dynamic causal modelling dcm for fmri n.
Download
Skip this Video
Loading SlideShow in 5 Seconds..
Dynamic Causal Modelling (DCM) for fMRI PowerPoint Presentation
Download Presentation
Dynamic Causal Modelling (DCM) for fMRI

Loading in 2 Seconds...

play fullscreen
1 / 27

Dynamic Causal Modelling (DCM) for fMRI - PowerPoint PPT Presentation


  • 408 Views
  • Uploaded on

Dynamic Causal Modelling (DCM) for fMRI. Andre Marreiros. Wellcome Trust Centre for Neuroimaging University College London. Thanks to. Stefan Kiebel Lee Harrison Klaas Stephan Karl Friston. Overview. Dynamic Causal Modelling of fMRI. Definitions & motivation.

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about 'Dynamic Causal Modelling (DCM) for fMRI' - kalila


Download Now An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
dynamic causal modelling dcm for fmri

Dynamic Causal Modelling (DCM) for fMRI

Andre Marreiros

Wellcome Trust Centre for Neuroimaging

University College London

slide2

Thanks to...

Stefan Kiebel

Lee Harrison

Klaas Stephan

Karl Friston

slide3

Overview

Dynamic Causal Modelling of fMRI

Definitions & motivation

    • The neuronal model(bilinear dynamics)
  • The Haemodynamic model
  • Estimation: Bayesian framework
  • DCM latest Extensions
slide4

Principles of organisation

Functional specialization

Functional integration

neurodynamics 2 nodes with input
Neurodynamics: 2 nodes with input

u1

u2

z1

z2

activity in is coupled to via

coefficient

neurodynamics positive modulation
Neurodynamics: positive modulation

u1

u2

z1

z2

modulatory input u2 activity through the coupling

neurodynamics reciprocal connections
Neurodynamics: reciprocal connections

u1

u2

z1

z2

reciprocal

connection

disclosed by

u2

haemodynamics reciprocal connections
Haemodynamics: reciprocal connections

a11

Simulated response

Bold

Response

a12

Bold

Response

a22

green: neuronal activity

red: bold response

haemodynamics reciprocal connections1
Haemodynamics: reciprocal connections

a11

Bold

with

Noise added

a12

Bold

with

Noise added

a22

green: neuronal activity

red: bold response

slide10

LG

left

LG

right

FG

right

FG

left

Example: modelled BOLD signal

Underlying model(modulatory inputs not shown)

left LG

right LG

RVF

LVF

LG = lingual gyrus Visual input in the FG = fusiform gyrus - left (LVF) - right (RVF) visual field.

blue: observed BOLD signal

red: modelled BOLD signal (DCM)

use differential equations to describe mechanistic model of a system
Use differential equations to describe mechanistic model of a system
  • System dynamics = change of state vector in time
  • Causal effects in the system:
    • interactions between elements
    • external inputs u
  • System parameters  :specify exact form of system

overall system staterepresented by state variables

change ofstate vectorin time

example linear dynamic system

LG

left

FG

right

LG

right

FG

left

Example: linear dynamic system

LG = lingual gyrus

FG = fusiform gyrus

Visual input in the - left (LVF) - right (RVF)visual field.

z4

z3

z1

z2

RVF

LVF

u2

u1

systemstate

input

parameters

state changes

effective

connectivity

externalinputs

extension bilinear dynamic system

LG

left

FG

right

LG

right

FG

left

Extension: bilinear dynamic system

z4

z3

z1

z2

CONTEXT

RVF

LVF

u2

u3

u1

bilinear state equation in dcm fmri
Bilinear state equation in DCM/fMRI

modulation of

connectivity

systemstate

direct

inputs

state changes

m externalinputs

connectivity

slide15

z

λ

y

Conceptual overview

Neuronal state equation

The bilinear model

effective connectivity

modulation of

connectivity

Input

u(t)

direct inputs

c1

b23

integration

neuronal

states

a12

activity

z2(t)

activity

z3(t)

activity

z1(t)

hemodynamic

model

y

y

y

BOLD

Friston et al. 2003,NeuroImage

slide16

q

=

k

g

t

a

r

h

{

,

,

,

,

}

The hemodynamic “Balloon” model

  • 5 hemodynamic parameters:

important for model fitting, but of no interest for statistical inference

  • Empirically determineda priori distributions.
  • Computed separately for each area
slide17

