MEDPHYS 580 Flashcards
Draw an X-ray tube.
Include: anode, cathode, focusing cup, vacuum envelope, tube housing, rotor, bearings, stator, transformer oil, output port
Explain the basic principles of operation of an x-ray tube. What component of the x-ray tube is the source of electrons? How are the electrons accelerated to the anode?
Electrons are ‘boiled’ off the cathode through thermionic emission. After electrons are emitted, they are electrostatically repelled from each other and accelerated towards the anode.
A negatively-biased focusing cup (-100 V in respect to the cathode) is used to focus this beam. Shape of the cup controls the width of the beam.
Electrons hit the rotating anode and through bremsstrahlung release x-ray photons.
What percent (%) of electron energy absorbed in the anode is converted to x-rays?
Only 1% of the electron energy absorbed in the anode is converted to x-rays.
The remaining ~ 99% is converted to heat in the anode via soft and hard collisions.
What modulates the number of electrons available in x-ray tube operation?
Filament current.
What are grid-controlled x-ray tubes used for ? What is specific to them?
Give two examples.
Grid-controlled x-ray tubes employ large negative biasing (e.g. -3000 V) to completely turn off the electron beam. This design is used when a very fast turn-on / turn-off of x-ray output is desired.
Examples: pulsed fluoroscopy and cardiac angiography.
What are the two geometries of anodes?
Two geometries:
- Reflective geometry (x-rays emerge on the same side as the incoming electrons)
- Transmission geometry (x-rays emerge on the opposite side as the incoming electrons)
List properties of a good anode material.
What is the best material to use?
- High Z
- High heat capacity
- High melting point
Best material to use is Tungsten (W) (Z=74) covered with a small amount of Rhenium (Re) to improve ductility.
What do kV, kVp, mA, ms, and mAs describe?
kV = accelerating voltage of the tube
kVp= peak kV
mA= tube current flowing from cathode to anode
ms= time tube is active for (often pulsed)
mAs= product of mA and ms
If the x-ray tube is operated with a particular accelerating potential, in kV, then what is the energy of each electron striking the anode, in units of keV?
Electrons striking the target will have kinetic energy in keV equal to the kV.
10 kV accelerating potential= 10keV electron energy
In the spectrum of photon energies produced in an x-ray tube what is the maximum photon energy? Where does the peak occur?
Spectrum of photons will have the maximum energy (in keV) equal to the kV, but peak energy about ⅓ of that amount.
When energetic electrons strike the target material in the anode, what are the types of electron-matter interactions that can occur? Which interaction leads to production of Bremsstrahlung radiation? Which interaction leads to characteristic x-rays?
Types of interactions: Bremsstrahlung (Coulomb effects) and Compton scattering
Deceleration of electrons due to Coulomb effects leads to Bremsstrahlung radiation (spectrum with highest photon energy equal to kV and peaks at ⅓ of the maximum).
Compton scattering produces characteristic photons via fluorescence yield form the knocked-out electrons.
What is the K-shell binding energy for tungsten? What are the four K-lines of tungsten listed in the notes?
~69.5, ~67, ~59, and ~57 keV
How characteristic x-rays are produced when electrons strike the target? How do the characteristic x-ray energy relate to electron binding energies. What energy must the incident electron have for the K-shell to participate in characteristic x-ray production?
When a Compton scatter interaction occurs in the anode, it may knock loose an electron from one of the orbital shells if the incident electron has enough kinetic energy to overcome the binding energy of the orbital electron.
Once knocked free, the vacant space in the orbital may be filled by an electron from a higher shell. When this happens, the dropping electron emits a characteristic photon of ~69.5, ~67, ~59, or ~57 keV (for Tungsten).
To produce these, the kV must exceed their energy.
What is the shape of the bremsstrahlung energy spectrum from a thick target, according to the simple Kramers model?
How does the total energy of the spectrum (area under the spectrum) depend on: mAs, kV, and Z?
Kramers model: Intensity vs photon energy; linear relationship with characteristic energy peaks. Curve intersects the x-axis at tube voltage (kV) in keV.
Higher kV shifts the spectrum further right, increasing total energy by a squared factor (double kV makes for quadruple area= quadruple energy).
kV ∝ (Area)2= (total energy)2
Higher mAs will shift spectrum slope/height. Changes total energy linearly (double mAs makes double energy).
mAs ∝ Area= total energy
Draw how the shape of the Kramers spectrum changes when the mAs is doubled.
