Download Physics: Magnetic Resonance Imaging

Physics:
Magnetic Resonance Imaging
Lecturers
Lawrence Panych, PhD
Lei Qin, PhD
Bruno Madore, PhD
Stephan Maier, MD, PhD
Robert Mulkern, PhD
Brigham and Women’s Hospital
Harvard Medical School
Avdelningen för radiologi
Sahlgrenska Universitetssjukhuset (S. Maier)
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Magnetism, Magnetic Fields and Nuclear Magnetic Resonance
MR Signal Properties - Manipulating the Magnetization
MR Signal Properties – Relaxation, Diffusion, Dephasing
Pulse Sequences – the Basics
Pulse Sequences – Image Contrast Mechanisms
Image Reconstruction – Basic Mathematics of MRI
Image Characteristics and their Manipulation
Special Acquisition Techniques
Contrast Agents and their Use
Image Artifacts
MR Instrumentation
Safety and Bioeffects of MR
Studieböker
MRI in Practice.
Catherine Westbrook.
“lättläst”
MRI The Basics
Ray H. Hashemi.
“lite mer teori”
Studieböker
The Essential Physics of Medical Imaging.
Jerrold T Bushberg.
“Utförligt handbok om alla bildgivande
metoder”
Review of Radiologic Physics
Walter Huda
“kompendium för examens förberedning av
radiologer i USA”
Magnetism, Magnetic Fields and
Nuclear Magnetic Resonance
Main Areas Covered in Lecture
• Magnetic susceptibility
• Types of magnetic materials
• Magnetic fields
• Net magnetization due to Bo and field strength
Study Questions
• What is the basic source of the signal in MRI ?
• How is a magnetic field generated ?
• What is magnetic susceptibility ?
Electric Charge
Charge (positive or negative) is a fundamental property
of certain elementary particles of matter (e.g. the electron).
Opposite charges attract and like charges repel.
An electric field is generated around a charge.
Current is comprised of flowing electrical charge.
Magnetic Field
A property of space caused by the motion of an electric charge.
A stationary charge will produce only an electric field in the
surrounding space.
If a charge is moving, a magnetic field is also produced.
- Encyclopedia Britannica
Magnetar
100 Billion Tesla
3T MRI = 30,000 Gauss
25 Tesla = 250,000 Gauss
Magnetic
Field
Strength
Types of Magnets in MRI
Permanent Magnet
Electro-Magnet
Types of Magnets in MRI
Permanent Magnet
Super-conducting
Electro-Magnet
Strengths of Magnets in MRI
1 T (Tesla) = 10,000 G (Gauss)
Ultra-Low Field
< 0.2T (2000G)
Low Field Midfield High Field Ultra-High Field
0.25T
Permanent Magnet
0.5T
3.0T
7.0T +
Super-conducting
Electro-Magnet
Magnetic Field
H is the magnetic field intensity and is measured in units of amps/meter.
.p
iδL,
incremental
current element
with charge
moving along the
path, δL
rP Ar
δ H at the point, p, is equal to:
( iδL X Ar ) / (4 π rP2)
where Ar is a unit vector from the
current element to the point, p.
δ H is a vector orthogonal to vectors, δL and Ar
δH
δL
Ar
Magnetic Field
Direction of the
Magnetic Field
Direction of the
Current Element
Magnetic Flux Density
B is the magnetic flux density and is measured in units of Tesla.
B=µH
where µ is the magnetic permeability,
a measure of the ability of a medium to support a magnetic field.
In free space µ = µo where µo is the permeability of free space,
a measure of the ability to form a magnetic field in a vacuum.
Natural Sources of Magnetic Fields
The orbital motion of the negatively charged electron around the
nucleus as well as its spin
are central to explaining the magnetic properties of materials.
Nature of Magnetic Materials
Types of material
classified in terms of magnetic properties:
1.Diamagnetic
2.Paramagnetic
3.Ferromagnetic
4.Antiferromagnetic
5.Ferrimagnetic
6.Superparamagnetic
1. Diamagnetism
In Diamagnetic atoms the small magnetic fields caused
by the electron orbital motion are cancelled by the
magnetic fields caused by the electron spin of the atom
and in the absence of an external magnetic field the
magnetic moment of each atom is zero.
