Medical Imaging Systems:

1
Medical Imaging Systems MRI Physics and Image
Formation
Instructor Walter F. Block, PhD 1-3 Notes
Walter Block and Frank R Korosec, PhD 2-3
Departments of Biomedical Engineering
1, Radiology 2 and Medical Physics 3 University
of Wisconsin - Madison
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Major MRI Scanner Vendors
Philips Intera CV
Siemens Sonata
General Electric CV/i
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Siemens Espree, 1.5 T, 70 cm bore, 125 cm length
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Extremity Scanner (0.2 T)
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OrthOneXT, 1.0 T Extremity Scanner
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Magnetic Field Strengths

• 3.0 T Growing high end market (Neuro, MSK)
• 4.0 T Few
• 7.0 T Few human research scanners
• 8.0 T Animal scanners
• 9.4 T Animal scanners

• 0.2 T Orthopedics
• 0.3 T Open scanners
• 0.5 T Some closed bore
• 0.7 T Open scanners
• 1.0 T Common
• 1.5 T Most common

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1.5 T vs. 3.0 T (3D MR Angiography)
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MRI Uses Three Magnetic Fields

• Static High Field (B0) (Chapter 12, Prince)
• Creates or polarizes signal
• 1000 Gauss to 100,000 Gauss
• Earths field is 0.5 G
• Radiofrequency Field (B1) (Chapter 12, Prince)
• Excites or perturbs signal into a measurable form
• On the order of O.1 G but in resonance with MR
  signal
• RF coils also measure MR signal
• Excited or perturbed signal returns to
  equilibrium
• Important contrast mechanism
• Gradient Fields (After Lunch, Chapter 13, Prince)
• 1-4 G/cm
• Used to image determine spatial position of MR
  signal

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Nuclear Magnetic Dipole Moment
Magnetic Dipole Representation
Vector Representation
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Nuclear Magnetic Dipole Moment Spinning Charge
N
N
P
P
P
P
P
N
Hydrogen
Helium
Helium-3
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Nuclear Magnetic Dipole Moment

• To have a magnetic dipole moment, it must have
• An odd number of protons or
• An odd number of neutrons or
• An odd number of both protons and neutrons

12
Imaging Criteria

• To be imaged, nuclei must
• have an odd number of neutrons, protons, or both
• be abundant in the body
• Hydrogen in the water molecule satisfies both
• The hydrogen nucleus is composed of a single
  proton (odd number of nucleons)
• Water comprises 70 of the body by weight (very
  abundant)
• Most widely imaged
• Termed spins in MRI

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Atoms That Can be Imaged with MRI
H
C
O
F
Na
P
K
1
13
17
19
23
31
39
1
6
8
9
11
15
19
.093
.016
1.0
.066
S
N
A
where
Z
N is the element abbreviation A is the total
number of protons and neutrons combined (atomic
mass) Z is the number of protons ( atomic number)
S relative MRI sensitivity compared to hydrogen
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No Magnetic Field

No Net Magnetization
Random Orientation
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Static Magnetic Field (B0)
Body RF (transmit/receive)
Bore (55 60 cm)
Gradients
Shim (B0 uniformity)
Magnetic field (B0)
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Classical Physics Top analogy

• Spins in a magnetic field analogous to a
  spinning top in a gravitational field.

Axis of top
gravity
Top precesses about the force caused by
gravity Dipoles (or spins) will precess about the
static magnetic field
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Reference Frame
y
x
z
Magnetic field (B0) aligned with z (longitudinal
axis and long axis of body)
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B0 Field Dipoles Separate Into 2 States
Magnetic Field (B0)
Positive Orientation (Lower Energy)
Negative Orientation (Higher energy)
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Larmor Equation
?????B
Precessional Frequency
Magnetic Field Strength

• for hydrogen 42.58 MHz/T
• 64MHz 42.58 MHz/T ? 1.5T
• With stronger gravity, top will precess faster
• Same with dipoles stronger B0 causes faster
  precession

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Dipole Moments from Entire Sample
B0
7 up
6 down
Non-Random Orientation
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Sum Dipole Moments -gt Bulk Magnetization
Net Magnetization
B0
M
The magnetic dipole moments can be summed to
determine the net or bulk magnetization, termed
the vector M.
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Bulk Magnetization

