Basic Introduction to Data Analysis. Block Design Demonstration. Robert Savoy

Transcription

1 Basic Introduction to Data Analysis Block Design Demonstration Robert Savoy

2 Sample Block Design Experiment Demonstration Use of Visual and Motor Task Separability of Responses

3 Combined Visual and Motor Task Paradigm Projection Screen Mirror S-VHS Projector Lens Computer with S-VHS video output MRI Room Motor Task (sequential finger opposition) Visual Task

4 Visual Task vis Time (seconds)

5 Visual Task vis fix Time (seconds)

6 Visual Task vis fix vis fix vis fix vis fix vis fix vis Time (seconds)

7 Visual Task 10 Seconds On 15 Seconds Off vis fix vis fix vis fix vis fix vis fix vis fix Time (seconds)

8 Motor Task sfo = sequential finger opposition sfo rest Time (seconds)

9 Motor Task Cued by Visual Task Visual Stimulus Onset Visual Task * * * * * * sfo rest Motor Task Time (seconds)

10 Combined Visual and Motor Task vis fix 10 Seconds On 15 Seconds Off Visual sfo rest 25 Seconds Off 25 Seconds On Motor Time (seconds)

11 64 voxels wide 2 bytes per voxel 64 voxels high 64 x 64 = 4096 voxels per slice

12

13 10 Slices Per Brain Image

14

15 80 brain images per 4 minute run

16 2 bytes per voxel x 4096 voxels per slice x 10 slices per brain image x 80 brain images per run x 18 runs per session = > 100,000,000 bytes per session

17 Feel for the data Exploratory Check for gross problems Confirmatory Systematic statistical analysis Significance testing

18

19

20 Primary Visual Cortex

21 Primary Motor Cortex

22 Primary Motor Cortex Primary Visual Cortex

23

24 Examine the data from one slice of the brain as a function of time

25 Examine the data from one slice of the brain as a function of time

26 Examine the data from one slice of the brain as a function of time

27

28 S.F.O. Rest Rest Sequential Finger Opposition Rest

29 Group This Data Together Group This Data Together

30 Combine these Combine these Consider THIS voxel across all time points

31 Combine these Combine these Consider THIS voxel across all time points

32 Combine these Combine these Are these voxel levels statistically different from each other?

33 Statistical Map

34 Statistical Map Gray Level Indicates Value Statistical Map Color Indicates Value Threshold and Code Statistic via Color

35 High Resolution Image Statistical Map Overlay Statistical Map on Anatomical Image Threshold and Code Statistic via Color

36 Combined Visual and Motor Task vis fix 10 Seconds On 15 Seconds Off Visual sfo rest 25 Seconds Off 25 Seconds On Motor Time (seconds)

37 Statistical map based on time course of Visual Stimuli Statistical map based on time course of Motor Task

38 Time Course of MR Signals Visual Task Motor Task Time (seconds) Percent MR Signal Change Relative to Mean Signal

39 What are a few of the problems with this simple account of confirmatory data analysis?

40 p <.05 means Significant Result 1 time in 20 Just By Chance!

41 40,000 Voxels Per Brain 64 x 64 = 4096 voxels per slice 10 Slices Per Brain Image

42 1/20 of 40,000 voxels is 2000 voxels that appear to be activated Just By Chance

43 Bonferroni Correction

44 Bonferroni Correction Divide statistic by number of voxels

45 Bonferroni Correction Divide statistic by number of voxels.05 40,000 ~ ~ 1 1,000,000

46 4096 voxels per slice but ~ half outside brain

47 4096 voxels per slice but ~ half outside brain

48 4096 voxels per slice...but... 1) Half outside brain 2) Not interested in white matter or ventricles.

49

50 Regions of True Activation are usually bigger than a single voxel

51 Varying Thresholds for Statistical Significance Low Medium High Robert Savoy

52 Functional MRI Workshops Introduction to the GLM in fmri Data Analysis An Overview of Data Processing Tasks in the Analysis of fmri-based Experiments Robert L. Savoy, Ph.D. The Athinoula A. Martinos Center for Biomedical Imaging HyperVision, Inc.

