in
external coils, proportional to the size of
magnetic moment and to the frequency.
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Bloch Equation
Mx i  My j (Mz  M0 )k
dM
 M  H 

dt
T2
T1
Motion of the magnetization vector is described
by the Bloch equation. The cross product term
leads to magnetic resonance, while T1 and T2
terms lead to relaxation (decay) of transient
effects. For living tissues, T1 ~ 0.2 to 1 sec, T2 ~
0.02 to 0.1 sec.
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Imaging: two boxes.
s(t)
2
1.5
1
a
b
3.9
3.6
3.3
3
2.7
2.4
2.1
1.8
1.5
1.2
0.9
0.6
-0.5
-1
0.3
0
0.5
0
-1.5
-2
Assume the ‘body’ consists of two samples, a in stronger field,
b in a weaker field. s(t) is the sum of sinewaves at the two
frequencies. The Fourier transform of s(t) will have two lines
corresponding to the frequencies (locations) of the two
samples. The strength of each line is proportional to the
amount of material in each location.
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Imaging: linear object
Fourier transform
of s(t)
Tube, parts are narrow, parts
are wide
‘Map’ of tube thickness
Tube of nonuniform thickness in linearly varying
magnetic field. The Fourier transform of the
resonance signal is proportional to the tube
thickness.
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Imaging: two-dimensional object
Hz  H0  Gx x  Gy y
s(t)  Ke i 0 t  m(x, y)e
 Ke
i 0 t
i (Gx x Gy )t
FT [m(x, y)]( x  Gx t,  y  Gyt)
Given a thin plate of magnetic moments in the x-y
plane. The magnetic fields has linear variation
(gradients) in the x and y directions. The resulting total
magnetic resonance signal is proportional to the Fourier
transform of m(x, y) along a line in the Fourier plane.
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Diagram of Fourier plane path
y
y

x
x
Gx  Gcos 
Gy  Gsin 
m(x, y)
By successively applying different combinations of
gradients we can measure the Fourier transform over
the whole plane. Then take the inverse transform to
compute m(x, y).
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Huge Magnetic Fields
• Magnetization proportional to external field
• Frequency proportional to external field
• Voltage proportional to the product of magnetization
and frequency
• Signal proportional to square of magnetic field
• Higher field —> better image quality!
• We can get good image quality (for some
procedures) by scanning for a longer time
– Problems with motion and with patient comfort
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Contrast Mechanisms
• Intrinsic contrast mechanisms: m, proton
density; T1 and T2, relaxation times.
• Chemical environment affects signals and
can produce contrast. For example, resonant
frequencies for fat and muscle are different.
• Motion affects MRI signal. Flow and diffusion
can be measured.
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MRI Scanner
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Open Bore MRI Scanner
• Avoid claustrophobia
• Lower image quality
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Summary of MRI
• Rich set of contrast mechanisms.
• Versatile slice selection. Tomographic and
projection images are possible.
• Non-ionizing. No known harmful effects,
except heating.
• Resolution not as good as in X-ray.
• Expensive and slow.
• New technique. Rapid and continuing
progress.
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