A-Level Physics: Medical Physics

Medical physics is the crucial bridge between abstract physical principles and real-world healthcare. It transforms equations and theories into technologies that diagnose disease, guide surgery, and treat cancer. For your A-Level studies, mastering this option means understanding not just how these technologies work, but why specific physics is chosen for each clinical application, from imaging soft tissues to targeting tumors with precision.

Principles of Imaging with Ionising Radiation: X-rays

X-rays are high-energy electromagnetic waves, typically produced by firing a beam of high-speed electrons at a metal target (usually tungsten) in a vacuum tube. When these electrons are rapidly decelerated by the target nuclei, they emit a continuous spectrum of bremsstrahlung radiation. Characteristic line spectra are also produced when the incident electrons knock inner-shell electrons from the target atoms.

For diagnostic imaging, the key physical principle is differential attenuation. Different body tissues attenuate (absorb and scatter) X-ray photons to varying degrees. Bone, with its high atomic number ($Z$) due to calcium, attenuates much more strongly than soft tissue or fat. This creates the contrast on a traditional photographic film or digital detector. To improve image contrast for soft tissues, contrast media like barium or iodine compounds—which have high $Z$—can be introduced into the body. Modern computed tomography (CT) scans rotate an X-ray source and detector around the patient, using computer processing to construct detailed 3D cross-sectional images from thousands of individual attenuation measurements.

Principles of Imaging with Non-Ionising Radiation: Ultrasound

Ultrasound imaging uses high-frequency sound waves, typically above 20 kHz, well beyond human hearing. A piezoelectric transducer generates the ultrasound pulse and detects the returning echoes. The two core principles are reflection and the pulse-echo technique.

When an ultrasound wave crosses a boundary between two media with different acoustic impedances ($Z$), a proportion of the wave is reflected. Acoustic impedance is defined as $Z=\rho c$, where $\rho$ is the density of the medium and $c$ is the speed of sound in it. The intensity reflection coefficient, the fraction of intensity reflected, is given by:

$$R={\left(\frac{Z_2-Z_1}{Z_2+Z_1}\right)}^2$$

By measuring the time delay between the emitted pulse and the received echo, and knowing the speed of sound in tissue (~1540 m s⁻¹), the depth of the boundary can be calculated: $\text{distance}=\text{speed}\times \frac{\text{time}}{2}$. The transducer builds up a 2D image by scanning across the body. Its major advantage is that it uses non-ionising radiation, making it safe for frequent use, such as in fetal imaging.

Advanced Imaging: MRI and PET Scanning

Magnetic Resonance Imaging (MRI) relies on the physics of nuclear spin, primarily of hydrogen nuclei (protons) in water and fat molecules. When placed in a powerful, uniform static magnetic field ($B_0$), these spins align, creating a net magnetisation. A pulse of radiofrequency (RF) energy is then applied at the specific Larmor frequency, causing the net magnetisation to flip. When the RF pulse is switched off, the nuclei relax back to alignment, emitting RF signals themselves. By applying gradient magnetic fields, the location of emitting protons can be encoded, allowing a 3D image to be constructed. Different tissue relaxation times (T1 and T2) provide excellent soft-tissue contrast without ionising radiation.

Positron Emission Tomography (PET) scanning is a functional imaging technique. A biologically active molecule, like glucose, is labelled with a radioactive tracer that emits positrons (e.g., fluorine-18). Upon emission, a positron annihilates with a nearby electron, producing two gamma photons travelling in opposite directions (180° apart). The scanner detects these coincident gamma pairs, allowing the computer to pinpoint the line along which the annihilation occurred. By detecting millions of events, it builds a 3D map of metabolic activity, crucial for detecting cancers and studying brain function.

