Medical Imaging 1 Final

The number of electrons accelerated across an x‐ray tube is most strongly influenced by

filament current

Increasing the filtration of an x‐ray beam reduces

Average energy and HVL

Which of the following generators will likely have the largest waveform ripple?

Single phase

The heel effect is most likely to increase when reducing the

Andode angle

Adding an aluminum filter to an x‐ray beam most likely increases x‐ray

Beam hardening

 At the same peak voltage, which generator deposits the most energy into an anode?

3 phase (12 pulse)

The x‐ray tube output increases when reducing the

 Filtration

The adequacy of the filtration of an x‐ray tube is best determined by measuring the

Half-value layer

For a fixed kVp, which type of X-ray generator likely results in the shortest exposure time?

High frequency

The maximum photon energy in the x‐ray beam is determined by the x‐ray tube:

Voltage

Characteristic x‐rays are characteristic of the material in the

Anode

100keV electrons most likely produce x‐ray photons with an average energy (keV) of:

45 keV

The power (W) dissipated in the x‐ray tube filament is approximately

400 W

The most likely X-ray tube target material is

tungsten

A high-frequency generator is capable of producing a maximum of 1200 mA at 100 kVp with 100 msec exposure. What is the rating of this generator?

P = 100kVp * 1.2A = 120kW

The ratio of primary to secondary turns, voltage and current in the transformer

Np/Ns=Vp/Vs=Is/Ip

Actual anode focal area to projected anode focal area.

a=A*sin(theta)

Electrons passing through matter lose energy primarily by producing:

Atomic ionizations

The likelihood of Compton interaction is best quantified using:

Electron density

An x-ray beam, attenuated by three half-value layers, is reduced by a factor of:

8

The total number of atomic ionizations produced following absorption of a 30 keV photon is approximately:

10000

The linear attenuation coefficient at a certain wavelength is 0.1 cm-1. How much radiation is lost in 1mm:

1%

The mass attenuation coefficient does not depend on the absorber:

Physical density

At what photon energy (keV) are photoelectric and Compton effects approximately equally probable in water?

25 keV

How many bits are required to store 4096 shades of gray?

12

The theoretical limit of the vertical resolution (in line pairs) achieved with a 525-line TV monitor is approximately:

262

The MTF value (%) for the lowest spatial frequencies is most likely:

100%

The energy dependence of the photoelectric absorption above the K edge varies as:

1/E^3

For a given absorber, if the Compton attenuation coefficient at 50 keV is 0.1 cm-1, its value at 100 keV is most likely:

0.05 cm^-1

The energy lost per unit length along the track of charged particles is most likely the measure of:

ionization

The most likely percentage of coherently scattered photons in an x-ray beam emerging from a patient having a chest x-ray is:

< 5

According to the Rose criterion for low-contrast detection, the SNR should be

> 5

The maximal frequency of the signal is 2MHz. To limit aliasing and avoid oversampling, the sampling frequency should be in the range:

5-6 MHz

Compton scattering equation

E = E_0/(1+(E0/(mc²))(1-cos(theta)))

The standard deviation of an NM image pixel is 10. What the average of this pixel would likely be:

100

The standard deviations of independent measurements A and B are 1 and 4, respectively. Therefore, the standard deviation of their difference is approximately:

4

Diagnostic procedure has no value if the area under the ROC curve (%) is:

50%

For the normally distributed measured parameter with the mean of 10 and the standard deviation of 4, its variance equals to:

16

A receiver operating characteristic curve likely measures:

Test performance

Relaxing the threshold criterion in an ROC study increases the false-positive fraction as well as the test:

Sensitivity

How much area under the normal curve does a 93% confidence interval cover? What is the probability of observing a value outside of this area?

Area = C = 0.93. The probability of observing a value outside this area is 7%.

What are the types of Errors?

Blunders, systematic errors, and random errors.

Blunders can be incorrect instrument settings and incorrect labeling of containers

Systematic errors can be length measurements with a warped ruler, instrument malfunction, or observer bias

Random errors can be differences between members of a population, radiation counting measurments, or electronic noise in a circuit

Precision vs Accuracy.

Precision is the reproducibility of a measurement

Accuracy is how close the measurement is to the true value of the quantity measured → (TP+TN)/Total

What are Mean, Median, Mode, and Range?

The mean is the average, the median is the value that separates the data into two equal subsets, the mode is the value with the most observations, and the  range is the difference between the largest and the smallest

Standard Deviation and Variance.

Standard deviation is a measure of variability: = sqrt(1/N(x_1-mean)^2 +...)

Variance = stdv^2

What is percent uncertainty?

% uncertainty = stdv/mean * 100

Poisson distribution.

P(N;m)=(e^-m * m^N)/N!

P is the probability of getting a result N when the true value is m

Variance is m, and standard deviation is the square root of m

When m is large Poisson → Gaussian

Gaussian distribution.

m is the mean, and 2 is the variance

It is a continuous probability distribution

Central limit theorem.

The mean of a sufficiently large number of independent, identically distributed random variables, each with a finite mean and variance, will be approximately normally distributed according to the Gaussian distribution.

Confidence level, common choices, and area.

C gives the probability that the interval produced by the method employed includes the true value of the parameter m. 

Common choices are 0.9, 0.95, and 0.99

Area under each tail of the curve = (1-C)/2 → For a 95% confidence interval the area under each tail = (1-0.95)/2 = 0.025

Standard deviation for Poisson and Gaussian.

Poisson: = m

Gaussian: can be any value. When m becomes large, = m

In what domains can images be represented?

