White Pixel Artifact
• Caused by a noise spike during acquisition
• Spike in K-space <--> sinusoid in image
space
Susceptibility Artifacts
• Off-resonance artifacts caused by adjacent regions with different
Susceptibility
• BOLD signal requires susceptibility weighting…
but this also leads to image artifacts
No
Susceptibility
Contrast
High
Susceptibility
Contrast
courtesy of Douglas Noll
Through-Plane
Magnetic Fields
Dephasing
Ideal
in the Head Low Field
Signal Loss
Li et al. Magn. Reson. Med. 36:710
High Field
(1996)
courtesy of Douglas Noll
Susceptibility Artifacts
• Local gradients cause:
– extra dephasing when the gradient occurs through the imaging plane
(destructive interference). Result is signal loss.
– distortion (skewing of the k-space trajectory in different voxels) when the
gradient happens in the plane. Signal loss and distortions of the image.
• Solution: this is an active research field, lots of tricks you can do, but
they all have an associated cost in time, SNR, computation, hardware..
– Simplest: design acquisition parameters such that the artifacts are
minimized.
– Z-shimming: apply set of additional gradients
– Active shims: create additional gradient using materials, coils
– iterative reconstructions: crunch the numbers
Physiological oscillations
Time
domain
Frequency
domain
courtesy of Douglas Noll
Cardiac and Respiratory Variance
Residual Variance w/o Residual Variance w/
anatomy Physio correction Physio correction
courtesy of Douglas Noll
Cardiac Noise
• Blood flow is pulsatile -> changes blood volume,
and velocity.
• Other blood flow effects on MR signal:
– Flow enhancement (incoming spins have not received
any RF , fully relaxed -> more signal)
– Flow void (sometimes spins flow so fast through the
plane that they don’t see the RF pulse, or they flow out
before they can be encoded -> less signal )
– Flow induced displacement (additional phase acquired
because of in-plane movement -> distorted/displaced
signal, ghosting)
Reduction of cardiac effects
during Acquisition
• Use a smaller flip angle - reduces flow
enhancements and voids.
• Use flow “spoilers” to remove vascular signals.
(pair of symmetric gradient pulses, a.k.a.
“crushers”, refocus the signal from stationary
spins but not from moving spins.)
• Use fast acquisition (single shot) to reduce
ghosting.
• “Cardiac Gating”
Reduction of cardiac artifacts
after acquisition
• Digital Filters …
• Measure cardiac waveform and include in analysis
as a confound.
• Note: watch out for aliasing!!
– heartbeat ~from 0.5-2 Hz, typically ~1 Hz
– typical Nyquist frequency < 0.5 Hz
Respiration
Superior
• Air and Tissue difference in χ :
B0
Distortion of B0 field Inferior
Phase difference between inspiration and
expiration for a coronal slice.
• Chest movement changes the shape of the B0 field.
Changes gradients too.
• Resonant frequency changes slightly ( Recall that
ω0 = γB0)
• Blood Pressure changes slightly with respiration
(pulsation of arteries and hence blood volume)
Corrections for Respiration
• Fast image acquisition (single shot)
• “Notch” or “band-stop” Filters
• Record Respiratory waveform and use as a confound.
(Note- sometimes it’s correlated with task of interest)
Intensity
Timecourse before (purple) and
after (black) regression correction.
Image number
• Aliasing is not as much of a problem as in cardiac
fluctuations, but might still interfere with design
– Respiration ~ from 0.1 to 0.5 Hz, typically 0.3 Hz
– BOLD ~ from 0.01 to 0.05 (broad)
– typical fMRI Nyquist frequency < 0.5 Hz
Timing Errors
• MR images are typically collected one slice at a
time (exception: 3D imaging)
• The slices can be collected sequentially or
interleaved.
