Basics of MRI Physics


MR Discussion Group
Magnetic Resonance Science Center, UCSF
July 16, 1999
prepared by,
Amir Schricker
http://amirschricker.org/school/mri/
Contents:

  1. Introduction
  2. Concept of spin
  3. Precession of spins
  4. Excitation using RF pulses
  5. Relaxation
  6. Final Thoughts

I. Introduction
Nuclear magnetic resonance (NMR) is a powerful physical technique for probing the properties of atoms and molecules based on their interaction with an external magnetic field. This magnetic field affects a certain property of the nuclei, and the observations of these changes is fundamental to MR. The principles of magnetic resonance can be exploited (among many other ways) as magnetic resonance imaging (MRI) and magnetic resonance spectroscopy (MRS). These notes briefly cover the basics of MR physics.

II. Concept of spin
The principles of MR can be described using either classical (Newtonian) physics or modern (quantum) physics; whenever possible, the classical model will be used in these notes.

Atoms with an odd number of protons and/or neutrons (including, but not limited to, 1H, 19F, 13C, and 31P) exhibit the MR phenomenon because they possess a fundamental property known as nuclear spin. These nuclei can quantitatively be pictured as spinning spheres. Since the nuclei are also charged, these spinning charged spheres give rise to a small magnetic dipole moment as determined by Faraday’s Law of Induction. The vector sum of all these magnetic dipoles is known as the net magnetization.

The characteristics of MR are based on the interaction of this nuclear spin with two different magnetic fields: 1) the main external magnetic field, B0, and 2) a radiofrequency field, B1. In the absence of an external magnetic field, the individual dipoles of the nuclei randomly orient themselves in all directions, and therefore the net magnetization of the sample is zero (i.e. there is no net magnetization in the sample.)

But the net magnetization of the sample is zero only until an external magnetic field, B0, is applied. Now two noticeable effects are created. First, the nuclei tend to point in a direction parallel to B0, creating a non-zero net magnetization.

III. Precession of Spins
Next, their spins begin to rotate, or precess, about an axis parallel to B0. To better understand precession, consider this analogy: think about a toy top and the motion it undergoes. Not only does it spin about its own axis, but it also rotates around an axis perpendicular to the ground. The nuclei precess with a well-defined frequency determined by the simple Larmor relation:

ω = γB
This very important expression relates the frequency of precession, ω, to the applied magnetic field, B. The variable γ is known as the gyromagnetic ratio, a known constant unique for each atom. For 1H, γ = 42.58 MHz/Tesla. (1 Tesla(T) = 104 Gauss(G). Earth’s magnetic field = 1 G).

Review of key concepts

  • Nuclei behave like tiny bar-magnets because of their nuclear spin.
  • In the absence of an external magnetic field, there is no net magnetization because their spins are randomly oriented.
  • In an external magnetic field, 2 changes occur:
    1. A non-zero longitudinal magnetization is created.
    2. The spins begin to precess
  • The frequency of precession is determined by ω = γB (the Larmor relation.)

One modification: in the presence of the external magnetic field B0, about half of the nuclei align parallel to B0 and half align anti-parallel to B0. There are actually a few more aligned parallel because it is a lower energy state than the anti-parallel direction. Very few. About 7 nuclei per every 1,000,000.

IV. Excitation using RF pulses
To receive an MR signal, a second magnetic field is needed, denoted B1. This magnetic field is produced by radiofrequency (RF) waves. After the main external field has been established, short bursts of radiofrequency waves (RF pulses) are applied to the system. These pulses lie in the xy-plane and have the exact same frequency as the frequency of precession of the spins, and because of this, the pulses disturb some of the spins by transferring enough energy to them to induce a “spin flip.” A spin flip is a change in energy that causes the spin to point anti-parallel to the main magnetic field. Since there is one more spin now pointing down and one less spin pointing up, the net longitudinal magnetization (the magnetization along the z-direction, or the direction of B0, also called Mz) is decreased because there is one more spin pointing anti-parallel to cancel the effect of the a spin pointing parallel.

The RF pulse also generates a transverse magnetization, Mxy, which points perpendicular to B0. This arises because the RF pulse makes the spins precess in phase with each other, giving them phase coherence. This coherence forms a magnetization in the xy-plane, and the RF pulse can be thought of as “tipping” over the spins.

Brief review of key concepts:

  • The first step in receiving an MR signal is to apply an RF pulse into the system.
  • The RF pulse forces the following 2 effects:
    1. A decrease in longitudinal magnetization because of the spin flips.
    2. The creation of a transverse magnetization because of phase-coherence.

RF pulses are characterized by the amount which they tip the magnetization vector. Common pulses are the 90° pulse, which tips the magnetizations vector into the xy-plane; and the 180° pulse, which tips the magnetization vector in the -z direction.

V. Relaxation
The behavior of these two magnetizations after the RF pulse is turned off is called relaxation. The protons which were flipped by the RF pulse slowly go back to their original, parallel alignment. Relaxation is characterized by the time it takes to return to their original states. There are two types of relaxation, corresponding to the relaxation of the lateral magnetization and transverse magnetization: T1 and T2 relaxation.

T1 relaxation describes the release of extra energy back into the surroundings by the nuclei that underwent a spin-flips as they revert back to their low energy, parallel-aligned state; it is also called longitudinal relaxation since it involves the regrowth of longitudinal magnetization. A plot of longitudinal magnetization vs. the time since the RF pulse has been turned off is known as a T1-curve, as below.



Typical T1-curve
T2 relaxation describes the spins as they lose their phase coherence. The absence of the RF pulse, which generated the phase coherence in the first place, results in the nuclei beginning to spin in an out-of-phase fashion; this decreases the net transverse magnetization. A typical T2-curve is pictured below.



Typical T2-curve

Brief review of key concepts

  • Relaxation describes the state of the 2 magnetizations after the RF pulse is switch off.
  • There are two types of relaxation:
    1. T1: the regrowth of the longitudinal magnetization back to its original value.
    2. T2: the decay of the transverse magnetization.

One last remark: the observation of the magnetization “given off” by the nuclei as they relax provides the relevant signal for MR.

VI. Final Thoughts
Receive a magnetic resonance signal in 3 easy steps:

  1. Align spins with an external magnetic field, B0.

  2. Disturb the spins with an RF pulse, B1.

  3. Record an MR signal by observing the relaxation behavior of the spins.

And if you take away nothing else from these notes, just remember:

ω = γB