• ? of aligned spins ? ? bulk magnetization ? ?
  MR signal

• ? strength of B0 ? ? MR signal

At 1.5 T and 310 K, there are only 9 excess
aligned spins 2 per million protons!
But, a 1 x 1 x 1 mm voxel of water contains 0.3
million billion excess aligned spins!!!
Endpoint We can understand MRI with simple
classical physics instead of quantum physics
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MRI Uses Three Magnetic Fields

• Static High Field (B0)
• Creates or polarizes signal
• 1000 Gauss to 100,000 Gauss
• Earths field is 0.5 G
• Radiofrequency Field (B1)
• Excites or perturbs signal into a measurable form
• On the order of O.1 G but in resonance with MR
  signal
• RF coils also measure MR signal
• Excited or perturbed signal returns to
  equilibrium
• Important contrast mechanism
• Gradient Fields (After Lunch)
• 1-4 G/cm
• Used to image determine spatial position of MR
  signal

24
B1 Radiofrequency Field

• Polarized signal is all well and good, but what
  can we do with it? We will now see how we can
  create a detectable signal.

To excite nuclei, tip them away from B0 field by
applying a small rotating B field in the x-y
plane (transverse plane). We create the rotating
B field by running a RF electrical signal
through a coil. By tuning the RF field to the
Larmor frequency, a small B field (0.1 G) can
create a significant torque on the magnetization.

Diagram Nishimura, Principles of MRI
25
Exciting the Magnetization Vector
z
B1 tips magnetization towards the transverse
plane. Strength and duration of B1 can be set
for any degree rotation. Here a 90 degree
rotation leaves M precessing entirely in the xy
(transverse) plane.
Laboratory Reference Frame
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Tip Bulk Magnetization
z'
y'
x'
Rotating Reference Frame Imagine you are
rotating at Larmor frequency in transverse plane
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Tip Bulk Magnetization
z'
y'
x'
Rotating Reference Frame
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Tip Bulk Magnetization
z'
y'
x'
Rotating Reference Frame
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Tip Bulk Magnetization
z'
y'
x'
Rotating Reference Frame
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Larmor Equation
?????B
Tip Angle
? ?Dt????B1Dt
Tip Angle
Amplitude of RF Pulse
Time of Application of RF Pulse
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Magnetization is tipped using an RF Pulse
Components of tipped Magnetization (M)
'
'
'
'
'
'
In general, any component of the magnetization
can be tipped into the transverse plane to give
rise to a signal. Next, how do we detect the
signal?
32
After B1 Mtrans ( Mxy ) precesses about B0
B0
t0
t 0
Laboratory Frame
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Signal From Precessing Magnetization
Receiver (antenna) integrates proton signal Farad
ays Law of Induction Change in magnetic flux in
time across a surface induces an electric
potential (voltage signal)
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Radiofrequency Receiver Coils

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Radiofrequency Receiver Coils
Transmit and Receive
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Electromagnetic Energy Spectrum
Graph Medical Imaging Systems Macovski, 1983
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Excitation Is it Permanent?

• Static High Field (B0)
• Creates or polarizes signal
• 1000 Gauss to 100,000 Gauss
• Earths field is 0.5 G
• Radiofrequency Field (B1)
• Excites or perturbs signal into a measurable form
• On the order of O.1 G but in resonance with MR
  signal
• RF coils also measure MR signal
• Excited or perturbed signal returns to
  equilibrium
• Important contrast mechanism
• Magnetization (spins) will return to equilibrium
  (Chapter 12, Prince)
• Very important image contrast mechanisms
• More important than proton density
• Soft tissue has little difference in proton
  density
• Cause of flat contrast in X-ray and CT soft
  tissue
• Gradient Fields (After Break)
• 1-4 G/cm
• Used to image determine spatial position of MR
  signal

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T2 Relaxation
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Tip Bulk Magnetization
z'
y'
x'
40
Tip Bulk Magnetization
z'
M M0
y'
x'
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Tip Bulk Magnetization
z'
y'
x'
42
Tip Bulk Magnetization
z'
y'
x'
43
Tip Bulk Magnetization
z'
y'
x'
44
Transverse Magnetization
z'
y'
Mxy
x'
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Transverse Magnetization
z'
2 up
y'
Mxy
2 down
x'
46
T2 Decay
-