-M:
magnetic moment
due to
electron spin
+M:
magnetic moment
due to electron orbital
motion
1. Diamagnetism
In the presence of an external magnetic field the
electron motion is altered and this slightly lowers the
moment due to the electronic orbital motion and there
will be a small net magnetic moment, δ, that is oriented
opposite to the external magnetic field.
-M:
magnetic moment
due to
electron’ spin
+M - δ:
magnetic moment
due to electron orbital
motion
External
magnetic field
1. Diamagnetism
Water, e.g. in living objects, is diamagnetic.
In strong magnetic fields, the magnetic forces can cause levitation!
2. Paramagnetism
In Paramagnetic atoms the small magnetic fields
caused by the electron orbital motion are NOT
cancelled and
each atom has a small magnetic moment, ∆.
-m:
magnetic moment
due to
electron’ spin
+m + ∆:
magnetic moment
due to electron orbital
motion
Net magnetic moment, ∆
2. Paramagnetism
In the absence of an external magnetic field
the magnetic moments of the paramagnetic atoms are
randomly aligned and the average effect is that
there is no net magnetic moment of the atoms.
2. Paramagnetism
In the presence of an external magnetic field
the magnetic moments of the paramagnetic atoms
tend to align and the average effect is that
there is a net magnetic moment in the same direction as
the external field.
External
Magnetic field
3. Ferromagnetism
In Ferromagnetic atoms there
is a relatively large magnetic dipole moment.
These moments align over regions called domains.
In the absence of an external field, however, the
domains are randomly aligned so there is no net field.
3. Ferromagnetism
In the presence of an external magnetic field,
the domains tend to align in the direction of the
external field.
External
Magnetic field
When the field is removed, the random alignment of
the domains is not immediately established and there is
a residual magnetization of the material.
3. Ferromagnetism
A permanent magnet is created from ferromagnetic
material that is processed in a strong magnetic field.
When the field is removed, the domains remain
strongly aligned creating a permanent magnetization of
the material.
4. Antiferromagnetism
In antiferromagnetic materials, neighboring atoms
align anti-parallel with each other,
therefore, there is no net moment.
Presence of an external field has little effect.
5. Ferrimagnetism
As with antiferromagnetic materials, neighboring atoms
align anti-parallel with each other,
however, neighboring dipoles are unequal
giving a net magnetic moment.
The presence of an external field has a significant effect.
6. Superparamagnetism
In superparamagnetism, ferromagnetic nanoparticles
are randomly aligned in a non-ferromagnetic matrix.
In a magnetic field the particles align with the field
giving a relatively strong magnetic moment. When the
field is removed there is no residual magnetization.
Nature of Magnetic Materials
Types of material
classified in terms of magnetic properties:
1.Diamagnetic (most tissues in the body)
2.Paramagnetic (gadolinium)
3.Ferromagnetic (iron, nickel, cobalt)
4.Antiferromagnetic (nickel oxide - NiO)
5.Ferrimagnetic (ferrites)
6.Superparamagnetic (iron oxide nano-particles)
Magnetic Susceptibility
χ m is the magnetic susceptibilty and is a measure of the
degree to which magnetization, M, of a material varies.
M = χm H
Ferromagnetic materials such as iron and nickel have
very large magnetic susceptibilities.
Magnetic Susceptibility Spectrum
Pyrex
Perspex
Nuclear Magnetism
and
Nuclear Magnetic Resonance
Source of the Signal in MRI:
Net Spin of the Nucleus
12
P
P
(6 protons and 6 neutrons)
N
N
N
N
P
P
N
P
C
N
P
• Nuclei of all elements contain protons and neutrons
• Protons and neutrons combine to give a net spin
• If even number of protons and an even number of neutrons
Then the net spin of the nucleus is zero:
Source of the Signal in MRI:
Net Spin of the Nucleus
13
P
N
P
N
N
(6 protons and 7 neutrons)
N
N
P
P
N
P
C
N
P
• If there is an odd number of protons or neutrons
Then the net spin of the nucleus is not zero:
• Circulating charge creates a magnetic dipole moment.
