Medical physics

X-rays are high-frequency, short-wavelength electromagnetic radiation, typically with wavelengths from 0.01 to 10 nanometres. They are produced in an X-ray tube when high-energy electrons are rapidly decelerated. In a standard X-ray tube, a heated cathode filament releases electrons through thermionic emission. These electrons are accelerated through a very high potential difference (voltage) towards a metal target, usually made of tungsten, which acts as the anode. Upon striking the target, the electrons decelerate suddenly, converting their kinetic energy into other forms. About 99% is converted into heat, while about 1% is converted into X-ray photons. This process of producing radiation by decelerating charged particles is called Bremsstrahlung, or 'braking radiation'. The maximum energy (and thus minimum wavelength) of the X-ray photons produced is determined by the accelerating voltage, as the maximum energy a photon can have is equal to the entire kinetic energy of one electron: E_max = eV.

As a beam of X-rays passes through a material, its intensity decreases. This reduction in intensity is called attenuation. Attenuation occurs due to two main processes: absorption (e.g., photoelectric effect) and scattering. For a parallel, monochromatic X-ray beam, the intensity decreases exponentially with the thickness of the material it passes through. This is described by the equation I = I₀e^(-μx), where I is the transmitted intensity, I₀ is the initial intensity, x is the thickness of the material, and μ is the linear attenuation coefficient. The attenuation coefficient μ is a property of the material and depends on the energy of the X-ray photons and the atomic number of the material. Denser materials and materials with higher atomic numbers (like bone or lead) have a much higher attenuation coefficient than less dense materials (like soft tissue), which is why they show up differently on an X-ray image.

Standard X-ray images are 2D projections and have limitations, especially in distinguishing between soft tissues which have similar attenuation coefficients. Image quality can be improved in two main ways. First, a contrast medium, such as barium or iodine, can be introduced into the body. These substances have high atomic numbers and significantly increase the attenuation in the specific tissues or organs they fill (like the digestive tract or blood vessels), making them stand out clearly. Second, image intensifiers can be used. These devices convert the few X-ray photons that pass through the patient into a much larger number of light photons, which are then converted into an electrical signal to create a brighter image, allowing for a lower initial X-ray dose.

Computerised Axial Tomography (CAT or CT) is a more advanced technique. Instead of one static image, a CT scanner takes a series of X-ray images from many different angles as the X-ray tube rotates around the patient. A computer then processes these multiple 2D 'slices' and reconstructs them into a detailed 3D image. This allows doctors to see the body's internal structures without the overlapping of organs found in a conventional 2D X-ray, providing far superior soft tissue detail and spatial information.

Ultrasound refers to sound waves with frequencies above the range of human hearing, typically greater than 20 kHz. In medical imaging, frequencies in the range of 2-10 MHz are used. These high-frequency waves are produced and detected by a device called a transducer, which relies on the piezoelectric effect. A piezoelectric crystal (like quartz or certain synthetic ceramics) has a unique property: when a potential difference is applied across it, it mechanically deforms (changes shape). If an alternating p.d. with a high frequency is applied, the crystal vibrates rapidly, producing ultrasound waves. Conversely, the effect is reversible. If an incoming ultrasound wave causes the crystal to vibrate, it generates an alternating potential difference across its faces. The transducer therefore acts as both a transmitter and a receiver of ultrasound, sending out a short pulse and then 'listening' for the returning echoes.

When an ultrasound wave reaches a boundary between two different materials, some of it is reflected and some is transmitted. The amount of reflection depends on the difference in the acoustic impedance (Z) of the two materials. Acoustic impedance is a property of a medium that describes how much it resists the passage of sound waves. It is calculated as the product of the density (ρ) of the medium and the speed of sound(c) in that medium: Z = ρc. The greater the difference (or 'mismatch') in acoustic impedance between two materials, the greater the fraction of the wave's intensity that is reflected. The ratio of reflected intensity (Ir) to incident intensity (I₀) is given by the formula Ir/I₀ = ((Z₂ - Z₁)/(Z₂ + Z₁))². Because the impedance mismatch between air and skin is very large, almost all ultrasound would be reflected at the skin's surface. To overcome this, a coupling gel is used. The gel has an acoustic impedance similar to that of skin, which displaces the air and ensures that most of the ultrasound intensity is transmitted into the body.

Positron Emission Tomography (PET) is a nuclear medicine imaging technique that shows the metabolic or biochemical function of tissues and organs. A patient is injected with a small amount of a radiotracer, which is a biologically active molecule (like glucose) tagged with a positron-emitting radioisotope. A common tracer is Fludeoxyglucose (FDG). The tracer travels through the body and is absorbed by tissues. Areas with high metabolic activity, such as cancer cells or active parts of the brain, absorb more of the tracer. The radioisotope undergoes beta-plus (β⁺) decay, emitting a positron (an anti-electron). This positron travels a very short distance before it encounters an electron in the tissue. The particle-antiparticle pair annihilate each other, converting their entire mass into energy in the form of two high-energy gamma photons. To conserve momentum, these two photons are always emitted in opposite directions (180° apart). The PET scanner consists of a ring of gamma detectors that detect these pairs of photons arriving simultaneously. By analysing the lines along which these photon pairs are detected, a computer can reconstruct a 3D image showing the location and concentration of the radiotracer in the body.