z'
z'
-
-

y'
y'
x'
x'
T2 relaxation is dephasing of transverse
magnetization
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Transverse Magnetization
z'
y'
Mxy
x'
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T2 Decay Slight dephasing
z'
y'
x'
T2 relaxation is dephasing of transverse
magnetization
49
T2 Decay More dephasing
z'
y'
x'
T2 relaxation is dephasing of transverse
magnetization
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T2 Decay
z'
y'
x'
T2 relaxation is dephasing of transverse
magnetization
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T2 Decay
z'
y'
x'
T2 relaxation is dephasing of transverse
magnetization
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T2 Decay Complete dephasing
z'
y'
0
Mxy
x'
T2 relaxation is dephasing of transverse
magnetization
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T2 Relaxation
M0
Mxy M0 e-t/T2
Mxy
Time
54
T2 Signal Contrast
M0
Proton Density
Moderate T2-weighting
Mxy
Heavy T2-weighting
0.37M0
Mxy M0 e-t/T2
T2
Time
T2
55
Post Exercise Arm Imaging
Proton density
Moderate T2
Moderate T2
Mary Sesto Wally Block Tom Best Robert Radwin
Heavy T2
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Sample tissue time constants T2
T2 of some normal tissue types

• Table Nishimura, Table 4.2

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T2 T2 Relaxation
T2
Mxy
T2
Time
58
Causes of Spin Dephasing
1
1


??B0
T2
T2

• Local magnetic fields produced by nuclear
  neighbors (T2)
• Inhomogeneities in the main magnetic field, B0
  (T2)
• Quality of magnet usually not a concern
• Bulk susceptibility differences (T2)
• Air/tissue interfaces
• Iron

59
Different Names, Same Phenomenon

• T2 relaxation
• Mxy or Mtrans decay
• Spin-spin relaxation

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T2-weighted Sagittal Spine
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T1 Relaxation
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Tip Bulk Magnetization
z'
y'
x'
63
Tip Bulk Magnetization
z'
y'
x'
64
Tip Bulk Magnetization
z'
y'
x'
65
Tip Bulk Magnetization
z'
y'
x'
66
Tip Bulk Magnetization
z'
y'
x'
67
Transverse Magnetization
z'
y'
Mxy
x'
68
T1 Relaxation
B0
z
z
2 up
y
y
x
x
2 down
No Net Longitudinal Magnetization
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T1 Relaxation
B0
z
z
3 up
y
y
x
x
1 down
Spins Flip to Regrow Net Longitudinal
Magnetization
70
T1 Relaxation
z'
y'
x'
T1 relaxation is regrowth of the longitudinal
magnetization
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T1 Relaxation
z'
y'
x'
T1 relaxation is regrowth of the longitudinal
magnetization
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T1 Relaxation
z'
y'
x'
T1 relaxation is regrowth of the longitudinal
magnetization
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T1 Relaxation
z'
y'
x'
T1 relaxation is regrowth of the longitudinal
magnetization
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T1 Relaxation
z'
y'
x'
T1 relaxation is regrowth of the longitudinal
magnetization
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T1 Relaxation
z'
Mlong M0
y'
x'
T1 relaxation is regrowth of the longitudinal
magnetization
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T1 Relaxation
M0
Mz M0(1-e-t/T1)
Mz
Time
77
Source of T1 Contrast Varying Mz
M0
0.63M0
Mz M0(1-e-t/T1)
Mz
Time
T1
78
Different Names, Same Phenomenon

• T1 relaxation
• Mz or Mlong recovery
• Spin-lattice relaxation

79
T1 T2 Relaxation Trends
T1 depends on tumbling rate (more tumbling at
Larmor Frequency shorter T1) Solids
Very Long T1 Viscous Short
T1 Non-Viscous Long T1 T2 depends on time
spent in vicinity of nuclear neighbors
(more time near same neighbors shorter
T2) Solids Very Short T2 Viscous
Short T2 Non-Viscous Long T2
80
Relative Relaxation Rates
81
T1 and T2 vs B0

• T1 ? B0
• T1 ? as B0 ?
• T1 ? as B0 ?
• T2 largely independent of B0

82
T1 Relaxation
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Components of M after Excitation
Laboratory Frame
84
T1-, ?-, and T2-weighted images
?-weighted
T2-weighted
T1-weighted
85
Brain Tumor Imaging
Whats changed between these images?
T1-weighted Sagittal
T1-weighted Axial
T2-weighted Axial
86
Images of the Knee
?-weighted
T2-weighted
87
MR Physics So far...

• What we can do so far
• 1) Excite spins using RF field at ?o
• 2) Record time signal (Known as FID)
• 3) Mxy decays, Mz grows
• 4) Repeat.

But so far RF coils only integrate signal from
entire body. We have no way of forming an
image. That brings us to the last of the three
magnetic fields in MRI and image formation.