Frequency and Phase Encoding
- What are the units for angular frequency (ω)?
- Hertz (Hz)
- Cycles per second (cps)
- Radians per cycle
- Radians per second
Angular frequency (ω), also known as radial or circular frequency, measures angular displacement per unit time. Its units are therefore degrees (or radians) per second. Link to Q&A discussion
- Approximately how many degrees are in one radian?
- 30.0º
- 45.0º
- 57.3º
- 71.7º
By definition, 2π radians span the arc of one circle, or 360º. So 1 radian = 360/2π ≈ 57.3º Link to Q&A discussion
- A 180º-pulse is sometimes expressed using radians as a
- π/2-pulse
- π-pulse
- 3π/2-pulse
- 2π-pulse
A 180º-pulse is half a circle, or a π-pulse. Link to Q&A discussion
- As gradients are turned on and off, the angular frequency (ω) of a spin changes with time (t), expressed by the function ω(t). The area under the graph of ω(t) vs t between two time points (A and B) represents
- The spin’s accumulated phase shift between A and B
- The spin’s change in frequency between A and B
- The energy acquired by the spin between A and B
- The change in field strength experienced by the spin between A and B
The area under the ω(t) vs t curve represents the accumulated phase of the spin during a certain interval. From a unit perspective, frequency is measured in radians or degrees per second while time is measured in seconds, so their product [ω(t) x t] will have units of radians (or degrees). Link to Q&A discussion
- The MR signal information received by the RF-coil can be classified as
- Frequency modulated
- Amplitude modulated
- Phase modulated
- Pulse modulated
MR signal information, typically encoded over a range of 50-100kHz, arrives at the receiver amplitude-modulated on the RF carrier wave (e.g. at 64 MHz). The first step in signal process is called demodulation, which removes the carrier. Link to Q&A discussion
- The real and imaginary components during of an MR signal in the I and Q channels of a receiver are measured at a specific time point to be 3.0 and 4.0 au (arbitrary units) respectively. What is the actual magnitude of the signal?
- 3.5 au
- 5.0 au
- 7.0 au
- 12.0 au
The magnitude (M) = [Re² + Im²]½ = [3² + 4²]½ [25]½ = 5.0 au. Link to Q&A discussion
- Concerning Fourier representation of the MR signal, which of the following statements is false?
- The Fourier expansion of a signal can be written in either trigonometric or exponential form.
- To represent any real signal exactly, an infinite number of frequency components must be included in its Fourier representation.
- The Fourier transformation converts a time-based signal into the frequency domain, but the change cannot be reversed.
- The Fourier series representation of an MR image is always cut short (truncated).
All are true except for (c). Fourier transformation is the mathematical procedure connecting a time domain signal, s(t), and its frequency domain representation, S(ω). The inverse Fourier transform converts S(ω) back to s(t). Link to Q&A discussion
- The time domain signal, s(t), that corresponds to a uniform/rectangular band of frequencies in S(ω) is called a
- Double exponential
- Sinc function
- Gaussian
- Lorentzian
The sinc function, sinc(t) = [sin t]/t, Fourier transforms into a uniform band of frequencies, such as those used to define a slice profile in conventional 2D MR imaging Link to Q&A discussion
- Which of the following scientists did not win the Nobel Prize for their work in NMR?
- Felix Bloch
- Raymond Damadian
- Paul Lauterbur
- Peter Mansfield
Raymond Damadian did not win the Nobel Prize for his work and considered it a personal injustice. He placed full-page ads in several large world newspapers urging the Nobel committee to change their minds, which they never did. Link to Q&A discussion
- Which of the following is not a method for spatial localization of the MR signal?
- Frequency encoding
- Phase encoding
- Location of receiver coils
- Amplitude modulation
Choice (d), amplitude modulation, refers to the shape of transmitted or received RF-pulses but is not by itself a method of spatial localization. Link to Q&A discussion
- Which of the following statements about frequency encoding is incorrect?
- It commonly used for in-plane localization for 2D imaging.
- It is commonly used for slice selection in 3D imaging.
- Each voxel actually contains a range of frequencies, not just a single frequency.
- For most applications a linear frequency encoding gradient is desired.
All are correct except (b). Frequency encoding is commonly used for slice selection in 2D imaging, but phase encoding is typically used for slice selection in 3D. Link to Q&A discussion
- What is a typical total receiver bandwidth for a 1.5T MR scanner?
- 1 kHz
- 50 kHz
- 250 kHz
- 500 kHz
Receiver bandwidth is an operator-selectable parameter, chosen by the technologist before the scan begins. Available values for total receiver BW range from about 5-100 kHz with 50kHz being typical. Link to Q&A discussion
- What is the width of a pixel in the frequency encoding direction if the field-of-view is 25.6 cm and 512 frequency-encoding steps are used?
