大脑的连接功能

nullModels of Effective Connectivity & Dynamic Causal ModellingModels of Effective Connectivity & Dynamic Causal ModellingHanneke den Ouden Wellcome Trust Centre for Neuroimaging, University College London, UK Donders Institute for Brain, Cognition and Behaviour, Nijmegen, the Netherlands SPM course Zurich, February 2009Thanks to Klaas Stephan and Meike Grol for slidesSystems analysis in functional neuroimagingSystems analysis in functional neuroimagingFunctional specialisation: What regions respond to a particular experimental input?Functional integration: How do regions influence each other?  Brain ConnectivityOverviewOverviewBrain connectivity: types & definitions anatomical connectivity functional connectivity effective connectivity Functional connectivity Psycho-physiological interactions (PPI) Dynamic causal models (DCMs) Applications of DCM to fMRI dataStructural, functional & effective connectivityStructural, functional & effective connectivityanatomical/structural connectivity = presence of axonal connections functional connectivity = statistical dependencies between regional time series effective connectivity = causal (directed) influences between neurons or neuronal populationsSporns 2007, ScholarpediaAnatomical connectivityAnatomical connectivitypresence of axonal connections neuronal communication via synaptic contacts visualisation by tracing techniques diffusion tensor imaging However, knowing anatomical connectivity is not enough...However, knowing anatomical connectivity is not enough...Connections are recruited in a context-dependent fashion: Local functions depend on network activity However, knowing anatomical connectivity is not enough...However, knowing anatomical connectivity is not enough...Connections show plasticity Synaptic plasticity = change in the structure and transmission properties of a synapse Critical for learning Can occur both rapidly and slowlyNeed to look at functional and effective connectivityConnections are recruited in a context-dependent fashion: Local functions depend on network activity OverviewOverviewBrain connectivity: types & definitions Functional connectivity Psycho-physiological interactions (PPI) Dynamic causal models (DCMs) Applications of DCM to fMRI dataDifferent approaches to analysing functional connectivityDifferent approaches to analysing functional connectivityDefinition: statistical dependencies between regional time series Seed voxel correlation analysis Eigen-decomposition (PCA, SVD) Independent component analysis (ICA) any other technique describing statistical dependencies amongst regional time seriesSeed-voxel correlation analysesSeed-voxel correlation analysesVery simple idea: hypothesis-driven choice of a seed voxel → extract reference time series voxel-wise correlation with time series from all other voxels in the brainseed voxelSVCA example: Task-induced changes in functional connectivitySVCA example: Task-induced changes in functional connectivity2 bimanual finger-tapping tasks: During task that required more bimanual coordination, SMA, PPC, M1 and PM showed increased functional connectivity (p<0.001) with left M1  No difference in SPMs!Sun et al. 2003, NeuroimageDoes functional connectivity not simply correspond to co-activation in SPMs?Does functional connectivity not simply correspond to co-activation in SPMs?No, it does not - see the fictitious example on the right: Here both areas A1 and A2 are correlated identically to task T, yet they have zero correlation among themselves: r(A1,T) = r(A2,T) = 0.71 but r(A1,A2) = 0 ! task Tregional response A2regional response A1Stephan 2004, J. Anat.Pros & Cons of functional connectivity analysesPros & Cons of functional connectivity analysesPros: useful when we have no experimental control over the system of interest and no model of what caused the data (e.g. sleep, hallucinatons, etc.) Cons: interpretation of resulting patterns is difficult / arbitrary no mechanistic insight into the neural system of interest usually suboptimal for situations where we have a priori knowledge and experimental control about the system of interestFor understanding brain function mechanistically, we need models of effective connectivity, i.e. models of causal interactions among neuronal populations to explain regional effects in terms of interregional connectivityFor understanding brain function mechanistically, we need models of effective connectivity, i.e. models of causal interactions among neuronal populations to explain regional effects in terms of interregional connectivitySome models for computing effective connectivity from fMRI dataSome models for computing effective connectivity from fMRI dataStructural Equation