How Does FMRI Data Get Turned into Brain Activation Maps ?

1. How Does FMRI Data Get Turned into Brain Activation Maps? Robert W Cox, PhD SSCC / NIMH / NIH / DHHS / USA / EARTH March 31, 2004

2. Outline • Prolegomenon • Temporal Models of Activation • Spatial Models of Activation • Spatio-Temporal Models • Noise Models & Statistics • Inter-Subject Analyses • FMRI Analysis Research • Software Tools • But hardly any equations

3. Prolegomenon • Goal: Find and Characterize Neural “Activations” (whatever that means) • Shocking Revelation #1: FMRI data are (mostly) crap • All other neuroimaging data are, too • Must know what you are doing! • Shocking Revelation #2: Most FMRI papers are weak on analysis

4. Caveats • Almost everything herein has an exception or complication • Special types of data or stimuli may require special analysis tools • e.g., perfusion-weighted FMRI • Special types of questions may require special data and analyses • e.g., relative timing of neural events

5. What We Can Know • The Data: • 10,000..50,000 image voxels inside brain (resolution  3 mm) • 100..1000+ time points in each voxel (time step  2 s) • Also know timing of stimuli delivered to subject (etc) • Probably some hypothesis

6. Graphs of 33 voxels through time One slice at one time; Blue box shows graphed voxels Sample Data: Visual Area V1

7. Same Data as Last Slide This is reallygood data Blowup of central time series graph: about 7% signal change with a very powerful neural stimulus

8. Meta-Method for Analysis • Develop a mathematical model relating what we know (stimulus timing and image data) to what we want to know (location, amount, timing, etc of neural activity) • Given data, use this model to solve for unknown parameters in the neural activity (e.g., when, where, how much, etc) • Then test for statistical significance

9. Why FMRI Analysis Is Hard • Don’t know the true relation between neural “activity” and measurable MRI signal • What is “activity”, anyway? • What is connection between “activity” and hemodynamics and MRI signal? • Noise in data is also poorly characterized • Makes statistical assessment hard

10. Why So Many Methods? • Different assumptions about activity-to-MRI signal connection • Different assumptions about noise (signal fluctuations of no interest) properties and statistics • Different experiments and questions • Result: Many “reasonable” FMRI analysis methods • Researchers must understand the tools!! (Models and software)

11. Temporal Models:Linear Convolution • Assumption: FMRI (hemodynamic) response to 2 separated-in-time activations in the same voxel is the separated-in-time sum of two copies of some individual response function • The FMRI response to a single activation is called the hemodynamic response function (HRF)

12. Brief Stimulus at time t = 1 Model function h(t) = t8.6e–t/0.547 (MS Cohen) Model HRF

13. “Event-Related” Stimuli at times t = 1,7,10 Signal = HRF  Stimulus

14. Ideal response to 1 brief stimulus 220 sec stimulus blocks Block Stimulus

15. Fixed Shape HRF Analysis • Assume some shape for HRF • Signal model is r(t) =HRF  Stimulus = “Convolution” of HRF with neural activity timing function (e.g., stimulus) • Model for each voxel data time series: v(t) = ar(t) + b + noise(t) • Estimate unknowns: a=amplitude, b=baseline, 2 =noise variance • Significance of a≠0 activation map

16. Sample Activation Map • Threshold on significance of amplitude • Color comes from amplitude • Upper Image: color overlay at resolution of EPI • Lower Image: color overlay interpolated to resolution of structural image

17. Variable Shape HRF Analysis • Allow shape of HRF to be unknown, as well as amplitude (deconvolution) • Analysis adapts to each subject and each voxel • Can compare brain regions based on HRF shapes • e.g., early vs. late response? • Must estimate more parameters • Need more data (all else being equal)

18. Multiple Stimulus Classes • Need to calculate HRF (amplitude or amplitude+shape) separately for each class of stimulus • Novice FMRI researcher pitfall: try to use too many stimulus classes • Event-related FMRI: need 25+ events per stimulus class • Block design FMRI: need 10+ blocks per stimulus class

19. Sample Variable HRF Analysis Where HRF What HRF • What-vs-Where tactile stimulation • Red  regions with What  Where

20. Inverse Modeling • Instead of using stimulus timing to get HRF, could use an assumed HRF to get stimulus timing = timing of neural activity in each voxel • Example: show a long video, see what regions are active when, then try to correlate to video contents • e.g., amygdala activation and images of guns

21. Spatial Models of Activation • 10,000+ image voxels in brain • Don’t really expect activation in a single voxel (usually) • Curse of multiple comparisons: • If have 10,000 statistical tests to perform, and 5% give false positive, would have 500 voxels “activated” by pure noise—way way too much! • Can group voxels together somehow to manage the curse

22. Spatial Grouping Methods • Smooth data in space before analysis • Average data across anatomically-selected regions of interest ROI (before or after analysis) • Labor intensive (send more postdocs) • Reject isolated small clusters of above-threshold voxels after analysis

23. Spatial Smoothing of Data • Reduces number of comparisons • Reduces noise (by averaging) • Reduces spatial resolution • Can make FMRI results look PET-ish • In that case, why bother gathering high resolution MR images? • Smart smoothing: average only over local gray matter voxels • Uses resolution of FMRI cleverly • Or average over selected ROIs

24. Spatial Clustering • Analyze data, create statistical map (e.g., t statistic in each voxel) • Threshold map at a lowish tvalue, in each voxel separately • Threshold map by rejecting clusters of voxels below a given size • Can control false-positive rate by adjusting t threshold and cluster-size thresholds together

