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Primer on paradigms and data analyses in fMRI

Primer on paradigms and data analyses in fMRI. April 18 th , 2012 Laurea University of Applied Sciences, Espoo, Finland. WHY fMRI? BOLD SIGNAL THE BASELINE PARADIGMS GLM ANNs. WHY fMRI? BOLD SIGNAL THE BASELINE PARADIGMS GLM ANNs. Advantages of fMRI:. - non invasive;

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Primer on paradigms and data analyses in fMRI

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  1. Primer on paradigms and data analyses in fMRI April 18th, 2012 Laurea University of Applied Sciences, Espoo, Finland

  2. WHY fMRI? BOLD SIGNAL THE BASELINE PARADIGMS GLM ANNs

  3. WHY fMRI? BOLD SIGNAL THE BASELINE PARADIGMS GLM ANNs Advantages of fMRI: - non invasive; - ethically acceptable in healthy participants; - good spatial definition; - more than 15 years of neuropsychological functional studies.

  4. WHY fMRI? BOLD SIGNAL THE BASELINE PARADIGMS GLM ANNs The drawbacks: - noisy; - hospital environment; - participant limiting (claustrophobia, metal particles in the body, metallic ornaments, psychotropic drugs, etc.); - limited interaction with participants.

  5. WHY fMRI? BOLD SIGNAL THE BASELINE PARADIGMS GLM ANNs The basis of Blood-Oxygen-Level Dependent (BOLD) signal: High firing rate Difference Low firing rate

  6. WHY fMRI? BOLD SIGNAL THE BASELINE PARADIGMS GLM ANNs The basis of Blood-Oxygen-Level Dependent (BOLD) signal: Very important issues in fMRI studies: - absolute paradigms are not allowed in common studies (only relative questions); - BOLD signal is an indirect measure of brain activity; fMRI measures disturbances in the magnetic field caused by differential ratios in hemoglobin / oxyhemoglobin caused by requirement of oxygen caused by increased neuronal spiking rate caused by cognitive recruitment.

  7. WHY fMRI? BOLD SIGNAL THE BASELINE PARADIGMS GLM ANNs Which baseline? Current visual baselines tend to generate self-reflexive thoughts that can disguise eventual brands’ social content (D’Argembeauet al., 2005; Iacoboniet al., 2004;Schilbachet al., 2008)

  8. WHY fMRI? BOLD SIGNAL THE BASELINE PARADIGMS GLM ANNs Which baseline? A baseline that we usually use in cognitive-based studies, non-emotional words: SUBSTANTIVES VERBS ACTIONS EMOTIONS

  9. WHY fMRI? BOLD SIGNAL THE BASELINE PARADIGMS GLM ANNs Paradigm: block design 30 seconds 30 seconds 30 seconds 30 seconds 30 seconds Baseline Stimulus Baseline Stimulus Stimulus + better signal in fMRI / simplicity - induce strategies in subjects

  10. WHY fMRI? BOLD SIGNAL THE BASELINE PARADIGMS GLM ANNs Paradigm: event related – fixed ISI Fixed ISI (interstimuli interval) 5 seconds 5 seconds 5 seconds 5 seconds 5 seconds 5 seconds 5 seconds 5 seconds 5 seconds + + + + + … Baseline Baseline Baseline Baseline Baseline + reduce strategies in subjects (psychologically more robust) - lower signal in fMRI (prone to noise)

  11. WHY fMRI? BOLD SIGNAL THE BASELINE PARADIGMS GLM ANNs Paradigm: event related – jittered ISI Jittered ISI (interstimuli interval) 5 seconds 5 seconds 2 seconds 5 seconds 7 seconds 5 seconds 4 seconds 5 seconds 5 seconds + + + + + … Baseline Baseline Baseline Baseline Baseline + reduce strategies in subjects (psychologically more robust) may improve temporal resolution - lower signal in fMRI (prone to noise) increased complexity in data analysis