- 0.5 mm
- 1.0 mm
- 2.0 mm
- 5.0 mm
Pixel width = FOVf ÷ # frequency encode steps = 256 mm ÷ 512 = 0.5 mm. Link to Q&A discussion
- If 256 complex measurements of a digitized MR signal are sampled in a period of 5.12 ms, what is the dwell time?
- 5 μs
- 10 μs
- 20 μs
- 200 μs
The dwell time is the interval between digitized samples. So if 256 samples were obtained over a 5.12 ms period, the dwell time would be 5.12 ms/256 = 20 μs. Link to Q&A discussion
- What is the total receiver bandwidth if the interval between digitized samples (dwell time) is 25 μs?
- 2,500 Hz
- 25,000 Hz
- 40,000 Hz
- 50,000 Hz
Total receiver BW is the same as the digitization rate of the MR signal. In equation form, BW = 1/td = 1/(25 μs) = 40,000 Hz. Link to Q&A discussion
- In clinical MR imaging at 1.5T, what frequency range would be typical for setting the receiver to “narrow bandwidth”?
- 1 – 5 kHz
- 5 – 20 kHz
- 50 – 52 kHz
- 100 – 101 kHz
A typical range for narrow receiver bandwidth would be choice (b), 5 – 20 kHz. Link to Q&A discussion
- Which of the following statements about narrow bandwidth is incorrect?
- Narrow BW implies reduced sampling time.
- Narrow BW increases signal-to-noise.
- Narrow BW accentuates chemical shift artifacts.
- Narrow BW accentuates susceptibility artifacts.
Option (a) is false. Bandwidth is inversely proportional to sampling time. A synonym for "narrow bandwidth" is therefore "extended sampling time". Link to Q&A discussion
- Which of the following statements about transmitter bandwidth is true?
- It is automatically determined once receiver bandwidth is specified.
- Transmitter BW per se is not directly adjusted by the technologist when specifying scan parameters.
- Typical values for transmit BW are 50-100 kHz.
- Most modern RF-pulses for 2D slice-select are sinc-shaped.
The transmit bandwidth is not usually user-adjustable, so choice (b) is true. Typical values are 1000-2000 Hz and are independent of receiver bandwidth. Simple sinc pulses are no longer used for slice select, being supplanted by more sophisticated designs using the SLR algorithm. Link to Q&A discussion
- Cross-talk can be reduced by all of the following methods except:
- Increasing gaps between slices
- Increasing the strength of the slice-select gradient
- Performing slice interleaving
- Improving the RF slice profile
Increasing the strength of the slice-select gradient will only serve to produce thinner slices, not improve cross-talk. Link to Q&A discussion
- The earliest commercial version of simultaneous slice excitation (offered by GE in the 1990s) applicable to single-channel RF coils was called
- Phase Offset MultiPlanar (POMP)
- MultiBand (MB)
- Simultaneous Multi-Slice (SMS)
- HyperBand (HB)
The historical precursor to modern MB/SMS methods was POMP (Phase Offset MultiPlanar) imaging. The POMP technique used a composite RF-pulse to simultaneously excite two slices, each of which were phase-encoded over only one-half of the total field-of-view (FOV). Phase alternation allowed the two slices to be separately reconstructed without overlap. Unlike SMS, POMP does not utilize parallel imaging technology and is hence applicable to single-channel RF coils. Link to Q&A discussion
- Which of the following statements about MultiBand/Simultaneous Multi-Slice imaging is false?
- Use of parallel imaging arrays is required.
- Acceleration factors of 2-4 are typical.
- The slices must be widely spaced apart (2-3 cm).
- The technique imposes a significant penalty in terms of signal-to-noise.
MB uses coil encoding together with either gradient- or RF-encoding to resolve data along the slice-select (z)-axis. Because modern coil arrays typically have only a few coil elements in the z-direction, coil sensitivity differences along that axis are rather poor. Accordingly the simultaneously excited slices must be spaced widely apart (typically at least 25−30 mm). Unlike standard parallel imaging acceleration techniques, MB/SMS acceleration results in little to no penalty in signal-to-noise. (Option d is false). This is because neither the echo train length, number of phase-encoding steps, nor number of k-space samples has been reduced as occurs in conventional parallel imaging acceleration methods. Link to Q&A discussion
- What is the approximate in-plane pixel dimensions of a 25 x 25 cm FOV image acquired using 192 phase-encoding steps and 512 samples in the frequency direction
- 1.3 x 0.5 mm
- 2.6 x 0.5 mm
- 1.3 x 5.0 mm
- 2.6 x 5.0 mm
The pixel width in the phase encode direction is 250 mm ÷ 192 ≈ 1.3 mm, while that in the frequency encode direction is 250 ÷ 512 ≈ 0.5 mm. Link to Q&A discussion
- Concerning 2D Fourier Transform imaging, which statement is false
- The number of unique echo signals equals the number of phase-encoding steps.
