The functional connectivity of cortical areas Or how to produce many numbers.
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The functional connectivity of cortical areas Or how to produce many numbers
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Transcript of The functional connectivity of cortical areas Or how to produce many numbers.
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