Modelling (SEM) McIntosh et al. 1991, 1994; Büchel & Friston 1997; Bullmore et al. 2000 regression models (e.g. psycho-physiological interactions, PPIs) Friston et al. 1997 Volterra kernels Friston & Büchel 2000 Time series models (e.g. MAR, Granger causality) Harrison et al. 2003, Goebel et al. 2003 Dynamic Causal Modelling (DCM) bilinear: Friston et al. 2003; nonlinear: Stephan et al. 2008OverviewOverviewBrain connectivity: types & definitions Functional connectivity Psycho-physiological interactions (PPI) Dynamic causal models (DCMs) Applications of DCM to fMRI dataPsycho-physiological interaction (PPI)Psycho-physiological interaction (PPI)bilinear model of how the influence of area A on area B changes by the psychological context C: A x C  B a PPI corresponds to differences in regression slopes for different contexts. Psycho-physiological interaction (PPI)Psycho-physiological interaction (PPI)We can replace one main effect in the GLM by the time series of an area that shows this main effect. Let's replace the main effect of stimulus type by the time series of area V1:Task factorTask ATask BStim 1Stim 2Stimulus factorTA/S1TB/S1TA/S2TB/S2GLM of a 2x2 factorial design:main effect of taskmain effect of stim. typeinteractionmain effect of taskV1 time series  main effect of stim. typepsycho- physiological interactionFriston et al. 1997, NeuroImageExample PPI: Attentional modulation of V1→V5Friston et al. 1997, NeuroImage Büchel & Friston 1997, Cereb. CortexV1 x Att.=AttentionExample PPI: Attentional modulation of V1→V5PPI: interpretationPPI: interpretationTwo possible interpretations of the PPI term:V1Modulation of V1V5 by attentionModulation of the impact of attention on V5 by V1V1attentionattentionPros & Cons of PPIsPros & Cons of PPIsPros: given a single source region, we can test for its context-dependent connectivity across the entire brain easy to implement Cons: very simplistic model: only allows to model contributions from a single area ignores time-series properties of data operates at the level of BOLD time seriessometimes very useful, but limited causal interpretability; in most cases, we need more powerful modelsDCM!OverviewOverviewBrain connectivity: types & definitions Functional connectivity Psycho-physiological interactions (PPI) Dynamic causal models (DCMs) Basic idea Neural level Hemodynamic level Priors & Parameter estimation Applications of DCM to fMRI data Basic idea of DCM for fMRI (Friston et al. 2003, NeuroImage)Basic idea of DCM for fMRI (Friston et al. 2003, NeuroImage)Investigate functional integration & modulation of specific cortical pathways Using a bilinear state equation, a cognitive system is modelled at its underlying neuronal level (which is not directly accessible for fMRI). The modelled neuronal dynamics (x) is transformed into area-specific BOLD signals (y) by a hemodynamic forward model (λ).The aim of DCM is to estimate parameters at the neuronal level such that the modelled and measured BOLD signals are maximally similar.OverviewOverviewBrain connectivity: types & definitions Functional connectivity Psycho-physiological interactions (PPI) Dynamic causal models (DCMs) Basic idea Neural level Hemodynamic level Priors & Parameter estimation Applications of DCM to fMRI dataExample: a linear system of dynamics in visual cortexRVFLVFLG = lingual gyrus FG = fusiform gyrus Visual input in the - left (LVF) - right (RVF) visual field.x1x2x4x3u2u1Example: a linear system of dynamics in visual cortexExample: a linear system of dynamics in visual cortexExample: a linear system of dynamics in visual cortexRVFLVFLG = lingual gyrus FG = fusiform gyrus Visual input in the - left (LVF) - right (RVF) visual field.x1x2x4x3u2u1state changeseffective connectivityexternal inputssystem stateinput parametersExtension: bilinear dynamic systemExtension: bilinear dynamic systemRVFLVFx1x2x4x3u2u1CONTEXTu3nullhemodynamic modelλxyintegrationBOLDyyyactivity x1(t)activity x2(t)activity x3(t)neuronal statesStephan & Friston (2007), Handbook of Brain ConnectivityOverviewOverviewBrain connectivity: types & definitions Functional connectivity Psycho-physiological interactions (PPI) Dynamic causal models (DCMs) Basic idea Neural level Hemodynamic level Priors & Parameter estimation Applications of DCM to fMRI data The hemodynamic model in DCMimportant for model fitting, but of no interest for statistical inferenceThe hemodynamic model in DCM6 hemodynamic parameters: Computed separately for each area (like the neural parameters)  region-specific HRFs!Friston et al. 2000, NeuroImage Stephan et al. 2007, NeuroImagestimulus functionsuneural state equationhemodynamic state equationsEstimated BOLD responseExample: modelled BOLD signalExample: