k-Space
Parameters that affect K-space filling
-TR -Phase Matrix -NSA Increasing all these will increase scan time as more data is being sampled.
Preliminary Steps needed for FFT to create an image of each slice:
1. Frequency and Amplitude Modulation 2. Analog-to-digital conversion (ADC) 3. Readout or Measure Gradient 4. Acquisition window
If the receive bandwidth is 32KHz across the whole echo, the above and below the centre frequency would be...
16KHz (Half of the receive bandwidth)
RF Exication pulses result in the system...
Centreing itself in the center of k-space
Single shot imaging
Collects all the data required to fill lines of k-space from a single echo train
The number of data points is determined by the..
Frequency matrix. e.g. if the frequency matrix is 256, then 256 data points is acquired during the sampling window
The central portion of k-space contains data that have...
High signal amplitude and low resolution It is filled using shallow phase encoding gradients
In k-space filling, data is stored in...
Horizontal lines that are parallel to the frequency axis.
In k-space filling, the amplitude of the frequency-encoding gradient determines...
How far to the left or right k-space is traversed, thus determines the size of the pixels in the frequency encoding direction.
In k-space filling, the amplitude of the phase encoding gradient determines...
How far up or down a line of k-space is filled, thus in turn determines the size of the pizels in the phase direction of the image.
k-space stores...
Information about the frequency of a signal and where it comes from (from spatial encoding)
The outer portion of k-space contains data that have...
Low signal amplitude and high resolution It is filled using steep phase encoding gradients It does not contribute signal and contrast to the image.
The multiple waveforms in the echo in frequency and amplitude modulation are simplified into
One waveform that represents the average amplitude of all the different frequencies in the echo (TE) at different time points.
Axes of k-space
Phase axis is vertical and centered in the middle. Frequency axis runs parallel.
How does phase encoding fill up k-space?
Phase encoding gradient picks which line of k-space to fill in a certain TR. Positive polarity pick lines from the top half and negative the bottom half. Polarity and slope of phase gradient is altered every TR to fill all lines.
Frequency and Amplitude Modulation
Simplifies the frequencies and amplitudes present in the echo. Multiple waveforms are simplified into one waveform.
Sampling is..
The collection of data point that is placed in a line of k-space.
FOV in k-space is determined by...
The difference between each data point in k-space in either direction. It is inversely proportional to the size of the FOV in that direction. Phase - incremental step between each data point in a column of data. Frequency - Distance between each data point in k-space or sampling interval between each row of data.
The Nyquist theorem calculates...
The minimum digital sampling frequency needed to acquire enough data points to create an accurate image.
The image matrix in k-space is determined by...
The number of data points in k-space. Phase - Howm any lines of k-space are filled with data points (columns) Frequency - Number of data in each row of k-space
Receive Bandwidth
The range of frequencies accurately sampled or digitised during the sampling window.
Digital Sampling Rate/Digital Sampling Frequency
The rate at which data sampling occurs. Rate at which data points are acquired per second during the sampling window. (Hz)
Partial Echo
The technique of sampling only a portion of the frequency components for K-Space and interpolating the remaining portion to fill K-Space. Maximixes T1 and PD weighting
Fast Fourier Transform (FFT)
A mathematical process that gets us from the data points in k-space to the image. Each pixel location has its own pattern of spatial frequency and pseudo frequency and different amplitudes. FFT works out these patterns and the spatial locations of the pattern and allocates a tone on a grayscale to each pixel.
Parallel Imaging
A scan time acceleration technique which requires the use of a phased array coil to reconstruct an image in less time than conventional imaging Each coil/element is assigned to a line of k-space and each is filled and repeated.
k-space
A spatial frequency domain
2D volumetric acquisition
Acquisition where a small amount of data is acquired from each slice before repeating the TR e.g. one line of k-space for slice 1 and then fill the same line of k-space for slice 2 and repeat.
3D volumetric acquisition
Acquisition where the whole imaging volume is excited so that the images can be viewed in any plane
Parallel imaging artifact
Aliasing due to bigger gap between each line in k-space.
Sampling less than once per cycle can lead too...
Aliasing.
