Chapter 3: Basic Principles of MR Signal Generation

 

Study Questions

 

 

1.   What is the difference between “magnetic moment” and “angular momentum”? How do physicists describe nuclei that possess both?

 

      The magnetic moment is the torque within a magnetic field that is induced by a loop current generated by the spin of the hydrogen proton. Angular momentum is the product of the mass of the spinning body and its angular velocity. If nuclei possess both characteristics, physicists can say the nuclei have nuclear magnetic resonance (NMR).

 

2.   What is precession? What kind of objects precess and why?

     

      Precession is the gyroscopic motion of a spinning object, in which the axis of spin itself rotates around a central axis. Objects like tops spin with precession, because they do not spin perfectly upright but to an angle. This is because these objects respond to applied forces by moving their axes in a direction perpendicular to the applied force.

 

3.   What is net magnetization?

 

      Net magnetization is the sum of the magnetic moments of all spins within a spin system. This quantity is very small under normal conditions because all protons have random orientations and magnetic moments which tend to cancel each other out (magnetic moment is a vector quantity, so directionality matters). To increase this value a strong magnetic field must be applied in order to align the spins of the protons within the magnetic field (thus providing a net magnetization).

 

4.   What is the difference between longitudinal magnetization and transverse magnetization?

 

      Longitudinal magnetization is one of two components of the net magnetization. It is parallel to the main magnetic field or z direction of the scanner. The transverse magnetization comprises the second component and is perpendicular to the main magnetic field in the x-y plane.

 

5.   What happens during excitation?

 

      To allow a spin to jump from a low energy state to a high one, it must absorb a photon with equivalent energy difference. To do this radiofrequency coils bombard spins with photons which are actually electromagnetic fields that oscillate at the resonant frequency of the nucleus of interest. Some low energy spins absorb this energy and jump to a higher level in the process of excitation.

 

6.   What is the gyromagnetic ratio? Why is it important for MRI?

 

      The gyromagnetic ratio is the ratio between the charge and mass of a spin and is constant for a given type of nucleus.  It is also the scalar multiplier between magnetic moment and angular momentum (i.e., angular momentum times gyromagnetic ratio equals magnetic moment).  It is necessary to calculate the larmor frequency and thus the frequency of electromagnetic radiation needed during excitation.

 

7.   What are the parallel and antiparallel states of a nucleus? How does a nucleus change from one state to the other?

 

      The parallel state of a nucleus is a low energy state where the atomic spin precesses around an axis parallel to the main magnetic field. The anti-parallel state is when the nucleus is in a high energy state and precesses in the opposite direction. To change the spin from a lower to higher energy level, energy must be applied.

 

8.   What is the Larmor Frequency? How does it relate to the gyromagnetic ratio? How does it relate to magnetic resonance?

 

      The Larmor frequency is the resonant frequency of a spin within a magnetic field of a specific strength. It is the quantity of electromagnetic radiation that is needed to change spins from one state to another. It can be calculated by dividing the gyromagnetic ratio by 2π and multiplying it by the magnetic field strength. It is linked to magnetic resonance by the notion that energy at a particular frequency is necessary to change nuclei from one state to another.

 

9.   How does the net magnetization of a spin system (e.g., a set of atomic nuclei in a voxel) change over time when exposed to a strong magnetic field?

 

      Through the application of electromagnetic radiation at the Larmor frequency, the motion of the net magnetization vector can be affected.

 

10. How is an excitation pulse calibrated to have maximum effect upon a spin system?

 

      It is calibrated at the same frequency as the spin precession (Larmor frequency), exerting torque on the spins to perturb them.  This is analogous to pushing someone on a swing.  If you               apply energy at the swing’s natural frequency by pushing each time the person is in the same place, even very small pushes will help increase the velocity of the swing and thereby increasing         the energy of the system. 

     

11. Why does the net magnetization need to be tipped from the longitudinal plane to the transverse plane?

 

      By tipping the net magnetization a measurable MR signal can be created. An excitation pulse can cause large changes in the direction of the magnetization over time as it rotates which are detected by external receiver coils.

 

12. What is off-resonance excitation, why does it occur, and what are its consequences?

 

      Off resonance excitation occurs when there is a presentation of an excitation pulse at a frequency other than the resonant frequency of the sample. This reduces the efficiency.

 

13. How do we measure MR signal?

     

        To measure MR signal another receiver or detector coil is needed. Receiver coils acquire signal through the mechanism of electromagnetic coupling (Faraday’s Law of Induction). After the magnetization of the sample is tipped to the transverse plane, its precession at the Larmor frequency sweeps across the receiver coil causing the magnetic flux experienced by the receiver coil to change over time. Effectively this measurement is the MR signal.

 

14. What is T₁ relaxation? Does it relate primarily to longitudinal or transverse magnetization? Is it best thought of as recovery or decay?

 

      It is the time constant that describes the recovery of the longitudinal component of the net magnetization over time. It governs the rate at which longitudinal magnetization recovers.

 

15. What is T₂ relaxation? Does it relate primarily to longitudinal or transverse magnetization? Is it best thought of as recovery or decay?

 

      It is the time constant that describes the decay of the transverse component of net magnetization due to accumulated phase differences caused by spin-spin interactions. This type of relaxation relates to transverse magnetization decays.

 

16. What is T₂^* relaxation? Why is it important for fMRI?

 

      It is the time constant that describes the decay of the transverse component of net magnetization due to both accumulated phase differences and local magnetic field inhomogeneities. It is vital for fMRI studies because BOLD contrast relies on this contrast. BOLD is based on the the magnetic susceptibility that deoxygenated hemoglobin possesses.

 

17. What is the Bloch equation, and why is it important?

 

The Bloch equation is an equation that describes how the net magnetization of a spin system changes over time in the presence of a time varying magnetic field. It encompasses the establishment of net magnetization of a spin system within a magnetic field, the excitation of those spins using electromagnetic pulses, the reception of MR signal in detector coils, and the relaxation of magnetization over time. It provides the theoretical foundation for all MRI experiments because once solved, the Bloch equation leads to mathematical representations of the evolution of magnetization at steady state, excitation, and relaxation.