MRI: Excitation, Detection, and Imaging Revision Notes | A Level AQA Physics

1. Why MRI Needs More Than a Big Magnet

A powerful static magnetic field aligns proton spins throughout the entire body — but that alone tells you nothing about where a signal comes from. To build an image, the scanner must interrogate one tiny region at a time. The clever engineering that makes this possible is the gradient field coil system, and understanding it is the key to understanding MRI imaging.

Picture the patient lying inside a uniform field $B_0$. Every proton in the body precesses at the same Larmor frequency $f_0$. If you fire an RF pulse at $f_0$, every proton in the body responds simultaneously — useless for localisation. The solution is to make the field strength vary with position, so that the resonant frequency becomes a postcode for each slice of tissue.

2. Gradient Field Coils: Giving Every Slice Its Own Frequency

Gradient field coils are sets of electromagnets wound inside the scanner bore. When energised, they add a small, linearly varying magnetic field on top of the main static field $B_0$. The total field at any position along, say, the $z$-axis becomes $B(z) = B_0 + G_z z$, where $G_z$ is the gradient strength in T m$^{-1}$.

Because the Larmor frequency is proportional to the local field strength — $f = \frac{\gamma B}{2\pi}$, where $\gamma$ is the gyromagnetic ratio of the proton — each position along the gradient now has a unique resonant frequency. A slice at position $z_1$ resonates at a slightly different frequency than a slice at $z_2$. The scanner exploits this by transmitting an RF pulse at precisely the frequency corresponding to the desired slice.

Three sets of gradient coils are used in a full scan: one for each spatial axis ($x$, $y$, $z$). By switching gradients on and off in sequence, the scanner can select a slice in one direction, then encode position within that slice in the other two directions. This is how a three-dimensional image is built up from many successive measurements of small regions.

With the gradient coils establishing a spatial map of frequencies, the scanner is ready for the next stage: actually exciting the protons in the chosen region. That requires a carefully tuned radiofrequency pulse.

3. RF Excitation: Flipping Proton Spin States

In the static field $B_0$, protons occupy one of two spin states: a lower-energy state aligned with the field (spin-up) and a higher-energy state opposed to it (spin-down). At thermal equilibrium, slightly more protons occupy the lower-energy state, producing a net magnetisation along $B_0$.

When a short RF pulse is transmitted at the Larmor frequency of the selected slice, the oscillating magnetic field of the RF wave is in resonance with the precessing protons. Energy is absorbed, and protons are promoted from the lower-energy spin state to the higher-energy spin state. This is the excitation event. The net magnetisation is tipped away from the $B_0$ direction — often by 90° for a standard pulse — into the transverse plane.

The pulse is short — typically microseconds to milliseconds — so that only the protons in the selected slice (those with the matching Larmor frequency) are significantly affected. Protons in adjacent slices, precessing at slightly different frequencies, are not in resonance and are not excited. This is the mechanism by which successive small regions are scanned: the gradient is adjusted, the resonant frequency shifts to the next slice, and a new RF pulse is applied.

Once the RF pulse ends, the excited protons do not stay in their higher-energy state. They begin to relax — and it is during this relaxation that the detectable signal is produced.

4. De-excitation: Protons Emit the Signal

After the RF pulse is switched off, the excited protons return to their equilibrium spin alignment — the lower-energy state — in a process called relaxation. As they do so, they release the energy they absorbed, emitting RF radiation at the same Larmor frequency. This emitted RF signal is the raw data of the MRI scan.

Two distinct relaxation processes occur simultaneously. Longitudinal relaxation ($T_1$) describes how the component of magnetisation along $B_0$ recovers. Transverse relaxation ($T_2$) describes how the magnetisation in the transverse plane decays as protons lose phase coherence with one another. Different tissues have characteristic $T_1$ and $T_2$ values, which is why MRI can distinguish between, for example, grey matter, white matter, and cerebrospinal fluid — even though all contain hydrogen protons.

The strength and timing of the emitted signal depend on the density of protons in the tissue and on the local chemical environment — which determines $T_1$ and $T_2$. This is why MRI provides excellent soft-tissue contrast: different tissues relax at different rates, producing signals of different amplitudes at different times after the pulse.

5. Detection and Image Reconstruction

The emitted RF signals are detected by receiver coils placed around the patient. These coils act as antennae: the oscillating magnetic field of the emitted RF radiation induces a small alternating voltage in the coil, which is then amplified and recorded. The same coil that transmits the excitation pulse often serves as the receiver — it is switched between transmit and receive modes during the scan sequence.

