Non-ionising imaging revision notes

Non‑Ionising Imaging

Non‑ionising imaging techniques are essential in modern medicine because they avoid the harmful effects of ionising radiation. In the AQA A Level Physics specification the three core methods are:

1. Ultrasound imaging – uses high‑frequency sound waves.
2. Fibre‑optic endoscopy – transmits light through optical fibres.
3. Magnetic resonance imaging (MRI) – relies on strong magnetic fields and radio‑frequency pulses.

Below each section explains the underlying physics, the key equations, and the practical implications for diagnosis.

1. Ultrasound Imaging

Ultrasound imaging is the most widely used non‑ionising diagnostic tool. It works by sending short bursts of high‑frequency sound (typically 1–15 MHz) into the body and analysing the echoes that return from tissue interfaces.

1.1 Generation and Detection of Ultrasound Pulses

• Transducer: A piezoelectric crystal converts an electrical signal into a mechanical vibration, producing a pressure wave.
• Pulse‑echo method: The transducer alternates between transmitting a pulse and listening for echoes.
• Detection: The same crystal reverses the process, converting returning pressure waves back into an electrical signal.

1.2 Reflection at Tissue Boundaries

• Acoustic impedance (Z) is defined as the product of tissue density (ρ) and the speed of sound (c) in that tissue:

where Z = ρ × c.

• When a sound wave encounters a boundary between two media with different impedances, part of the wave is reflected and part is transmitted.
• The reflection coefficient (R) quantifies the fraction of the wave that is reflected:

where Z1 and Z2 are the impedances of the first and second media.

• A large impedance mismatch (e.g., tissue–air) produces a strong echo, which is why the lungs appear black on an ultrasound screen.

1.3 Calculating Depth from Pulse Return Time

• The echo travels to the interface and back, covering twice the depth.
• The depth (d) is calculated using the speed of sound in soft tissue (≈ 1540 m s⁻¹) and the round‑trip time (t):

*Example*: If an echo returns after 2 µs, the depth is

≈ 1.54 mm.

1.4 Advantages and Limitations

| Advantage | Limitation | |-----------|------------| | No ionising radiation – safe for repeated scans | Limited penetration in bone or air‑filled cavities | | Real‑time imaging – useful for guiding procedures | Image quality depends on operator skill | | Portable and relatively inexpensive | Lower spatial resolution compared with CT or MRI |

2. Fibre Optics and Endoscopy

Endoscopes bring a camera and light source into the body, allowing direct visualisation of internal organs. They rely on optical fibres to transmit light and images.

2.1 Total Internal Reflection in Optical Fibres

• An optical fibre consists of a core (high refractive index) surrounded by a cladding (lower refractive index).
• Light travelling from the core to the cladding is confined by total internal reflection when the angle of incidence exceeds the critical angle:

where n1 is the core index and n2 the cladding index.

• This principle allows light to travel long distances with minimal loss.

2.2 How Endoscopes Use Fibre Optics

• Illumination: A bundle of fibres carries light from a source to the tip of the endoscope.
• Image transmission: A separate bundle carries reflected light from the tip back to a camera.
• Image quality: Determined by the number of fibres, core diameter, and the quality of the fibre coatings.

2.3 Image and Illumination Transmission

• Bidirectional transmission: Some endoscopes use a single fibre bundle for both illumination and imaging, but this limits image resolution.
• Separate bundles: Provide higher resolution images and brighter illumination.
• Colour imaging: Requires fibres that can transmit the full visible spectrum; often achieved with a combination of blue, green and red fibres.

2.4 Advantages of Endoscopy for Diagnosis

• Direct visual inspection of mucosal surfaces.
• Minimally invasive – reduces recovery time.
• Real‑time feedback during procedures (e.g., biopsies).
• Ability to combine imaging with therapeutic tools (e.g., cautery, laser).

3. Magnetic Resonance Imaging (MRI)

MRI is a powerful imaging modality that uses strong static magnetic fields and radio‑frequency (RF) pulses to generate detailed images of soft tissues.

3.1 Role of Strong Magnetic Fields

• A uniform static field B₀ (typically 1.5–3 T) aligns the magnetic moments of hydrogen nuclei (protons) in the body.
• The alignment creates a net magnetisation vector along the field direction.

3.2 Resonance and Radio‑Frequency Pulses

• When an RF pulse at the Larmor frequency f = γB₀/(2π) is applied, protons are tipped away from the B₀ axis.
• γ is the gyromagnetic ratio of the proton (≈ 42.58 MHz T⁻¹).
• After the pulse, protons precess around B₀ and gradually return to equilibrium, emitting RF signals.

3.3 Signal Detection and Image Formation

• Gradient coils vary B₀ spatially, causing the Larmor frequency to depend on position.
• By sampling the emitted RF signal at different gradient settings, the scanner reconstructs a spatial map of proton density and relaxation times.
• Spin‑echo sequences refocus dephasing spins, improving image contrast.
• The final image is a 2‑D or 3‑D map of tissue properties, not a direct visual of anatomy.

3.4 Advantages and Limitations

| Advantage | Limitation | |-----------|------------| | Excellent soft‑tissue contrast | Expensive equipment and long scan times | | No ionising radiation | Contraindicated for patients with ferromagnetic implants | | Ability to acquire functional and diffusion images | Susceptible to motion artefacts | | Non‑invasive and painless | Requires patient to remain still for several minutes |

Key Take‑Away Points

• Ultrasound relies on acoustic impedance mismatches; depth is calculated from echo time.
• Endoscopy uses total internal reflection to guide light; separate fibre bundles optimise image quality.
• MRI depends on a strong static field to align spins and RF pulses to excite them; spatial encoding is achieved with gradient coils.
• Each modality offers unique diagnostic strengths while avoiding ionising radiation.

Exam‑Ready Tips

• Remember that depth in ultrasound is d = (c × t)/2 and that c ≈ 1540 m s⁻¹ in soft tissue.
• Clarify the difference between acoustic impedance and density when discussing reflections.
• For fibre optics, emphasise the critical angle condition and the role of the cladding.
• In MRI, distinguish the static B₀ field from the RF pulse and explain the concept of Larmor frequency.
• Highlight the importance of signal‑to‑noise ratio in MRI image quality.

Common Mistakes to Avoid

• Confusing acoustic impedance with density.
• Forgetting the factor of ½ when calculating ultrasound depth.
• Assuming light can exit an optical fibre without total internal reflection.
• Misinterpreting the static magnetic field as a source of RF energy.
• Overlooking the role of gradient coils in spatial encoding for MRI.