- The phase shifts between successive echoes are multiples of 180º.
- For low-amplitude phase-encodings the MR signal is strong but provides little information about spatial detail.
- For high-amplitude phase-encodings the MR signal is weak and provides little information about image contrast.
Choice (b) is false. The phase shifts between the rows are not simple multiples of 180°, but vary from echo to echo depending on the size of the phase-encoding step. The number of echo signals acquired equals the number of phase encode steps, which is usually 192 or 256. For low order phase-encodings, the MR signal is strong. The frequency projection approximates the general shape of the object but lacks edge definition. The higher order phase encode steps have smaller MR signals but provide more information about spatial detail, such as the location of edges. Link to Q&A discussion
- Why is the phase-encode direction often chosen along the shortest anatomic dimension?
- This reduces wrap-around artifact.
- This reduces flow-related artifact.
- This reduces artifacts from gross patient motion.
- It is a requirement for parallel imaging.
Wrap-around (also called aliasing) occurs when the size of the body part imaged exceeds the defined field-of-view (FOV) in the phase-encode direction. This causes anatomy outside the FOV to be folded in over the main part of the image. To avoid wrap-around the phase-encoding direction is usually chosen to be along the shortest anatomic dimension. Flow-related and other motion artifacts may be moved around by changing the phase-encode direction, but the best direction is based on the location and types of these artifacts, which may or may not be best along the shortest dimension. For parallel imaging there may be some restrictions on possible phase-encode directions allowed, but setting phase-encode along the shortest axis is not necessarily required. Link to Q&A discussion
Scanning and Quality Control
- Which steps in setting up an MR scan are in the proper chronological order?
- Set landmark → Perform prescan → Acquire localizer → Position slices
- Acquire localizer → Position slices → Set landmark → Perform prescan
- Set landmark → Acquire localizer → Position slices → Perform prescan
- Perform prescan → Acquire localizer → Set landmark → Position slices
Choice (c) shows the correct order. Link to Q&A discussion
- Which process in the list below is not a part of automatic prescan?
- Specific Absorption Rate (SAR) estimation
- Quick shimming
- Center frequency adjustment
- Transmitter gain adjustment
- Receiver gain adjustment
Specific Absorption Rate (SAR) is estimated by the scanner based on the patient’s body weight, pulse sequence, and pulse sequence parameters selected. This occurs before automatic prescan, allowing the operator to adjust parameters to keep SAR within established limits. Automatic prescan is essentially the last step before the actual scan begins. Link to Q&A discussion
- In which of the following situations is manual shimming (in addition to prescan quick shimming) nearly always required?
- Diffusion-weighted imaging
- MR Spectroscopy
- Fast-spin echo imaging
- Dixon fat-water imaging
Very detailed high-order shimming is mandatory for spectroscopy. Although spectroscopy shimming can be automated, the settings always require review and often tweaking by the MR technologist. Link to Q&A discussion
- In which of the following situations is center frequency adjustment most critical?
- When using spatial saturation pulses
- When using flow saturation pulses
- When using arterial spin labeling pulses
- When using fat saturation pulses
The center frequency may be set on water protons, fat protons, or some average of the two. Accurate center frequency setting is particularly important when spectral fat saturation pulses are employed to make sure the fat peak is adequately suppressed. Link to Q&A discussion
- What artifact will occur if the receiver attenuator value is set too low during prescan?
- Data clipping
- Wrap around
- Ghosts
- Diffuse noise
If the attenuator value is set too low (i.e., receiver gain is set too high), then the signal will overload the analog-to-digital converter, and data clipping will occur. Since the largest peaks of the MR signal typically are the low order phase-encode steps at the center of k-space, data clipping interferes with image contrast. The result is an image with an "eerie" appearance Link to Q&A discussion
- What is the purpose of dummy cycles during prescan?
- To adjust RF-voltage to achieve a perfect 90º-pulse
- To allow warm-up of the transmit and receive circuitry
- To optimally match coil impedance with that of the patient
- To allow steady state longitudinal and transverse magnetization to be established
Once RF-excitation begins, the longitudinal and transverse magnetizations need time to reach their steady-state values. During prescan the scanner plays out several cycles of the sequence without recording a signal. These are called dummy cycles, disabled, or discarded acquisitions (DDA). The precise number of dummy cycles depends on the TR and the sequence chosen. Only once the system is near equilibrium does data collection begin. Link to Q&A discussion
- To sell an MR scanner in the United States, a company must receive what kind of premarket clearance from the Food and Drug Administration?