  12. WHY fMRI? BOLD SIGNAL THE BASELINE PARADIGMS GLM ANNs Paradigm: event related – jittered ISI 1 TR 1 TR 1 TR 1 TR 1 TR 1 TR 1 TR 1 TR 1 TR 1 TR 1 TR 1 TR 1 TR 1 TR 1 TR 1 TR 1 TR 1 TR 5 seconds 5 seconds 5 seconds 5 seconds 5 seconds 5 seconds 5 seconds 5 seconds 5 seconds + + + + + … 5 seconds 5 seconds 2 s 5 seconds 7 seconds 5 seconds 4 s 5 seconds 5 seconds + + + + + … Usually 1 TR (repetition time, i.e. time that the scanner needs to acquire a full volume) is 2 – 3 seconds. With jittering, stimulus onset and volume acquisition is dis-synchronized (example 1 TR = 2500 ms)

  13. WHY fMRI? BOLD SIGNAL THE BASELINE PARADIGMS GLM ANNs Paradigm: mixed design Positive basic shapes Indifferent basic shapes + tries to get the best of both worlds: powerful signal without parasitic behavioral strategies - difficult to analyze (hemodynamic response may overlap)

  14. WHY fMRI? BOLD SIGNAL THE BASELINE PARADIGMS GLM ANNs Pixels and Voxels: The digital photo is in fact a matrix, where each matrix’s element is a pixel

  15. WHY fMRI? BOLD SIGNAL THE BASELINE PARADIGMS GLM ANNs Pixels and Voxels: Voxels = pixels with thickness The brain is divided in voxels (usually around 200,000 with 2  2  2 mm3), and in each voxel one GLM analysis is run.

  16. WHY fMRI? BOLD SIGNAL THE BASELINE PARADIGMS GLM ANNs The General Linear Model equation: Y = β X +  fMRI signal regression parameters paradigm’s manipulation y1 = β10 + β11 x1 + β12 x2 + … + β1mxm + 1 y2 = β20 + β21 x1 + β22 x2 + … + β2mxm + 2 (…) yn = βn0 + βn1 x1 + βn2 x2 + … + βnmxm + n n: number of voxels m: number of variables used in the paradigm

  17. WHY fMRI? BOLD SIGNAL THE BASELINE PARADIGMS GLM ANNs The General Linear Model equation: Y = β X +  fMRI signal regression parameters paradigm’s manipulation y1, y2, …, yn signal in voxel 1, 2, …, n x1, x2, …, xn regressors 1, 2, …, m (a regressor introduces in the model our expectation of the evolution of the hemodynamic response for one certain stimulus) βn0, βn1, βn2, …, βnm parameters that represent the magnitude of the associated regressor (which are calculated during the analysis)

  18. WHY fMRI? BOLD SIGNAL THE BASELINE PARADIGMS GLM ANNs The General Linear Model equation: x1, x2, …, xn regressors 1, 2, …, m (a regressor introduces in the model our expectation of the evolution of the hemodynamic response for one certain stimulus) Example of two stimuli (EV1 and EV2) in an event-related paradigm; stimuli onsets were convolved with a double gamma function to simulate the BOLD signal:

  19. WHY fMRI? BOLD SIGNAL THE BASELINE PARADIGMS GLM ANNs The General Linear Model equation: βn0, βn1, βn2, …, βnm parameters that represent the magnitude of the associated regressor (which are calculated during the analysis) If βnm is different from 0, then the voxel n is active for the stimulus m. But, how much different from 0? Calculating the t statistic: t = βnm / SDβnm (in practice t  p-value  z) Higher βnm leads to higher t Higher SDβnm leads to lower t

  20. WHY fMRI? BOLD SIGNAL THE BASELINE PARADIGMS GLM ANNs The General Linear Model equation: The fMRI signal is acquired for each voxel. Let choose 3 voxels…

