fmri 實 驗 設 計 與 統 計 分 析 簡 介 Introduction to fmri Experiment Design & Statistical Analysis

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1 成 功 大 學 心 智 影 像 研 究 中 心 功 能 性 磁 振 造 影 工 作 坊 fmri 實 驗 設 計 與 統 計 分 析 簡 介 Introduction to fmri Experiment Design & Statistical Analysis 陳 德 祐 7/5/2013 成 功 大 學. 國 際 會 議 廳 Primary Reference: Functional Magnetic Resonance Imaging. Scott A. Huettel, Allen W. Song, and Gregory McCarthy (Sinauer, 2009, Second Edition) AFNI documents & class handouts

2 Hypothesis and Experiment Research hypothesis A proposition about the nature of the world that makes predictions about the results of an experiment. For a hypothesis to be well formed, there must be some experiment whose outcome could prove it to be false. Experiment The controlled test of a hypothesis. Experiments manipulate one or more independent variables, measure one or more dependent variables, and evaluate those measurements using tests of statistical significance. Experimental design The organization of an experiment to allow effective testing of the research hypothesis.

3 Experimental Design: Terminologies Variables Independent (IV) vs. Dependent (DV) Categorical vs. Continuous Causality vs Correlation Experimental vs. Control Comparisons of subjects Between- vs. Within-subjects Confounding factors Randomization, counterbalancing Practice effect & fatigue effect

4 What is a Good Experimental Design? Test specific hypothesis Specify how IVs and DV relate to each other Rule out alternative explanations Minimize the cost for running experiments

5 What is fmri Experimental Design? Controlling the timing and quality of cognitive operations (IVs) to influence brain activation (DVs) In other words: Conditions (IVs) fmri signals and behavioral performance What can/should we control? Stimulus properties (what is presented?) Stimulus timing (when is it presented?) Subject instructions (what do subjects do with it?) What are the goals of experimental design? To test specific hypotheses (i.e., hypothesis-driven) To generate new hypotheses (i.e., data-driven)

6 A basic plan for an fmri study 1. Define mental process to examine Hypotheses 2. Design tasks to manipulate that process Experiments 3. Measure fmri and behavioral data during tasks Data collection 4. Compare fmri data between tasks Statistics

7 Two aspects of fmri experimental design 1. Conceptual design How do we design tasks to measure the processes of interest? The issues are similar to those in cognitive psychology 2. Methodological design How do we construct a task paradigm to optimize our ability to measure the effects of interest, within the specific constraints of the fmri scanning environment?

8 General Considerations Sugges&ons Detail Prac&cal concerns 1. Construct hypothesis 2. Timing arrangement 3. Increase subject number 4. Choose adequate s=muli 5. Organize presenta=on order 6. Record behavioral scores Determine the brain area/network of interests. Acquisi&on &me is spent on the key task condi&ons, not wasted. Especially true for comparisons between groups Maximize the fmri contrasts based on adopted materials and &ming Increase efficiency with minimal confounding factors Not count on fmri only, mul&- measurements are crucial Brain coverage Total scan &me Subject recruitment Delivery of s&muli & controls Enhance efficiency of design matrix Ques&onnaire Response &me

9 Hypotheses for an fmri study Psychological hypothesis: mental or cognitive process Neuronal hypothesis: brain regions (mental process => neuronal activity) Hemodynamic hypothesis: (linearity of hemodynamic response in different regions may be different)

10 Between-subject vs Within-subject Design 1. Between-subject design (or independent groups design) Different group of subjects are assigned to different conditions as defined by the independent variable Control group or random assignment? 2. Within-subject design (or repeated measured design) The same group of subjects serves in more than one treatment Carryover effects: practice effect or fatigue Randomization or counterbalance

11 Overview of fmri Experimental Paradigm

12 Run (or session) Typically 5~10 min for each run/session

13 Block & Trials

14 Trial and Stimulus Color-delayed recognition task Yee et al (2010) J Neurophysiol 103: , 2010.

15 Basic Types of fmri Experiment

16 Blocked Design Definition Inherited from PET experiments Simple & Powerful Combination of trials under the same process Block length ~ sec X A+X X A+X Between blocks Task vs. Baseline conditions Cognitive subtraction assumption Counterbalance blocks of single subject (ABCBCA ) B1 B2 B3 B4 Process of A: (A+X) - (X) Counterbalance blocks across subjects (ABCABC...) (BCABCA...)...

