NeuroImaging. (spatial and statistical processing, maybe) Philippe Peigneux, PhD. UR2NF - Neuropsychology and Functional

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1 NeuroImaging (spatial and statistical processing, maybe) Philippe Peigneux, PhD UR2NF - Neuropsychology and Functional Neuroimaging Research Unit, ULB

2 CREDITS These slides have been presented during an introductory course to neuroimaging techniques held at the Université Libre de Bruxelles (ULB) October-December Some are original slides, but many are taken from online material available at the following : FMRI 4 NEWBIES SPM - Statistical Parametric Mapping Thanks to the many generous authors who have build this educational material!

3 Philips Achieva 3T, Hôpital Erasme, ULB

4 Attending a poster session at a recent meeting, I was reminded of the old adage To the man who has only a hammer, the whole world looks like a nail. In this case, however, instead of a hammer we had a magnetic resonance imaging (MRI) machine and instead of nails we had a study. Many of the studies summarized in the posters did not seem to be designed to answer questions about the functioning of the brain; neither did they seem to bear on specific questions about the roles of particular brain regions. Rather, they could best be described as exploratory. People were asked to engage in some task while the activity in their brains was monitored, and this activity was then interpreted post hoc. -- Stephen M. Kosslyn (1999). If neuroimaging is the answer, what is the question? Phil Trans R Soc Lond B, 354,

5 Brains Needed "...the single most critical piece of equipment is still the researcher's own brain. All the equipment in the world will not help us if we do not know how to use it properly, which requires more than just knowing how to operate it. Aristotle would not necessarily have been more profound had he owned a laptop and known how to program. What is badly needed now, with all these scanners whirring away, is an understanding of exactly what we are observing, and seeing, and measuring, and wondering about." -- Endel Tulving, interview in Cognitive Neuroscience (2002, Gazzaniga, Ivry & Mangun, Eds., NY: Norton, p. 323)

6 Terminology of fmri Structural (T1) images: - high resolution - to distinguish different types of tissue Functional (T2*) images: - lower spatial resolution - to relate changes in BOLD signal to an experimental manipulation Time series: A large number of images that are acquired in temporal order at a specific rate t Condition A Condition B

7 Terminology of fmri subjects sessions runs single run (U.S.) volume TR = repetition time time required to scan one volume slices voxel

8 Terminology of fmri Scan Volume: Field of View (FOV), e.g. 192 mm Axial slices Slice thickness e.g., 3 mm Matrix Size e.g., 64 x 64 3 mm In-plane resolution 192 mm / 64 = 3 mm 3 mm 3 mm Voxel Size (volumetric pixel)

9 Why is fmri analysis so (bloody) complicated? Temporal issues 1. BOLD dynamics 2. Non-linear effects 3. Serial autocorrelations Spatial issues 1. Subject s inter-scan movement 2. Inter-subject brain differences 3. Multiple comparisons across the brain Other issues 1. Low signal-to-noise ratio (SNR) 2. Very expensive 3. Very boring

10 Data analysis : getting good data! Image time-series Kernel Design matrix Statistical parametric map (SPM) Realignment Smoothing General linear model Normalisation Statistical inference Gaussian field theory Template Parameter estimates p <0.05

11 High and Low Frequency Noise

12 High-Pass Filter Events: SOA = 15s (e.g., stimulus) Blocks: SOA = 120s (e.g., attention) High-pass filter cut-off = min[2 * max(soa)]

13 High-Pass Filter Before filtering After filtering Events (0.07Hz) Blocks (0.01Hz) HP cutoff = 1/30s = 0.03 Hz

14 High-Pass Filter Good: Cleans data, removing low-frequency drifts unrelated to the experimental paradigm Bad: It can remove signal-related frequencies What to do: Check the frequency spectrum of the design matrix (xx.x), and the smoothed design matrix (xx.xkxs.x), to ensure that the filter is doing the right job AND/OR think well in advance how your stimuli are displayed!

