Anatomical Background of Dynamic Causal Modeling and Effective Connectivity Analyses Jakob Heinzle Translational Neuromodeling Unit (TNU), Institute for Biomedical Engineering University and ETH Zürich HBM 24, Educational Course: Anatomy Outline Relation between structure and function Effective connectivity Dynamic causal modeling (DCM) Anatomical Background for DCM 2 Connectional fingerprints determine local function Unique anatomical connectivity patterns (connectional fingerprints) for cortical areas Families of cortical areas (clusters) with similar patterns Analogous results for electrophysiological response patterns Anatomical connectivity is the major determinant for the response profile of neuronal ensembles. Passingham et al., Nat Rev Neurosci, 22 Anatomical Background for DCM 3
Anatomical connections define processing hierarchies Markov & Kennedy, TICS, 24 Literature based database: http://cocomac.g-node.org/ Stephan et al., Phil. Trans. B, 2; Kötter, Neuroinformatics, 24 Felleman & Van Essen, Cereb Cortex, 99 Hilgetag et al, Phil Trans. B, 2 Anatomical Background for DCM 4 Weighted and directed connectivity matrix in macaque From area Fraction of labeled neurons per area weight Markov et al., Cereb Cortex, 22; J Comp Neurol 24; To area Anatomical Background for DCM 5 Activation, intrinsic functional connectivity and anatomy Spontaneous correlation pattern Evoked response pattern: eye movement task Anatomical connectivity pattern Vincent et al, Nature, 27 Anatomical Background for DCM 6 2
Tight link between functional and anatomical connectivity - human fmri Average CCRF Intrinsic functional connectivity in humans is visuotopically organized matches monkey anatomy! Heinzle et al, Neuroimage, 2 Anatomical Background for DCM 7 Some naming conventions Anatomical connectivity - Fibre bundles, Close Contacts, Synapses Functional connectivity - Statistical relation, e.g. Correlation, Mutual information Effective connectivity - Directed influence, e.g. DCM, Transfer Entropy, Granger Causality Anatomical Background for DCM 8 Outline Relation between structure and function Effective connectivity Dynamic causal modeling (DCM) Anatomical Background for DCM 9 3
Why effective connectivity? Anatomical connectivity is critical for understanding brain function but not sufficient on its own. Functional connections synapses Context dependent modulation of connection strengths, synaptic plasticity, neuronal adaptation mechanisms, etc. Anatomical Background for DCM Synaptic connections show plasticity Numerous mechanisms at different time scales (ms to days) incl. very rapid changes! Regulated in several ways (e.g. modulatory effects of DA) peak PSP (mv) Matsuzaki et al., Nature, 24 Reynolds et al., Nature, 2 Anatomical Background for DCM Connections are recruited in a contextdependent fashion.4.3.2. 2 3 4 5 6 7 8 9.6.4.2 2 3 4 5 6 7 8 9.3.2. 2 3 4 5 6 7 8 9 Synaptic strengths are context-sensitive: They depend on the spatio-temporal distribution of presynaptic inputs and post-synaptic events. Anatomical Background for DCM 2 4
