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# Copy of A2 Physics - Medical Imaging

OCR A2 Physics course revision - with example exam questions
by

## Otto Physicsbeast

on 18 March 2014

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#### Transcript of Copy of A2 Physics - Medical Imaging

Medical Imaging
X-rays
Electromagnetic waves of wavelengths between 10^-12 and 10^-9m
Production requires high voltage and a good vacuum in a tube with an anode and a cathode. Electrons from –ve cathode need to be accelerated from cathode and should not hit any gas molecules towards the anode. If they have enough energy when they hit the anode, some x-rays will be emitted
E(max) = hf(max) in eV h = planck constant = 6.6x10^-34
Interaction of X-rays with matter
X-rays as particles
Photoelectric effect:
The work function is so small It can be ignored. The emitted photoelectrons when produced using x-rays have a max KE equal to the photon energy of the x-rays. These emitted electrons cause ionisation in the same way as β particles do
Pair production:
It’s possible for a photon of x-rays to collide with a particle and spontaneously produce a positron and an e-.
Energy of x-ray photon = 0e-1 + 0e+1 (effect only seen in particularly high voltage systems
Compton effect:
Deflected x-rays had longer wavelength that initially. He explained using quantum theory – x-rays a stream of particles colliding with free e- in C and bounding off them. Photon deflected through large angle will have lost more energy and so longer wavelength. Small angle = not much energy lost so little increase in wavelength
X-ray intensity
Intensity, I of a beam of X-rays is defined as the power per unit c.s.a
I = Io x e^-ux
Typical values of u:
Vacuum, 0
Flesh, 100m-1
Bone, 300m-1
The image can be enhanced using a Barium meal because it absorbs the X-rays providing better contrast
3D X-ray images
Computerised axial tomography (CAT) scan:
The final images is usually a ‘slice’ of the body taken horizontally. The x-ray beam is fan-shaped and has very little thickness so the x-rays irradiate only a thin slice at a time. The x-rays are then detected after going through the patient by a thousand detectors. The source is rotated 1 revolution and the detectors are moved up a cm which means on the next revolution it looks at the next slice of the body. The computer takes all the images and constructs a 3D one.
- Can be taken quickly so a large number of patients can be done each day.
-The initial cost is less than MRI
However, they do require a dose of radiation to the patient, but the does is less than it used to be because of increased sensitivity in sensors
Gamma rays have to be used because alpha and beta would be absorbed by (and damage) the body
The half life of the source must be long enough to carry out the investigation, but no longer
The gamma camera is a detector of gamma photons emitted by a source inside a patient. Tens of thousands of vertical holes collimate the beam so only photons travelling vertically can pass through the lead block. Once through the lead, the gamma photons enter a large crystal of NaI 400mm x 10mm thick. NaI is fluorescent material and scintillates when absorbed gamma photon
Gamma cameras are used to diagnose diseases of thyroid, liver, brain, kidneys…
Modern cameras can have more than one scintillating crystal, to gain a 3-D image of the organ
PET is an extension of gamma ray photography used to detect abnormal metabolic or chemical activity in the body
Magnetic resonance
Nuclei have a property called spin. They spin in a similar way to gyroscopes (a precess). The spinning gives a proton a very small magnetic property called magnetic moment
The frequency of precession is called the Larmor frequency = 4.25x10^7 x B where B is the total magnetic flux density
When the applied magnetic flux density is altered, an interesting resonance occurs. The effect of applying various frequencies to the coils shown in the diagram. When the radio frequency equals the Larmor frequency, a large amount of energy is absorbed by the proton
Once proton gains the energy from a pulse of the radio waves at the Larmor frequency it is in semi-stable state. Will relax back to lower energy state which is key to MRI
Relaxation times depend on the mag. field at the position of any proton which is different in every material
The energy gained when the axis flips has to be lost, as radio waves which can be detected, amplified and interpreted
MRI
MRI scanner made up of: the main magnet, additional magnets to keep magnetic field constant, radiofrequency coil, computer and a display
Quality of image is high
Good distinction between different types of soft tissue
Bone not a barrier to radio waves so pictures inside places like brain are clear
No side effects from having a scan
No metallic objects can be scanned or they heat up
The equipment can have no external sources of radio waves within it
Machines are expensive and take a long time to do one patient
Non-invasive techniques
The endoscope: optic fibres that can be inserted into body openings
Ultrasound: Frequencies just above audible range, cause no ionisation, safe on pregnant women, distinguishes between muscle and blood and can show blood movement, intensity must still be as low as possible or can be destructive
Doppler effect in sound: When sound emitted from stationary source the sound waves spread out in concentric circles, but ig you move towards it you will not hear the same frequency because extra waves will have passed into your ears in a certain time. When source is moving, behind it the wavelength increases and is reduced in front
f’ = cf/(c-v)
Ultrasound
The piezoelectric effect:
When certain crystals have a p.d applied to them, they contract a little. When a high-f alternating p.d is applied, called a signal, the crystals oscillate at the frequency of the signal and send out ultrasound waves. Because the process can work in reverse, the same crystal can also act as a receiver of ultrasound. The crystal cut so it’s a whole number of wavelengths. If a compression from an ultrasound wave arrives at the crystal, a p.d is created across it and can be amplified electronically
The ultrasound transducer:
The piezoelectric crystal is in the hand held equipment. Its curved faceplate shapes the ultrasound waves into a narrow beam. A tuning device controls the frequency of the ultrasound waves. A gel is applied between the transducer and the skin to ensure the ultrasound enters the body
Ultrasound is reflected from surfaces rather than going through the body. Echoes are used. A boundary between tissue/liquid or tissue/bone or air/skin reflects the waves
Ultrasound sent into the body must be pulsed. Once a pulse is sent into body there is a pause while reflected echoes are picked up by the transducer
Acoustic impedance
Z used to determine fraction of intensity refracted at boundary between 2 materials of different acoustic impedances Z = ρc
The equation for ration of intensity reflected, Ir against incident intensity, Io when ultrasound is at a boundary and leaving one material of acoustic impedance Z1 and entering another of Z2

Impedance matching:
The need to match up similar impedances to get good transmission/reflection values
Exam
Questions

Q: State an interaction mechanism
and what happens to an x-ray
photon when interacting with a
single atom in that mechanism [2]
A:
Pair Production: incoming photon produces
electron/positron pair
OR
Compton scattering: incoming photon collides
with electron which is deflected and scattered
Q: Describe how ultrasound is used
to determine the speed of blood in
the artery [3]
A:
Signal sent from transducer is reflected on the blood boundary
The wavelength of the ultrasound is changed
Change in wavelength is proportional to the speed of the blood
Q: Outline physical principles
employed in production of an MRI
scan [10]
A:
Atoms with uneven number of protons/neutrons spin - Hydrogen used for this reason
This means they can act as tiny magnets
They align with and external magnetic field and precession occurs
Radio frequency sent in at Larmour frequency
Resonance occurs and the protons and neutrons flip
Radiofrequency turned off and amplitude of precession starts to drop
Atoms emit radio frequency when returning to equilibrium state
The time it takes to return to this equilibrium state is called the relaxation time
The radio frequency is detected by pick up coils
Precession frequency is proportional to magnetic field
magnetic field gradient means precessions frequency depends upon position
Hence a 3-D scan possible
Full transcript