53 Thanks and Acknowledgements Tom Zeffiro (General; SPM; Visualization tools for SPM) Rainer Goebel (BrainVoyager) Robert Cox (AFNI) Doug Greve and Bruce Fischl (FreeSurfer) Steve Smith (FSL) Team of teachers associated with SPM, especially the slides from the Zurich courses:

54 Outline Some nomenclature and conventions Connecting two famous cartoons... fmri as taught by Savoy & Adding one more soon-to-be famous image... The General Linear Model as used in fmri Data Analysis as taught by the SPM group

55 The next few slides were from a the beginning of a lecture on Spatial Preprocessing by Ged Redgway at the Zurich SPM Course in 2009 Ged Ridgway Centre for Medical Image Computing University College London Thanks to: John Ashburner, Klaas Enno Stephan, and the FIL Methods Group. Meike Grol, Chloe Hutton, Jesper Andersson, Floris de Lange, Miranda van Turennout, Lennart Verhagen,

56 Terminology of fmri (slide 1 of 3) Structural (T1-weighted contrast) images: - high resolution - to distinguish different types of tissue Functional (T2* -weighted contrast) 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 Condition A Condition B time

57 Terminology of fmri (slide 2 of 3) subjects sessions runs single run TR = repetition time time required to scan one volume volume slices voxel

58 Terminology of fmri (slide 3 of 3) Scan Volume: Field of View (FOV), e.g. 192 mm Matrix Size e.g., 64 x 64 In-plane resolution 192 mm / 64 = 3 mm (if 200 mm, 200/64 = 3.125) Axial slices Slice thickness e.g., 3 mm 3 mm 3 mm 3 mm Voxel Size (volumetric pixel)

59 Outline Connecting two famous cartoons... & Titles for 5 (or 6) Data Analysis Lectures! Optimizing Data Acquisition! Preprocessing! Modeling for First Level Estimation! Modeling for Second Level Estimation! Inference and Critical Thresholds! (Sixth Lecture: Connectivity and Multivariate Analysis) Now to draw connections between above two cartoons...apologizing that they may make more sense after the course...

60 NMR Data Analysis Practicalities MRI Psychophysiological Laboratory Experimental Task Hemodynamics Functional Neuroanatomy Experimental Design Comparing Brains Computational Neuroanatomy

61 NMR Data Analysis Data Analysis Practicalities MRI Psychophysiological Laboratory Experimental Task Hemodynamics Functional Neuroanatomy Comparing Brains Computational Neuroanatomy

62 Overview of SPM Image time-series Spatial Smoothing Kernel Design matrix Statistical parametric map (SPM) Realignment Smoothing GLM: General Linear Model Spatial Normalisation Statistical inference Gaussian field theory Standardized Anatomical Template Parameter estimates p <0.05

63 Lecture 1 Optimizing Data Acquisition This is the attempt to get the best quality images that you can from your scanner, subject, and experiment.

64 Lecture 2 Preprocessing: Realignment Primarily, this is to compensate, on a global level, for the fact that living subjects move. It is realigning images with similarly collected images---images like themselves.

65 Lecture 2 Preprocessing: Spatial Smoothing This is almost always done, because the size of the activated region is typically larger than a single voxel. It benefits the statistical analysis in a number of ways...in most experiments.

66 Lecture 2 Preprocessing: Spatial Normalization Putting brain data in a standard 3-dimensional coordinate space permits group analysis and reporting findings. Realignment can be associated with spatial normalization when going between imaging modalities (PET & fmri; T1 & T2*)

67 Lecture 3 Modeling for First Level Estimation This is the search for task-related activity in each individual subject.

68 Lecture 4 Modeling for Second Level Estimation Experimental Design Second Level modeling can refer to many things. Most commonly, it refers to group analyses of various kinds.

69 Lecture 5 Inference and Critical Thresholds No Statistics Here! Inference and critical thresholds are a core part of the history of the SPM software package. Gaussian Random Field theory was an attempt to deal with the problem of multiple comparisons without invoking the overly stringent Bonferonni correction.

70 fmr Model Specification and Estimation Basic fmri Course Human Brain Mapping Conference Florence, Italy, 11 th June 2006 Rainer Goebel CEO & Chief Software Developer Brain Innovation B.V. Maastricht, The Netherlands Maastricht Brain Imaging Center!!! F.C. Donders Center for Department of Cognitive Neuroscience!! Cognitive Neuroimaging Maastricht University!!!!! Nijmegen, The Netherlands Maastricht, The Netherlands!!!!

71 View 1: A series of volumes (scans, 3D images ) Useful for seeking spatio-temporal patterns, e.g., via PCA, ICA, etc. View 2: Multiple voxel time series Useful for seeking temporal patterns in each individual voxel of the volumes. Standard hypothesis-driven statistical analysis (e.g., GLM) goes with view 2 since it is applied independently for each voxel time course, i.e., voxel-wise statistical analysis. Two Views on fmri Data

72 Inference: Use Uncertainty of Parameter Estimates a) b) noise noise noise noise Mean 2 Mean 1 Rest Stim Rest Stim Same mean values in Rest and Stim condition in cases a) and b) Simple subtraction (difference = Mean 2 Mean 1) yields same result! Simple subtraction does NOT consider variance of means (noise) Statistical analysis (e.g., t test) relates estimate (mean difference) to uncertainty of estimate = pooled variance of values within conditions, i.e.