To understand brain (dys)function... we need models of effective connectivity that: incorporate anatomical and physiological principles connect these to computational mechanisms allow for inference on neuronal mechanisms (e.g., synaptic plasticity) from measured brain responses Anatomical Background for DCM 3 Outline Relation between structure and function Effective connectivity Dynamic causal modeling (DCM) Anatomical Background for DCM 4 Dynamic causal modeling (DCM) EEG, MEG fmri Forward model: Predicting measured activity given a putative neuronal state y g(x, ) Model inversion: Estimating neuronal mechanisms from brain activity measures dx f( x, u, ) dt David et al., Neuroimage, 26 Moran et al., NeuroImage, 28 Friston et al., Neuroimage, 23 Stephan et al., Neuroimage, 28 Stephan et al., Neuroimage, 2 Anatomical Background for DCM 5 5
.4.3.2..6.4.2.3.2. 3 2 4 3 2 2 3 4 5 6 7 8 9 2 3 4 5 6 7 8 9 2 3 4 5 6 7 8 9 2 3 4 5 6 7 8 9-2 3 4 5 6 7 8 9 3 2 2 3 4 5 6 7 8 9 Nonlinear DCM for fmri neural model u u 2 x 3 Neural population activity dx A dt m ( i) u B n x x 2 ( x D i j i j j) x Cu Weights are constrained / reflect by anatomy fmri signal change (%) Stephan et al., Neuroimage, 28 Anatomical Background for DCM 6 Hemodynamics DCM forward model neural state equation u stimulus functions t m dx ( j) A u jb x Cu dt j.4.2 vasodilatory signal s x s γ( f ) s f s flow induction (rcbf) f hemodynamic s f state equations Balloon model changes in volume v changes in dhb /α /α τv f v τq f E ( f,e ) qe v q/v v q 2 4 6 8 2 4 RBM N, =.5 CBM N, =.5 RBM N, = CBM N, =.5 RBM N, = 2 CBM N, = 2 2 4 6 8 2 4.2 -.2 -.4 -.6 2 4 6 8 2 4 S q ( q, v) V k q k2 k3 v S v k 4.3 ETE k2 r ETE BOLD signal k3 change equation Stephan et al., Neuroimage, 27 Anatomical Background for DCM 7 Conductance-based DCMs (for EEG) inhibitory interneurons pyramid al cells spiny stellate cells pyramid al cells pyramidal cells CV g ( VL V ) g ( VE V ) g f ( V )( VE V ) V L E NMDA Mg g E ( E) 2,3 V E E( ( VR g, ) ) E g NMDA ( I ) 2,3 V NMDA NMDA( ( VR g, ) ) NMDA ( I ) 3,2 () () () () () () ( V ) ( V ) ( V ) CV g V g V g V u V L L E E I I g ( E) () E(,3 ( V VR, ) ge ) () E E g ( E) () I(,2 ( V VR, ) gi ) () I I ( I ),2 ( E ),3 ( E ) 3, ( E ) 2,3 CV g V V i i i CV g ( VL V ) g ( VE V ) g ( VI V ) g f ( V )( VE V ) V L E I NMDA Mg g ( E) () () E( 3, ( V VR, ) ge ) E E g ( I ) I( 3,2( V VR, ) gi ) I I g NMDA ( I ) () () ( 3, ( V VR, ) g ) NMDA NMDA NMDA Marreiros et al., Neuroimage, 2 Moran et al., Neuroimage, 2 Anatomical Background for DCM 8 6
Conductance-based DCMs (for EEG) inhibitory interneurons pyramid al cells spiny stellate cells pyramid al cells pyramidal cells CV g ( VL V ) g ( VE V ) g f ( V )( VE V ) V L E NMDA Mg g E ( E) 2,3 V E E( ( VR g, ) ) E g NMDA ( I ) 2,3 V NMDA NMDA( ( VR g, ) ) NMDA ( I ) 3,2 () () () () () () ( V ) ( V ) ( V ) CV g V g V g V u V L L E E I I g ( E) () E(,3 ( V VR, ) ge ) () E E g ( E) () I(,2 ( V VR, ) gi ) () I I ( I ),2 ( E ),3 ( E ) 3, ( E ) 2,3 CV g V V i i i CV g ( VL V ) g ( VE V ) g ( VI V ) g f ( V )( VE V ) V L E I NMDA Mg g ( E) () () E( 3, ( V VR, ) ge ) E E g ( I ) I( 3,2( V VR, ) gi ) I I g NMDA ( I ) () () ( 3, ( V VR, ) g ) NMDA NMDA NMDA Weights are constrained by anatomy Marreiros et al., Neuroimage, 2 Moran et al., Neuroimage, 2 Anatomical Background for DCM 9 Generative models, model selection and model validation Any given DCM = a particular generative model of how