  21. WHY fMRI? BOLD SIGNAL THE BASELINE PARADIGMS GLM ANNs The General Linear Model equation: Now, add the course of the paradigm (as paradigms are manipulated). For each voxel, it is possible to compute statistics that compare the MRI signal and the paradigm. Z = -0.20 Z = -3.59 Z = +4.49

  22. WHY fMRI? BOLD SIGNAL THE BASELINE PARADIGMS GLM ANNs The General Linear Model equation: These statistics allow to emphasize the voxels that most follow the paradigm course according to a established criterion. In this case: - activation: z > 2.3 - deactivation: z < -2.3 Nothing 52% postcentral gyrus Z = -0.20 Deactivation 47% precuneous cortex Z = -3.59 Activation 57% paracingulate gyrus Z = +4.49

  23. WHY fMRI? BOLD SIGNAL THE BASELINE PARADIGMS GLM ANNs Is this approach acceptable or interesting? 1. Modeling the signal with GLM framework Y = β X +  2. Statistical parameter maps 3. Inferences about cognitive processes - valuation; - Theory of Mind; - choice; - recalling; - autobiography; - … paradigm’s manipulation signal regression parameters PROBLEMATIC!!!  difficult to accept

  24. WHY fMRI? BOLD SIGNAL THE BASELINE PARADIGMS GLM ANNs Why is this problematic? Theory of Mind activates the paracingulate gyrus 2. Statistical parameter maps   ? My task also activates the paracingulate gyrus My task  Theory of Mind ? NO! Very careful with GLM-based conclusions!!!

  25. WHY fMRI? BOLD SIGNAL THE BASELINE PARADIGMS GLM ANNs Is this approach acceptable or interesting? Y = β X +  In GLM: given X it is possible to model Y calculating β But in Behavioral Sciences I would prefer: X = β1 Y + 1  not interesting

  26. WHY fMRI? BOLD SIGNAL THE BASELINE PARADIGMS GLM ANNs Why Artificial Neural Networks (ANNs) are fine? We PERCEIVE the SMILE because we read the pixels’ distribution pattern and NOT because we analyze each pixel individually (univariate approach) If we expect to understand how the brain works, we should consider multivariate methods because voxels do not work separately in the brain; their function is interdependent.

  27. WHY fMRI? BOLD SIGNAL THE BASELINE PARADIGMS GLM ANNs The Perceptron: The Perceptron emulates the functioning neuron, i.e. it has several inputs, makes a decision, and outputs that decision: These inputs are weighted. Input x1 influences the perceptron weighted by w1. In fact, the influence is the product w1 x1 . The total influence, u, is: X1 • W1 • W2 X2 U … u= w1 x1 + w2 x2 + ... + wn xn • Wn Xn

  28. WHY fMRI? BOLD SIGNAL THE BASELINE PARADIGMS GLM ANNs The Perceptron: u= w1 x1 + w2 x2 + ... + wn xn A step function will decide if the neuron (perceptron) fires or not fires, comparing u with a  threshold: X1 • W1 • W2 X2 U … • Wn Xn

  29. WHY fMRI? BOLD SIGNAL THE BASELINE PARADIGMS GLM ANNs The Perceptron: u= w1 x1 + w2 x2 + ... + wn xn However the step function is discontinuous and presents mathematical problems. Other step-like functions are preferred, as the sigmoid: X1 • W1 • W2 X2 U … • Wn Xn

  30. WHY fMRI? BOLD SIGNAL THE BASELINE PARADIGMS GLM ANNs The MLP (multi-layer perceptron): The Perceptron may be used to decide between two states providing some information. If several Perceptrons are connected, then more complex decisions processes can be modeled: I1 H1 O1 I2 I3 H2 O2 I4 I5 H3 O3 X1 • W1 I6 • W2 X2 I7 U H4 O4 … I8 • Wn Xn Hidden layer Output I9 Input

