Design Matrix

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DESCRIPTION

The General Linear Model. Data. Design Matrix. filter. intrinsic correlations and non-sphericity correction. contrast images. SPM{ T }. SPM{T}. isoluminant stimuli (even). isochromatic stimuli (odd). V5. speed. contrast. 100. SPM{T}. PPM. 200. 300. 1. 2. 3. 4. Design matrix. - PowerPoint PPT Presentation

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1

Design MatrixDesign Matrix

intrinsic correlations andnon-sphericity correction

intrinsic correlations andnon-sphericity correction

filterfilter

DataData

SPM{T}SPM{T}

The General Linear Model

vT

T

T

TcV

c

SYSX

SSVN

SSXSY

XY

~}ˆ{ˆ

ˆ

)(ˆ

,),0{~ 2

adjustmentXX

none

whitening

S

001

1

21

}{

){

}{ˆ

)(1

)()(ˆ}ˆ{ˆ

2

2

2

RVRVtrace

RVtracev

RVtrace

RYY

SXSXR

cSXVSXccV

T

TTT

contrast images

contrast images

2

SPM{T}SPM{T}

speed

isoluminant stimuli (even)

isochromatic stimuli (odd)V5V5

3

Design matrix1 2 3 4

100

200

300

contrast

z = 3mm

SPM{T} PPM

z = 3mm

4

Basis functions

Single HRF

FIR model

Temporal basis functions

i

ii ttuty

ttth

)()(

)()()( 2211

)()(

)()(

tuTty

uTth

))(()(

)()()( 2211

iii tuTty

tTtTth

Stimulus function

)(uTi

)(uT

)( it

)(tuTi

Design matrixDesign matrix

SPM{F}SPM{F}

)(tu

5

sf

tionflow induc

v,q y

)(tu

s

v

f

hidden states

neuronal input

BOLD response

v

q

},,,{ qvfs

q/vvf,Efqτ /α

dHbchanges in

1)( /αvfvτ

volumechanges in

1

f

q

)1( fγsus

ignalependent sactivity-d

hemodynamicshemodynamics

6

Nonlinear saturation

7

V1 IFG

V5

SPC

Motion

Photic

Attention

..82(100%)

.42(100%)

.37(90%)

.69 (100%)

.47(100%)

.65 (100%)

.52 (98%)

.56(99%)

8

spiny stellate

cells

inhibitory interneurons

pyramidal cells

4 3

236

746

63

225

1205

52

650

214

014

41

278

038

87

2)(

2))()()((

2))()((

2))()((

iii

i

ee

LB

e

e

ee

LF

e

e

ee

LB

e

e

xxxS

Hx

xx

xxxSxSAA

Hx

xx

xxx

xxCuxSIAA

Hx

xx

xxxSIAA

Hx

xx

1 2)( 0xSAF

)( 0xSAL

)( 0xSAB

Extrinsicforward

connections

Extrinsic backward connections

Intrinsic connections

Neuronal model

Extrinsic lateral connections

9

spiny stellate

cells

inhibitory interneurons

pyramidal cells

IntrinsicForward

BackwardLateral time

input

.56

/.6

1

.59

/.8

7

.05

/.0

4

.00/.09

.01/3.68

P300 Real andmodelled

frequentrare

Time {s}

Time {s}

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