1. fMRI Methods Lecture6 – Signal & Noise

2. Tiny signals in lots of noise
Rest
Pressing hands
% signal difference
Absolute difference

3. 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?

4. What’s the noise Thermal noise System noise
Head motion, respiration, heart beat (physiological) noise
Hemodynamics variability
Neural variability
Behavioral/Cognitive variability
Are 5&6 really noise?

5. 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.

6. System noise
Variability in the function of the imaging hardware across space and time.
Static field inhomogeneities Scanner drift

7. Susceptibility artifacts
Field inhomogeneities are particularly strong at tissue/air boundaries (sinuses). Increase with field strength.
1.5 T
4 T

8. Comparing “extrinsic” noise
Thermal and system noise can be measured and estimated using a phantom made of a known material.

9. Head motion Moving the head during a scan causes two types of noise:
Spatial changes throughout the scan.

10. Now even done online by the scanner! Rather than post-hoc
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

11. Head motion
Image intensity artifacts in time (intensity “spikes”).

12. 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?

13. 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 =

14. 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

15. Preventing head motion

16. Physiological noise
There are non-neural mechanisms causing hemodynamic or inhomogeneity changes during a scan. Luckily they are periodical…

17. Respiration artifacts
The lungs create a changing susceptibility artifact, similar to that seen below in the sinuses (stronger in larger fields).
1.5 T
4 T
Only the lungs effect the signal throughout the brain…

18. Physiological noise
Increases at higher static magnetic fields for the same reason the signal increases…

19. Fourier transform
Decompose complex signals into sinusoidal components
Frequency domain
Frequency
power + + a* b* c*
Frequency
phase
Temporal domain

20. Temporal filtering
Get rid of very low frequencies (drift, respiration). Others?
Fourier transform + + a* b* c*
Noise? multiply by zero

21. 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).

22. Hemodynamics variability
Different subjects exhibit different HRFs

23. Hemodynamics variability
HRFs vary across sessions
Across brain areas?

24. Hemodynamics variability
To address this we can estimate the subject’s HIRF in a separate run and use it to model the responses.

25. Neural variability
The brain is never at “rest”, spontaneous neural activity fluctuations are as large as stimulus evoked responses.

26. 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.

27. Behavioral/Cognitive variability
The more complex an experiment, the more variable the behavioral responses:
Subjects can choose different strategies.
Changes in attention/arousal (caffeine).
Response time distributions of
two subjects performing a
simple decision task.

28. Behavioral/Cognitive variability
Again, variability is typically handled by averaging across trials.
However, this variability also offers an opportunity:
Does neural response
amplitude predict reaction
time or accuracy?
fMRI response
Reaction time

29. Intra-subject variability
Finger tapping task

30. Intra-subject variability
Generate random numbers

31. 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?

32. Improve SNR by averaging
Estimating HRF using different trial numbers:

33. 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!

34. 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.

35. 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

36. Preprocessing
Standard steps everyone does to reduce noise/variability:

37. Always look at the raw data

38. Slices are acquired during different times within a TR:
Slice time correction
Slices are acquired during different times within a TR:

39. 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.

40. Head motion correction
To avoid this sequential TR images are co-registered spatially and estimated head motion parameters are projected out of the data.

41. Distortion correction
One can do a magnetic field mapping to determine inhomogeneities in the static magnetic field that cause geometric distortions

42. 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.

43. To the lab!

44. 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: 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”