  31. WHY fMRI? BOLD SIGNAL THE BASELINE PARADIGMS GLM ANNs The MLP (multi-layer perceptron): The MLP is trained with data in order to calculate the all the weights of the network. Commonly, the training is supervised, i.e. inputs and outputs are given in order to make the calculations. I1 H1 O1 I2 After the training stage, more input data can be fed into the MLP, now without outputs. In the test stage, the MLP calculates the outputs given the inputs and the calculated weights. The MLP can make predictions. I3 H2 O2 I4 I5 H3 O3 I6 I7 H4 O4 I8 Hidden layer Output I9 Input

  32. WHY fMRI? BOLD SIGNAL THE BASELINE PARADIGMS GLM ANNs An example with ANNs: Stimuli 35 Positive rated brands’ logos Stimuli 35 Indifferent rated brands’ logos 35 Fictitious logos

  33. WHY fMRI? BOLD SIGNAL THE BASELINE PARADIGMS GLM ANNs An example with ANNs: Data pre-processing Original BOLD timecourses ICs’ maps output by PICA Binaries of ICs’ maps Test data: Masked averages of original BOLD timecourses ICs’ timecourses output by PICA Train data:

  34. WHY fMRI? BOLD SIGNAL THE BASELINE PARADIGMS GLM ANNs An example with ANNs: Dimensionality reduction We used Probabilistic Independent Component Analysis (PICA) in a data set that encompasses all individuals’ data sets concatenated. In the end of this stage we had 161 independent components (ICs). It is assumed that the voxels inside the same IC have similar timecourses.

  35. WHY fMRI? BOLD SIGNAL THE BASELINE PARADIGMS GLM ANNs An example with ANNs: Feature extraction Stimuli: positive indifferent Ideal signal: positive indifferent Real signal: The signal is noisy and sparsely discrete (TR = 3 seconds) Comparison of two strategies to average consecutive fMRI volumes. The green line represents the canonical hemodynamic response function. The areas represented by blue and red bars represent the amount of the contribution to the average in time periods. In strategy 2 (blue color) the second and third volumes after stimulus onset are averaged. In strategy 3 (red color) the second, third, and forth volumes after stimulus onset are averaged.

  36. WHY fMRI? BOLD SIGNAL THE BASELINE PARADIGMS GLM ANNs An example with ANNs: Results Conclusion: We have good reasons to think that this procedure constructed an ANN that is able to extract pertinent information from BOLD signal in order to make behavioral predictions above the chance level.

  37. WHY fMRI? BOLD SIGNAL THE BASELINE PARADIGMS GLM ANNs An example with ANNs: More results (interpreting the hidden layer)

  38. WHY fMRI? BOLD SIGNAL THE BASELINE PARADIGMS GLM ANNs An example with ANNs: More results (interpreting the hidden layer) IC19 Precentral gyrus (motor cortex) Action execution

  39. WHY fMRI? BOLD SIGNAL THE BASELINE PARADIGMS GLM ANNs An example with ANNs: More results (interpreting the hidden layer) IC10 Precentral gyrus (motor cortex) Action execution

  40. WHY fMRI? BOLD SIGNAL THE BASELINE PARADIGMS GLM ANNs An example with ANNs: More results (interpreting the hidden layer) IC25 Posterior cingulate gyrus and precuneus Autobiographical memories IC45 Default network Self-reflexive processes IC68 Ventral medial prefrontal cortex and frontal pole Judgments of preference

  41. THE END • Moutinho, Luiz • Foundation Chair of Marketing, Business School, University of Glasgow, Scotland, UK • Santos, José Paulo (jpsantos@ismai.pt) • ISMAI – Superior Institute of Maia, Portugal • Socius – Research Centre in Economic and Organizational Sociology, ISEG/UTL, Portugal • Seixas, Daniela • Institute of Histology and Embriology, Faculty of Medicine of Oporto Univ., Portugal • Institute for Molecular and Cell Biology, Oporto, Portugal • Neuroradiology Department, São João Hospital, Oporto, Portugal • Brandão, Sofia • Radiology Dep., Magnetic Resonance Imaging Unit, São João Hospital, Oporto, Portugal

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