OCR A-Level Physics/Fields, Particles and Frontiers of Physics/Medical Physics

Currently X-Rays and PET scans are completed. The rest are not yet complete or not yet even started. Feel free to add content or edit the existing content to make it better

X-Ray Imaging

X-Ray Production

• X-Rays are produced by firing a beam of electrons at a tungsten target.
• The beam of electrons is produced by heating a filament. This releases electrons via thermionic emission.
• The electrons are accelerated due to an electric field from a cathode towards a tungsten anode. There is a high potential difference between the anode and cathode.
• When the electrons hit the tungsten, their kinetic energy is converted into X-Ray radiation.
• However, only a very small amount of energy is converted into X-Rays. Most of it is converted into heat. The heat would be so great that it would be able to melt the tungsten which has a high melting point.
• The tungsten is rotated (around 3000 rpm) to avoid overheating. This allows parts of the tungsten to cool down when they are not being hit.
• The X-Rays leave the tube as a collimated beam, which is a parallel-sided beam. This is done by a collimat, which is a device that makes the beam parallel-sided.

X-Ray Absorption

Photoelectric Effect

• An X-Ray Photon enters an atom and is absorbed by the electron
• The electron is ejected from the atom, leaving a space in an electron shell. This gap is filled by another electron which emits a photon.
• The energy the incident photon is less than 100keV

Pair Production

• An X-Ray photon enters an atom's electric field and produces a positron-electron pair.
• The positron is annihilated with another electron.
• Photon energy greater than 1.02MeV

Compton Scattering

• An X-Ray photon enters an atom and is partially absorbed by an electron
• The electron is ejected and the photon is scattered with a lower intensity, frequency and energy, and therefore a longer wavelength.
• Photon energy range of 0.5 to 5.0 MeV

X-Ray Attenuation

Intensity - Power per unit cross-sectional area

When X-Rays enter matter, the intensity decreases exponentially.
$I=I_{0}e^{-\mu x}$
Where $I_{0}$ is the initial intensity, $\mu$ is the attenuation coefficient an $x$ is the thicknes of the material.

Half-Value Thickness

Half Value Thickness - The thickness required to decrease the initial intensity by half

How to derive the half value thickness:

1. ${\frac {1}{2}}I_{0}=I_{0}e^{-\mu x_{\frac {1}{2}}}$

1. ${\frac {1}{2}}=e^{-\mu x_{\frac {1}{2}}}$

1. $ln({\frac {1}{2}})=-\mu x_{\frac {1}{2}}$

1. $ln{1}-ln{2}=-\mu x_{\frac {1}{2}}$

1. $x_{\frac {1}{2}}=>{\frac {ln{2}}{\mu }}$

Remembering Ln(1) is zero

Improving X-Ray Images

X-Ray images can appear on the screen as quite faint. So how would you be able to improve it? One option is to increase the intensity of X-Rays that is exposed to the patient, however this is not good for the patient as it exposes the patient to more harmful radiation. So increasing the intensity is not a good way to improve the image.

• Intensifier screens are a good way of producing a better image. These are sheets of a phosphorous material sandwiched in between two intensifier screens. the phosphor in the material emits visible light when it absorbs X-Rays.
• In digital systems, incoming X-Rays hit a phosphorus screen which releases electrons which are accelerated by an electric field so that they can strike a screen to produce visible light which can be displayed on a television screen by recording the striking screen with a camera.
• Contrast media are substances that are used to allow a good view of soft tissues. This is done because the contrast medium is a good absorber of X-Rays, due to having a high atomic number like iodine or barium.
  • You may have heard of a barium meal. The meal is digested and can show the intestine of a patient.

CAT Scans

Computerised Axial Tomography(CAT or CT) Scans produce a 3D image using X-rays.

• Patient lies in a vertical ring of X-Ray detectors
• The X-Ray tube moves around the patient, exposing them to a thin, fan-shaped beam of X-Ray photons
• The detectors on the opposite side to the X-Ray tube detect the X-Rays and record them to a computer
• Slices of the patient can be viewed
• Computer software can build a 3D image of the patient

Advantages

• Can distinguish tissues with similar attenuation coefficients (densities)
• non-invasive (nothing is inserted into the body)
• Can produce a 3D image

Disadvantages

• Exposes the user to harmful radiation

PET Scans

• Positron Emission Tomography
• A tracer, known as a radiopharmaceutical, is inserted into the body by either swallowing or injection.
• The tracer is glucose with fluorine-18 attached to it. Fluorine-18 emits positrons when it decays.
• The tracer is used by the body in respiration so active parts of the body release more positrons.
• When a positron is emitted, it is immediately annihilated by an electron. This gives off two gamma rays which travel in opposite directions.
• Detectors that are situated all the way around the patient detect the two gamma rays.
• The difference in time it takes for the gamma rays to be detected determines the location of activity in the body.
• PET scans are mainly used in the brain.

MRI Scans

Gamma Sources must be used because alpha and beta particles would be absorbed by the body rather than passing straight through.We use a gamma camera to track the movement of the gamma-emitting source.

