MRI102 Ch6 Quiz Review

Question-and-Answer cards covering MRI sampling, Nyquist, bandwidth, k-space organization, matrices, gradients, NEX, and scan-time calculations.

What is the primary purpose of sampling in MRI?

To convert the physical (analog) MR echo into a digital signal that the computer can store and process.

During which step of the imaging process does sampling occur?

Sampling is performed while the echo is being read (during the acquisition/sampling window).

Define sampling frequency (Fs).

The rate at which data points are taken from the echo— numerically identical to the receiver bandwidth when the Nyquist criterion is met.

Define sampling interval (Δt).

The time between consecutive samples; it is the inverse of the sampling frequency (Δt = 1/Fs).

How are sampling frequency and sampling interval related?

They are inversely related— if sampling frequency increases, the sampling interval decreases, and vice-versa.

List two consequences of increasing the sampling frequency too much.

1) Shorter sampling interval → more data points → larger raw data set and longer reconstruction time. 2) More noise is sampled, potentially darkening the image and (sometimes) lengthening scan time.

What is the effect of decreasing the sampling frequency below optimum?

Under-sampling occurs, leading to aliasing artifacts and loss of resolution/information.

State the Nyquist theorem as used in MRI.

To avoid aliasing, the echo must be sampled at a frequency at least twice the highest frequency present in the signal.

Why is the Nyquist theorem important in MR sampling?

It defines the minimum acceptable sampling frequency to faithfully digitize the echo without aliasing and determines the required receiver bandwidth.

What artifact arises when the sampling frequency is set too low?

Aliasing (wrap-around) caused by under-sampling.

Define received bandwidth (RBW).

The range of frequencies allowed to pass through the receiver filter and be sampled during the acquisition window.

How are received bandwidth and sampling frequency related when Nyquist is satisfied?

They have the same numerical value (RBW = Fs).

Describe the ‘filtering’ function of received bandwidth.

RBW acts like a band-pass filter, accepting frequencies within its range and rejecting frequencies above and below it, thereby controlling how much signal and noise are sampled.

How does increasing RBW affect SNR?

A wider RBW allows more noise as well as more signal, so overall SNR decreases.

What happens to the center frequency when RBW is widened?

The center frequency shifts (typically to the right on the spectrum diagram) to keep the acquisition window symmetric about the echo peak.

Define a data point in MR sampling.

A single digitized sample of the echo amplitude stored as a number in k-space.

What is k-space?

A storage matrix that holds raw frequency and phase information about the image before reconstruction.

How does k-space differ from the final MR image?

K-space is not the image; it contains raw data that the Fourier transform converts into the spatial domain image.

Which axis of k-space corresponds to phase encoding?

The vertical axis.

Which axis of k-space corresponds to frequency encoding?

The horizontal axis.

How many k-spaces are generated in a scan?

One k-space per slice (e.g., 15 slices → 15 separate k-spaces).

What does the Fast Fourier Transform (FFT) do in MRI?

It converts filled k-space data into the spatial domain image, assigning bright pixels to high signal amplitudes and dark pixels to low amplitudes.

Which gradient selects the k-space line filled during each TR?

The phase-encoding gradient; its amplitude determines which line (positive or negative side).

How does gradient polarity during frequency encoding affect data fill?

Positive polarity fills a line from the center to the right edge; negative polarity fills from the center to the left edge.

Where are high-amplitude signals stored in k-space and what information do they provide?

In the central lines; they govern image signal and contrast.

Where are low-amplitude signals stored in k-space and what information do they provide?

In peripheral (outer) lines; they determine spatial resolution (detail).

Explain conjugate symmetry in k-space.

The right and left halves (and top/bottom halves) of k-space are mirror images; this property allows partial-k techniques to replicate missing data.

Name a scan-time-reduction method that exploits conjugate symmetry.

Half-Fourier (partial-Fourier) or fractional k-space filling.

Main drawback of partial-k techniques (e.g., ¾ or ½ Fourier).

Any artifacts in the acquired data are mirrored/replicated, potentially magnifying the artifact in the final image.

Define frequency matrix.

The number of data points (pixels/voxels) sampled along each line of k-space— equivalent to the number of pixels in the frequency (long-axis) direction of the image.

Define phase matrix.

The number of phase-encoding lines filled in k-space— equivalent to the number of pixels in the phase (short-axis) direction of the image.

How does matrix size affect spatial resolution (assuming constant FOV)?

Larger matrix → more, smaller pixels → higher resolution; smaller matrix → fewer, larger pixels → lower resolution.

Write the basic 2-D scan-time equation.

Scan Time = TR × NEX (NSA) × Phase-encoding steps (phase matrix).

What is NEX (or NSA) and what is its effect?

Number of signal averages; repeating and averaging each line increases SNR but lengthens scan time according to the scan-time equation.

How does increasing TR or NEX affect patient throughput?

They lengthen scan time, slowing patient throughput, but TR can alter contrast and NEX improves SNR.

What determines the field of view (FOV) in the frequency direction?

The strength (slope) of the frequency-encoding gradient: a lower gradient amplitude yields a larger FOV; a steeper gradient yields a smaller FOV.

Why must the entire k-space be filled (or mathematically completed) for diagnostic quality?

Complete data— including both central contrast lines and peripheral resolution lines— are required to reconstruct an image with correct contrast and sharpness.

How does a steep frequency-encoding gradient affect data points collected?

Steeper gradient spreads frequencies wider, usually requiring more sampled points to cover the band, thus increasing frequency matrix size.

How do steep vs. shallow phase-encoding gradients affect k-space fill?

Steep amplitude fills outer (high-phase) lines with low-amplitude signal; shallow amplitude fills central lines with high-amplitude signal.

How can you estimate total pixels/voxels in an image?

Multiply frequency matrix × phase matrix (e.g., 380 × 256 ≈ 97,280 pixels).