The functional connectivityof cortical areas

Or how to produce many numbers

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Coordination of different modules

Structural equation modelling

Popular in behavioral sciences- e.g. „whats role of intelligence in performance?“

Identify latent factors in data- structure in covariance matrix- confirmatory vs exploratory

Roots in path analysis (Wright, 1921)

General model: DATA = MODEL + ERROR - reduce error

http://www.gsu.edu/~mkteer/semfaq.html

Graphical representation

Measure 1

Measure 2

Measure 3

Factor 1

Factor 2

Causal Correlates

Error 1

Error 1

Error 1

Formal representation

δ+ξΛ=

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

δδδδ

+⎥⎦

⎤⎢⎣

⎡ξξ

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

λλ

λλ

=

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

x

0

0

0

0

x

x

x

x

4

3

2

1

2

1

42

32

21

11

4

3

2

1

Measurement = weighted latent factors + error

Aplication to fMRI data

Effective connectivity vs functional connectivity

Ec: influence of one neuronal system on anotherFc: temporal correlation of two neurophysiological events

Anatomy can inform choice of factor loadings

How to estimate effects over time?

Simple regression model:Y = xB + u

Include time:Yt = xtBt + ut

Estimate evolution B using Kalman filter- predictor-corrector algorithm

The paradigm

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I. Toni, J. Rowe, K.E. Stephan & R.E.Passingham. (2002). Changes of cortico-striatal effective connectivity during visuomotor learning. Cerebral Cortex 12:1040-1047

What are the modules?

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The model

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The result

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What have we learned?

Your turn!

An application to fMRI