Maximum energy stays the same; curve cuts y-axis higher up; area under the curve doubles
Draw how the shape of the Kramers spectrum changes when the kV is doubled.
Maximum energy doubles (x-axis intercept doubles); y-intercept doubles; area under the curve quadruples
Why do we need a collimator?
What is the purpose of the oil in the tube?
The objective of the collimator is to produce a beam that is proper “quality” , desired dimensions and positioned correctly on the patient.
Tube housing is filled with oil for better heat dissipation. Radiolucent window allows x-rays to go out.
What is beam hardening?
Beam hardening is the removal of lower energy photons from the x-ray beam.
Filtration hardens the beam, removing non penetrating dose-depositing low-energy photons.
What is the electron source in the x-ray tube?
Filament is electron source- electrons are ‘boiled off’ through thermionic emission* due to the current run through it via a separate, low (~10) V circuit.
Higher filament current emits more electrons, but raises temperature- too hot breaks it.
Line focus principle. How does an angled anode enable a large actual focal spot, but a small projected focal spot (as viewed from the detector).
Why is this geometry beneficial? How is the effective focal spot size related to the actual focal spot size, for a given anode angle?
Larger focal spot handles heating better and can be used for higher energy applications, but smaller focal spots provide higher-resolution images. This reflective geometry allows some of both.
Larger anode angles make for larger focal spots. Note this geometry only affects one axis.
Effective focal spot: F X F
Actual focal spot on the anode surface: F X L where L=F/sin∅ (∅ is the anode angle)
How does field-of-view (FOV) depend on anode angle?
Maximum field of view along the cathode-anode axis (left and right) depends on anode angle. Larger angles enable larger FOVs.
Heel effect. How does intensity vary along the cathode-anode axis? What is the cause of the heel effect? How does the severity of the heel effect depend on anode angle?
X-Rays are generated within the target, and must first travel out. Heel Effect refers to how some are absorbed before they can escape. Electrons ‘deeper’ in the anode (further from cathode) must travel further to escape. Shallower anode angles result in larger heel effect.
In this way, emitted spectrum is weaker further from the cathode.
What is the purpose of the rotor and stator?
Anode rotates to help dissipate heat from the interactions (note: only 1% of electron energy goes to photons, the rest to heat!). Rotor and stator make a motor to rotate the anode. Stator uses magnetic induction to make rotor spin.
How long must the cathode filament be to achieve a 1 x 1 mm effective focal spot size with a 10 degree anode angle?
see image
Automatic exposure control: What is the basic principle of operation of a radiography phototimer system, and what parameters can the operator control? How does a fluoroscopic automatic exposure control (AEC) compare to the radiography phototimer?
AEC modulates kV, mA, and t (mA*t =mAs) to maintain constant detector (not necessarily patient!) exposure under changing conditions (like moving table relative to source, imaging thicker body part, etc.) Operator chooses kV.
Radiography Phototimer: integrates over detector charge to terminate tube once a set point of exposure is reached. Simply changes t (mAs), nothing else. Often comes with many preset conditions.
Fluoroscopic Phototimer: adjusts all 3 parameters in real-time, since fluoro is in real time, and may involve moving patient couch or machine arm.
Know the definitions of fluence and energy fluence, and their units. How do fluence and energy fluence vary with distance from a point-like source of x-rays? Be able to scale the fluence specified at a particular distance rA to some new distance rB. How do fluence and energy fluence scale with mAs?
Fluence is photons/mm2, Energy Fluence is that times energy keV*photons/mm2
Both fall off as 1/R2 due to geometric beam divergence.
Both are linearly proportional to mAs.
Understand exponential attenuation. Calculate the number of primary x-rays transmitted through a slab of material, given: thickness, linear attenuation coefficient, and the number of incident x-rays.
N= x-rays transmitted
N0= incident x-rays
t= thickness
mu= linear attenuation coefficient
What are the three important x-ray-matter interactions, in the diagnostic energy range? Understand the concept of partial attenuation coefficients and partial mass attenuation coefficients.
