fMRI: Biological Basis and Experiment DesignLecture 23: GLM in multiple voxels

• Errata• Final project review• Keeping track of space• Multi-voxel GLM

Before

After

x

Erratum: ICE9% Repeat the "experiment" a few times%%%!!! Wrong way ... shouldn't run the same design again and again - then%%%the experimental conditions aren't nearly as randomized as they could%%%be!nScans = 10;clear datafor n = 1:nScans data(n,:) = caoSimulateData(neural,TR,BOLDamp,SNR,1); end

% "Analyze" data ...%%Check out code that does TTA ...TTAlength = 20;[TTA TTAsem count] = caoComputeTTA(design,data,TTAlength);TTA_minus_baseline = TTA - repmat(TTA(:,1),[1 size(TTA,2)]);subplot(2,1,1)errorbar(repmat((0:(TTAlength-1))',[1 size(TTA,2)]),TTA,TTAsem); title(['nScans = ' num2str(nScans)]); axis tightsubplot(2,1,2)errorbar(repmat((0:(TTAlength-1))',[1 size(TTA,2)]),TTA_minus_baseline,TTAsem); title(['nScans = ' num2str(nScans)]); axis tightlegend(num2str(count))

Erratum: ICE9% Repeat the "experiment" a few times%% Right way - new trial order each repetitionnScans = 10;fixedLength = 500;design = zeros(nScans,fixedLength);neural = zeros(nScans,fixedLength);data = zeros(nScans,fixedLength);for n = 1:nScans %% For this, I'd built in a flag that would make the design vector the %% same length each time (adding 0's at end) to deal with the fact that %% randomized ISI's yield unpredictable scan lengths design(n,:) = caoMakeER(waitUpFront,nStimTypes,ISIrange,nStim,500); for nt = 1:length(design) if design(n,nt) % if there's a stimulus neural(n,nt) = relResp(design(n,nt)); % pick the appropriate response end end data(n,:) = caoSimulateData(neural(n,:),TR,BOLDamp,SNR,1); end

Basic assignment, final project(all projects need these components)

• Abstract (250 words)• Background - experiment design and neuroscience question

motivating the experiment (1 page, 1 - 3 references)• Methods (2 – 4 pages)

– MR Methods section (resolution, TR, TE, protocol)– Prediction of neural activity– Prediction of BOLD response (noiseless model)– Simulated data (BOLD + noise - physiological and/or thermal)– ROI selection– GLM

• Results (1 – 3 pages)– Paragraph describing simulation output + 1 figure– Paragraph describing GLM results + 1 figure

• Discussion (1 - 2 pages)– 3 things that might not be as expected if you ran the experiment

Building blocks, final project(weekly assignments, 2nd half of semester)

• Abstract (250 words)• Background - experiment design and neuroscience question

motivating the experiment (1 page, 1 - 3 references)• Methods (2 – 4 pages)

– MR Methods section (resolution, TR, TE, protocol) – WA 8– Prediction of neural activity – WA7– Prediction of BOLD response (noiseless model) – WA7– Simulated data (BOLD + noise - physiological and/or thermal) – WA8– ROI selection– GLM – WA10 & WA11

• Results (1 – 3 pages)– Paragraph describing simulation output + 1 figure – WA8– Paragraph describing GLM results + 1 figure – WA10 & WA11

• Discussion (1 - 2 pages)– 3 things that might not be as expected if you ran the experiment

Presentation schedule

• Groups– Denkinger

– Han, Honwanishkul, Roher

– Haut, Johnson

– Kruse, White

– Kwon

– Liu, Schmidt

– Seo, Vizueta

– Theodorou

– Thompson

• Times– May 2

• 9:45 – 10:05 Kwon• 10:05 – 10:25 Theodorou• 10:25 – 10:45 Denkinger• 10:45 – 11:15 Big group HHR

– May 4• 9:45 – 10:05 Thompson• 10:05 – 10:25 Big group• 10:25 – 10:45 Seo, Vizueta• 10:45 – 11:15 Haut, Johnson

A1,1 A2,1 A3,1 A4,1

A1,2 A2,2 A3,2 A4,2

A1,3 A2,3 A3,3 A4,3

A1,m A2,m A3,m A4,m

Linear model for BOLD in a single voxel

A = x =

x1

x2

x3

x4

y =

y1

y2

y3

ym

Ax = yDesign matrix, [m x n] - m time-points - n stimulus types

Data [m x 1] - response through time

Responses [n x 1] - for each stimulus, a scalar (single number) representing how well that voxel responds to that stimulus

...

...

...

...

...

A1,1 A2,1 A3,1 A4,1

A1,2 A2,2 A3,2 A4,2

A1,3 A2,3 A3,3 A4,3

A1,m A2,m A3,m A4,m

Linear model for BOLD in multiple voxels

A = x =

x1,1

x2,1

x3,1

x4,1

y =

y1,1

y2,1

y3,1

ym,1

Ax = yDesign matrix, [m x n] - m time-points - n stimulus types

Data [m x p] - response through time

Responses [n x p] - for each stimulus, a scalar (single number) representing how well that voxel responds to that stimulus

x1,2

x2,2

x3,2

x4,2

x1,p

x2,p

x3,p

x4,p

y1,2

y2,2

y3,2

ym,2

y1,p

y2,p

y3,p

ym,p

...

...

...

...

...

...

...

...

...

...

......

...

...

...

Keeping track of voxels

2D (or 3D) array of data1D vector X & Y (& Z) coords

= +

Fake experiment – distributed neural activityBrain (3 types of responses)

3 types of stimuli; 3 types of "neuron" (voxel?)

Fake experiment – simulated dataBrain (3 types of responses) voxels

(Baseline trends, noise dominate visualization)

Design Matrix

- Stimulus 1 - Stimulus 2 - Stimulus 3 - Linear drift - Half-cycle cos drift - 1.5 cycle cos drift

Design Matrix + (sim.) data

X = ?

time

voxels

voxels

(An aside on rows and columns)

• Why do [nTpts nVoxels] instead of [nVoxels nTpts]?– Typical experiment

• 6 scans, 200 tpts per scan --> nTpts = 1200

• 1 brain, 64 x 64 x 30 voxels --> nVoxels = 122,880

– Size of A• [nTpts nVoxels]: [122,880 1200]

• [nVoxels nTpts]: [1200 122,880]

– Size of ATA• [nTpts nVoxels]: [1200 1200]

• [nVoxels nTpts]: [122,880 122,880] !

Estimate of voxel responses

X =

time

voxels

voxels

xest = x + = (ATA)-1AT (y + )

Estimate of voxel responses

Response to Stim1 Response to Stim3Response to Stim2

Estimated

Input

WA10 – Build design matrix & GLM analysis tool