the measured data (may) have been caused Model selection = hypothesis testing = comparing competing models (i.e. different ideas about mechanisms underlying observed data) Evaluate the relative plausibility of competing explanations for an established effect (e.g., activation) Careful definition of model (hypothesis) space crucial! model selection model validation! Model validation requires external criteria (external to the measured data) Anatomical Background for DCM 2 Bayesian model selection (BMS) Model evidence: p( ym ) py (, mp ) ( md ) Gharamani, 24 log pym ( ) log py (, m),,, KLq p m KLq p ym p(y m) y all possible datasets accounts for both accuracy and complexity of the model a measure of how well the model generalizes Various approximations, e.g.: - negative free energy, AIC, BIC McKay, Neural Comp, 992 Penny et al., Neuroimage, 24 Anatomical Background for DCM 2 7
.6.5.4.3.2..6.4.2.8.6.4.2.6.4.2.8.6.4.2-2 - 2-2 - 2 2 3 4 5 6.5.5.5.5.5.5.5 m: a=-32,b=-32.5 m: a=-8,b=-24.5 m9: a=-4,b=-2.5 m28: a=,b=-6.5 m37: a=,b=2.5 m46: a=4,b=6.5 m55: a=8,b=28.5 2.8.6.4.2.8.6.4.2 34.2% v.5268 6.5% v.384 5.7% v.7 43.6% v.7746-3 -2-2 3.5.5.5.5.5.5.5 m 2: a=-6,b=-32.5 m : a=-8,b=-2.5 m 2: a=-4,b=-8.5 m 29: a=,b=-2.5 m 38: a=,b=24.5 m 47: a=4,b=2.5 m 56: a=8,b=32.5.5.5.5.5.5.5.5 m3: a=-6,b=-28.5 m2: a=-8,b=-6.5 m 2: a=-4,b=-4.5 m 3: a=,b=-8.5 m39: a=,b=28.5 m48: a=4,b=24.5 m 57: a=2,b=2.5.5.5.5.5.5.5.5 m 4: a=-2,b=-32.5 m3: a=-8,b=-2.5 m 22: a=-4,b=.5 m 3: a=,b=-4.5 m 4: a=,b=32.5 m 49: a=4,b=28.5 m58: a=2,b=24.5.5.5.5.5.5.5.5 m 5: a=-2,b=-28.5 m 4: a=-4,b=-32.5 m 23: a=-4,b=4.5 m 32: a=,b=.5 m 4: a=4,b=-32.5 m5: a=4,b=32.5 m 59: a=2,b=28.5.5.5.5.5.5.5.5 m 6: a=-2,b=-24.5 m5: a=-4,b=-28.5 m 24: a=,b=-32.5 m 33: a=,b=4.5 m 42: a=4,b=.5 m 5: a=8,b=2.5 m6: a=2,b=32.5.5.5.5.5.5.5.5 m7: a=-2,b=-2.5 m 6: a=-4,b=-24.5 m 25: a=,b=-28.5 m34: a=,b=8.5 m43: a=4,b=4.5 m 52: a=8,b=6.5 m 6: a=6,b=28.5.5.5.5.5.5.5.5 m8: a=-8,b=-32.5 m 7: a=-4,b=-2.5 m 26: a=,b=-24.5 m 35: a=,b=2.5 m44: a=4,b=8.5 m 53: a=8,b=2.5 m62: a=6,b=32.5.5.5.5.5.5.5.5 m9: a=-8,b=-28.5 m 8: a=-4,b=-6.5 m 27: a=,b=-2.5 m 36: a=,b=6.5 m 45: a=4,b=2.5 m 54: a=8,b=24.5 m 63 & m 64.5 Examples for the use of DCM Anatomical priors for DCM for fmri Modulation of connectivity by prediction errors Conductance based DCM if time permits: DCM validation in patients or layered DCM Anatomical Background for DCM 22 Anatomically informed priors DCM FG FG probabilistic tractography FG left 34 6.5% FG right 3 5.7% 24 43.6% LG LG LG left 2 34.2% LG right connectionspecific priors for coupling parameters anatomical probability Stephan et al., Neuroimage, 29 Anatomical Background for DCM 23 Anatomically informed priors R R R 2 R 2 Models with anatomically informed priors were clearly superior : Bayes Factor > 9 Posterior model probabilities prior variance anatomical probability Stephan et al., Neuroimage, 29 Stephan et al., Neuroimage, 29 Anatomical Background for DCM 24 8