17 Blocked Design Setting Up Determine conditions first (Nc 2) Not too short / too long for each block! Design the timing & sequence btw conditions Concern time points/condition & total acquisition time. Alternating blocks (2 conditions: A & B) Additional control blocks (3 conditions: A & B & Rest) long blocks short blocks

18 Blocked Design : Pros & Cons Advantage Detection power (statistics) Strong BOLD signal (summation, > 2%) Disadvantage Insensitive to the shape and timing of HRF Expectation effects Pure insertion assumption Incorrect response?

19 Event-Related Definition Inherited from EEG experiments Similar to ERP (Event-Related Potentials) since 1920s Signal averaging / Time-locking trials Smaller response (<1%) than blocks (2-3%) Identify timing mismatch between regions word stems -> generate complete words Buckner et al. PNAS 1996

20 Early use of Event-Related fmri Detect Rare Stimuli Most O stimuli, responded to rare X target Dorsolateral Prefrontal Cortex Lateral Parietal Cortex

21 Event-Related Setting Up Hemodynamics Response Short TR limited coverage or slice thickness Inter-subject/trial variations single trial averaging Less Contrast Sensitivity of detection optimal stimulus duration and interval 1000 msec 100 msec 34 msec Aguirre et al. Neuroimage 1998 Time (sec) Savoy et al. ISMRM 1995

22 Event-Related Periodic event-related designs Inter-Stimulus Interval (ISI or ITI) Stimulus Duration (SD) Long ISI ~ 15 sec, very inefficient Rapid event-related designs Setting Up Stimulus Duration (SD) InterStimulus Interval (ISI) small activation at longest ITI, may due to reduced number of trials flickering checkerboard to only left or right visual field Dale & Buckner, 1997

23 Effect of ISI on Event Related fmri short interval: overlap between consecutive HDR reduces the variability in BOLD signal 10 to 12s ISI with 2s SD: periodic activation was still present ISI too short will cause the BOLD signal to saturate Finger tapping task while flashing visual stimuli Bandettini & Cox Magn Reson Med 2000

24 Jittered Events ER-design with variable ISI Miezin et al. Neuroimage 2000 Advantage Better estimation of BOLD response Uncorrelated time points during task Minimize expectation effects S 6 more variability in time, more degree of freedom for statistics S 7

25 Event-Related Design Advantage Great flexibility Reduce habituation Less sensitive to noise Disadvantage Design complexity Weak BOLD response Higher inter-trial/subject variability

26 fmr Adaptation (Mixed) Assumption: Grouping of events into a task block will cause the subject to adopt and maintain a particular cognitive state The process occurs rapidly within the block will evoke transient brain activation under sustained brain activity

27 Conclusion

28 常 見 的 fmri 分 析 軟 體 SPM (Statistical Parametric Mapping) Wellcome Trust Centre for Neuroimaging, UCL, UK Free software running on MATLAB AFNI (Analysis of Functional NeuroImages) NIH, USA Free software, UNIX/Linux, Mac FSL (FMRIB Software Library) FMRIB, Oxford, UK Free software, UNIX/Linux, Mac Brain Voyager Brain Innovation B.V., Netherlands commercial software