25. Cluster-Based Detection

26. Clustering Fun Clustering ON Clustering OFF “ShowThru” Volume Rendering

27. Spatio-Temporal Models:Data Driven Analyses • Component models: PCA, ICA • Temporal clustering • Functional (effective, dynamic, etc.) connectivity • Have 4D voxel data v(x,y,z,t) • Try to factor it into simpler pieces that make some sense

28. Component Analyses • Spatio-temporal components: v(x,y,z,t)  w1(x,y,z)  u1(t) + w2(x,y,z)  u2(t) +  • Each ui(t) is a time series component • Each wi(x,y,z) is a spatial map = amplitude of ui(t) in voxel at (x,y,z) • Idea: Explore what’s in the data • Problem: Can be hard to interpret

29. 16th component Data time series “What” stimuli start eigenimage Sample PCA • What-vs-Where tactile stimulation • 16th principal component (of 1040) • Somewhat confusing (at least to me)

30. Temporal Clustering • Idea: Find voxel time series that are “alike” — in some sense • e.g., highly correlated • Average them together to make a “cluster” and iterate • Results: set of component time series, and classification of each voxel location (x,y,z) as belonging to one component

31. Connectivity Analyses • Idea: look for correlated fluctuations in FMRI signal amplitude between different regions during “same” state • Usually start with a preliminary linear analysis to select regions AND / OR • Usually start with some model of connectivity between regions • e.g., region A feeds directly into region B but not into region C

32. Sample Connectivity Model v(t) v(t)=data v(t)=data v(t)=data v(t)=data KJ Friston et al, NeuroImage 19: 1273–1302 (2003)

33. Noise Models & Statistics • Subject head movement • Biggest practical annoyance in FMRI • Physiological noise • Heartbeat and respiration affect signal in complex ways • Magnetic field fluctuations • Scanner glitches can produce gigantic (10 ) spikes in data

34. Correcting Head Movement • Best: don’t let subjects move head! • Almost impossible • Next Best: detect movement during scan, alter MRI acquisition to compensate (prospective correction) • Requires special hardware and/or MRI pulse programming • The Usual: computationally realign (register) images after the fact (retrospective correction)

35. Sample Movement Data Motion parameters vs. time • Less than 1o of head movement • Time between images = 5 seconds

36. Physiological “Noise” • MRI signal changes due to non-neural physiology during scan • Can be approximately filtered out with external measurements • e.g., EKG, respiratory bellows, pulse oximeter • Somewhat harder than it sounds, and is not commonly used (yet)

37. Fluctuations: 16 images/sec 0.22 Hz 1.08 Hz

38. Temporal (‘Serial’) Correlation • Most statistical tests assume separate data samples are independent • Physiological noise is inherently correlated in time • Statistical thresholds (p-values) and power are affected

39. Adapting to Correlated Noise • Can adjust degrees-of-freedom in statistical parameters to approximate for correlation • Can do this with attempts to band-pass filter out physiological noise • Can “prewhiten” data time series to approximately remove correlation • In both methods, must estimate various correlation parameters

40. Avoiding Some Assumptions • All statistical methods require assumptions about noise • Gaussianity, independence, … • Can use modern statistical resampling methods to reduce the number of assumptions • Very computationally intensive • Substituting number crunching for mathematical theory

41. Spatially Structured Noise • Physiological noise is also spatially correlated • But in spotty ways (e.g., among major blood vessels) that are hard to allow for • This issue is usually ignored since it is very hard to model • Exception: “spiral” imaging methods

42. Inter-Subject Analyses • Cortical folding patterns are (at least) as unique as fingerprints • Inter-subject comparisons requires some way to bring brain regions into alignment • Solutions: Brain Warping and ROIs

43. caudate, putamen ROIs • Manually draw anatomically defined brain regions on 3D structural MRIs • Can be tediously boring • Use ROIs to select data from each subject • Combine averages from ROIs as desired • e.g., ANOVA on signal levels

44. Easy Brain Warping • Align brain volume so that inter-hemispheric fissure is vertical (z), and Anterior-Posterior Commissure line is horizontal (y) • Stretch/shrink brain to fit Talairach-Tournoux Atlas dimensions • Use (x,y,z) coordinates based at AC=(0,0,0) • Accuracy: Not so hot (5-15 mm)

45. Hard Brain Warping (3D) • Nonlinearly distort (warp, morph) brain volume images in 3D to match sulcus-to-sulcus, gyrus-to-gyrus • Very computationally intensive • Accuracy: hard to gauge, since method is not widely used • Software for this is not easily available

46. Hard Brain Warping (2D) • Idea: Warp brain only along cortical sheet (curved 2D surface) rather than in general 3D way • Hope: 2D is a little easier than 3D and may be more anatomically meaningful • Not widely used at present • More on this next week!

47. Preview of Surface Stuff Gray-White matter boundary

48. Individual “Brainotyping”? • Most FMRI work to date has been on finding group differences • e.g., patients vs. normals, old vs. young • Is it possible to classify an individual using FMRI brain mapping? • e.g., into disease sub-types? • No one knows how to do this, but it would be cool and useful

49. FMRI Analysis Research • Lots of “reasonable” analyses • Too many good ideas to list here! • Methodology for comparing them • Closer integration of analysis to neural-level hypotheses • Cognitive models; signaling networks • Understand physiology better! • “Brainotyping”: methods for grouping and discriminating among brain maps

50. Software Tools • Several widely used packages • In order of popularity; authors • SPM - Wellcome Institute/London • John Ashburner • AFNI - NIMH IRP/Bethesda • Robert Cox • FSL - FMRIB/Oxford • Steve Smith • Homegrown and/or pastiche