Prediction errors drive synaptic plasticity PE(t) R x 3 a McLaren 989 x x 2 t t k k t w w PE w a PE( ) d synaptic plasticity during learning = f (prediction error) t Anatomical Background for DCM 25 Learning of dynamic audio-visual associations Model behavior with a hierarchical Bayesian Model estimate of prediction errors PE (Behrens et al., Nat Neurosci, 27) den Ouden et al., J Neurosci, 2 Anatomical Background for DCM 26 Prediction error (PE) activity in the putamen PE during active sensory learning PE during incidental sensory learning p <.5 (SVC) den Ouden et al., Cereb Cortex, 29 PE during RF learning O'Doherty et al., Science, 24 PE = teaching signal for synaptic plasticity during learning Could the putamen be regulating trial-by-trial changes of task-relevant connections? Anatomical Background for DCM 27 9
PE control plasticity during adaptive cognition Hierarchical Bayesian learning model Influence of visual areas on premotor cortex: stronger for surprising stimuli weaker for expected stimuli PUT p =. p =.7 PMd PPA FFA den Ouden et al., J Neurosci, 2 ongoing pharmacological and genetic studies Anatomical Background for DCM 28 What is a good model? essentially, all models are wrong, but some are useful. George E.P. Box Anatomical Background for DCM 29 Strategies for model validation in silico humans animals & humans patients numerical analysis & simulation studies experiments of known cognitive/neurophys. processes experimentally controlled system perturbations clinical facts Examples: Validation of DCM in animal studies: infers site of seizure origin (David et al. 28) infers primary recipient of vagal nerve stimulation (Reyt et al. 2) infers synaptic changes as predicted by microdialysis (Moran et al. 28) infers fear conditioning induced plasticity in amygdala (Moran et al. 29) tracks anaesthesia levels (Moran et al. 2) predicts sensory stimulation (Brodersen et al. 2) Anatomical Background for DCM 3
Dopaminergic modulation of AMPA/NMDA receptors a AMPA NMDA GABA exogenous inputs to layer IV NMDA inputs to layer III pyramidal cells and interneurons Moran et al., Curr Biol, 2 Anatomical Background for DCM 3 Estimates of AMPA/NMDA correlate with behaviour Moran et al., Curr Biol, 2 Anatomical Background for DCM 32 Validating models against clinical facts model of neuronal (patho)physiology individual diagnosis predicting individual outcome individual therapeutic response Brodersen et al., PLoS Comp Biol, 2; Brodersen et al, Neuroimage Clin. 23 Anatomical Background for DCM 33
Summary Anatomical connectivity information is important, but not everything Models of effective connectivity neural system mechanisms can be inferred from neuroimaging data DCM is one (not the only) method for this: Neuronal interactions are modeled at the hidden neuronal level Bayesian system identification method Key role for model selection Can be integrated with measures of anatomical connectivity Can be integrated with computational models Validation is critical (for any modeling approach) Anatomical Background for DCM 34 Acknowledgments TNU-Team E. Aponte T. Baumgartner D. Cole A. Diaconescu S. Grässli H. Haker Rössler Q. Huys S. Iglesias L. Kasper E. Lomakina C. Mathys S. Paliwal F. Petzschner S. Princz S. Raman D. Renz G. Stefanics K.E. Stephan L. Weber T. Wentz S. Wilde Collaborators J.-D. Haynes, Berlin T. Kahnt, Chicago H. den Ouden, Nijmegen P. Koopmans, Oxford K.A.C. Martin, Zürich Many thanks to K.E. Stephan for sharing slides. Translational Neuromodeling Unit Anatomical Background for DCM 35 2