29 SPM (Statistical Parametric Mapping)

30 AFNI (Analysis of Functional NeuroImages)

31 FSL (FMRIB Software Library)

32 Brain Voyager

33 BOLD (Blood Oxygenation Level Dependent) Response Hemodynamic response (HDR) Ø Brain response to stimulus/task/condition o Ideally we want to know the response (activation) at neuronal level, but that is beyond the FMRI capability Ø Indirect measure of neural response: dynamic regulation of blood flow Hemodynamic response function (HDF) Ø Mathematical formulation/idealization of HDR Ø BOLD signal is further an indirect measure of brain response Ø HDF bridges between neural response and BOLD signal Instant stimulus 33

34 BOLD fmri Signal and Analysis Hemodynamic function convolved with experiment design

35 Activity Evaluation Active Rest Signal change Standard deviation Use concept of normal distribution to model each condition in BOLD signal. Find which voxels have time courses that match the predicted response. An unrelated brain region should have no response!

36 Statistics: Correlation Quantify how well the data match HRF response. Strategy: 1. Paradigm + fmri data 2. Covariance 3. Normalization (divide by std) μx & μy: population mean σx & σy: standard deviation Degree of freedom: (nx + ny -2) Correlation coefficients range: (-1, +1) irrelevant to amplitude Correlation

37 Statistical Comparison v Comparison between Conditions Conditions induced by IVs (task or population) DV: (fmri data) 1. Grp1-Grp2 Baseline threshold Activation 2. Task-Rest Baseline (OFF) Activation (ON) α< 0.05 α< 0.05

38 Statistics: t-test Identify differences in the means Single condition (compared to 0) μ0: population mean s: sample standard deviation n: sample size Degree of freedom: (n-1) Two conditions (unequal sample size, unequal variance) X1 & X2: population mean n1 & n2: sample size SX1X2: standard deviation of 2 samples Degree of freedom: (n1 + n2-2) t é p ê more likely has significant difference

39 Review of Statistics H1 : ON OFF H0 : ON = OFF threshold β α Power = 1-β α< 0.05 β false alarm Strategy control α and decrease β significance level: p < 0.05 (magic number) missed

40 Basics of Linear Model: Regression Regression: relationship between a response/outcome (dependent) variable and one or more explanatory (independent) variables (regressors) Ø Simple regression: fit data with a straight line y y =! + "x + #! is the intercept (constant), " is the slope (like amplitude) Ø Some statisticians just call it linear model Mathematical crystallization x Ø y i =! + "x i + # i, or y i =! + " 1 x 1i + + " k x ki + # i Ø y = X! + ", X = [1, x 1, x 2,, x k ] Ø Assumption o linearity o white noise (independence) and Gaussianity " ~ N(0, $ 2 I)

41 Statistics: Regression Observed data (yi) regressors (xi) variable weighting (βi) residual noise (ε) Regressors for fmri Curve fitting If β is non-zero, then voxel is active β has amplitude info. Data

42 Solution for linear regression y = X! + " Ø Project data y onto the space of explanatory variables (X) Ø OLS Meaning of coefficient: " value, slope, marginal effect or effect size associated with a regressor Various statistical tests: Ø Omnibus or overall F-test for the whole model, e.g, H 0 : all " values are 0, or H 0 : all " values of interest are 0 Ø Student t-test for each " (H 0 : " 3 = 0) Ø Student t-test for linear combination of " values - general linear test (GLT), e.g., H 0 : " 3 " 5 = 0, or H 0 : 0.5*(" 3 + " 4 ) " 5 = 0 Ø F-test for composite null hypothesis, e.g., H 0 : " 3 = " 4 = " 5 or H 0 : " 3 = " 4 = " 5 = 0 Basics of Linear Model 42

43 General Linear Model with FMRI Time series regression: data y is time series Ø Regressors: idealized response o We get what we re looking for o It may miss something when we fail to recognize it o Regressor construction is quite challenging Ø Special handling: noise not white " ~ N(0, $ 2 #) with temporal or serial correlation o Banded variance-covariance matrix # Ø AKA general linear model (GLM) in many fmri packages Same model for all voxels in the brain Ø Simultaneously solve the models: voxel-wise analysis, massively univariate method 43

