MPY205 Flashcards
Difference between Fourier series and Fourier transform
series is discrete and transform is continuous
Define the point spread function
The point spread function (PSF) describes the response of an imaging system to a point source or point object.
A more general term for the PSF is a system’s impulse response, the PSF being the impulse response of a focused optical system.
Define the modulation transfer function
Fourier transform of PSF
The MTF determines how much contrast in the original object is maintained by the detector.
What does ADC stand for?
Analogue to digital converter
produces binary version of data (intensities)
What is the Nyquist frequency defined as?
Half the sampling rate
What is the convolution integral?
A convolution is an integral that expresses the amount of overlap of one function as it is shifted over another function
Define an impulse signal
a signal composed of all zeros, except a single nonzero point
What is an image?
A map (or image) is a spatial distribution of a parameter where the value of that parameter is encoded as a colour or a brightness
analogue….
quantity can be of any value
digital….
data expressed as series of the digits 0 and 1
data is damaged when it is forced to be discrete
continuous quantity…….
digital imaging
sensor–> transducer (converts input (mag of physical interaction) to output (mV or mA) –>ADC–>latch–>number (integer in computer)
What is the point spread function?
An object can be considered to be made up of lots of points of diff intensities and providing the imaging system images a point as a point the image will faithfully represent the object. In reality, the energy in the object is smeared over a finite area in the image space, (the energy of the object is smeared and there is conjugacy with associate degradation of the image). this smeared representation of the point is called the point spread function
What does the convolution integral describe?
- the image of an object by the transfer function
- it is the basis on digital filtering and image processing
What is the relationship between the Fourier transform and convolution?
F[f*g]=F[f].F[g]
the Fourier transform of a convolution of two functions = the product of the Fourier transform of those functions
What does fourier transform do?
coverts to frequency spectrum
Define HVL
the thickness of the material at which the intensity of radiation entering it is reduced by one half.
Define reaction cross-section
the probability of an interaction interpreted as an effective area of interaction per particle
Define the differential cross-section
a refined version of the reaction cross section to account for dependence on other parameters
What was said about conjugacy?
Good image formation requires a point to be imaged as a point. The object point and image point of a lens system are said to be conjugant points
What does an imaging system do?
It creates a distribution of intensities that are the same distribution of intensities as the object
What is the function that transfers the object to the image called?
transfer function
What are the Dirichlet conditions?
- f(x) is defined and single-valued, except possibly at a finite number of points (in the range -L to L)
- f(x) is periodic with period 2L
- f(x) and f’(x) are piecewise continuous in -L,L
What did Fourier notice could be done with the Fourier series?
multiplying by sin or cos and integrating over a while number of terms could reduce many of the Fourier terms to zero
What is the fourier transform of the delta function?
a constant
What is the fourier transform of the gaussian function?
gaussian
What is the fourier transform of the sin or cos at a single frequency function?
delta function
What did maxwell realise about a moving charge?
the force is due to the accelerating charge, therefore, an accelerating charge radiates
What is an EM wave?
perpendicular electric and magnetic waves
the electric component does mast of the interacting as world is made up of charges
What are the properties that describe EM waves?
Duality- can be considered both particulate and wave-like in nature
Polarisation- imposing of a well-defined plane of oscillation on the electric vectors of electromagnetic waves
Coherence- the extent to which one part of the Em-field can be described
Intensity- a measure of the number of photons striking unit area in unit time
Describe absorption
the transfer of a photon’s energy to surrounding material
Describe scatter
the random re-direction of a photon’s path
Describe attenuation
the decreasing photon flux resulting from interaction processes as light travels through a medium
Describe reflection
the ordered redirection of EM radiation that occurs when it bounces off a smooth surface
Describe refraction
the bending of radiation as it crosses a refractive index boundary
Describe diffraction
the spreading of light that occurs as it passes an edge
What is flux?
flow of energy per unit time
What is fluence?
flow ‘concentration’ per unit area
What is energy flux?
number of photons per unit time
Watts
What is flux density?
the number of photons striking unit area (normal) in unit time
particles/m^2
What is intensity?
the energy incident per unit (normal) area per unit time
W/m^2
What is radiant energy?
The energy radiated by a source
Joules
Define an atom
the smallest unit into which an element may be divided and still retain the properties of the original element
Define a molecule
a group of atoms producing a discrete complex having particular physical/chemical properties
Define an ion
An electrically charged atom or group of atoms, typically caused by the removal of one or more electrons
What is the atomic number?
Z number of protons
What is the mass number?
