13. Medical physics A.md

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Understand: How does a piezo-electric crystal work? Answer: A piezoelectric crystal is a type of material that changes its shape when a potential difference (p.d.) is applied across it. This is due to the piezoelectric effect. Conversely, when the shape of the crystal changes, it generates an electromotive force (e.m.f.). This is known as the inverse piezoelectric effect.

Understand: How are ultrasound waves generated and detected by a piezoelectric transducer? Answer: Ultrasound waves are generated by a piezoelectric transducer by applying an alternating voltage to a piezoelectric crystal. This voltage causes the crystal to vibrate at the frequency of the voltage, thereby producing ultrasound waves. The transducer detects these waves by making use of the inverse piezoelectric effect. The incoming ultrasound waves cause the crystal to vibrate, which in turn generates a voltage that can be measured.

Understand: How can the reflection of ultrasound pulses at tissue boundaries be used to obtain diagnostic information about internal structures? Answer: When ultrasound waves encounter a boundary between different types of tissues, part of the wave is reflected back towards the transducer. The time it takes for the reflected wave to reach the transducer can be used to calculate the distance to the boundary. This information can be used to build up a picture of the internal structures in the body, allowing for non-invasive diagnosis and monitoring.

Define: What is the specific acoustic impedance of a medium? Answer: The specific acoustic impedance (Z) of a medium is defined as the product of the density of the medium (ρ) and the speed of sound in that medium (c). Mathematically, this is expressed as .

Use: How is the intensity reflection coefficient of a boundary between two media calculated? Answer: The intensity reflection coefficient () for a boundary between two media with specific acoustic impedances Z1 and Z2 can be calculated using the equation .

Recall and Use: What is the equation for the attenuation of ultrasound in matter? Answer: The equation for the attenuation of ultrasound in matter is , where I is the intensity of the ultrasound after it has travelled a distance x through the matter, I0 is the initial intensity of the ultrasound, and μ is the attenuation coefficient of the matter.

Production and use of X-rays 7. Explain: How are X-rays produced and how can the minimum wavelength of X-rays be calculated from the accelerating potential difference? Answer: X-rays are produced when high energy electrons collide with a metal target. The energy of the electrons is transformed into X-ray photons as the electrons are decelerated in the metal. The minimum wavelength λmin of the X-rays produced can be calculated from the accelerating potential difference V using the equation , where h is Planck's constant, c is the speed of light, and e is the charge of an electron.

Understand: How are X-rays used in imaging internal body structures and what does the term contrast mean in X-ray imaging? Answer: X-rays are used in imaging internal body structures because they can penetrate tissues and are absorbed to different extents by different types of tissue. This difference in absorption results in different levels of blackening on an X-ray film, allowing internal structures to be visualized. The term contrast in X-ray imaging refers to the difference in the degrees of blackening between different areas on the X-ray image, which reflects the difference in absorption of X-rays by different tissues.

Recall and Use: What is the equation for the attenuation of X-rays in matter? Answer: The equation for the attenuation of X-rays in matter is , where I is the intensity of the X-rays after they have travelled a distance x through the matter, I0 is the initial intensity of the X-rays, and μ is the attenuation coefficient of the matter.

Understand: How does computed tomography (CT) scanning produce a 3D image of an internal structure? Answer: Computed tomography (CT) scanning produces a 3D image of an internal structure by first taking multiple X-ray images of the same section from different angles. These images are then combined to form a 2D image of the section. This process is repeated along an axis to obtain 2D images of multiple sections. These 2D images are then combined to produce a 3D image of the internal structure.

PET scanning 11. Understand: What is a tracer and how is it used in medical imaging? Answer: A tracer is a substance containing radioactive nuclei that can be introduced into the body. It is absorbed by the tissue being studied. By detecting the radiation emitted by the tracer, information about the physiological processes in the body can be obtained.

Recall: What type of tracer is used in positron emission tomography (PET scanning)? Answer: A tracer that decays by β+ decay is used in positron emission tomography (PET scanning). This means the tracer emits positrons, which are particles of antimatter with the same mass as an electron but a positive charge.

Understand: What occurs during annihilation and what principles are conserved in this process? Answer: Annihilation occurs when a particle interacts with its antiparticle, resulting in their mutual destruction and the release of energy. Both mass-energy and momentum are conserved in this process.

Explain: How does PET scanning work? Answer: In PET scanning, a tracer that decays by β+ decay is introduced into the body. The positrons emitted by the decay of the tracer annihilate when they interact with electrons in the tissue, producing a pair of gamma-ray photons travelling in opposite directions. These gamma-ray photons can then be detected and used to create an image of the tracer concentration in the tissue.

Calculate: How can the energy of the gamma-ray photons emitted during the annihilation of an electron-positron pair be calculated? Answer: The energy of the gamma-ray photons emitted during the annihilation of an electron-positron pair is equivalent to the rest mass energy of the electron and positron. This can be calculated using the equation , where m is the rest mass of the electron (or positron) and c is the speed of light.

Understand: How are the gamma-ray photons from an annihilation event used to create an image of the tracer concentration in the tissue? Answer: The gamma-ray photons from an annihilation event travel outside the body and can be detected by detectors arranged around the body. The arrival times and directions of the gamma-ray photons can then be processed to determine the location of the annihilation event, and hence the location of the tracer in the body. By repeating this process, an image of the tracer concentration in the tissue can be created.