15 Serial autocorrelations (Low-Pass Filter) Individual observations are not mutually independent!! The effective degrees of freedom (d.f.) are reduced Options: Temporal smoothing (impose a known correlation) Good: Does not require a model of correlations Bad: Lower d.f. Gaussian Matched-filter Theorem (e.g., hrf) auto-regressive model of order 1 Estimate intrinsic autocorrelation [e.g. AR(1)] Good: Maximize d.f. Bad: The model used can be wrong Uniform Voxel-specific

16 30 slices

17 Intra-volume time acquisition correction (slice timing)

18 Slice timing Interleaved sequence Ascending sequence

19 Inter-scan movement: Realignment People move, even if they don t realize! Need for motion correction Two steps: 1. Registration: Determine the 6 parameters that describe the rigid-body transformation between each image and a reference image (usu. first in series). 2. Transformation: Resampling each image according to the determined transformation parameters.

20 Inter-scan movement: Realignment Same location in the brain Same location in the grid Rigid body movement: 3 translation parameters 3 rotation parameters z roll x pitch y yaw

21 Realignment: Transformation

22 Realignment: Registration Small movements are corrected well TRANSLATION mm z y x ROTATION rad pitch (x) yaw (y) roll (z) Sudden movements are more problematic (especially if correlated with experimental paradigm)

23 Slide from Duke course can be catastrophically bad

24 Motion Intensity Changes A B C Slide modified from Duke course

25 Motion Spurious Activation at Edges lateral motion in x direction motion in z direction (e.g., padding sinks) brain position time1 time2 stat map time 1 > time 2 time 1 < time 2

26 Structural differences between subjects: Normalization Different People Different Brains!!

27 Normalization Also useful for reporting coordinates in a standard space (e.g., Talairach and Tournoux)

28 Standard space The Talairach Atlas The MNI/ICBM AVG152 Template The MNI template follows the convention of T&T, but doesn t match the particular brain Recommended reading:

29 Why smooth? Remove residual inter-subject brain differences Allow for the use of Gaussian random field theory (coming through )

30 Effects of Spatial Smoothing on Activity Unsmoothed Data Smoothed Data (kernel width 5 voxels) Slide from Duke course

31 Should you spatially smooth? Advantages Increases Signal to Noise Ratio (SNR) Matched Filter Theorem: Maximum increase in SNR by filter with same shape/size as signal Reduces number of comparisons Allows application of Gaussian Field Theory May improve comparisons across subjects Signal may be spread widely across cortex, due to intersubject variability Disadvantages Reduces spatial resolution Challenging to smooth accurately if size/shape of signal is not known Slide from Duke course

32 Other Artifacts Ghosts Zebra Brains Metallic Objects (e.g., hair tie) Spikes

33 Data analysis : a good design cannot harm Image time-series Kernel Design matrix Statistical parametric map (SPM) Realignment Smoothing General linear model Normalisation Statistical inference Gaussian field theory Template Parameter estimates p <0.05

34 Voxel-wise time series analysis model specification Time Time parameter estimation hypothesis statistic single voxel time time series BOLD signal SPM

35 Why do we need stats? We could, in principle, analyze data by voxel surfing: move the cursor over different areas and see if any of the time courses look interesting Slice 9, Voxel 0, 0 Even where there s no brain, there s noise Slice 9, Voxel 1, 0 Slice 9, Voxel 22, 7 The signal is much higher where there is brain, but there s still noise Slice 9, Voxel 9, 27 Here s a voxel that responds well whenever there s visual stimulation Slice 9, Voxel 18, 36 Here s a couple that sort of show the right pattern but is it real? Slice 9, Voxel 13, 41 Here s one that responds well whenever there s intact objects Slice 9, Voxel 14, 42 fmri for Dummies

36 Why do we need stats? Clearly voxel surfing isn t a viable option. We d have to do it 49,152 times in this data set and it would require a lot of subjective decisions about whether activation was real This is why we need statistics The lies and damned lies come in when you write the manuscript Statistics: tell us where to look for activation that is related to our paradigm help us decide how likely it is that activation is real fmri for Dummies