The Gamma Camera

The gamma camera detects gamma photons that have been emitted by a source inside the patient's body. A block of lead with ten of thousands vertical holes, the Collimator, is positioned close to the patient, these parallel tubes align the beam so only particles traveling along the axis of the collimator can pass through to the detector, the lead will absorb any Photons moving in any other direction.

Once through the Collimator, the gamma photons strike the Scintillator, which is a large crystal of sodium iodide. The sodium iodide is a fluorescent material and emits many photons of visible light when it absorbs a gamma photon.

Behind the sodium iodide crystal is an array of photomultiplier tubes, arranged in a hexagonal position. Each photomultiplier tube initially emits one electron for every photon, by the photoelectric effect. The tubes amplify the effect to release many more electrons, giving an electrical pulse output for every incident photon of light. More photomultiplier tubes are added for better clarity of picture

Ultrasound

In medical applications the most commonly used values for medical purposes are in the rang 1 to 15 MHz

Most women are offered at least two ultrasound scans during pregnancy: The first scan (8–14 weeks) can determine, for measurements of the dimensions of the foetus, when the baby is due to be born. and the second scan (usually around 18–21 weeks) checks for structural abnormalities particularly in the baby's head or spine. it can also help to detect kidney stones or gall stones in the gall bladder.

Ultrasound scanning uses sound waves rather than EM radiation such as X-rays. Ultrasound scanning is different in the two main facts that; ultrasound is reflected from surfaces rather than going through them. Echoes are used A boundary between tissue and liquid, or tissue and bones, etc. reflects the waves. And that ultrasound must be pulsed, after a pulse of ultrasound is sent into the body from the transducer. there is a pause while reflected echoes come back to be picked up by the transducer

Ultrasound Transducer and the Piezoelectric effect

A transducer contains a piezoelectric crystal and acts as both a transmitter and receiver of ultrasound. Normally, audible sound is produced by a body vibrating at a frequency between 20 Hz and 20 kHz. To produce ultrasound at frequencies of around 1 MHz, a physical effect called the Piezoelectric effect is used.

When certain crystals have a potential difference applied to them, they contract a little. When a high-frequency alternating p.d. is applied, the crystals oscillate at the frequency of the signal and emit ultrasound waves. Because the process can work in reverse, the same crystal can also act as a receiver. If a compression from an ultrasound wave arrives at the crystal, a p.d. is created across it. This can be amplified electronically.

Acoustic Impedance

Ultrasound scan depends on ultrasound being reflected at a boundary between materials. If at the first boundary between two materials all the ultrasound is reflected, then there will be no ultrasound left to be reflected at any further boundary. The key to be able to get multiple reflections from different boundaries depends on the fraction of the intensity of reflected ultrasound to the fraction transmitted. Ultrasound is reflected when there is a change in the density of materials, so it cannot pass through air spaces.

Acoustic Impedance, Z, is used in determining the fraction of the signal intensity that is reflected at a boundary between two materials of different acoustic impedances. Acoustis impedance is defined by the equation

Z = ρc

Where ρ is the density of the material and c is the speed of sound in the material. The equation for the ratio of the intensity reflected, $I_{r}$, against the incident intensity, $I_{0}$, when ultrasound is at a boundary and leaving one material of acoustic impedance $Z_{1}$, and entering another of acoustic impedance, $Z_{2}$.

${I_{r} \over \ I_{0}}={({Z_{2}-Z_{1}})^{2} \over \ (Z_{2}+Z_{1})^{2}}$

If gel isn't used then most of the ultrasound will be reflected and never enter the body at all. The need to match up similar impedances to get good transmission/reflection values is called Impedance Matching

A-Scan

Also known as the Amplitude scan, a short pulse of ultrasound waves is sent into the body at the same time that an electron beam travels across the screen of a cathode ray oscilloscope.

The transducer receives reflected pulses which cause vertical spikes on the CRO screen. The horizontal, or x-axis shows the time that the echo took to be detected by the transducer and can be used to work out the depths of thicknesses of reflecting tissue in the body.

No photo is produced, but measurements can be taken from it to determine dimensions

B-Scan

Also known as the Brightness scan, is much more common.

A real time 2D or 3D image of the area being scanned is built up from many returning echoes recorded from several transducers in an array, or a transducer is moved to different positions or angles around the patient.

The greater the amplitude of the reflected pulse, the brighter each dot will be, so a range of brightnesses will be shown in a scan where different bone, liquid, and soft tissue reflect different proportions of the transmitted ultrasound beam.

The Doppler Effect

The Doppler effect works in the same same for ultrasound waves as it works for a moving source of sound and light waves. $f'={c \over \ (c-2\upsilon )}*f$

Where $f'$, is the new frequency of the reflected pulse detected at the receiver, $c$ is the velocity of the electromagnetic radiation from the speed gun, $v$ is the speed of the moving object, and $f$ is the frequency of the transmitted waves. This means that the speed of the moving reflector can be calculated from the cage in the frequency of waves.

This can also be used with ultrasound to determine speed of blood flow in the heart or artery. The red blood cells reflect the ultrasound. For this we use:

${\Delta \ f \over \ f_{0}}={2vcos\theta \over \ c}$