- 401(k)
- 501(k)
- 1099
- 457(b)
In the United States the Food and Drug Administration (FDA) has statutory authority to regulate the sale and use of MRI equipment. MRI scanners are considered Class II devices, meaning that they have the potential for human harm and require pre-market 501(k) clearance prior to marketing. The FDA has issued guidance documents with non-binding (but strongly suggested) criteria — including those related to hardware, software, performance, site planning, and safety — to attain this premarket approval. The other numbers are all IRS forms and investment accounts unrelated to MRI Link to Q&A discussion
- Which of the following organizations does not offer MRI accreditation in the United States?
- American College of Radiology (ACR)
- Centers for Medicare & Medicaid Services (CMS)
- RadSite
- The Joint Commission (TJC)
In the US there are four MRI accrediting organizations that are currently sanctioned by the Centers for Medicare & Medicaid Services (CMS) – the American College of Radiology (ACR), the Intersocietal Accreditation Commission (IAC), The Joint Commission (TJC), and RadSite. Link to Q&A discussion
- Which of the following quality control measurements must be performed at least weekly on an MR scanner?
- Center frequency
- Magnetic field homogeneity
- Slice thickness accuracy
- Monitor resolution
Daily QC activities include visual inspection of all scanner hardware, the function of safety and communication devices, and general assessment of image quality including identification of artifacts. On at least a weekly basis, a special MR phantom is placed in the scanner and various measurements are made and recorded. Such measurements include landmark accuracy (table position), center frequency, image uniformity, transmitter gain or attenuation, geometric distortion, spatial resolution, artifact evaluation, and signal-to-noise ratio. Other more sophisticated testing should be performed semiannually or yearly by a medical physicist. Link to Q&A discussion
- The most common cause of geometric errors is
- Warping of the MR phantom
- Abnormal RF-coil impedance
- Miscalibration of one or more imaging gradients
- Center frequency drift
The most common cause of geometric errors is miscalibration of one or more imaging gradients. Gradients tend to drift over time and require periodic re-calibration by service engineers. Occasionally the problem is caused by Bo inhomogeneity due to improper shim adjustments or an occult ferromagnetic object lodged in the scanner bore. Link to Q&A discussion
- Detailed procedures and standards for the two most commonly used methods of measuring signal-to-noise in a phantom come from which organization?
- The National Electrical Manufacturers Association (NEMA)
- The International Electrotechnical Commission (IEC)
- The International Commission on Non-Ionizing Radiation Protection (ICNIRP)
- The American Society for Testing and Materials (ASTM International)
The National Electrical Manufacturers Association (NEMA) provides detailed methods and standards for evaluating all types of electrical devices. Those relating specifically to MRI quality include how to measure signal-to-noise (MS 1, 6, & 9), geometric distortion (MS 2 & 12), and uniformity (MS 3). Link to Q&A discussion
- When complex-valued MR signal data is converted into a magnitude image, the noise statistics are best described using a
- Gaussian (normal) distribution
- Poisson distribution
- Gamma distribution
- Rician distribution
Because region-of-interest (ROI) measurements are typically made on magnitude-reconstructed images, some correction to the statistics must take place. Recall that "raw" MR data is a complex number with real and imaginary parts. When converted to a magnitude only image, the pixel values corresponding to noise are no longer Gaussian, but skewed into a so-called Rician distribution. Link to Q&A discussion
- The section of an MR phantom consisting of closely spaced lines or holes containing material with strong difference in signal intensity from the background is used to measure
- Low-contrast object detectability
- Geometric distortion
- High-contrast spatial resolution
- Image uniformity
The high-contrast portion of MR phantoms contains closely spaced lines, edges, or holes containing material with strong differences in signal intensity from background. Low-contrast resolution refers to the ability to identify small holes in the phantom with only slightly different relaxation times from background. Link to Q&A discussion
- The section of an MR phantom consisting of triangular ramps or wedges oriented at a known angle is used to measure
- Slice thickness
- Slice position
- Linear accuracy
- Low-contrast resolution
The most common method to estimate slice thickness is to use a phantom containing triangular ramps or wedges whose surfaces are oriented at a known angle (θ) to the plane of the slice. When a slice passes through the ramp, it produces a stretched "shadow" image whose full width half maximum (FWHM) can be estimated. Link to Q&A discussion