A-Level Physics: Medical Physics and Imaging

Medical physics bridges fundamental physical principles with life-saving clinical practice. For you, as an A-Level student, it provides a compelling application of waves, particle physics, and energy transfer. Understanding how different imaging modalities work—and why one is chosen over another for a specific diagnosis—is crucial, both for your exams and for appreciating the technology behind modern healthcare.

The Principles of X-ray Imaging

X-rays are high-energy, short-wavelength electromagnetic waves, typically produced within an X-ray tube. Here, electrons are accelerated by a high voltage (e.g., 100 kV) towards a metal target, such as tungsten. When these high-speed electrons decelerate rapidly upon collision, their kinetic energy is converted into X-ray photons via a process called bremsstrahlung (braking radiation).

The key to forming an image is differential absorption. Denser materials like bone, which have a higher atomic number ($Z$), absorb X-rays more effectively than softer tissues like muscle or fat. This creates a shadowgraph where bones appear white (high absorption) and soft tissues appear in shades of grey. Image contrast can be enhanced using contrast media, such as barium or iodine compounds, which are ingested or injected to absorb X-rays strongly, outlining specific organs like the digestive tract or blood vessels. The intensity of an X-ray beam after passing through tissue decreases exponentially, governed by the attenuation equation $I=I_0{e}^{-\mu x}$, where $I_0$ is initial intensity, $\mu$ is the linear attenuation coefficient, and $x$ is the thickness of material.

From 2D to 3D: Computed Tomography (CT) Scans

A standard X-ray provides a compressed 2D image, where structures can overlap. A CT (Computed Tomography) scanner overcomes this by building a 3D image from a series of 2D X-ray "slices." The patient lies on a table that moves through a rotating gantry. An X-ray tube and detectors on opposite sides of the ring rotate around the patient, taking hundreds of measurements from different angles for each slice.

A powerful computer then processes this vast dataset using a mathematical technique called back projection. It reconstructs a detailed cross-sectional image (a tomogram) of the body, assigning a CT number (Hounsfield unit) to each tiny volume element (voxel) based on its attenuation coefficient relative to water. This allows for exceptional differentiation between soft tissues that appear similar on a standard X-ray. The process is akin to mathematically reassembling a sliced loaf of bread to see the detail within each slice without overlap.

Ultrasound Imaging and Acoustic Impedance

Ultrasound imaging uses high-frequency sound waves, typically above 20 kHz, well beyond human hearing. A piezoelectric transducer both generates the ultrasound pulses and detects the reflected echoes. The fundamental principle is the reflection of these waves at boundaries between different tissues.

The amount of reflection depends on the difference in acoustic impedance ($Z$) between two media. Acoustic impedance is defined as $Z=\rho c$, where $\rho$ is the density of the material and $c$ is the speed of sound within it. The greater the difference in impedance at a boundary, the greater the fraction of ultrasound intensity that is reflected. For instance, the boundary between soft tissue and bone causes near-total reflection, creating a bright echo. The time delay between transmitting a pulse and receiving its echo is used to calculate the depth of the boundary: $\text{distance}=\text{speed}\times \text{time}/2$. By scanning the transducer, a 2D image called a B-scan is built up.

Functional Imaging: Positron Emission Tomography (PET)

While CT and ultrasound show anatomy, PET (Positron Emission Tomography) scans reveal metabolic activity and function. A positron-emitting tracer, such as fluorodeoxyglucose (FDG), is introduced into the body. FDG is a glucose analog, so it is absorbed more by cells with high metabolic rates, like active brain neurons or rapidly dividing cancer cells.

The radioactive tracer nucleus emits a positron (a particle with the same mass as an electron but a positive charge). This positron travels a short distance in tissue before annihilating with an electron. This annihilation event converts the mass of both particles into two gamma-ray photons, each with energy 511 keV, which travel in almost exactly opposite directions (180° apart). The PET scanner's ring of detectors registers these simultaneous, opposing photons—a process called coincidence detection. By mapping millions of these events, a computer constructs a 3D image showing the concentration of the tracer, highlighting areas of abnormal biochemical activity.

Comparing Imaging Modalities for Clinical Diagnosis

Each modality has distinct advantages and limitations, guiding clinical choice.

• X-ray (including Fluoroscopy): Advantages: Quick, inexpensive, excellent for visualising bone fractures, chest infections, and dental issues. Real-time imaging (fluoroscopy) is used for procedures like angiography. Limitations: Provides only 2D images with overlapping structures; poor soft-tissue contrast; involves ionising radiation.

• CT Scan: Advantages: Outstanding 3D anatomical detail of both bone and soft tissue (e.g., brain haemorrhages, tumours, complex fractures). Fast scanning times. Limitations: Very high dose of ionising radiation compared to a standard X-ray; more expensive.

• Ultrasound: Advantages: No ionising radiation, making it safe for foetal imaging; provides real-time moving images (e.g., heart valves); relatively inexpensive and portable. Limitations: Cannot penetrate bone or gas-filled areas (like lungs), so its "window" into the body is limited; image quality is operator-dependent.

• PET Scan: Advantages: Uniquely shows metabolic and biochemical function, crucial for oncology (cancer staging), neurology, and cardiology. Limitations: Very expensive; requires a nearby cyclotron to produce short-lived tracers; poor anatomical detail, so it is often combined with a CT scan (PET-CT) to overlay function on structure; uses ionising radiation.

Common Pitfalls

1. Confusing Attenuation with Reflection: A common error is stating that X-rays are "reflected" by bone. They are not; they are absorbed or attenuated. Ultrasound, however, relies on reflection at boundaries due to acoustic impedance mismatch.
2. Misunderstanding Acoustic Impedance: It is not simply "density." While related, acoustic impedance $Z$ is the product of density and the speed of sound in that medium ($Z=\rho c$). A large difference in either property at a boundary will cause strong reflection.
3. Muddling PET Tracer and Radiation: Students often think the injected tracer itself is "gamma radiation." The tracer emits positrons. The gamma rays are produced outside the nucleus from the positron-electron annihilation event, and it is these paired gamma photons that are detected.
4. Overlooking the Key Distinction (Anatomy vs. Function): When comparing techniques, the most fundamental distinction is that X-ray, CT, and Ultrasound primarily show anatomy (structure), while PET shows function (metabolic activity). CT shows where a mass is, PET can indicate if it is actively growing.

Summary

• X-ray imaging relies on differential absorption of high-energy photons by tissues of different densities and atomic numbers, described by the exponential attenuation law $I=I_0{e}^{-\mu x}$.
• CT scanning uses X-rays from multiple angles and computer reconstruction to create detailed 3D cross-sectional images, eliminating the overlap problem of 2D X-rays.
• Ultrasound creates images from echoes produced by the reflection of high-frequency sound waves at tissue boundaries, where the degree of reflection depends on the difference in acoustic impedance ($Z=\rho c$).
• PET scanning detects pairs of gamma photons produced from positron-electron annihilation, mapping the distribution of a radioactive tracer to reveal areas of high metabolic activity.
• Clinical choice depends on balancing factors: ionising radiation risk, cost, need for anatomical detail versus functional information, and the specific area of the body being examined.