Diagram

Dynamic Causal Modelling of fMRI

Network

dynamics

Haemodynamic

response

Priors

Model

comparison

State space

Model

Model inversion

using

Expectation-maximization

Posterior distribution

of parameters

fMRI

data y

slide18

Estimation: Bayesian framework

  • Models of
  • Hemodynamics in a single region
  • Neuronal interactions
  • Constraints on
  • Connections
  • Hemodynamic parameters

prior

likelihood term

posterior

Bayesian estimation

slide19

stimulus function u

Overview:parameter estimation

neuronal state

equation

  • Specify model (neuronal and hemodynamic level)
  • Make it an observation model by adding measurement errore and confounds X (e.g. drift).
  • Bayesian parameter estimation using Bayesian version of an expectation-maximization algorithm.
  • Result:(Normal) posterior parameter distributions, given by mean ηθ|y and Covariance Cθ|y.

parameters

hidden states

state equation

ηθ|y

observation model

modelled BOLD response

haemodynamics 2 nodes with input
Haemodynamics: 2 nodes with input

Dashed Line: Real BOLD response

a11

a22

Activity in z1 is coupled to

z2 via coefficient a21

slide21

Inference about DCM parameters:single-subject analysis

  • Bayesian parameter estimation in DCM: Gaussian assumptions about the posterior distributions of the parameters
  • Use of the cumulative normal distribution to test the probability by which a certain parameter (or contrast of parameters cT ηθ|y) is above a chosen threshold γ:



ηθ|y

model comparison and selection

Pitt & Miyung (2002), TICS

Model comparison and selection

Given competing hypotheses, which model is the best?

slide23

SPC

SPC

V1

V1

V5

V5

Comparison of three simple models

Model 1:attentional modulationof V1→V5

Model 2:attentional modulationof SPC→V5

Model 3:attentional modulationof V1→V5 and SPC→V5

Attention

Attention

Photic

Photic

Photic

SPC

0.55

0.03

0.85

0.86

0.85

0.70

0.75

0.70

0.84

1.36

1.42

1.36

0.89

0.85

V1

-0.02

-0.02

-0.02

0.56

0.57

0.57

V5

Motion

Motion

Motion

0.23

0.23

Attention

Attention

Bayesian model selection: Model 1 better than model 2,

model 1 and model 3 equal

→ Decision for model 1: in this experiment, attention primarily modulates V1→V5

slide24

Extension I: Slice timing model

  • potential timing problem in DCM:

temporal shift between regional time series because of multi-slice acquisition

2

slice acquisition

1

visualinput

  • Solution:
    • Modelling of (known) slice timing of each area.
  • Slice timing extension now allows for any slice timing differences.
  • Long TRs (> 2 sec) no longer a limitation.
  • (Kiebel et al., 2007)
slide25

Single-state DCM

Two-state DCM

input

Extrinsic (between-region) coupling

Intrinsic (within-region) coupling

Extension II: Two-state model

slide26

Extension III: Nonlinear DCM for fMRI

Here DCM can model activity-dependent changes in connectivity; how connections are enabled or gated by activity in one or more areas.

The D matrices encode which of the n neural units gate which connections in the system.

attention

0.19

(100%)

Can V5 activity during attention to motion be explained by allowing activity in SPC to modulate the V1-to-V5 connection?

The posterior density of indicates that this gating existed with 97.4% confidence.

SPC

0.03

(100%)

0.01

(97.4%)

1.65

(100%)

V1

V5

0.04

(100%)

motion

slide27

Conclusions

Dynamic Causal Modelling (DCM) of fMRI is mechanistic model that is informed by anatomical and physiological principles.

DCM uses a deterministic differential equation to model neuro-dynamics (represented by matrices A,B and C)

DCM uses a Bayesian framework to estimate these

DCM combines state-equations for dynamics with observation model (fMRI: BOLD response, M/EEG: lead field).

DCM is not model or modality specific (Models will change and the method extended to other modalities e.g. ERPs)