A number of protons + neutrons
What is the atomic mass unit?
a unit of mass used to express atomic and molecular weights, equal to one twelfth of the mass of an atom of carbon-12.
What is the binding energy?
energy required to separate an atomic nucleus completely into its constituent protons and neutrons,
it is the mass deficit, the energy of a nucleus is less than the sum of the energy of the individual particles in that nucleus as energy is lost trying to hold the nucleus together
When does maxwell not apply?
if you can fit a whole no. of wavelengths into an orbit around a nucleus, you get non-radiative losses
What is an isotope?
Same Z, different A
What is an isobar?
Same A, different Z
What is an isomer?
same species, different energy
Where to x-rays and gamma rays originate from?
x-rays atomic origin
gamma rays nuclear origin
What is alpha decay?
2 protons and 2 neutrons
a helium nucleus
What is beta decay?
an electron or a positron
n–> p+ + e- + v* beta- (proton stays in nucleus)
p+–> n +e+ + v beta+ (neutron stays in nucleus)
What is gamma decay?
high energy electromagnetic radiation
Which properties of an ionising particle determine its ability to ionise matter? as it is independent of energy
particle charge, mass, speed
What is the quantitive parameter that describes the amount of energy dumped per unit length?
dE/dx= Linear Energy Transfer coefficient
rate of energy change with distance
Newtons or keV/μm
Rate the radiations by there ability to damage and travel
alpha- v damaging as v big, but cant travel v far
beta- middle
photon- v small so less likely to interact but can travel further
What is KERMA?
the point of interaction
Kinetic Energy Released in the Material
dE/dm
What is the absorbed dose?
Distributed energy transfer, energy dumped in unit mass of material dE/dm
measure in Gray or J/Kg
What is exposure?
charge liberated per unit mass
Roentgen
1 roentgen = 2.58x10^-4 C/Kg
Why are we concerned about damage to DNA by radiation?
Damaged DNA will pass on damaged DNA
Ionised chain- single-strand break can repair but may repair itself wrong
- a double-strand break is the most damage
Explain the stochastic effect
Based on probability and random variables
no such thing as a safe dose, only less probable that damage will be done
more photons increases likely hood of damage but it does not increase severity only probability
What is LD50?
The lethal dose of radiation for 50% of the population to die
List the side effects with varying gray dose
1 Gray - Acute radiation sickness 5 Gray- LD50 10 Gray- Death in days 50 Gray- Death in hours Radiation kills the cells ability to reproduce so no new cells are being made
What are the three qualifications of radiation damage?
energy (absorbed dose) higher speed = more energy = more lethal
Nicked (dose equivalent) increased damage as radiation spreads through the body
Location (effective dose) systemic effect
What is the RBE equation?
Relative biological effectiveness
Dose from standard radiation to produce given biological effect/ Dose from test radiation to produce given biological effect
What is the dose equivalent?
measure in sievert
Dose Eq = Absorbed dose x Q (radiation weighting factor) x modifying factor
Q correlated with LET
CELLULAR
What is the effective dose?
any radiation insult can be normalised to an effective (whole-body) dose that delivers the same ‘health detriment’
eg if you shot 10000 ppl w/ one sievert to the lung 20 will die as 0.002
SYSTEMIC
What is the ALARP principle?
As low as reasonably practicable/achievable with economic and social factors taken into account
minimise the time of exposure
maximise distance from source
shielding and effective working protocols
List some x-ray control variables
principal control variables - kV, mA, time
kV- potential between cathode and anode
mA- refers to the magnitude of electron current passing through tube
other factors- focal spot size, field size
What does the kV across the anode and cathode in an x-ray tube dictate?
dictates spectrum
controls energy of electrons and therefore the likely hood of absorption as absorption is dependant on Z and energy of photons
Exposure =
no. of photons per second x time
current controls no. of photons per sec
What is filtration (tube)?
a measure of the quality of the emitted x-ray spectrum
characterised by HVL
spectral content is controlled using filters, usually aluminium, as it has similar properties to the human body
x-rays that would’ve have been absorbed by the body get absorbed by aluminium decreasing the dose
What is a DAP?
Dose area product
it is built into the x-ray tube and measures exposure used to infer patient dose
What is contrast?