Temporal: display in terms of time → Oscilloscope display or time lapse (blood flow)

Spatial domain: display in terms of position (2D or 3D) → photographs, radiographic images

Frequency domain: reduces image to underlying frequencies and shows how much of the signal lies within each frequency.

Transform between image domains.

Can transform from spatial or temporal to frequency using the Fourier transform

What are the three types of contrast?

Subject (radiographic) 

Detector

Display

Subject (Radiographic) contrast, and what does it depend on for the following imaging modalities: X-ray, Nuclear medicine, MR, US, optical, and Terahertz.

Contrast due to changes in the subject. 

X-ray: tissue composition

NM: the ability of tissue to concentrate the radioactive material

MR: proton density and relaxation phenomena

US: acoustic properties

Optical: photochemical reactions, tissue composition, and ability of the tissue to concentrate molecular markers

Terahertz: tissue composition

Subject contrast equation:

C=(Nb-Nc)/Nb

Number of photons passed the background material 

Number of photons passed the background and contrast material

Nb=N0*e^-mu*L

Nc=N0*e^-mu(L+x)

C=1-e^-mu*x

Detector contrast.

Determined by the response of the detector to an incoming signal. Conversion efficiency depends on the exposure and the wavelength of the input signal

Contrast to noise ratio and optical density equation:

CNR=(Na-Nb)/stdv

OD=log(I0/I)

Display contrast:

Contrast the reproducibility of the display mechanism → A computer screen can be a limiting factor for contrast

Window width and window level:

Significant in Display contrast. Window width is the range of the grayscale values that can be displayed, and the window level is the center of the window width.

Spatial resolution:

The ability of an image system to distinctly depict two objects as they become smaller and closer together

Different functions to measure spatial resolution.

Point spread function (PSF)

Line Spread function (LSF)

Edge spread function (ESF)

Types of PSFs:

Point stimulus

Isotropic PSF

Non-isotropic PSF

Explain full-width half max with the equation.

Width of a function at half of the maximum → the minimum distance that the two points must be separated to be distinguishable

Positive predictive value:

Representation of the probability that a positive result is a true positive

Negative predictive value:

Representation of the probability that a negative result is a true negative

Sensitivity:

Measures the proportion of true positives identified correctly → A high positivity means that the positives were correctly identified

Specificity:

Measures the proportion of true negatives identified correctly → A high specificity means that the negatives were correctly identified

Contrast Transfer function and limiting resolution:

Shows the ability of an imaging system to transfer contrast of objects of different sizes in the presence of blur. 

The shape of the CTF curve depends on the sources and distribution of blur within the system. 

The CTF curve has a specific point at which the contrast becomes zero. This is referred to as the disappearance frequency and represents the resolution limit 

The limiting resolution of a system is given in lp/mm, typically 3-20%

What imaging modality has the highest resolution?

Radiography

Modulation transfer function:

a measure of how well an optical system, like a lens, transfers contrast from an object to an image.

It quantifies the system's ability to reproduce contrast at different spatial frequencies, effectively indicating its resolution and contrast sensitivity. A high MTF means the lens can reproduce fine details with good contrast, while a low MTF means it struggles to reproduce fine details, resulting in a blurrier image.

Typically, higher frequencies are dampened more than the lower frequencies due to stronger blurring by the detector. 

Max at low spatial frequencies and min at high spatial frequencies → max contrast at spatial frequencies close to 0, preserving contrast for larger objects

What does radiographic contrast depend on?

Subject mass attenuation coefficient, Elemental composition of subject, electron density, physical density, subject thickness, incident x-ray spectrum

What does detector contrast depend on?

exit x-ray beam spectrum, detector attenuation coefficient

What does display contrast depend on?

Window and level in electronic image display

How does photon energy effect radiographic contrast?

Low energy photons result in high radiographic contrast

Explain filtering for contrast enhancement

“Shaping” of an x-ray spectrum by adding a filter. A metallic filter should have a k-edge slightly higher than the contrast agent. Photons transmitted through the filter will be attenuated by the contrast agent.

Dual energy subtraction imaging

Image = Image2 - k*(Image1). Take images at two different energies and subtract to emphasize an object

Three possible results for x-ray incident on matter

Penetration, Absorption, Scatter

The ratio of scattered x-rays to primary x-rays can be what value? It increases with:

5 or higher

It increases with beam width and object thickness

Scatter fraction of x-rays

SF = S/(S+P)

Scatter reduction

Anti-scatter grid - narrow bars of lead placed between object and detector. scattered x-rays are absorbed and primary x-rays pass through.

Grid ratio

H/W: strip height to gap between strips

Bucky factor

Ratio of radiation incident on the grid to the transmitted radiation. typical values: 2-6

Explain Screen/Film systems

X-rays emitted and pass through patient. remaining x-rays reach intensifying screens inside the cassette. intensifying screen converts x-rays into light which exposes the film, the film is processed.

Calculate the approximate # of green photons (with energy of 2.7 eV/photon) that will be generated by 50keV x-ray photon is the efficiency is 15%

50000 eV * 0.15 = 7500 eV

7500 eV / 2.7 eV/photon = 2800 photons

How does the thickness of the screen in the screen/film systems affect the image

A thicker screen will produce a lot more photons but there will be less resolution

Computed radiography

Cassette based system. A plate is loaded in cassette and a latent image is captured by imaging plate. plate is processed to release latent image

Digital radiography

projection x-ray imaging based on digital detectors. Digital detectors are charge integrated digital detectors or photon counting digital detectors