fMRI Methods
Lecture6 – Signal & Noise
Tiny signals in lots of noise
Rest
Pressing
hands
Absolute
difference
% signal
difference
What’s the signal
The signal we’re really measuring is tiny changes of
current induced in our detector coils.
What induces the current?
What makes the signal in a voxel stronger (larger image
intensity)?
What is the “signal” we’re really interested in?
What’s the noise
1. Thermal noise
2. System noise
3. Head motion, respiration, heart beat (physiological)
noise
4. Hemodynamics variability
5. Neural variability
6. Behavioral/Cognitive variability
Are 5&6
really noise?
Thermal noise
Thermal motion of electrons, collisions, random
exchange of energy, larger at higher temperatures…
It is generally considered homogeneous and random and
so can be reduced by averaging across multiple
samples.
It increases linearly with
static field strength.
System noise
Variability in the function of the imaging hardware across
space and time.
Static field inhomogeneities
Scanner drift
Susceptibility artifacts
Field inhomogeneities are particularly strong at tissue/air
boundaries (sinuses). Increase with field strength.
1.5 T
4T
Comparing “extrinsic” noise
Thermal and system noise can be measured and
estimated using a phantom made of a known material.
Head motion
Moving the head during a scan causes two types of noise:
1. Spatial changes throughout the scan.
Head motion
Spatial changes can be estimated and fixed by locating
brain edges and moving/rotating them appropriately.
Now even done online by the scanner! Rather than post-hoc
Head motion
2. Image intensity artifacts in time (intensity “spikes”).
Head motion
Intensity artifacts are more difficult to correct.
Can either be “projected out”, interpolated over, or cut out.
What happens when head motion and task are correlated?
Add motion parameters to model
Add 6 predictors (3 translation and 3 rotation) to the
model and hope they “soak” up the relevant variability.
=
*
a1 a2 a3 a4
…
+ error
Or project/regress out
Ensure zero correlation between the noise estimate (x)
and the data (y).
a = y*x
y(after) = y(before) – a*x
Preventing head motion
Physiological noise
There are non-neural mechanisms causing hemodynamic
or inhomogeneity changes during a scan. Luckily they are
periodical…
Respiration artifacts
The lungs create a changing susceptibility artifact, similar
to that seen below in the sinuses (stronger in larger
fields).
1.5 T
4T
Only the lungs effect the signal throughout the brain…
Physiological noise
Increases at higher static magnetic fields for the same
reason the signal increases…
Fourier transform
Decompose complex signals into sinusoidal components
+ b*
Temporal domain
+ c*
Frequency
phase
a*
power
Frequency
domain
Frequency
Temporal filtering
Get rid of very low frequencies (drift, respiration). Others?
Fourier transform
a*
+ b*
Noise? multiply by zero
+ c*
Temporal filtering
High pass filter – lets the high frequencies pass, stops the
low frequencies.
Low pass filter – lets the low frequencies pass, stops the
high frequencies.
Band pass filter – lets a particular range of frequencies
through (often by sequentially running a low high and low
pass filter).
Hemodynamics variability
Different subjects exhibit different HRFs
Hemodynamics variability
HRFs vary across sessions
Across brain areas?
Hemodynamics variability
To address this we can estimate the subject’s HIRF in a
separate run and use it to model the responses.
Neural variability
The brain is never at “rest”, spontaneous neural activity
fluctuations are as large as stimulus evoked responses.
Neural variability
Some think the stimulus evoked responses “ride” on top of
spontaneous cortical fluctuations, others think stimulus
evoked responses replace spontaneous fluctuations.
We typically get rid of them by averaging across multiple
trials.
Behavioral/Cognitive variability
The more complex an experiment, the more variable the
behavioral responses:
1. Subjects can choose different strategies.
2. Changes in attention/arousal (caffeine).
Response time distributions of
two subjects performing a
simple decision task.
Behavioral/Cognitive variability
Again, variability is typically handled by averaging across
trials.
Does neural response
amplitude predict reaction
time or accuracy?
fMRI response
However, this variability also offers an opportunity:
Reaction time
Intra-subject variability
Finger tapping task
Intra-subject variability
Generate random numbers
Improve SNR by averaging
The main approach to canceling out noise is to average
across multiple trials.
This assumes that
the neural response
is constant (locked to
the stimulus/task)
and that the noise is
randomly distributed.
Are they?
Improve SNR by averaging
Estimating HRF using different trial numbers:
Improve SNR by averaging
Estimating voxel significance
using different trial numbers:
Never compare statistics
across conditions/groups.
A difference in statistical
significance does not equal
a difference in signal
strength!
Higher fields
The signal is dependant on the magnetization of the
hydrogen atoms, which increases with field strength (more
atoms align with the static field).
The gain in signal is quadratic.
The increase in noise is linear.
So the signal/noise ratio
scales linearly with scanner
strength.
Higher fields
Stronger signal = finer spatial resolution (smaller voxels).
But remember that we are limited to the resolution of the
vasculature. There is already a lot of correlation among
neighboring 3*3*3 mm voxels.
Larger susceptibility artifacts.
Shorter T2*
Longer T1
Preprocessing
Standard steps everyone does to reduce noise/variability:
Always look at the raw data
Slice time correction
Slices are acquired during different times within a TR:
Head motion correction
Head motion artifacts are particularly evident at edges:
The movement can generate a large change in image
intensity, which can be correlated with the experiment
design.
Head motion correction
To avoid this sequential TR images are co-registered
spatially and estimated head motion parameters are
projected out of the data.
Distortion correction
One can do a magnetic field mapping to determine
inhomogeneities in the static magnetic field that cause
geometric distortions
Temporal filtering
Extract the part of the signal that’s related to your task. Or
at least get rid of parts that aren’t (e.g. scanner drift).
Squeeze hand
for 20 seconds
and then rest for
20 seconds.
To the lab!
Lab #6
Open a folder for your code on the local computer. Try to
keep the path name simple (e.g. “C:\Your_name”).
Download code and MRI data from:
www.dinshi.com
Save Lab6.zip in the folder you’ve created and unzip.
Open Matlab. Change the “current directory” to the
directory you’ve created.
Open: “Lab6_Randomization.m”
Then continue with: “Lab6_ProjectingOutNoise.m”