Contrast is defined as the difference in optical density between the regions of interest
What is optical density used for?
to characterise the blackness of the film
brightness is directly related to x-ray flux striking film
Name some factors that will reduce contrast and how to correct them?
poor differential absorption in the tissue of interest - reduce volume of tissue in beam
overlying tissue
scatter - low kVs are associated with low scatter, scatter reduction grid
noise
Describe the scatter reduction grid
improves image quality at the expense of dose
collimating device that sits above the film detector
consists of fine lead strips that stop scatter radiation reaching film/detector
What is fluoroscopy?
real-time x-ray image displayed on a video monitor
Describe digital x-rays
computed radiography- film replaced with digital plate, the plate is developed to reveal image
digital radiography- film replaced with CCD-type chip technology
What is the difference between planar and spiral CT?
plane of info move person and stack slices (slice)
spiral- never acquire full plane- just spiral (volume)
much faster and more flexible
synthesize plane from info of either side and reconstruct
Outline the MRI process
MRI Bo field –> hydrogen proton dipoles –> gradient fields –> sample excitation –>dipole relaxation –>gradient field –> signal detection –> k space –> Fourier transform –> image
What is a paramagnetic material?
- weak magnetism
- resultant force in the sample region as the sample is aligned with mag field
- temporary if you remove the field the ample will no longer be magnetised
What is a diamagnetic material?
- weak magnetism
- anti-aligned
- net mag field reduces in vicinity of sample
- temporary
What is a ferromagnetic material?
- strong magnetism in the vicinity of object
- aligned
- permanent
What is an electromagnetic material?
- current through the wire (movement of charges)
- material made to exhibit mag properties by passing a current through it
What is a dipole?
a pair of equal and oppositely charged or magnetised poles separated by a distance
List some artefacts of MRI
when the data is not what is claims to be, a result of conditions in which principal assumptions about the imaging process are violated
- noise (RF interference)
- motion artefact (respiratory cardiac flow)
- chemical shift (water/fat)
- susceptibility (distortions)
- field non-uniformity
Name some safety considerations in MRI
Large static fields - danger from flying objects
Large switching fields- current induction in nerves (cardiac risk)
Large RF fields - heating
the localised dose is bigger than the systemic dose
5 gauss line - marked on the floor, no ferromagnetic objects beyond
no metal objects in patients or pacemakers
What is the relationship between mass and linear attenuation ceofficient?
I = Io * e^-𝛍x
𝛍 is the linear attenuation coefficient
mass attenuation coefficient is 𝛍/𝛒
What is the Larmor frequency?
The rate of precession of the magnetic moment of the proton around an external magnetic field
What is K space?
k-space is an array of numbers representing spatial frequencies in the MR image.
Fourier transform to get the image
What is circular polarization?
each point on the electromagnetic field of the wave has a constant magnitude but its direction rotates at a constant rate perpendicular to the direction of the wave
What is the gyroscopic ratio for a hydrogen proton?
42.6 MHz/T
What is T1?
longitudinal relaxation (slow)
spin-lattice relaxation
energy loss mechanism
100s-1000s millisecs
What is T2?
Transverse relaxation (fast)
spin-spin dephasing (i.e. loss of coherence)
each proton feels the influence of fluctuating field from neighbouring spins
10-100s msecs
What is T2*?
Anything that causes a fluctuation in Larmor freq will accelerate dephasing
B field is slightly non-uniform this accelerates T2 by order of magnitude
Use 180-degree bursts to track rapid decay (spin-echo sequence)
Is the hydrogen proton diamagnetic?
Yup
What is tomography?
Tomography is imaging by sections or sectioning, through the use of any kind of penetrating wave.
How are electron emitted from the cathode?
thermionic emission
- free electrons are emitted from the surface of a metal when external energy is applied
Name the two ways x-rays are produced
- bremsstrahlung
- characteristic radiation
Describe bremsstrahlung
Electrons accelerating towards the anode are suddenly brought to rest by a head-on collision with a nucleus in the anode.
All the electrons energy of motion is converted to radiation (photon) of maximum energy
What does the energy of a photon emitted by bremsstrahlung depend on?
voltage of electron
- either hitting a nucleus straight on
- or being deflected by positive nuclei and emitting photons of diff wavelength
What are some properties of the anode in x-ray tubes?
- high-density material to increase the chance of absorption
- gets v hot as lots of energy is absorbed
- rotated on a rotor to smear energy around the circumference
- made from tungsten, works at white heat
- bevelled so image focal point is small
Describe characteristic radiation
- high energy photons are more likely to escape anode ad low energy photons get absorbed
- high-speed electrons impact on the anode and knock out an inner shell electron
- this causes an electron from an outer shell to drop down into the vacant inner shell and in doing so releases a photon
In characteristic radiation what is the wavelength of the photon characteristic of?
shells of anode nucleus
Describe photoelectric absorption
- a low energy photon interacts with an electron in the atom and removes it from its shell
When is the probability of photoelectric absorption maximum?