In the diagnostic range, we see Rayleigh Scattering, Compton Scattering, and Photoelectric Effect.
Each of these has its own attenuation coefficient for how each process individually attenuates, summing these gives total attenuation coefficient.
To decouple attenuation from medium phase, divide by density to get mass attenuation coefficients.
How does dose correlate to collision Kerma and exposure?
Collision Kerma is energy lost from electrons in J/kg, while Exposure is charge over mass C/kg.
What is 1 Roentgen equal to, in SI units (Coulombs/kg) ?
1 Roentgen is 0.876 cGy in air kerma
What different components of an x-ray tube which filter the x-ray beam
Beam is filtered initially by the anode (Heel Effect), then the oil, then the window. Filters can also be added.
What does a “K-edge filter” do to an x-ray spectrum?
A k-edge causes a large spike in the spectrum due to an energy threshold now permitting more electrons to interact.
Draw a typical filtered x-ray spectrum.
See picture
What is the definition of half value layer?
A half-value layer (HVL) refers to the thickness of a specific material needed to reduce the exposure of a beam to one half of what it’d be without the material.
Calculate the half value layer of a monoenergetic x-ray beam, given the attenuation coefficient at the appropriate energy.
see equation
-ln(0.5)= 0.693
Understand the concept of equivalent photon energy and the “1/3 to ½ kVp” rule of thumb.
Equivalent energy of a diagnostic x-ray beam is generally ⅓ to ½ the maximum of the spectrum (kV).
Know a value for mR/mAs @ 100 cm, for some kV and total Al filtration. Apply this value to calculate an exposure value.
100kV and 10mR/mAs at 100cm is 2mm Al. (inherent 1mm Al, plus 1mm added).
What is the dependence of beam intensity (or energy fluence) on kV at the following locations: i) at the anode (Kramers theory), ii) after inherent and added filtration but before the patient, and iii) after patient filtration?
see picture
Intensity dependance on kV increases (powers i)V2, ii) V3-4, iii)V4-6)
Understand the basic stages found in all x-ray detectors (input x-rays, converter, secondary quanta, sensor, readout)
1.
- Input x-rays that were made in the anode fall to the converter/absorber
-
Converter converts x-rays into many secondary quanta
- Indirect conversion: uses phosphor to make optical photon quanta
- Direct conversion: uses photoconductors to make electrical quanta
- Secondary quanta fall onto an array of sensors or film that form a spatial distribution of the input quanta
- Spatially distributed secondary quanta from the sensor result in a readout image
What are the names of the two main types of converters, and what kind of secondary quanta do they produce?
- Indirect Conversion - uses a phosphor layer to generate many optical-range photons from incident x-ray photons. Photosensitive elements react to this light. May cause some blurring in initial conversion.
- Direct Conversion - uses a photoconductor to produce electron-hole pairs from incident x-ray photons. This charge is stored on element capacitors.
Understand the basic operating principles of screen/film, image intensifier/TV, imaging plate, flat panel detector, and solid-state CT detectors.
Screen/Film - silver halide crystals react to photons, become dark spots on an otherwise transparent film. Produces a permanent non-digital image. Indirect Conversion.
Image Intensifier/TV - bottle-shaped, takes input photons, converts to optical photons via CsI phosphor, then electrons, then accelerates down tube via bias- amplifies signal, then makes optical photons for viewing/recording via camera. Indirect Conversion.
Imaging Plate - Like screen, but does not re-emit absorbed light immediately, read off later with laser. Indirect Conversion, makes a digital image from readout.
Flat Panel Detector - May be direct or indirect, uses many small a-Si elements to store electric charge after secondary quanta for a digital output.
Solid-State CT - Uses segmented scintillator to produce secondary light photons, read off with 2D array of photodiodes.
Compare spreading of secondary quanta versus converter thickness, for i) unstructured phosphors, ii) structured phosphors, and iii) photoconductors.
In indirect conversion, unstructured phosphors allow secondary quanta to spread more than structured ones like CsI, which restricts it to the columnar shapes the phosphor is grown into. Photoconductors, in direct conversion, don’t allow any spreading of the signal.
What aspect of detector performance is affected by spreading of secondary quanta?
Spreading of secondary quanta like this lessens spatial resolution, blurring signal.
What aspect of detector performance is affected by converter thickness?