modelled BOLD signalblack: observed BOLD signal red: modelled BOLD signalOverviewOverviewBrain connectivity: types & definitions Functional connectivity Psycho-physiological interactions (PPI) Dynamic causal models (DCMs) Basic idea Neural level Hemodynamic level Priors & Parameter estimation Applications of DCM to fMRI data nullBayesian statisticsposterior  likelihood ∙ priorBayes theorem allows us to express our prior knowledge or “belief” about parameters of the modelThe posterior probability of the parameters given the data is an optimal combination of prior knowledge and new data, weighted by their relative precision.new dataprior knowledgenullembody constraints on parameter estimation hemodynamic parameters: empirical priors coupling parameters of self-connections: principled priors coupling parameters other connections: shrinkage priorsPriors in DCMSmall & variable effectLarge & variable effectSmall but clear effectLarge & clear effectDCM parameters = rate constantsDCM parameters = rate constantsThe coupling parameter a thus describes the speed of the exponential change in x(t)Integration of a first-order linear differential equation gives an exponential function:Coupling parameter is inversely proportional to the half life  of x(t):If AB is 0.10 s-1 this means that, per unit time, the increase in activity in B corresponds to 10% of the activity in AExample: context-dependent decay-x2stimuli u1context u2x1++---+Example: context-dependent decayu1u2x2x1Penny, Stephan, Mechelli, Friston NeuroImage (2004)DCM SummaryDCM SummarySelect areas you want to model Extract timeseries of these areas (x(t)) Specify at neuronal level what drives areas (c) how areas interact (a) what modulates interactions (b) State-space model with 2 levels: Hidden neural dynamics Predicted BOLD response Estimate model parameters: Gaussian a posteriori parameter distributions, characterised by mean ηθ|y and covariance Cθ|y.neuronal statesactivity x1(t)activity x2(t)Inference about DCM parameters: Bayesian single-subject analysisInference about DCM parameters: Bayesian single-subject analysisGaussian assumptions about the posterior distributions of the parameters Use of the cumulative normal distribution to test the probability that a certain parameter (or contrast of parameters cT ηθ|y) is above a chosen threshold γ: By default, γ is chosen as zero ("does the effect exist?").ηθ|yInference about DCM parameters: group analysis (classical)Inference about DCM parameters: group analysis (classical)In analogy to “random effects” analyses in SPM, 2nd level analyses can be applied to DCM parameters:Separate fitting of identical models for each subjectSelection of bilinear parameters of interestone-sample t-test: parameter > 0 ?paired t-test: parameter 1 > parameter 2 ?rmANOVA: e.g. in case of multiple sessions per subjectOverviewOverviewBrain connectivity: types & definitions Functional connectivity Psycho-physiological interactions (PPI) Dynamic causal models (DCMs) Applications of DCM to fMRI data Design of experiments and models Some empirical examples and simulationsPlanning a DCM-compatible studyPlanning a DCM-compatible studySuitable experimental design: any design that is suitable for a GLM preferably multi-factorial (e.g. 2 x 2) e.g. one factor that varies the driving (sensory) input and one factor that varies the contextual input Hypothesis and model: Define specific a priori hypothesis Which parameters are relevant to test this hypothesis? If you want to verify that intended model is suitable to test this hypothesis, then use simulations Define criteria for inference What are the alternative models to test?Multifactorial design: explaining interactions with DCMMultifactorial design: explaining interactions with DCMLet’s assume that an SPM analysis shows a main effect of stimulus in X1 and a stimulus  task interaction in X2. How do we model this using DCM?Simulated dataA1A2Stim2Stim1Task ATask BStim 1 Task AStim 2 Task AStim 1 Task BStim 2 Task BSimulated data++++++++++++A1A2nullStim 1 Task AStim 2 Task AStim 1 Task BStim 2 Task Bplus added noise (SNR=1)X1X2Final point: GLM vs. DCMFinal point: GLM vs. DCMDCM tries to model the same phenomena as a GLM, just in a different way: It is a model, based on connectivity and its modulation, for explaining experimentally controlled variance in local responses. If there is no evidence for an experimental effect (no activation detected by a GLM) → inclusion of this region in a DCM is not meaningful.Thank youThank youStay tuned to find out how to … select the best model comparing various DCMs … test whether one region influences the connection between other regions … do DCM on your M/EEG & LFP data … and lots more!