37 Predicted Responses fmri is based on the Blood Oxygenation Level Dependent (BOLD) response It takes about 5 sec for the blood to catch up with the brain We can model the predicted activation in one of two ways: 1. shift the boxcar by approximately 5 seconds (2 images x 2 seconds/image = 4 sec, close enough) 2. convolve the boxcar with the hemodynamic response to model the shape of the true function as well as the delay PREDICTED ACTIVATION IN VISUAL AREA PREDICTED ACTIVATION IN OBJECT AREA BOXCAR SHIFTED CONVOLVED WITH HRF fmri for Dummies

38 Basis Functions Synthetic hemodynamic response function (HRF) Raw data

39 Basis Functions HRF, temporal derivative and dispersion Gamma functions Fourier set (sines and cosines)

40 Basis Functions Options: Few, model-based functions (e.g., synthetic HRF) Good: Easy to analyze and interpret in terms of hemodynamic activity Bad: May fail to capture real responses that do not fit the assumed behaviour Many, general basis functions (e.g., Fourier set) Good: No a priori assumptions about the shape of the response. Can capture unexpected responses (e.g., longer delay/duration) Bad: Difficult to interpret physiologically. Difficult to take to a second level (random) analysis

41 Effect of Thresholds r =.80 64% of variance p < r =.50 25% of variance p < r =.40 16% of variance p < r =.24 6% of variance p <.05 r = 0 0% of variance p < 1 fmri for Dummies

42 Complications Not only is it hard to determine what s real, but there are all sorts of statistical problems Potential problems What s wrong with these data? 1. data may be contaminated by artifacts (e.g., head motion, breathing artifacts) * 49,152 = 2457 significant voxels by chance alone r =.24 6% of variance p < many assumptions of statistics (adjacent voxels uncorrelated with each other; adjacent time points uncorrelated with one another) are false fmri for Dummies

43 The General Linear Model T-tests, correlations and Fourier analysis work for simple designs and were common in the early days of imaging The General Linear Model (GLM) is now available in many software packages and tends to be the analysis of choice Why is the GLM so great? the GLM is an overarching tool that can do anything that the simpler tests do you can examine any combination of contrasts (e.g., intact - scrambled, scrambled - baseline) with one GLM rather than multiple correlations the GLM allows much greater flexibility for combining data within subjects and between subjects it also makes it much easier to counterbalance orders and discard bad sections of data the GLM allows you to model things that may account for variability in the data even though they aren t interesting in and of themselves (e.g., head motion) as we will see later in the course, the GLM also allows you to use more complex designs (e.g., factorial designs) fmri for Dummies

44 A Simple Experiment Lateral Occipital Complex responds when subject views objects Blank Screen Intact Objects TIME One volume (12 slices) every 2 seconds for 272 seconds (4 minutes, 32 seconds) Condition changes every 16 seconds (8 volumes) Scrambled Objects fmri for Dummies

45 What s real? A. C. B. D. fmri for Dummies

46 What s real? I created each of those time courses based by taking the predictor function and adding a variable amount of random noise signal = + noise fmri for Dummies

47 What s real? Which of the data sets below is more convincing? fmri for Dummies

48 Statistical Significance Significance depends on signal (differences between conditions) noise (other variability) sample size (more time points are more convincing) fmri for Dummies

49 Let s create a time course for one LO voxel fmri for Dummies

50 We ll begin with activation Response to Intact Objects is 4X greater than Scrambled Objects fmri for Dummies

51 Then we ll assume that our modelled activation is off because a transient component fmri for Dummies

52 Our modelled activation could be off for other reasons All of the following could lead to inaccurate models different shape of function different width of function different latency of function fmri for Dummies

53 Variability of HRF Aguirre, Zarahn & D Esposito, 1998 HRF shows considerable variability between subjects different subjects Within subjects, responses are more consistent, although there is still some variability between sessions same subject, same session same subject, different session fmri for Dummies

54 Now let s add some variability due to head motion fmri for Dummies

55 though really motion is more complex Head motion can be quantified with 6 parameters given in any motion correction algorithm x translation y translation z translation xy rotation xz rotation yz rotation For simplicity, I ve only included parameter one in our model Head motion can lead to other problems not predictable by these parameters fmri for Dummies

56 Now let s throw in a pinch of linear drift linear drift could arise from magnet noise (e.g., parts warm up) or physiological noise (e.g., subject s head sinks) fmri for Dummies

