MRI: Magnetic Fields, Gradients, and Susceptibility

MRI Fundamentals Study Guide Part 1

Quiz

1. What is the primary difference between a Tesla (T) and a Gauss (G) as units of magnetic field measurement?
2. Describe a magnetic gradient and provide a simple example of its calculation.
3. What is magnetic susceptibility and how is it quantified?
4. What is the difference between diamagnetism and paramagnetism?
5. Which subatomic particle primarily determines the overall magnetic susceptibility of a material, and why?
6. Explain the concept of Langevin (Larmor) diamagnetism.
7. What is Curie Paramagnetism and what types of materials exhibit this property?
8. How does a 3.0T MRI scanner’s magnetic field strength compare to that of a refrigerator magnet or the Earth’s magnetic field?
9. What are the physical units that define a Tesla?
10. Explain the difference between the magnetic induction field (B) and the magnetic field intensity (H).

Answer Key

1. Tesla (T) is the SI unit for magnetic field measurement, while Gauss (G) is the unit used in the older CGS system. 1 Tesla is equal to 10,000 Gauss.
2. A magnetic gradient exists when a magnetic field changes in magnitude or direction between two points. It is calculated as the change in field (ΔB) divided by the change in distance (Δs). For example, a 2 mT/meter gradient in the z-direction means the magnetic field strength changes by 2 millitesla for every meter along the z-axis.
3. Magnetic susceptibility is a measure of how much a substance becomes magnetized in an external magnetic field. It is a dimensionless number (χ) defined as the ratio of the internal polarization (J) to the external field strength (B₀), χ = J/B₀.
4. Diamagnetism is a property where a substance’s induced magnetization opposes the external magnetic field, resulting in a negative susceptibility. Paramagnetism is a property where the induced magnetization aligns with the external field, resulting in a positive susceptibility.
5. Electrons primarily determine a material’s overall magnetic susceptibility because electron-field interactions are thousands of times stronger than nuclear ones due to their smaller size.
6. Langevin (Larmor) diamagnetism is a weak magnetic effect present in all materials, caused by the orbital angular momentum of paired electrons in filled orbitals. This effect generates an internal field that opposes the external applied field.
7. Curie Paramagnetism is a moderately powerful magnetic mechanism that occurs in atoms and molecules with unpaired electrons. These unpaired electrons align with the external field, augmenting it, and is important in materials like those containing certain metals or protein conglomerates.
8. A 3.0T scanner’s field is significantly stronger than a refrigerator magnet (5 mT, hundreds of times smaller) and the Earth’s magnetic field (30-70 μT, a hundred times smaller). A junkyard magnet might be close to 1T.
9. The physical units for Tesla (T) are newtons per ampere-meter (N/Am). This is derived from the Lorentz force law (F = i * l * B), where Force (F) is in Newtons, current (i) is in Amperes, and length (l) is in meters.
10. The magnetic induction field (B) represents the actual magnetic field induced within a region of space, taking into account the presence of matter. The magnetic field intensity (H) can be thought of as the externally applied “magnetizing force” independent of the material in the space.

Essay Format Questions

1. Discuss the various types of magnetic susceptibility, including diamagnetism, paramagnetism, superparamagnetism, and ferromagnetism, explaining the underlying physical causes and providing examples of materials exhibiting each type.
2. Describe the concept of a magnetic gradient in detail, including its vector nature, how it is defined mathematically, and its practical application in MR imaging.
3. Compare and contrast the units of Tesla and Gauss for measuring magnetic field strength. Explain the historical context and why Tesla is the preferred SI unit while Gauss is still sometimes used.
4. Elaborate on the interactions between electrons and nuclei with an externally applied magnetic field that give rise to magnetic susceptibility. Discuss the roles of electron spin, orbital angular momentum, paired and unpaired electrons, and nuclear paramagnetism.
5. Explain the relationship between the magnetic induction field (B) and the magnetic field intensity (H) when matter is present. Define magnetic permeability and susceptibility and describe how they relate B and H.

Glossary of Key Terms

Tesla (T): The preferred Système Internationale (SI) unit of measurement for magnetic field strength (B). One Tesla is equal to 10,000 Gauss.

Gauss (G): An older CGS (centimeter-gram-second) unit of measurement for magnetic field strength (B). One Gauss is equal to 0.1 millitesla (mT).

Gradient: A spatial variation in the magnitude or direction of a magnetic field between two points. It is defined as the change in field (ΔB) divided by the change in distance (Δs).

Magnetic Susceptibility (χ): A dimensionless measure of the extent to which a substance becomes magnetized when placed in an external magnetic field. It is the ratio of the internal polarization (J) to the external field strength (B₀).

Diamagnetism: A type of magnetism where a substance’s induced magnetization opposes the external magnetic field, resulting in a negative magnetic susceptibility (χ < 0). Nearly all biological tissues are weakly diamagnetic.

Paramagnetism: A type of magnetism where a substance’s induced magnetization aligns with the external magnetic field, resulting in a positive magnetic susceptibility (χ > 0). Materials with unpaired electrons can exhibit paramagnetism.

Superparamagnetism: A type of magnetism exhibiting strong paramagnetic behavior at low fields, where magnetic moments of small particles align with the field. This effect is stronger than simple paramagnetism.

Ferromagnetism: A type of magnetism exhibiting very strong alignment of magnetic moments with an external field, even after the field is removed. Ferromagnetic substances have large positive susceptibilities.

Langevin (Larmor) Diamagnetism: A weak diamagnetic effect present in all materials, caused by the orbital motion of paired electrons generating an internal field opposing the applied field.

Curie Paramagnetism: A moderately powerful paramagnetic effect occurring in atoms and molecules with one or more unpaired electrons that align with the external field.

Magnetic Induction Field (B): The actual magnetic field within a region of space, including the effects of any matter present. It is a vector field with magnitude and direction. Measured in Tesla or Gauss.

Magnetic Field Intensity (H): An external “magnetizing force” that gives rise to a magnetic field. It is independent of the material filling the space. Measured in amperes per meter (A/m) in SI units.

Magnetic Permeability (µ): A dimensionless factor that describes how a material concentrates or disperses magnetic lines of force relative to a vacuum. It is related to magnetic susceptibility by the equation µ = 1 + χ.