The receive bandwidth is determined by
Applying a filter to the frequencies encoded by the frequency encoding gradient.
Sampling time and TE relationship
As TE increases, sampling time is increased.
The simplest method of k-space filling is
Cartesian filling
Partial Fourier Imaging
Data is partially filled in k-space (e.g. 75%) and the rest is extrapolated through the use of conjugate symmetry of k-space. Can display motion artefacts.
Analog-to-Digital Conversion
Digitizes the modulation (aka echo). A process of converting continuous information into discrete data; some information is typically lost.
The sampling interval is calculated by...
Dividing the sampling frequency by 1.
If the sampling frequency is too high...
Files might be too large and sampling might take too long. Artefacts may also occur as more noise is acquired in k-space.
In k-space, resolution is referred to as
Frequency Resolution
The number of data points horizontally in each line equals the...
Frequency matrix
Outer portion of k-space have higher resolution because...
Large changes of phase along the phase-encoding gradient mean that two points close together in the patient are likely to have a phase difference and are differentiated from each other.
The most optimum digital sampling frequency is determined by the
Nyquist Theorem
The number of data points vertically in each line equals the...
Phase matrix
Elements of k-space filling
RF pulse and Gradients
Radial k-space filling
Radial k space filling is used as a way to reduce motion. By collecting data like cutting a pie into slices and then rotating it around, we are able to remove motion in our slice plane. This however is only limited to the slice plane and any motion outside of our slice plane would demonstrate motion artifact.
During the sampling window, the system...
Samples or measures the echo at certain time points. Everytime a sample is taken, this is stored as a data point in k-space.
The rate of which sampling occurs is called the
Sampling rate/Sampling frequency
The duration of the frequency-encoding gradient is called...
Sampling time/Sampling Window/Acqusition Window
Conjugate Symmetry
Symmetry of data in K space. The data in top half of k-space are identical to those in the bottom half. This is due to the slope of phase encoding gradients required to select a certain line in one half of k-space is identical to the opposite side.
Once a specific line is filled in for each slice...
TR is repeated and the slice gradient selects the initial slice and a different line of k-space is filled in.
Slice Gradient in k-space selects...
The 'slice' of the k-space in at specific time interval (TR)
Frequency Encoding in k-space selects...
The amount of data that is inputted in each phase matrix/line.
Readout/Measurement Gradient
The frequency encoding gradient is switched on while the system reads the echo and digitizes it.
Spiral K space filling
The frequency encoding gradient oscillates to fill lines from left to right and then right to left, starting from the centre. Phase encoding oscillates to fill top and bottom.
The Nyquist sampling theorem states that...
The highest frequency present in the modulation must be sampled at least twice as frequently to accurately digitize or represent it.
The lines are numbered with...
The lowest number near the central axis and the highest numbers towards the outer edges. (Positive end to negative end)
The digital sampling frequency determines...
The time interval between each data point.
The combination of RF pulses and gradients governs...
The type of pulse sequence which in turn determines how k-space is traversed.
If the sampling frequency is too low...
Then there may not be enough data points in k-space ot create an accurate image.
In k-space filling, the slice select gradient determines which area of k-space is being...
Traversed.
In k-space filling, the polarity of the phase encoding gradient determines
Whether a line in the top of bottom half of k-space is filled. Phase-postive pole: Fills top half of k-space Phase-negative pole: Fills bottom half of k-space.
In k-space filling, the polarity of the frequency encoding gradient determines...
Whether k-space is traversed from left to right or right to left. Positive gradient - LEFT to RIGHT Negative gradient - RIGHT to LEFT
Phase Encoding in k-space selects...
Which 'line' of k-space to fill up in a certain TR.
Sequential acquisition
acquisition where all the data from each slice is acquired before going on to the next
k-space phase matrix
is the number of 'lines of data' selected in the scan protocol. Determines how many lines are filled with data to complete the scan e.g. a phase matrix of 128 will have 128 lines of data.
Cartesian filling
k-space is filled in a linear manner from top to bottom or vice versa. note, each chest of drawer represents the same slice at different time intervals (by TR)
The lines of k-space are...
numbered so that the system always knows where it is in the k-space