MRI Physics Chapter 6 k-Space

After reading this chapter, you will be able to: Describe the characteristics of k-space. Explain different ways in which k-space is filled. Understand how pulse sequences determine how and when k-space is filled with data. Apply this understanding when altering parameters in the scan protocol.

The system now has a way of locating an individual signal within the image by measuring the number of times the magnetic moments of spins cross the receiver coil (frequency) and their position around their ___________path (phase).

precessional 

Fast Fourier transform

mathematical conversion of frequency/time domain to frequency/amplitude.

K-space: an area in the array processor where data on _________frequencies are stored.

spatial 

The number of data points is determined by the frequency ___________(more on this later).

matrix 

Steep gradients, both positive and negative, select the most _______lines, while ________gradients select the _______lines.

outer, shallow, central 

The _______line (line 0) is always filled with data.

central 

The number of data points is determined by the frequency
_______.

matrix 

The _______variable is still time, but digital watches display it as numbers.

measured 

Analog is a term used for information about a variable illustrated as a(n) ________. 

waveform 

Amplitude modulation

modulation or simplification of waveforms according to their amplitude.

What is the definition of "Nyquist frequency"?

Highest frequency that is accurately sampled. Occurs if the digital sampling frequency is at least twice the frequency being sampled.

The digital sampling frequency determines the time ______between each data point.

interval 

As long as the highest frequency present is sampled twice, it is represented correctly in the ______.

data

The ______sampling frequency is not directly selected in the scan protocol, but it affects several other parameters that are selected, so read on!

digital

As the receive bandwidth is a selectable parameter in the scan protocol, it is used to determine the _______sampling frequency.

digital 

There is insufficient range of different frequencies to separate out signals from the different _____stations.

radio 

If a receive ______of 64 _________is selected, then the echo is sampled 64 000 times per second during the sampling ________. 

bandwidth, KHz, window 

Transmit bandwidth

range of frequencies transmitted in an RF excitation pulse.

The _____of the echo therefore occurs half way into the ___________________after 4 ms.

peak, sampling window 

Others choose to display it as the receive bandwidth per ________in the frequency direction of the image.

pixel 

The default is shown in the top line where a sampling _______of 8 ms is used with a 32 __________bandwidth with a frequency ________ of 256. 

window, KHz, matrix 

The opposite is true if the sampling _______decreases.

window 

The waveforms on each k-space line are created in different TRs by different _______of phase-encoding gradient, and so their phase information is different.

slopes 

Unlike frequency encoding, which relies on what happened during the short time-frame of the sampling ______, the phase encoding process relies on what happened during the entire scan.

window 

If the data look the same every TR, then the system places the data in the same line every TR, and the ________image has a _______of only 1 __________in the phase direction of the image.

resultant, resolution, pixel 

Phase encoding

locating a signal according to its phase.

By minimizing phase change with a(n) _________phase-encoding gradient slope, the resultant echo has a high signal amplitude and contributes largely to signal and contrast in the image.

shallow 

There are many different permutations of k-space filling where the _______proportion of _______ to_________lines filled is altered.

relative, central, outer 

One data point does not equal 1 ________. 

pixel 

Conjugate symmetry

symmetry of data in k-space.

Usually, to fill each line more than once, the same _______of phase-encoding gradient is used over two or more successive TRs, rather than filling all the lines once and then returning to repeat the process again.

slope 

The data in each line are acquired after application of a different ________of phase-encoding gradient applied in each TR period.

slope 

In the frequency axis of k-space, the __________between each data point in each row is inversely proportional to the _________of the frequency FOV (Equation (6.11)).

sampling interval, size 

In the phase axis of k-space, the difference in phase shift between each data point in each column is inversely _________to the size of the phase FOV (Equation (6.10)).

proportional 

What is the definition of "Image matrix"?

Number of pixels in the frequency and phase axes of the image.

Is this the correct definition of Receive bandwidth?

range of frequencies transmitted in an RF excitation pulse.

no

In practice, the FOV in the frequency direction is usually altered by changing the _________of the frequency-encoding gradient rather than changing the receive bandwidth.

slope 

Pixel size in the phase axis of the image depends on the vertical ________of k-space.

dimension

The __________of the phase-encoding gradient and the negative lobe of the frequency-encoding gradient determine at what point in k-space data storage begins.

combination

The _________traveled depends on the amplitude of the positive _________of the gradient and determines the pixel _________in the frequency direction of the image.

distance, lobe, size 

Time of the total acquisition. The time to fill k-space.

Scan time

__________averaging is used where a reduction in scan time is necessary and where the ________signal loss is not of _________importance.

partial, resultant, paramount 

The coil ________can be used to increase spatial _______, e.g. achieve a phase _______of 512 in the time of a 128.

configuration, resolution, matrix 

Parallel imaging or sensitivity encoding is a(n) _______that fills k-space more efficiently than conventional imaging.

technique 

Multiple channels are selected, and the _______number depends on the level and sophistication of the hardware and software of the system.

maximum 

_______shift may increase as different resonant frequencies are mapped across each coil.

chemical 

What is the definition of "Single-shot imaging"?

