Physics:Magnetic Resonance Imaging

LecturersLawrence Panych, PhD

Lei Qin, PhDBruno Madore, PhD

Stephan Maier, MD, PhDRobert Mulkern, PhD

Brigham and Women’s HospitalHarvard Medical SchoolAvdelningen för radiologiSahlgrenska Universitetssjukhuset (S. Maier)

• 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 PhysicsWalter 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

Magnetar100 Billion Tesla

3T MRI = 30,000 Gauss

Magnetic Field

Strength

25 Tesla = 250,000 Gauss

Types of Magnets in MRI

Permanent Magnet Electro-Magnet

Types of Magnets in MRI

Permanent Magnet Super-conductingElectro-Magnet

Strengths of Magnets in MRI

Permanent Magnet Super-conductingElectro-Magnet

Ultra-Low Field Low Field Midfield High Field Ultra-High Field

< 0.2T (2000G) 0.25T 0.5T 3.0T 7.0T +

1 T (Tesla) = 10,000 G (Gauss)

Magnetic FieldH is the magnetic field intensity and is measured in units of amps/meter.

iδL,incremental

current elementwith charge

moving along the

path, δL

. prP Ar δH 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.

δH is a vector orthogonal to vectors, δL and Ar

δLδH

Ar

Magnetic Field

Direction of theMagnetic Field

Direction of theCurrent Element

Magnetic Flux Density

B is the magnetic flux density and is measured in units of Tesla.

B = µ H

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.Diamagnetic2.Paramagnetic3.Ferromagnetic

4.Antiferromagnetic5.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 momentdue to electron spin

+M:magnetic momentdue to electron orbital motion

1. DiamagnetismIn 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 momentdue to electron’ spin

+M - δ:magnetic momentdue to electron orbital motion

Externalmagnetic 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 momentdue to electron’ spin

+m + ∆ :magnetic momentdue to electron orbital motion

Net magnetic moment, ∆

2. Paramagnetism

In the absence of an external magnetic fieldthe 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 fieldthe 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.

ExternalMagnetic field

3. FerromagnetismIn 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. FerromagnetismIn the presence of an external magnetic field,

the domains tend to align in the direction of the external 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.

ExternalMagnetic field

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.

3. Ferromagnetism

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

χm 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 havevery large magnetic susceptibilities.

Magnetic Susceptibility Spectrum

PyrexPerspex

Nuclear Magnetismand

Nuclear Magnetic Resonance

Source of the Signal in MRI: Net Spin of the Nucleus

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:

12C (6 protons and 6 neutrons)P

NN

N

P

PP N

N

N

P

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.

13C (6 protons and 7 neutrons)P

N NN

N

P

PP N

N

N

P

Source of the Signal in MRI: Net Spin of the Nucleus

Some Nuclei with MR SignalNucleus Abundance of

Element in the Human Body

Natural Abundance of

Isotope

Percent of All Atoms in the Human Body

13C 9.4% 1.11% 0.1%

23Na 0.04% 100% 0.04%

31P 0.24% 100% 0.24%

1H 63% 99.985% 63%

Some Nuclei with MR SignalNucleus Abundance of

Element in the Human Body

Natural Abundance of

Isotope

Percent of All Atoms in the Human Body

13C 9.4% 1.11% 0.1%

23Na 0.04% 100% 0.04%

31P 0.24% 100% 0.24%

1H 63% 99.985% 63%

Some Nuclei with MR SignalNucleus Abundance of

Element in the Human Body

Natural Abundance of

Isotope

Percent of All Atoms in the Human Body

13C 9.4% 1.11% 0.1%

23Na 0.04% 100% 0.04%

31P 0.24% 100% 0.24%

1H 63% 99.985% 63%

Some Nuclei with MR SignalNucleus Abundance of

Element in the Human Body

Natural Abundance of

Isotope

Percent of All Atoms in the Human Body

13C 9.4% 1.11% 0.1%

23Na 0.04% 100% 0.04%

31P 0.24% 100% 0.24%

1H 63% 99.985% 63%

1H 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.

P

1H

• 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.

“Proton” MRI

PP

1H 1H

Bo

• 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.

Quantum States

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.

Alignment of Nuclear Spins

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.

Distribution of States

Net number of protons aligned with a 1.5T field

in 1 mm3 of water:

330 trillion

mz

mx

my

M

Most of MRI can be explained using a magnetization vector. The magnetization vector, M, represents the net moment.

Magnetization Vector

Net magnetic moment from billions of nuclear

spins

Small volume element << 1mm3

Bo

Next Lecture MRI Signal Properties Manipulating the

Magnetization Vector

mz

mx

my

M

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 ?