# Introduction to MRI

## 1. Hydrogen nuclei as magnets

A hydrogen nucleus contains a single proton so it has a charge of +1. The nucleus also has an intrinsic "spin". Because they have a charge and motion they create an electric current and this, in turn, creates a magnetic field. What this means is that hydrogen nuclei act like tiny magnets and will be affected by any magnetic field applied to them. Similarly, a magnetic field arising from tissue creates an electric current in the RF coils. In this way magnetic signals from tissue can be measured as an induced electric current in the RF coils of the MR machine.

Hydrogen nuclei are the most useful atoms to use in imaging mainly because they form the majority of atoms in the body. Any nucleus with an odd number of protons can be used (an unpaired proton is needed to provide the magnetic moment due to the spin of the unpaired proton).

## 2. Precession

As well as "spinning" about their own axis, when a magnetic field is applied the nuclei will "rotate" about the axis of the magnetic field. This is called precession. The example usually given is of a gyroscope or spinning top. Spinning a gyroscope causes it to rotate about its own axis but gravity will also cause it to lean and spin about another axis dependent on the gravitational field strength (for a demonstration see Paul Callaghan's video on Precession and Resonance which is very good at demonstrating this concept).

The frequency of this spinning is the precessional / Larmor / rotational frequency. In MR imaging we induce precession by applying a magnetic field (conventionally in the Z axis and called B0, along the long axis of the patient). This magnetic field is permanently switched on in the MRI scanner.

The precessional frequency is calculated by the Larmor Equation

F = K x B0
Key:
F = precessional frequency (Larmor frequency)
K = the gyromagnetic ratio (a constant that is different for different nuclei)
B0 = strength of the static magnetic field

For a field strength of 1 Tesla the Larmor frequency of hydrogen is 42 Megahertz (MHz) or 42 million cycles per second.

As the main magnetic field (B0) is applied, the nuclei precess in the Z-axis along the applied magnetic field. Most will precess aligned with it (the low energy state) but a few will precess in the opposite direction (the high energy state). However, the majority will be aligned, creating a net longitudinal magnetisation (Mz) in the Z-axis direction.

Out now in paperback and on Kindle

Note: Not available in all regions.

## 3. Transverse magnetisation

However, we cannot measure the longitudinal magnetisation and so we need to "flip" the magnetisation, usually to 90°, in order to be able to measure it and create our MRI signal. To flip the magnetisation a rapidly oscillating magnetic field at 90° to B0 is applied (B1 / radiofrequency pulse / RF pulse). This flips the net magnetisation into a transverse plane (Mxy). In order to do this the B1 magnetic field needs to oscillate at the same frequency as the precessing nuclei, the resonant frequency, as this ensures the most efficient transference of energy to the nuclei. Remember, this is 42 MHz for a 1 Tesla scanner and 63 MHz for a 1.5 Tesla scanner.

### Point of interest: why can't we measure longitudinal magnetisation?

1. The net magnetisation vector is too small to measure when it is aligned with the main magnetic field because the main field is so large.

2. When net magnetisation is at an angle to the main magnetic field, it precesses, and this generates a measureable signal perpendicular to the field.

### Point of interest: radiofrequency pulse

For a 1.5T machine, the resonant frequency is 63 MHz which is within the range of radiowaves. Therefore, the exciting field (B1) is called the radiofrequency or RF field.

## 4. Relaxation

As long as the RF pulse is applied the nuclei continue to precess in the transverse plane in phase creating a net transverse magnetisation (large Mxy). As soon as the RF is switched off, the transverse magnetisation begins to disappear and the nuclei relax back to their resting state of net longitudinal magnetisation (B0, large Mz). This happens via two mechanisms and forms the basis for the T1 and T2 signals.

1. Spin-Lattice Relaxation or T1 Recovery

2. Spin-Spin Relaxation or T2 Decay

We will go into more detail on the next page.

#### Next page: T1 and T2 signal

Buy FRCR Physics Notes in paperback or on Kindle and follow us for the latest developments and updates via social media.