44 FMRI Data Data partition: Data = Signal + Noise Ø Data = acquisition from scanner (voxel-wise time series) o What we have Ø Signal = BOLD response to stimulus; effects of interest + no interest o We don t really know the real signal!!! o Look for idealized components, or search for signal via repeated trials o Of interest: effect size (response amplitude) for each condition: beta o Of no interest: baseline, slow drift, head motion effects, Ø Noise = components in data that interfere with signal o Practically the part we have don t know and/or we don t care about; that is, noise is the part we can t explain in the model o Will have to make some assumptions about its distribution Data = baseline + slow drift + other effects of no interest + response response k + noise Ø How to construct the regressors of interest (responses)? 44

45 Linear Model with Fixed-Shape IRF Ø FMRI data = baseline + drift + other effects of no interest + response response k + noise Ø baseline = baseline + drift + other effects of no interest o Drift: psychological/physiological effect, thermal fluctuation o Data = baseline + effects of interest + noise o Baseline condition (and drift) is treated in AFNI as baseline, an additive effect, not an effect of interest (cf. SPM and FSL)! Ø y i =! 0 +! 1 t i +! 1 t i 2 + " 1 x 1i + + " k x ki + + # i Ø y = X! + ", X = [1, t, t2, x 1, x 2,, x k, ] Ø In AFNI baseline + slow drift is modeled with polynomials o A longer run needs a higher order of polynomials probably one order per 150 sec o With m runs, m separate sets of polynomials needed to account for temporal discontinuities across runs m(p+1) columns for baseline + slow drift: with p-order polynomials Ø Other typical effects of no interest: head motion effects 45

46 Design Matrix with Fixed-Shape IRF Voxel-wise (massively univariate) linear model: y = X"+# Ø X: explanatory variables (regressors) same across voxels Ø y: data (time series) at a voxel different across voxels Ø ": regression coefficients (effects) different across voxels Ø #: anything we can t account for different across voxels Visualizing design matrix X = [1, t, t 2, x 1, x 2,, x k, ] in grayscale baseline + drift s&muli head mo&on } 6 dri) effect regressors Ø linear baseline Ø 3 runs x 2 parameters/run 2 regressors of interest 6 head mo=on regressors Ø 3 rota=ons + 3 shi)s 46

47 Everything is about contrast! Ø Even true for happiness in life Statistical Testing Effects (regression coefficients) of interest Ø β: effect relative to baseline condition o β A = Effect A - β base Ø t-statistic: significance Pairwise comparisons (contrasts) Ø Conditions β A vs. β B (e.g., house vs. face) o β A β B = (Effect A - β base ) (Effect B - β base ) = Effect A - Effect B Ø t-statistic: significance General linear test linear combination of multiple effects Ø t-statistic: 0.5*happy + 0.5*sad neutral Composite tests Ø F-statistic for composite null hypotheses: happy = sad = neutral = 0; or, happy = sad = neutral 47

48 Group Analysis (2nd-level Analysis) Summarize results from all subjects H Prerequisite: reasonable alignment to some template Conventional approach: taking β(or linear combination of multiple β s) only for group analysis H H H Assumption: all subjects have same precision (reliability, standard error, confidence interval) about β All subjects are treated equally Student t-test: paired, one- and two-sample: not random-effects models in strict sense as usually claimed Alternative: taking both effect estimates and t-statistics H H t-statistic contains precision information about effect estimates Each subject is weighted based on precision of effect estimate

49 Examples of Groups Analysis One-Sample Case One group of subjects (n 10) One condition (house or face) effect Linear combination of multiple effects (house - face) Null hypothesis H : average effect = 0 0 Rejecting H 0 is of interest! Results Average effect at group level Significance: t-statistic Two-Sample Case Two groups of subjects (n 10): ex:males and females One condition (house or face) effect Linear combination of multiple effects (house - face) Example: Gender difference in emotion effect? Null hypothesis H 0 : Group1 = Group2 Results Group difference in average effect o Significance: t-statistic

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