57 and then we ll add a dash of low frequency noise low frequency noise can arise from magnet noise or physiological noise (e.g., subject s cycles of alertness/drowsiness) low frequency noise would occur over a range of frequencies but for simplicity, I ve only included one frequency (1 cycle per run) here fmri for Dummies Linear drift is really just very low frequency noise

58 and our last ingredient some high frequency noise high frequency noise can arise from magnet noise or physiological noise (e.g., subject s breathing rate and heartrate) fmri for Dummies

59 When we add these all together, we get a realistic time course fmri for Dummies

60 Now let s be the experimenter First, we take our time course and normalize it using z scores z = (x - mean)/sd normalization leads to data where mean = zero SD = 1 fmri for Dummies

61 We create a GLM with 2 predictors β 1 = + + β 2 fmri Signal = Design Matrix x Betas + what we CAN explain how much of it we CAN explain our data = x + Residuals what we CANNOT explain Statistical significance is basically a ratio of explained to unexplained variance fmri for Dummies

62 Implementation of GLM in SPM Many thanks to Øystein Bech Gadmar for creating this figure in SPM Time Intact Predictor Scrambled Predictor SPM represents time as going down SPM represents predictors within the design matrix as grayscale plots (where black = low, white = high) over time SPM includes a constant to take care of the average activation level throughout each run fmri for Dummies

63 We create a GLM with 2 predictors when β 1 =2 = + + when β 2 =0.5 fmri Signal our data = Design Matrix x Betas what we CAN explain how much of it we CAN explain = x + + Residuals what we CANNOT explain Statistical significance is basically a ratio of explained to unexplained variance fmri for Dummies

64 Correlated Predictors Where possible, avoid predictors that are highly correlated with one another This is why we NEVER include a baseline predictor baseline predictor is almost completely correlated with the sum of existing predictors + r = -.53 = r = -.53 Two stimulus predictors r = -.95 Baseline predictor

65 Which model accounts for this data? x β = 1 x β = 0 + OR + x β = 1 x β = x β = 0 x β = -1 Because the predictors are highly correlated, you can t tell which model is best

66 A Real Voxel Here s the time course from a voxel that was significant in the +Intact - Scrambled comparison fmri for Dummies

67 Maximizing Your Power signal = + As we saw earlier, the GLM is basically comparing the amount of signal to the amount of noise How can we improve our stats? increase signal decrease noise increase sample size (keep subject in longer) fmri for Dummies noise

68 How to Reduce Noise If you can t get rid of an artifact, you can include it as a predictor of no interest to soak up variance Example: Some people include predictors from the outcome of motion correction algorithms Corollary: Never leave out predictors for conditions that will affect your data fmri for Dummies

69 What s this #*%&ing reviewer complaining about?! Particularly if you do voxelwise stats, you have to be careful to follow the accepted standards of the field. In the past few years the following approaches have been recommended by the stats mavens: 1. Correction for multiple comparisons 2. Correction for serial correlations 3. Random effects analyses fmri for Dummies

70 Correction for Multiple Comparisons With conventional probability levels (e.g., p <.05) and a huge number of comparisons (e.g., 64 x 64 x 12 = 49,152), a lot of voxels will be significant purely by chance e.g.,.05 * 49,152 = 2458 voxels significant due to chance How can we avoid this? 1) Bonferroni correction divide desired p value by number of comparisons Example: desired p value: p <.05 number of voxels: 50,000 required p value: p <.05 / 50,000 p < quite conservative can use less stringent values e.g., Brain Voyager can use the number of voxels in the cortical surface small volume correction: use more liberal thresholds in areas of the brain which you expected to be active fmri for Dummies

71 Correction for Multiple Comparisons 2) Gaussian field theory Fundamental to SPM If data are very smooth, then the chance of noise points passing threshold is reduced Can correct for the number of resolvable elements ( resels ) rather than number of voxels Slide modified from Duke course fmri for Dummies