Some Nuclei with MR Signal
Nucleus
Abundance of
Element in the
Human Body
Natural
Abundance of
Isotope
Percent of All
Atoms in the
Human Body
C
9.4%
1.11%
0.1%
Na
0.04%
100%
0.04%
P
0.24%
100%
0.24%
H
63%
99.985%
63%
13
23
31
1
Some Nuclei with MR Signal
Nucleus
Abundance of
Element in the
Human Body
Natural
Abundance of
Isotope
Percent of All
Atoms in the
Human Body
C
9.4%
1.11%
0.1%
Na
0.04%
100%
0.04%
P
0.24%
100%
0.24%
H
63%
99.985%
63%
13
23
31
1
Some Nuclei with MR Signal
Nucleus
Abundance of
Element in the
Human Body
Natural
Abundance of
Isotope
Percent of All
Atoms in the
Human Body
C
9.4%
1.11%
0.1%
Na
0.04%
100%
0.04%
P
0.24%
100%
0.24%
H
63%
99.985%
63%
13
23
31
1
Some Nuclei with MR Signal
Nucleus
Abundance of
Element in the
Human Body
Natural
Abundance of
Isotope
Percent of All
Atoms in the
Human Body
C
9.4%
1.11%
0.1%
Na
0.04%
100%
0.04%
P
0.24%
100%
0.24%
H
63%
99.985%
63%
13
23
31
1
H is a very good candidate nucleus for MRI because (1) there is a lot of
hydrogen in the body, (2) 1H is the most common isotope of hydrogen and
(3) the magnetic moment is relatively strong compared to other nuclei.
1
“Proton” MRI
1
H
P
• In medical imaging we deal almost exclusively with the signal
from the hydrogen atom, which is comprised of one proton.
• This is why in MRI we often hear the term proton imaging.
• Hydrogen atoms in the body are primarily in water and fat.
Quantum States
1
Bo
P
H
1
H
P
• In a background magnetic field, Bo, the spin magnetic
moments of the hydrogen atoms will tend to align with the field.
• The possible spin states are quantized.
• The magnetic moments must align with the field or against it.
• The energy needed to change states depends on field strength.
Alignment of Nuclear Spins
Bo
• The preferred, low-energy state is for nuclear magnetic
moments to align with the external magnetic field.
Alignment of Nuclear Spins
Bo
• Although the preferred, low-energy state is to align with the
field, because of thermal fluctuations, some spin moments may
occasionally align opposite to the field in the higher energy state.
Distribution of States
Bo
• At high-temperature the moments constantly flip back and forth
and only a small net magnetic moment of very many nuclei is
aligned with the field.
• At body temperature, given 1 million hydrogen spins at 1.5T,
only 5 more spins are aligned with the field than against the field.
Net number of protons
aligned with a 1.5T field
in 1 mm3 of water:
330 trillion
Magnetization Vector
mz
Bo
Net magnetic moment
from billions of nuclear
spins
M
my
mx
Small volume element << 1mm3
Most of MRI can be explained using a magnetization vector.
The magnetization vector, M, represents the net moment.
Next Lecture
MRI Signal Properties Manipulating the
Magnetization Vector
mz
M
my
mx
Study Questions
• What is the basic source of the signal in MRI ?
• How is a magnetic field generated ?
• What is magnetic susceptibility ?
Study Questions
• What is the basic source of the signal in MRI ?
The magnetic moment of the hydrogen nuclei.
• How is a magnetic field generated ?
• What is magnetic susceptibility ?
Study Questions
• What is the basic source of the signal in MRI ?
The magnetic moment of the hydrogen nuclei.
• How is a magnetic field generated ?
By moving electrical charge (current).
• What is magnetic susceptibility ?
Study Questions
• What is the basic source of the signal in MRI ?
Magnetic moment of the hydrogen nuclei (proton).
• How is a magnetic field generated ?
By moving electrical charge (current).
• What is magnetic susceptibility ?
A measure of the degree to which a material can be
magnetized.
Additional Study Questions
• What materials in the body are the main sources
of ‘proton’ MRI ?
• What would be considered ‘high field’ and what
kind of magnet is employed to generate it ?
• What type of material has the highest magnetic
susceptibility ?
Additional Study Questions
• What materials in the body are the main sources
of ‘proton’ MRI ?
Water and fat.
• What would be considered ‘high field’ and what
kind of magnet is employed to generate it ?
3 T (=30,000 G), super-conducting electro-magnet.
• What type of material has the highest magnetic
susceptibility ? Ferromagnetic material, e.g. iron.
Home Study Questions
• How many ‘states’ can the hydrogen nuclei be in
when in an external magnetic field ?
• Do all carbon nuclei have a net nuclear magnetic
moment ?
• What is the rule for determining if a nucleus has a
net magnetic moment ?
• What will increase the strength of the NMR signal ?