Image formation 1: k-space Flashcards
How do you visualise phase?
Imagining a vector V of magnitude A rotating at a constant rate
What is the component of the vector in the x direction?
(co)sine wave
What is the phase of the wave?
The angle the vector makes with the axis at time t=0
How are pixels arranged in an MR image?
rows and columns in a matrix
What does each pixel in the reconstructed image contain?
A number related to signal intensity (location in the computer memory)
What does matrix control?
Not only image size but also raw data space (k-space)
What happens each time the sequence is repeated?
A full line of k-space is acquired
- Frequency encode direction [ x-direction]
This is repeated for every line in the phase encode [y-direction]
What happens as sequence is acquired?
K-space if filled line by line
What does the phase encode matrix define?
How many times the sequence must be repeated and therefore acquisition time
What doesn’t frequency encode matrix have?
Effect on scan time
• In each direction of pixel size = FOV/matrix
- E.g. PE pixel size = PE FOV/PE matrix
* E.g. FE pixel size = FE FOV/FE matrix
What is k-space?
Array of numbers representing spatial frequencies in the MR image
What is each star in k-space?
data point derived directly from MR signal
What does all the points in k-space contain?
Little information about every voxel
What does each individual point in image space depend on?
All of the points contained in k-space
What does k-space data related to?
Image data by Fourier Transform
How are the cells of k-space commonly displayed?
Rectangular grid with principal axes kx and ky
What does kx and ky axes of k-space correspond to?
Horizontal to horizontal and vertical axes of the image
What does k-axes represent?
spatial frequencies in the x- and y- directions rather than positions
What does individual points (kx,ky) in k-space do not correspond to?
one-to-one with individual pixels in image
What does each k-space point contain?
spatial frequency and phase information about every pixel in the final image
What does each pixel in image map to?
every point in k-space
What does the centre of k-space contain?
signal-to-noise and contrast information
What does data from the edges of k-space contain?
Information about resolution (edges and boundaries)
What happens when a frequency encoding gradient is applied during evolution of MR signal?
successive data points in the echo reflect progressively increasing spatial frequencies
What is Free Induction Decay (FID)?
The signal unaffected by any gradient
What is the time constant that determines the rate of decay?
T2
What does FID not have?
Positional information
What does FID induce?
A current in the receiver coil at the Larmor frequency
How can you think voltage as?
pure sine wave at f0 , modul0ated by much lower frequency signals that represent the slight differences in resonant frequency caused by
• applied gradients
• inherent susceptibility
• magnet inhomogeneity, etc.
Why are magnetic field gradients required?
Translate signals into seperate locations
What are magnetic field gradient?
Variations in the magnetic field with respect to position
What is a one-dimensional magnetic field gradient?
Variation with respect to one direction
What does a one-dimensional magnetic field gradient along x-axis in a magnetic field B0 indicate?
Magnetic field is increasing in the x direction
What is a gradient?
A measure of the change in something over a specific distance
- Linear variation in static field strength
- Can be applied in any direction - 3 gradient coils, Gx, GymGz
What happens when a gradient is applied?
The total field experienced by nuclei will be dependent upon position in space e.g. in the x-direction • B(x) = B0 + x Gx
What is the equation of gradient?
42.57*(field+(gradient x position)= resonant freq
Where is all of information of interest in?
426Hz and -213Hz frequency differences (from Larmor freq)
What is resultant effect?
Sum of two signals at the two different frequencies
What does field gradient cause?
A variation of MR signal frequency
What does frequency variation cause?
spins to precess at different rates
What happens when spins precess faster?
Appear to dephase
What does the amount of dephasing depend on?
gradient strength
How can you re-phase spin?
Reverse this effect using equal and opposite grafient
What can dephasing be caused by?
B0 field inhomogeneities
- results in change in frequency
What are the 3 steps that signal can be localised?
- Slice selection
- Frequency encoding
- Phase encoding
What is frequency encoding?
Encode spatial information along the rows
What is phase encoding?