72 3) Cluster correction falsely activated voxels should be randomly dispersed set minimum cluster size to be large enough to make it unlikely that a cluster of that size would occur by chance assumes that data from adjacent voxels are uncorrelated (not true) 4) Test-retest reliability Perform statistical tests on each half of the data The probability of a given voxel appearing in both purely by chance is the square of the p value used in each half e.g.,.001 x.001 = Alternatively, use the first half to select an ROI and evaluate your hypothesis in the second half. fmri for Dummies

73 Correction for Temporal Correlations Statistical methods assume that each of our time points is independent. In the case of fmri, this assumption is false. Even in a screen saver scan, activation in a voxel at one time is correlated with it s activation within ~6 sec This fact can artificially inflate your statistical significance. fmri for Dummies

74 Autocorrelation function original shift by 1 volume shift by 2 volumes To calculate the magnitude of the problem, we can compute the autocorrelation function For a voxel or ROI, correlate its time course with itself shifted in time Plot these correlations by the degree of shift time If there s no autocorrelation, function should drop from 1 to 0 abruptly pink line the points circled in yellow suggest there is some autocorrelation, especially at a shift of 1, called AR(1) fmri for Dummies

75 Collapsed Fixed Effects Models assume that the experimental manipulation has same effect in each subject treats all data as one concatenated set with one beta per predictor (collapsed across all subjects) e.g., Intact = 2 Scrambled =.5 strong effect in one subject can lead to significance even when others show weak or no effects you can say that effect was significant in your group of subjects but cannot generalize to other subjects that you didn t test fmri for Dummies

76 Contrasts in the GLM We can examine whether a single predictor is significant (compared to the baseline) We can also examine whether a single predictor is significantly greater than another predictor fmri for Dummies

77 Separate Subjects Models one beta per predictor per subject e.g., JC: Intact = 2.1 JC: Scrambled = 0.2 DQ: Intact = 1.5 DQ: Scrambled = 1.0 KV: Intact = 1.2 KV: Scrambled = 1.3 weights each subject equally makes data less susceptible to effects of one rogue subject fmri for Dummies

78 Random Effects Analysis Typical fmri stats test whether the differences between conditions are significant in the sample of subjects we have tested Often, we want to be able to generalize to the population as a whole including all potential subjects, not just the ones we tested Random effects analyses allow you to generalize to the population you tested underpaid graduate students in need of a few bucks! Random effects analyses can really squash your data, especially if you don t have many subjects. Sometimes we refer to the random effects button as the make my activation go away button. Reviewers are now requesting random effects analyses more frequently You don t have to worry about it if you re using the ROI approach because (1) presumably the ROI has already been well-established across multiple labs; and (2) posthoc analyses of results in an ROI approach allow you to generalize to the population (assuming you include individual variance) fmri for Dummies

79 Fixed vs. Random Effects GLM Sample Data #1 Sample Data #2 Subject Intact beta Scram beta Diff Subject Intact beta Scram beta Diff SUM SUM Fixed Effects GLM cannot tell the difference between these data sets because (Intact sum - Scram sum) is the same in both cases In Random Effects GLM, Data set #1 would be more likely to be significant because all 3 subjects show a trend in the same direction (intact > scrambled), whereas in data set #2, only 2 of 3 subjects show a difference in that direction

80 Methodological Fundamentalism The latest review I received

81 Approach #1: Voxelwise Statistics 1. You don t necessarily need a priori hypotheses (though sometimes you can use less conservative stats if you have them) 2. Average all of your data together in Talairach space 3. Compare two (or more) conditions using precise statistical procedures within every voxel of the brain. Any area that passes a carefully determined threshold is considered real. 4. Make a list of these areas and publish it. This is the tricky part! fmri for Dummies

82 Voxelwise Approach: Example Malach et al., 1995, PNAS Question: Are there areas of the human brain that are more responsive to objects than scrambled objects You will recognize this as what we now call an LO localizer, but Malach was the first to identify LO LO activation is shown in red, behind MT+ activation in green LO (red) responds more to objects, abstract sculptures and faces than to textures, unlike visual cortex (blue) which responds well to all stimuli fmri for Dummies

83 The Danger of Voxelwise Approaches This is one of two tables from a paper Some papers publish tables of activation two pages long How can anyone make sense of so many areas? Source: Decety et al., 1994, Nature fmri for Dummies