Therapeutic Applications: Radiation in Medicine

Radiation is used therapeutically primarily in radiation therapy for cancer. The goal is to deliver a lethal dose of ionising radiation to a tumor while minimising damage to surrounding healthy tissue. This is achieved through techniques like external beam radiotherapy, where multiple beams are cross-fired at the tumor from different angles. Each individual beam passes through healthy tissue at a low dose, but the doses sum to a very high dose at the tumor intersection point.

The effectiveness of radiation on tissue is quantified by the absorbed dose, measured in Grays (Gy), where $1\text{ Gy}=1{\text{ J kg}}^{-1}$. However, different types of radiation cause different biological damage for the same absorbed dose. This is accounted for by the relative biological effectiveness (RBE) and the equivalent dose, measured in Sieverts (Sv), where $\text{equivalent dose (Sv)}=\text{absorbed dose (Gy)}\times w_R$. Precise planning using CT or MRI scans is essential for targeting, and methods like intensity-modulated radiotherapy (IMRT) allow the beam shape and intensity to be conformed to the tumor's 3D shape.

Optical Physics in Medicine: Vision Correction and Endoscopy

Physics underpins the correction of common vision defects. Myopia (short-sightedness) occurs when the eye's lens system is too powerful or the eyeball is too long, causing images to focus in front of the retina. It is corrected using a diverging (concave) lens. Hyperopia (long-sightedness) is the opposite, requiring a converging (convex) lens. The required lens power in dioptres ($D$) is simply the inverse of the focal length in metres ($P=1/f$).

Fiber optics are central to keyhole surgery via endoscopes. An endoscope uses two bundles of flexible optical fibers. One bundle transmits intense cold light into the body cavity (illumination). The other bundle, the image guide, carries the reflected light back to the eyepiece or camera. Total internal reflection is the governing principle: light travels along the core of each thin glass fiber by continually reflecting off the core-cladding boundary, provided the angle of incidence exceeds the critical angle. This allows surgeons to see and operate internally with minimal invasion.

Common Pitfalls

1. Confusing Acoustic Impedance with Electrical Impedance: While both use the symbol $Z$, acoustic impedance ($Z=\rho c$) is a property of a medium affecting sound waves, not electrical current. Remember its units are $kg{m}^{-2}{s}^{-1}$ (Rayls).
2. Misunderstanding MRI's Radiation Source: A common error is stating that MRI uses ionising radiation like X-rays or gamma rays. It does not. MRI uses strong magnetic fields and radio waves, which are non-ionising. The "nuclear" refers to the nucleus of the atom, not radioactivity.
3. Mixing Up Lens Correction for Eye Defects: Students often recommend the wrong lens type. A simple memory aid: a short-sighted (myopic) person can see well over short distances, so they need a lens that diverges light to push the focus further back. A long-sighted person needs the opposite.
4. Equating Absorbed Dose and Equivalent Dose: The absorbed dose (Gy) measures the energy deposited per kilogram. The equivalent dose (Sv) adjusts this for the type of radiation's biological impact. For example, an alpha particle dose of 1 Gy causes far more damage than 1 Gy of X-rays, resulting in a much higher equivalent dose in Sv.

Summary

• Medical physics applies core principles—such as wave attenuation, reflection, nuclear magnetism, and radioactive decay—to create technologies for diagnosis and therapy.
• X-rays and CT rely on differential attenuation of ionising radiation by tissues, while ultrasound uses the pulse-echo technique and reflection at acoustic impedance boundaries.
• MRI exploits the magnetic properties of hydrogen nuclei in strong magnetic fields, providing superb soft-tissue contrast without ionising radiation.
• PET scanning tracks metabolic activity by detecting gamma photons from positron-electron annihilation, following the administration of a radioactive tracer.
• Radiation therapy aims to maximise tumor dose while sparing healthy tissue, using concepts of absorbed dose (Gy) and equivalent dose (Sv).
• Optical physics corrects vision defects with lenses (using dioptre power $P=1/f$) and enables minimally invasive surgery through fiber optic endoscopes via total internal reflection.