73 From Experimental Timing to Expected fmri Time Course Neural pathway Hemodynamics MR scanner Convolution kernel

74 The General Linear Model (GLM) β 0 X 0 fmri signal = β 1 X residuals Time β 2 X 2 Time design matrix Time The design matrix models expected signal time courses for individual conditions (effects of interest), but may also include additional predictor time courses (confounds, effects of no interest) helping to improve explaining the data. In this example, two main predictors are defined (X 1 and X 2 ). A constant predictor (X 0 ) is required to fit the base level of the signal time course. The expected time courses are obtained by convolving the condition box-car functions (red / green) with the assumed impulse response (HRF, two-gamma function).

75 The General Linear Model (GLM) β 0 X 0 fmri signal = β 1 X residuals Time β 2 X 2 Time design matrix Time...The expected time courses are obtained by convolving the condition box-car functions (red / green) with the assumed impulse response (HRF, twogamma function).

76 The General Linear Model (GLM) Time = β 0 + β 1 + β 2 + Time fmri signal design matrix residuals The time courses of the signal, predictors and residuals can be rearranged in column form with time running from top to bottom. This view is helpful to understand the matrix form of the General Linear Model.

77 The General Linear Model (GLM) estimate! β 0 β 1 β 2 Time = fmri signal = data design matrix = model (defined by YOU) residuals = error

78 The General Linear Model (GLM) estimate! β 0 β 1 β 2 Time = fmri signal = data design matrix = model (defined by YOU) residuals = error The GLM time courses, especially the design matrix is often shown in a graphical view using a black-to-white colour range for coding (expected) signal intensities.

79 Time = fmri signal = data design matrix = model (defined by YOU) residuals = error Time = fmri signal = data design matrix = model (defined by YOU) residuals = error

80 With many thanks for slides & images to: FIL Methods group

81

82 Convolve stimulus function with a canonical hemodynamic response function (HRF): Stimulus timing shown in RED Stimulus timing convolved with the canonical HRF Shown in GREEN MR data shown in BLUE

83 The General Linear Model (GLM)

84 The GLM in Matrix Notation observed variable, fmri time course design matrix beta weights, coefficients errors, residuals predictor, explanatory variable, regressor, covariate, basis function another predictor... one of k functions to help fit the data in the GLM

85 The GLM in Matrix Notation

86 The GLM in Matrix Notation Observed fmri signal: Predicted fmri signal: Prediction error:

87 Fitting a GLM

88 The GLM - Contrasts

89 Observed fmri signal Predicted fmri signal residuals b 0 = design matrix GLM Example, block design

90 Observed fmri signal Predicted fmri signal residuals b 0 = b 1 = 1.8 design matrix GLM - Example

91 Observed fmri signal Predicted fmri signal residuals b 0 = b 1 = 4.5 design matrix GLM - Example

92 Observed fmri signal Predicted fmri signal residuals b 0 = b 1 = b 2 = 5.5 GLM - Example design matrix

93 Lessons from the GLM Example To obtain optimal GLM fits, all known effects should be modelled in the design matrix. Non-modelled effects are moved to the residuals, substantially increasing the error variance. This leads to poor fits and reduced statistical power (the error variance is one component of the standard error of contrasts). Inspection of the residuals is a good diagnostic to assess the goodness-of-fit of a GLM: If one observes prominent, low-frequency fluctuations, it is likely that not all effects have been modelled or that the modelled time courses do not fit to the data. The latter might be for example, due to delayed fmri responses with respect to predictors. Confound predictors may be added to improve the fit, for example, predictors capturing low-frequency drifts (Fourier basis functions or Discrete Cosine Transform, DCT, basis functions), if drifts are not removed already during data preprocessing.

94 Overview of SPM Image time-series Spatial Smoothing Kernel Design matrix Statistical parametric map (SPM) Realignment Spatial Normalisation Smoothing GLM: General Linear Model Preprocessing Modeling Inference Statistical inference Gaussian field theory Standardized Anatomical Template Parameter estimates p <0.05

95 effects of interest error variance effects of no interest effects of interest statistic = error variance

96 effects of interest error variance effects of no interest The Jewel we seek! Explained Variance The Unexplained Variance, called noise effects of interest statistic = error variance

97 Functional MRI Workshops Introduction to the GLM in fmri Data Analysis An Overview of Data Processing Tasks in the Analysis of fmri-based Experiments Robert L. Savoy, Ph.D. The Athinoula A. Martinos Center for Biomedical Imaging HyperVision, Inc.