- the energy of the photons is equal to the binding energy of the electron in its shell (resonant coupling)
- the electron is tightly bound
Describe Compton- scatter
increase in wavelength of x-rays & other electromagnetic radiations that have been elastically scattered by electrons
- incident photon deflected with energy transfer to free electron
What is pair production and why is it irrelevant to diagnostic imaging?
- photon in excess of 1.02MeV passes close to the nucleus of an atom and spontaneously converts to electron-positron pair
- not used in diagnostic imaging as typical energy is 40-100keV
Name some methods of ionising detection
- GM tube
- Scintillation detection (NaI(Ti) crystal interaction creates photon shower)
- photographic emulsion (film sensitive to ionising rad- silver bromide)
- thermoluminescence dosimetry
What is done to the voltage in x-ray production?
- transformation - high voltage for high e electrons
- rectification - ac supply for transformer so rectify to unidirectional current as anode must be positive
Define isotropy and homogeneity
Homogeneity - the same thing is observed by different observers at different locations
Isotropy - same thing is observed by looking in any direction in the universe
Effective dose for CT scan
10 mSv
Effective dose for background radiation
2.5 mSv per yr
cornwall -8
Effective dose chest xray
0.04 mSv
What is SAR?
Specific Absorption Rate a measure of the rate at which energy is absorbed by the human body when exposed to a radio frequency (RF) electromagnetic field.
What does DAC stand for?
Digital to analogue converter
What is phase encoding?
encode a phase axis
then encode other axes as frequency
multiple repeats and use double Fourier transform to decode
Phase encoding is used in the MRI images to determine the relative pixel brightness in the orthogonal plane used by frequency encoding, as each section will have a slightly different phase
Difference between dose and exposure?
Exposure rate is the amount of ionizing radiation per hour in a person’s vicinity (measured in milliRoentgen per hour, mR/h)
dose rate is the biological effect on the body from exposure to that radiation (measured in nanoSieverts per hour, nSv/h).
Pitch of CT scan
distance in mm that ct table moves in one revolution of the x-ray tube around patient
MRI HP
Hydrogen proton is a spinning (intrinsic) charged particle
therefore it can be seen as a current loop
and a current loop has an associated magnetic field
so HP is a mini magnet
When mag field is applied protons try to align
Proton is also spinning rigid body so when torque (mag field) is applied it precesses
Map to common origin to get (anti-aligned as diamagnetic)
Need incoherence in the precessional plane for a signal so…
flood proton with RF at Larmor freq into the precessional plane to get proton to precess 90deg
the remove RF so it relaxes
(RF weaker than B-field so 90deg precession is slower the b field precession)
Describe frequency encoding
gradient fields, vary from left-right, up-down, and front-back, creating a unique magnetic field strength in each element of the patient being scanned. Therefore, the mishmash of signals that come out of the patient can be decoded by the computer to assign a signal strength (pixel brightness) to each part of the 3-D anatomy. This is frequency encoding.
What is an image intensifier in x-ray imaging?
- converts x-rays into visible light at higher intensity
- used in x-ray imaging systems (such as fluoroscopes) to allow low-intensity x-rays to be converted to a conveniently bright visible light output.
Describe the process of a CT scan
- X-ray tube rotates around the patient with the detector
- slices stacked
- A measure of the attenuation coefficient in regions
- More views reduce ambiguity
- no unique solution
- computer makes best guess
How do the x-ray film and cassette work?
- AgBr is the active material for image formation
- plastic film coated with AgBr
- ionising radiation reduces to AgBr —-> Ag+ + Br
Why are fluorescent screens used in x-ray?
the film is of low density and atomic number and it is, therefore, a poor detector of X-rays
The probability of X-ray detection is greatly
increased by sandwiching it between two
fluorescent screens.
- These are of high density and high atomic
number (eg. calcium tungstate).
- The presence of an ionising event within the
screen releases a shower of visible photons that
expose the film.
- A reflective layer bounces photons back onto the
film if necessary.
- The spread of the photon shower at the film is
minimised by sandwiching the whole assembly
tightly together within a cassette.
What is a projection (CT)?
a representation of the object in a lesser
dimensional space
Explain the Hounsfield unit
HU is displayed as the intensity
HU range is mapped to display an intensity range
The window can be widened or shortened to produce better contrast in the image
The relative scale of attenuation coeff with respect to water
Typical matrix size in CT
512
