Unit 20: Medical Physics — Long Questions

The piezoelectric effect is the property of certain crystals (e.g. quartz, tourmaline, Rochelle salt, or synthetic ceramics such as PZT) that lack a centre of symmetry, in which internal regions of positive and negative charge are normally balanced. There are two forms of the effect:
• Direct piezoelectric effect: when mechanical pressure is applied to the crystal, the balance of charge is disturbed and the charges shift slightly, producing an electric field (voltage) on the surface of the crystal.
• Converse piezoelectric effect: when an electric field is applied to the crystal, it changes shape slightly (mechanical deformation/vibration).
In an ultrasound transducer, the converse effect is used to generate ultrasound: an applied alternating voltage makes the crystal vibrate rapidly, emitting pulses of high-frequency sound waves into the body. After the wave reflects off internal tissue boundaries and returns as an echo, the returning pressure wave strikes the crystal and, through the direct piezoelectric effect, generates a small electric voltage. This electrical signal is processed by the machine's computer, which calculates the time delay and intensity of the echoes to construct the image. Thus the same crystal first converts electricity to sound (transmission) and then sound back to electricity (detection).

The piezoelectric transducer first emits short pulses of high-frequency ultrasound (typically 1 MHz–15 MHz) into the body through a gel, which removes air gaps between the transducer and skin and improves sound transmission. These waves travel through the tissues at speeds that depend on the type of tissue. When a wave meets the boundary between two tissues of different acoustic impedance (determined by tissue density and the speed of sound in that tissue), part of the wave is reflected back towards the transducer as an echo, while the rest continues onward. The transducer then switches to receive mode and detects these returning echoes via the direct piezoelectric effect, converting the pressure variations into electrical signals. A computer measures the time delay of each returning echo (which indicates the depth of the reflecting boundary) and its intensity (which indicates the strength of the reflection). Boundaries with a larger acoustic impedance difference, such as soft tissue and bone, produce stronger echoes and appear brighter in the final image, allowing the internal structures of organs and tissues to be visualized in real time.

As X-rays pass through the body, they lose energy by interacting with and ionizing atoms, a process called attenuation; the intensity of the beam decreases exponentially with the thickness of material passed through, following I = I₀e⁻^(μx), where I₀ is the initial intensity, I is the intensity after passing through thickness x, and μ is the attenuation coefficient, which depends on the material and the X-ray energy. Denser, thicker tissues (such as bone) have a higher attenuation coefficient and absorb more X-rays, so less radiation reaches the detector behind them, making them appear brighter/whiter on the image. Less dense tissues (such as soft tissue or air) absorb fewer X-rays, so more radiation passes through, making them appear darker. This difference in the amount of transmitted intensity between tissue types is what is seen as contrast. For example, hard (high-energy) X-rays are used for bone imaging because bone strongly absorbs them, giving good contrast against surrounding soft tissue, while soft (low-energy) X-rays are better for imaging soft tissue such as the breast; and contrast media like iodine (Z = 53) or barium (Z = 56), which have high atomic numbers and absorb X-rays strongly, can be introduced to increase the contrast of structures (e.g. blood vessels or the digestive tract) that would otherwise be hard to distinguish.

A conventional X-ray is quick and simple to produce but gives only a flat, two-dimensional projection image in which organs and bones along the beam path overlap each other, making it difficult to distinguish individual structures clearly, especially tissues of similar density. A CT scan, by contrast, rotates an X-ray tube around the patient while detectors record images of the same cross-section from many different angles; a computer combines these into a detailed cross-sectional slice, and many such slices are stacked to form a full three-dimensional image. This allows doctors to see the exact size, shape, and location of organs, bones, and abnormalities such as tumours, and to distinguish tissues that would appear identical on a plain X-ray — which is of much greater diagnostic value, for example in accurately locating a tumour for treatment or detecting a stroke quickly. The trade-off is that a CT scan involves more X-ray exposure (ionizing radiation) than a single plain X-ray, roughly equal to about one-third of a year's natural background radiation, so it is used with appropriate precautions, particularly in pregnant women or patients with existing health concerns.

Tomography comes from the Greek word tomos, meaning "slice"; it refers to imaging the body in thin cross-sectional slices rather than as a single flat projection. In a CT (Computed Tomography) scanner, the X-ray tube rotates around the patient while detectors stay fixed, collecting many X-ray images of the same cross-section of the body from different angles — this gives complete information about that slice from all sides. A computer processes ("computes") this angular data and combines it into one detailed 2D cross-sectional image, or slice. The scanner then moves slightly along the body's axis and repeats the entire process to obtain the next slice, and so on along the length of the region being examined. Finally, the computer stacks all these individual 2D slices together, like layers of a cake or the pages of a digital apple sliced layer by layer, to reconstruct a complete three-dimensional image of the internal structure.

In an X-ray tube, electrons emitted from a heated filament are accelerated through a potential difference V towards a heavy-metal target (e.g. tungsten), striking it with kinetic energy (K.E.)max = eV.
Characteristic X-rays (inner shell transitions): A fast electron can knock an electron out of an inner shell (K or L) of a target atom, leaving a vacancy. An electron from a higher shell then falls to fill this vacancy, and the energy lost in the transition is emitted as a photon. If an L-shell electron fills a K-shell vacancy, the emitted photon is a Kα X-ray; if an M-shell electron fills it, it is a Kβ X-ray; and so on for transitions from still higher shells, with further vacancies in the L and M shells similarly being filled and producing more lines. Because these photon energies are fixed by the energy-level differences of the target element, they appear as sharp, discrete lines and are called characteristic X-rays.
Continuous X-rays (bremsstrahlung): Separately, when the bombarding electrons are suddenly decelerated as they strike and pass near the nuclei of the target atoms, they emit electromagnetic radiation because an accelerating (or decelerating) charge radiates energy — this is called bremsstrahlung or "braking radiation." An electron that loses all its kinetic energy in a single collision emits a single photon of maximum energy, hfmax = (K.E.)max = eV, giving the shortest wavelength λmin in the spectrum. Electrons that lose their energy over several collisions emit photons of smaller energy (longer wavelength). Since electrons are decelerated by varying amounts, a whole continuous range of X-ray wavelengths is produced, forming the continuous background spectrum on which the discrete characteristic lines are superimposed.