Technique that fills k-space in one shot.

Algorithms are needed so that data are placed in the correct location in k-space as the strips of data rotate around the _________ axis. 

central 

The amplitude gradually increases until it reaches maximum negative _________, and the bottom line of k-space is filled.

polarity 

What is k-space in MRI?

An area in the array processor where data on spatial frequencies are stored

What factor determines the number of lines in k-space?

Phase matrix

What factor determines the number of data points to be collected in k-space?

Frequency matrix

How are lines of k-space numbered?

Lowest numbers near the central axis, highest numbers toward the outer edges; top half positive, bottom half negative

Which gradient changes amplitude (slope) from one TR period to the next?

Phase encoding gradient

How does the phase gradient select each line of k-space?

Steep slope selects outer lines with low signal; shallow slope selects central lines with high signal

How is k-space filled using steep and shallow phase encoding gradients?

Central lines are filled using shallow slopes; outer lines are filled using steep positive and negative slopes

What is another name for the frequency encoding gradient?

Readout or measurement gradient

What is sampling time in MRI?

The duration of the frequency or readout; also known as the acquisition window

What is sampling rate in MRI?

The rate at which frequencies are sampled or digitized during the acquisition window; number of data points per second

What does the Nyquist theorem state?

A frequency must be sampled at least twice to reproduce it reliably

What artifact occurs when the Nyquist theorem is not followed?

Aliasing (wrap around)

What is receive bandwidth in MRI?

Range of frequencies sampled during readout; includes the range and speed of digitization

What is Fast Fourier Transformation (FFT) in MRI?

Mathematical conversion of frequency/time domain to frequency/amplitude

What is the frequency matrix in MRI?

The number of pixels along the frequency axis of the image and the number of data points per row of k-space

What is the phase matrix in MRI?

The number of pixels along the phase axis of the image and the number of data points per column of k-space

Is k-space the image?

No, k-space is not an image

What is conjugate symmetry in k-space?

Identical top and bottom, left and right; used to reduce scan times

Which part of k-space has low signal amplitude and high spatial resolution?

Outer portion

Which part of k-space has high signal amplitude and low spatial resolution?

Center portion

Which area of k-space determines image contrast?

Central line portion due to low resolution

Which area of k-space determines image resolution?

Outer line portion due to high resolution

Which parameters control scan time in MRI?

TR, Phase Matrix, and NEX

What is the scan time formula in MRI?

ST = TR × PM × NEX

What is the number of excitations (NEX)?

Number of times a line of k-space is filled with data; also called NSA or NEX

How can signal be sampled more than once in MRI?

By maintaining the same slope of the phase gradient over several TRs

What is spatial resolution in MRI?

The ability to distinguish two points in the image as separate

What is frequency resolution in MRI?

The resolution of spatial frequencies in k-space

What factors determine pixel size in MRI?

Image matrix and FOV

How does FOV affect pixel size?

It is inversely proportional to the spacing between data points in k-space

What does the RF excitation pulse do in relation to k-space?

Centers the system in the middle of k-space

What does the amplitude of the phase encoding gradient determine?

How far up and down a line is filled in k-space and the pixel size in the phase direction

What does the polarity of the phase encoding gradient determine?

Whether a line in the top or bottom of k-space is filled (positive = top, negative = bottom)

What does the amplitude of the frequency encoding gradient determine?

How far left and right k-space is filled and the pixel size in the frequency direction

What does the polarity of the frequency encoding gradient determine?

Whether k-space is filled left to right or right to left

What is partial averaging in MRI?

Filling only a portion of k-space with data and putting zeros in the remainder

What is partial echo in MRI?

Reading only part of the echo during frequency encoding and extrapolating the remainder in k-space

What is parallel imaging in MRI?

Technique that uses multiple coils to fill segments of k-space

What is single-shot (SS) imaging?

Technique that fills k-space in one shot using a single echo train

How does spiral filling reduce scan time?

Readout and phase gradients switch polarity rapidly, starting at the center and spiraling outward

How does propeller filling reduce motion artifact?

Central portion of k-space is acquired every TR, improving SNR and CNR through motion averaging

What is the difference between 2D and 3D imaging in MRI?

2D fills one line of k-space for slice 1, then the same line for slice 2, etc.

What is a key characteristic of 3D imaging in MRI?

Data are acquired from an entire volume of tissue; slices can be contiguous and without gaps

Acceleration factor

ratio of the number of k-space lines in a fully sampled acquisition to the number actually collected

Acquisition window

time that the readout gradient is switched on for.

Algorithm

a set of steps used by a computer to solve a problem

Aliasing

artifact produced when data are undersampled.

Amplitude modulation

modulation or simplification of waveforms according to their amplitude.

Analog-to-digital conversion

changing a waveform into binary numbers via digitization.

Blipping

used in single shot to step down through phase-encoding steps.

Cartesian filling

linear filling of k-space.