• Delay between slice excitations is typically
TR / (num. slices)
• Therefore, the time series are time-shifted
differently in each slice
FMRI data “layout”
TR 2TR 3TR
slice 1
slice 4
time
Acquisition
TR 2TR 3TR
slice 1
slice 4
time
Acquisition
TR 2TR 3TR
slice 1
slice 4
time
Sampling Error in Time
The data you think you have
The data you really have
Sampling Error in Time
How the data looks
The true data
so shift it back!
Movement
In 2 Dimensions:
• shift from (x1,y1) to (x2,y2):
x2 = x1 + Δx
y2 = y1 + Δy
• Rotation from (x1, y1) to (x2,y2):
x2 = x1cos(θ) + y1sin(θ)
y2 = -x1sin(θ) + y1cos(θ)
2-D Transformation matrix
• Both Together (note that the order matters)
x2 = x1 cos(θ) + y1 sin(θ) + Δx
y2 = -x1 sin(θ) + y1 cos(θ) + Δy
or In Matrix Form …
x2 cos(θ) sin(θ) Δx x1
y2 = -sin(θ) cos(θ) Δy y1
1 0 0 1 1
2-D Transformation matrix
(x2,y2) = A(x1, y1)
this extends to N-dimensions too
3-D Rotation matrices
cos(θ) sin(θ) 0 0 cos(θ) 0 sin(θ) 0 1 0 0 0
-sin(θ) cos(θ) 0 0 0 1 0 0 cos(θ) 1 sin(θ) 0
0 0 1 0 -sin(θ) 0 cos(θ) 0 -sin(θ) 0 cos(θ) 0
0 0 0 1 0 0 0 1 0 0 0 1
xy plane xz plane yz plane
rotation rotation rotation
Estimation of Movement
1. Choose a set of translations, rotations
2. Combine the six transformations matrices (linear
operators) into one “rigid body” transformation
r2 = A r1
3. Resample the images at the new locations
4. Are the two images more alike?
5. Repeat and search for the best matrix A
Movement
Interpolate this
point from its
neighbors
Resampling the image
• Think of realignment as transforming the
sampling grid, rather than the image.
• Interpolation:
– Choose weighting function (kernel):
• Nearest neighbor
• bi-linear, tri-linear interpolation
• sinc interpolation
Comparing images: cost function
• How do you know two images match?
1. Least squares difference
Σ ( I 1 - I 2 )2
2. Normalized correlation, correlation ratio
Σ(I1 I2) Var(E[I1 I2])
(Var(I1) (Var( I2) )1/2 Var(I2)
3. Mutual information
⎛ p(I1,I2 ) ⎞
M(I1,I2 ) = ∑ p(I1,I2 )log 2 ⎜ ⎟
i, j ⎝ p(I1 ) p(I2 ) ⎠
4. others ….M. Jenkinson and S.M. Smith. Medical Image Analysis,
5(2):143-156, June 2001
€
Search Strategies
• least squares (Y=βX) …
• Steepest descent: vary parameters and compute
the gradient in the cost function (error). Keep
going as long as it gets better.
• There are variations on this theme:
– simplex
– Newton’s method / gradient descent
– Adaptive methods
– others…
Sample Movement Parameters
Movement Noise
• In addition to mixing voxels, you introduce a
fluctuation in signal intensity during realignment
• This is a complicated function of the movement:
– affects the k-space data acquisition
– mixes partial volumes,
– interpolation methods also have an effect on intensity.
Movement Noise corrections
• Minimize movement while acquiring data
whenever possible !!
• Include movement parameters as confounding
regressors.
– Complicated function, but the signal fluctuation is well
correlated with the movement parameters.
– Including movement regressors will strongly reduce
variance.
– If movement is correlated with task = BIG TROUBLE!
Putting it all together :
pre-processing stream
Functional Time Series Anatomical Images
B0 map correction
Reconstruction
Physio correction B1 homogeneity correction
Reconstruction brain extraction
Slice Timing correction registration
Motion- realignment normalization
SPM Statistical Map
in Standard
Space
