Exam Notes 4.6

X-Ray Scanning

X-rays are generated by bombarding a heavy metal target, such as Tungsten, with electrons.

CT/CAT Scan (Computerised Axial Tomography)

A CT/CAT scan involves rotating an X-ray tube around the patient to capture cross-sectional images of their internal structures.

• Process: The X-rays are detected by an array of detectors, which are then used to construct 2D cross-sections of the patient's internal structures.

• Attenuation: As X-rays pass through different substances, they are attenuated (absorbed, intensity reduced) differently. For example, bone and soft tissue attenuate X-rays to varying degrees.

• Contrast: Sometimes, a liquid contrast agent, such as Barium, is administered to the patient to enhance image clarity, particularly in areas with low natural contrast, like blood vessels.

X-Ray Interactions with Matter

• Rayleigh/Simple Scattering: The photon changes direction, but it is not absorbed.

• Compton Scattering: The photon liberates an electron and is then re-emitted with a longer wavelength.

• Photoelectric Effect: The photon is completely absorbed, and an electron is liberated (ionization).

• Pair Production: The photon transforms into a particle and its corresponding antiparticle (e.g., an electron and a positron).

Intensity of Transmitted X-rays

The intensity of transmitted X-rays decreases exponentially with distance, described by the following equation:

I = I_0 e^{-\mu x}

Where:

• I is the intensity of the transmitted X-rays.

• I_0 is the initial intensity of the X-rays.

• \mu is the attenuation/absorption coefficient (m⁻¹).

• x is the distance traveled (m).

Gamma Camera & PET Scans

Gamma Camera

A gamma camera is used to detect gamma rays emitted by a radioactive source injected into the patient.

• Process: A purely gamma-emitting source is injected into the patient. The emitted gamma rays are detected by a gamma camera.

• Components:

  • Scintillator: Absorbs gamma photons and re-emits many visible photons.

  • Photomultiplier Tubes: Convert the energy of visible photons into an electrical signal.

  • Collimator: Ensures that only gamma rays traveling parallel to the camera are detected, improving image resolution.

  • Computer: Processes the electrical signals to generate an image.

PET (Positron Emission Tomography) Scan

A PET scan involves injecting a positron-rich substance into the patient. Positrons annihilate with electrons, producing pairs of photons which are then detected.

• Process: A positron-rich substance is injected into the patient. When positrons encounter electrons, they annihilate each other, producing a pair of photons that travel in opposite directions.

• Detection: These photons are detected by an array of detectors, and their point of origin is calculated. This information is used to build up an image of the targeted area.

Ultrasound Scans

Ultrasound refers to any sound with a frequency greater than 20 kHz.

Acoustic Impedance

When ultrasound encounters a medium with a different acoustic impedance, it is partially reflected. Acoustic impedance (Z) is defined as:

Z = \rho v

where \rho is the density of the medium and v is the speed of sound in the medium.

Transducer

The transducer generates ultrasound by applying a varying potential difference (p.d.) to an array of piezo-electric crystals, causing them to vibrate at the applied frequency.

Reflection of Ultrasound

The intensity of reflected ultrasound (Ir) depends on the acoustic impedances of the two mediums (Z1 and Z2), this is given by the equation:

\frac{Ir}{Ii} = \frac{(Z2 - Z1)^2}{(Z2 + Z1)^2}

Where I_i is the intensity of the incident ultrasound.

If two mediums have the same impedance, they are said to be acoustically matched, and no sound will be reflected. This is why gel is used between the transducer and skin to minimize reflections before the ultrasound enters the body.

The crystals also produce a tiny current when the reflected sound waves cause them to vibrate, which is detected and used to construct the image.

Types of Ultrasound Scans

• A-scan: A stationary transducer measures depth by analyzing the time it takes for the ultrasound to reflect back.

• B-scan: Multiple A-scans are performed while moving the transducer sideways to build up a 2D image.

• Doppler Scan: Measures flow rate by detecting the change in wavelength/frequency of ultrasound reflected off red blood cells. The Doppler shift (Δf) is given by:

\frac{\Delta f}{f} = \frac{2v \cos{\theta}}{c}

Where:

• f is the original frequency of the ultrasound.

• v is the velocity of the blood flow.

• \theta is the angle between the ultrasound beam and the direction of blood flow.

• c is the speed of sound in the medium.