84 Approach #2: Region of interest (ROI) analysis If you are looking at a well-established area (such as visual cortex, motor cortex, or the lateral occipital complex), it s fairly easy to activate and identify the area 1. Do the stats and play with the threshold till you get something believable in the right vicinity based on anatomical location (e.g., sulcal landmarks) or functional location (e.g., Talairach coordinates from prior studies) 2. Once you have found the ROI, do independent experiments, extract the time course information and determine whether activation differences between conditions are significant Because the runs that are used to generate the area are independent from those used to test the hypothesis, liberal statistics (p <.05) can be used fmri for Dummies

85 Example of ROI Approach Culham et al., 2003, Experimental Brain Research Does the Lateral Occipital Complex compute object shape for grasping? Step 1: Localize LOC Intact Objects Scrambled Objects

86 Example of ROI Approach Culham et al., 2003, Experimental Brain Research Does the Lateral Occipital Complex compute object shape for grasping? Step 2: Extract LOC data from experimental runs Grasping Reaching NS p =.35 NS p =.31

87 Example of ROI Approach Very Simple Stats Subject 1 % BOLD Signal Change Left Hem. LOC Grasping 0.02 Reaching 0.03 Then simply do a paired t-test to see whether the peaks are significantly different between conditions Extract average peak from each subject for each condition NS p = NS p = Instead of using % BOLD Signal Change, you can use beta weights You can also do a planned contrast in Brain Voyager using a module called the ROI GLM

88 Utility of Doing Both Approaches We also verified the result with a voxelwise approach Why might ROI alone not suffice? Why might voxelwise alone not suffice? Verification of no LOC activation for grasping > reaching even at moderate threshold (p <.001)

89 Example: The Danger of ROI Approaches Example 1: LOC may be a heterogeneous area with subdivisions; ROI analyses gloss over this Example 2: We looked at another example of an ROI analysis last week: Kanwisher et al. s paper on the fusiform face area (FFA). Since then, growing evidence suggests another area, the occipital face area (OFA) may also be critical to face perception. The OFA was overlooked in the original study because it was less robust and reliable than the FFA. fmri for Dummies

90 Comparing the two approaches Voxelwise Analyses Requires no prior hypotheses about areas involved Includes entire brain Often neglects individual differences Can lose spatial resolution with intersubject averaging Can produce meaningless laundry lists of areas that are difficult to interpret You have to be fairly stats-savvy and include all the appropriate statistical corrections to be certain your activation is really significant Popular in Europe Region of Interest (ROI) Analyses Extraction of ROI data can be subjected to simple stats (no need for multiple comparisons, autocorrelation or random effects corrections) Gives you more statistical power (e.g., p <.05) Hypothesis-driven Useful when hypotheses are motivated by other techniques (e.g., electrophysiology) in specific brain regions ROI is not smeared due to intersubject averaging Easy to analyze and interpret Neglects other areas which may play a fundamental role If multiple ROIs need to be considered, you can spend a lot of scan time collecting localizer data (thus limiting the time available for experimental runs) Popular in North America fmri for Dummies

91 A Proposed Resolution There is no reason not to do BOTH ROI analyses and voxelwise analyses ROI analyses for well-defined key regions Voxelwise analyses to see if other regions are also involved Ideally, the conclusions will not differ If the conclusions do differ, there may be sensible reasons Effect in ROI but not voxelwise perhaps region is highly variable in stereotaxic location between subjects perhaps voxelwise approach is not powerful enough Effect in voxelwise but not ROI perhaps ROI is not homogenous or is context-specific

92 Hypothesis- vs. Data-Driven Approaches Hypothesis-driven Examples: t-tests, correlations, general linear model (GLM) a priori model of activation is suggested data is checked to see how closely it matches components of the model most commonly used approach Data-driven Example: Independent Component Analysis (ICA) no prior hypotheses are necessary multivariate techniques determine the patterns in the data that account for the most variance across all voxels can be used to validate a model (see if the math comes up with the components you would ve predicted) can be inspected to see if there are things happening in your data that you didn t predict can be used to identify confounds (e.g., head motion) need a way to organize the many possible components fmri for Dummies