In indirect conversion, Greater thickness allows for more spreading of the secondary quanta (bad), but increases detector efficiency (good), since it allows for more assurance that photons will interact within the medium. (trade off resolution vs signal strength).
List desirable properties of a converter material.
- high Z
- high density
- high yield of secondary quanta per unit x-ray energy absorbed
- ability to fabricate in large area
- fast response / low afterglow
Describe the difference between an energy-integrating detector, a photon-counting detector, and an energy-resolved photon-counting detector.
Energy-Integrating: As above, the signal is the sum total of all the x-ray energy deposited in the medium.
Photon-Counting: Instead, counts the individual pulses of signal
Energy-Resolved Photon-Counting: can weight each counted pulse by its energy, can ditch low-energy pulses to optimize SNR
Be able to calculate the contrast of an object, given the appropriate material thicknesses, densities, and mass attenuation coefficients.
See picture.
Know the approximate expression for contrast in the low-contrast limit, for both added and embedded objects.
See picture.
Know the tissues/materials in the body that give rise to radiographic contrast. For each material, what physical properties are responsible for the contrast?
Mainly: Soft Tissue, Fat, Bone, Air, and Contrast Agents
Mass Attenuation coefficient, density, and thickness determine how each affects contrast.
What is the relationship between the mean and variance of a Poisson-distributed random variable.
Mean and variance are the same in Poisson distribution = lambda
What does the autocovariance function quantify?
SDNR combines contrast and SNR (sometimes SDNR is called CNR).
See image.
Use the Rose model to calculate the required fluence to detect an object with given area and contrast (or given quantities that allow you to determine contrast and area). What is a typical value for the parameter “k”? What does “k” represent?
Rose Model determines detectability threshold where N is photons incident, R is the whole image area, A is the area with differing contrast C (that we want to detect), and DQE is intrinsic detector efficiency.
K is whatever SDNR threshold is required to detect the object. Example value of 5 or so.
How can you interpret contrast-detail curve?
Objects on or above the curve are detectable in the system at hand. A lower curve is better, as it allows more things to be detected in the system.
What is SPR?
SPR stands for scatter to primary ratio. It shows how many scattered photons there are in respect to the primary photons.
What is SF?
SF stands for scatter fraction. It shows what fraction of the beam energy is from scatter, and what’s from primary photons
How does the presence of scatter reduce contrast? Be able to write expressions for contrast with and without scatter.
What is CDF?
CDF stands for Contrast degradation factor.
Given the mean x-ray fluence incident on an ideal counting aperture, and the area of the aperture, be able to calculate: mean counts, variance in the counts, standard deviation in the counts, counts signal-to-noise ratio, and the noise in normalized image data.
In a normalized image, a simple scalar (g) is multiplied onto mean counts and standard deviation. SNR is unchanged, but, when normalized, noise becomes proportional to 1/sqrt(N), the inverse of SNR.
What is the definition of grid primary transmission?
Primary transmission= (Transmitted primary)/ (Incident primary)
Secondary transmission= (Transmitted secondary)/ (Incident secondary)
What is grid selectivity?
What is Bucky factor?
Grids reduce all incoming radiation. In film detectors, some baseline amount of radiation is needed to form a proper image- this is corrected by increasing the mAs by this factor B.
When a grid is used, how does the detected scatter fraction change?
Does a grid reduce patient exposure requirements to achieve a given SDNR?
Grids usually lower exposure for a given SDNR, but there are some tradeoffs and it is not guaranteed.
What is the convolution model of blurring, and the concept of a point spread function (PSF), and scaling relationships?
In image space, convolving a Point Spread Function (PSF) with points on the image to account for blurring that occurs due to physical limitations (focal spot not a perfect point, detector elements not perfect points, patient motion). These are further affected by any magnification in the setup.
For a rectangular focal spot of width ‘fs’ at the source plane, what is the focal spot PSF width at the image plane? What is the focal spot PSF width referenced back to the object plane?
The focal spot PSF is a rect function with width equal to the focal spot, with some adjustment for magnification.
At image plane: fs(m-1)
At object plane: fs(m-1)/m
For a model of linear object motion in a plane, what is the width of the PSF in the image plane and at the object plane? How does this PSF depend on object velocity and exposure time?