Encode spatial information along the columns
What is decoding of spatial information performed by?
Inverse Fourier Transform
What is the slice selection gradient perpendicular to?
desired slice plane
Simultaneously with RF excitation pulse
What does the RF pulse contain?
Narrow bandwidth centred at Larmor frequency
What is the slice thickness determined by?
Bandwidth of RF pulse and slice select gradient strength
What is the process of slice selection?
- A magnetic field gradient is applied in the z-axis
- The Larmor frequencies of the nuclei varies along the z-axis
- An RF pulse with a frequency matching the Larmor frequency of the nuclei we want to select is applied
- In this way a slice along the z-axis is selected (correlates with an axial slice of the patient)
- The phases of the nuclei are reset by reversing the gradients
How can you flip the precession of the nuclei?
The RF pulse frequency should be the same as the Larmor frequency of the nuclei
What does changing the RF pulse frequency move?
Slice selected up and down the z axis
What does altering the gradient strength alter?
The steepness of the gradient
- Larger gradient = smaller image slice
- Smaller gradient = larger image slice
What does the Phase Encoding (PE)
The spin resonance frequencies - induces dephasing
What do all of the protons precess at?
same frequency but with different phases
- Y direction
Where is FE gradient applied?
Perpendicular to the phase encoding direction
What does FE gradient alter?
main magnetic fiekd
causing the resonance frequency to vary as a function of position \
-X direction
What is the duration of 2D acquisition?
RTNPENFE
What are the two ways signals can be described?
- Give all the frequencies that make it up, along with their relative proportion
- Give amplitude of the total signal at each instant of time
What can any image be decomposed into?
spectrum of periodic (sinusoidal) brightness variation
High spatial frequencies
- Describes things that are changing rapidly from pixel to pixel in an image
- Detail of the image (edges)
Low spatial frequencies
- Describes things that are changing slowly from pixel to pixel
- Overall form of the image (contrast)
What does zero spatial frequency describe?
Overall intensity of the whole image
What is the contrast of image largely determined by?
Spatial frequencies close to zero
What does the centre of k-space contain?
Low spatial frequency information
-Determines the overall image contrast, brightness and general shapes
What does the periphery of k-space contain?
High spatial frequency
- edges, details, sharp transitions
What does small objects have?
Ripples far out into the periphery of k-space
What does larger objects have?
Their spectral energies more concentrated at the centre
• What happens if we don’t measure the signal at all the points in a ‘square’ of k-space?
- Simply don’t acquire largest phase encoded k-space lines
- Replace omitted lines by zero filling
- Time saving proportional to no of lines missed out
- Loss of spatial resolution in PE axis (y resolution reduced -> blurring) –k ymax reduced
- small improvement in SNR
- NO change in field of view –Spacing between k-space lines unchanged
What is the spatial resolution given by?
Selected FOV divided by matrix size in either direction
How is the spatial resolution gradually improved?
Increasing numbers of Fourier lines around the centre of K-space
What happens if we reduce the number of phase encode steps, but leave their range the same?
- Reduced matrix size
- Changed FOV
- Not changed Y-resolution
- This is a rectangular field of view with square pixels
What happens if we change both the range and spacing of PE gradient steps?
- Still end up with a rectangular field of view
- Reduced matrix size
- Changed FOV
- Changed Y-resoltuon
When is spin echo symmetric about its centre?
Perfectly homogenous field
What happens if the echo is symmetric?
Only have to sample half of the k-space
How can you fill in the missing points of echo?
Taking the complex conjugate of the data points we have measured
Why is the number of PE steps necessary?
Reconstruct image reduced
Scan time reduced
Scan percentage at 30%
reduction of the spatial resolution in the image as well as in a increase of the SNR in the image
How do you increase the resolution for fixed FOV?
- Increase gradient strengths
- Increase the acquisition matrix size
- Increase sampling time (in frequency encoding directions only)
How can you reduce the FOV for fixed matrix size?
- Increase gradient
2. Increase sampling time
What is SNR proportional to?
Voxel volume
