fMRI Methods Lecture7 – Review: analyses & statistics

1. fMRI MethodsLecture7 – Review: analyses & statistics

2. Neurons Neural computation Neural selectivity Hierarchy of neural processing

3. Integration of information Retinal ganglion cell receptive fields Integrate V1 neuron receptive field (Hubel & Wiesel)

4. Cortical columns Neighboring neurons often share the same selectivity and are strongly connected. “units of computation” At least in the visual system Many columns in a voxel.

5. Hemodynamic changes

6. Birth of the HRF Boynton et. al. 1996

7. Linear shift invariant system Stimulus HRF HRF Time Invariance Scaling Measured Response: Additivity

8. Convolution Multiply each timepoint of the neural activity by a copy of the HRF

9. Estimating neural activity We actually want to go the other way around. So we assume that neuro-vascular coupling is constant across brain areas, tasks, and states

10. Estimating neural activity If we find a reduced/increased hemodynamic response in one experimental condition versus another, what can we deduce about the neural activity generating it? Objects Faces

11. Experiment designs Present stimuli or tasks in a particular temporal structure and see where responses are related/correlated with this temporal structure. Block design: Sparse event related design: Time Rapid event related design:

12. Experiment designs

13. Experiment designs

14. Experiment designs

15. Analyses We have 4 ways of analyzing the data: Correlation with an HRF convolved model Regression with an HRF convolved model Regression with an un-convolved model (deconvolution) Trigger averaging

16. General linear model A mathematical model describing the expected response predictor 1 predictor 2 predictor 1 predictor 2 1 0 0 1 0 0 0 1 1 0 0 1 0 0 1 1 0 0 1 0 1 0 0 1 0 0 Design matrix

17. General linear model Predictors as vectors Dimensions = time-points in data Direction = temporal structure Length = variability of structure If predictors have the same number of “trials”/”blocks”, they will have the same length

18. General linear model The time-course of a voxel is also a vector data What is the relationship between the data and the model? How do we best scale the predictors/model to fit the data?

19. HRF convolved model Our data contains hemodynamic changes, not neural responses. Assume a canonical HRF and convolve the predictors/model:

20. 1. Correlation Correlate each predictor with the data (voxel time-course): predictor 2 predictor 1 data data

21. 2. Regression (take 1) Use linear regression to determine scaling factor for each predictor: design matrix beta data residuals * + a1 a2 error =

22. Unconvolved model Estimate the amplitude and shape of the response at the same time: 1 0 0 1 0 0 0 1 1 0 0 1 0

23. 3. Regression (take 2) Use regression to determine scaling of each predictor: * = a1 a2 … an

24. Randomization/Jitter It’s important to randomize trial timing:

25. 4. Trial triggered average Cut out the trials from your time-course: Normalize each trial to its first two samples The idea is that you expect the same relative response in each trial.

26. Trial triggered average Inspired by ERP Jitter and randomness very important Error bars are simply the standard error of the mean

27. Statistics How do we know whether the beta values are significantly different from zero or from one another? In a single subject analysis and a multi subject fixed effects analysis this depends on the beta value’s variability: Contrast vector

28. Statistics Translate the t-value to a p-value according to the number of “degrees of freedom” T distribution (100 DOF)

29. Fixed effects analysis Commonly done by building a long GLM; stacking the data = * + a1 a2 error

30. Random effects analysis When comparing responses in the same subjects, perform paired “repeated measure” t-test on beta values Beta 1 0.1 0.3 0.7 0.2 0.3 -0.2 Beta 2 1.2 1.4 0.4 2.2 0.8 1 Diff 1.1 1.1 -0.3 2 0.5 1.2

31. Random effects analysis When comparing responses across different subjects, perform regular “two sample” t-test on beta values Group 1 0.1 0.3 0.7 0.2 0.3 -0.2 Group 2 1.2 1.4 0.4 2.2 0.8 1

32. Statistical parameter maps Perform the analysis for each voxel separately and color the voxels by their statistical significance (p values) Around 64,000 voxels in a standard fMRI scan…. Bonferroni Random field theory Cluster thresholding False discovery rate

33. Beware of statistical thresholding Threshold is always arbitrary! From looking at these maps you don’t know how big the difference between betas really is or anything about the actual responses… “Strong” response?

34. Comparing statistical “maps” P values are a function of the average response strength and its variability: Do not compare response strength across subjects, conditions, experiments, using SPM maps!

35. Example A real example from an experiment with autistic individuals:

36. Example When estimating the response within each ROI:

37. Response variability What could cause differences in response variability? Signal and noise

38. System noise Can we compare responses across different scanners? Static field inhomogeneities Scanner drift

39. Head motion Were subjects moving differently during the scan?

40. Head motion In the lab we’ll try different methods of correcting for head motion. Inclusion in the GLM, projecting out, cutting the data

41. Physiological noise Hemodynamic changes caused by heart rate, blood pressure, and respiration.

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

43. Behavioral/Cognitive variability Complex experiment = variable behavioral responses Subjects can choose different strategies. Changes in attention/arousal (caffeine). Response times Effects of caffeine.

44. To the lab!

45. Lab #7 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:http://www.weizmann.ac.il/neurobiology/labs/malach/ilan/lecture_notes.htmlSave Lab6.zip in the folder you’ve created and unzip.Open Matlab. Change the “current directory” to the directory you’ve created.Open: “Lab6_ProjectingOutNoise.m”

46. Scans Create experiments to test the following questions: What is the subject’s real HIRF and how similar is it to a canonical HIRF? How should one arrange the stimuli in a rapid event related experiment? Test different ways of arranging the stimuli (jitter, randomization). What is the minimal inter-stimulus interval that enables accurate separation of responses? You can do the experiments in the visual or auditory domains.