Rect function with width reliant on velocity and exposure time (it’s assumed that the motion is of constant velocity during scan)
At image plane: mvt
At object plane: vt
For a detector aperture of width ‘a’ at the image plane, what is the width of the PSF at the image plane and at the object plane?
At image plane: a
At object plane: a/m
What is the Fourier transform of the rect function? If the rect function has width ‘a’, what is the spatial frequency of the “first zero” of the sinc function? If the rect is normalized to unit area, what is the value of the sinc function at zero spatial frequency?
The Fourier Transform of a rect function is a Sinc function.
If the rect has width a, the sinc has zeros at n/a, so larger width rectangles make the first zeros come quicker and faster. Physically, this is as if larger PSF make MTFs discard higher frequencies ‘sooner’
A unit area rect makes sinc(0) = 1
Sinc(0)=a*h (where h is the height of rect)
Focal spot vs. detector blurring.
- How does a) focal spot, b) detector and c) motion blurring behave with respect to magnification?
- Given a focal spot size (f) and detector aperture size (a), determine the optimal magnification.
a) Focal spot MTF goes down with magnification
b) Detector MTF goes up with magnification
c) Motion MTF doesn’t depend on magnification
2. Optimal magnification occurs where the first zero of the focal spot MTF (at the object plane) is equal to the first zero of the detector aperture MTF (at the object plane).
What should the sampling interval be to ensure no loss of information?
Given maximum frequency uNyquist, the sampling spacing ∇x should follow:
Given a particular sampling interval, what is the Nyquist frequency?
What happens when the analog signal to be sampled contains spatial frequencies above the Nyquist frequency?
In general, uNyquist ≤ 1/ (2 ∇x)
Failing to meet these criteria results in signal aliasing, making replications over our proper image.
What is DQE?
DQE stands for Detective Quantum Efficiency
Also DQE= NEQ/ N
What is NQE?
NQE stands for Noise-equivalent quanta
Conceptualize as: “An image generated by an imperfect system looks the same as an image that was generated by a perfect system using fewer photons. The NEQ is the mean of that reduced number of photons.”
What is QDE?
QDE is the quantum detector efficiency.
It is the best case scenario for DQE, refers to how many of the incident photons actually interact within the detector.
What are the signal and noise propagation equations in respective detector gain stages?
See image.
How does stochastic gain degrade DQE?
Stochastic gain degrades DQE by adding in the variance of its own gain, as well as amplifying existing variances by the gain
Derive an expression for the line integral of attenuation coefficient in terms of the number of x-rays transmitted along a ray and the number of x-rays entering the patient.
What is the definition of the Hounsfield Unit (CT number).
Hounsfield units are derived from the attenuation coefficient relative to water at some point, normalized.
Write an equation for a line parallel to the yr-axis and intersecting the xr-axis at a specific value.
Holding xr constant, this makes a line (equation).
This simulates the x-ray beams’ orientation
If a measurement is made along a specific line in object space, what does that correspond to in sinogram space?
A line intergal through object space maps to a point in the sinogram space.
The point in sinogram space will be located at (phi, xr), as per the line image space.
What do all of the lines through a fixed object point map to, in sinogram space?
All the lines through a fixes object point map to a cosine curve in the sinogram space.
According to: xr = r×cos(theta- phi) , this maps out a cosine curve with amplitude r, and initial ‘phase shift’ theta.
If we were mapping to a yr-phi system, we’d have a sine curve instead.
Calculate the required angular interval given the detector sampling pitch and the field-of-view size.
This can also be called ‘the number of views’ needed.
For units of degrees:
What are the definitions and relationships between CTDI100, CTDIw, and CTDIvol.
CTDI stands for CT Dose Index.
What is the pitch of a helical scan?
Where N = number of slices collected, T = slice thickness, and I = table increment between scans.
What is the CTDIvol for a helical scan based on CTDIw?
What is the effective mAs for a scan?
Effective mAs scales each slice by how long it is exposed. Pitch <1 (lingers/double doses) results in an increased mAs, while pitch >1 (skips sections) will lower it.
How does the noise level in the reconstructed image (standard deviation in HU) depend on the effective mAs?
Increasing effective mAs reduces noise by a factor of 1/root(mAs)
Also based on slice thickness and, though unchangeable, DQE