Because the gradient coils encode position as frequency, the detected signal from a single RF pulse contains contributions from all the protons in the selected slice, each at a slightly different frequency depending on their position within the slice. A mathematical technique called a Fourier transform is applied by the computer to decompose this complex signal into its constituent frequencies, assigning an intensity value to each spatial location.

The computer repeats this process for many different gradient settings and RF pulse timings, building up a complete data set. From this data set, it reconstructs a two-dimensional map of signal intensity across the cross-section. Higher signal intensity — reflecting more protons or favourable relaxation characteristics depending on the pulse sequence weighting used — appears brighter on the image. The result is the greyscale MRI image familiar from clinical practice.

Worked example: Tracing the MRI Signal Chain for One Slice

Describe, in sequence, the physical processes that occur from the moment the gradient coils are energised to the moment a signal is recorded for a single cross-sectional slice.

1. $B(z) = B_0 + G_z z$ — The gradient coil superimposes a linearly varying field on $B_0$. Each position $z$ now has a unique total field strength, and therefore a unique Larmor frequency $f(z) = \frac{\gamma (B_0 + G_z z)}{2\pi}$. The desired slice at position $z_s$ has Larmor frequency $f_s$.
2. RF pulse frequency $= f_s$ — The transmitter coil emits a short RF pulse tuned to $f_s$. Only protons in the slice at $z_s$ are in resonance; protons at other positions have different Larmor frequencies and are not significantly excited.
3. Spin-up $\rightarrow$ spin-down (energy absorbed) — Protons in the selected slice absorb energy from the RF pulse and are promoted to the higher-energy spin state. The net magnetisation is tipped into the transverse plane. This is the excitation event.
4. Spin-down $\rightarrow$ spin-up (energy emitted as RF) — Protons relax back to equilibrium, emitting RF radiation at $f_s$. The amplitude and decay rate of this signal depend on proton density and the $T_1$/$T_2$ relaxation times of the tissue.
5. Induced EMF $\propto$ rate of change of flux from emitted RF — The oscillating magnetic field of the emitted RF induces an alternating voltage in the receiver coil by electromagnetic induction. This voltage is amplified and digitised.
6. Fourier transform applied to raw signal data — The computer applies a Fourier transform to decompose the detected signal by frequency (and therefore by position within the slice). Signal intensities are mapped to spatial coordinates, producing the image of that cross-section.

Answer: Gradient coils create a position-dependent Larmor frequency → RF pulse excites the target slice → protons change spin state → protons de-excite and emit RF → receiver coil detects the signal → computer reconstructs the image.

6. Scanning Successive Regions: The Full Picture

A complete MRI scan is not a single measurement — it is a carefully choreographed sequence of gradient switching and RF pulsing, repeated for every slice and every phase-encoding step within each slice. After one slice is excited and its signal recorded, the gradient coil current is adjusted to shift the resonant frequency to the next slice position, and the process repeats. This is what the AQA specification means by 'successive small regions': the scanner works through the volume of interest systematically, one region at a time.

Within a single slice, two additional gradient directions encode the $x$ and $y$ positions of individual voxels (volume elements). The frequency-encoding gradient is applied during signal readout, spreading different columns across different frequencies. The phase-encoding gradient is applied briefly before readout, imprinting a phase shift that encodes row position. Together, these three gradient directions allow the computer to assign every detected signal to a precise three-dimensional location.

7. Exam Technique: Securing Every Mark

MRI questions at A-level frequently use the command words 'describe' and 'explain'. Examiners draw a sharp distinction between the two. A 'describe' answer states what happens in sequence — no reasons required. An 'explain' answer must include the scientific mechanism: why the gradient makes frequencies position-dependent, why only the resonant slice is excited, why de-exciting protons emit RF radiation.

Three specific language choices consistently earn marks. First, use the phrase 'change of spin state' (or 'spin flip') when describing excitation — not vague terms like 'protons are disturbed'. Second, state explicitly that the emitted RF signal has the same frequency as the excitation pulse (the Larmor frequency). Third, when describing image formation, name the computer processing step: the signals are 'processed by a computer to produce a visual image', and stronger answers mention that different tissues produce signals of different intensity due to differing proton density or relaxation times.