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Effective Connectivity: Basics

Effective Connectivity: Basics. Aim: Estimate the influence that one neural system exerts over another Estimate how this influence is affected by experimental manipulations Requirements: - an anatomical model of which regions are connected

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Effective Connectivity: Basics

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  1. Effective Connectivity: Basics • Aim: • Estimate the influence that one neural system exerts over another • Estimate how this influence is affected by experimental manipulations • Requirements: - an anatomical model of which regions are connected - a mathematical model of how the different regions interact • Procedure: • Choose between two model types: • STATIC, linear regression models using PPIs and SEM. • DYNAMIC, used for Dynamic Causal Modelling (DCM)

  2. Effective Connectivity: linear regression methods PPIs = Psycho-Physiological Interactions • A PPI corresponds to a context-dependent difference in the slope of the regression between two regional time series. • E.g. V1 and V5 activity in two contexts: (1) No attention (2) With attention + with attention no attention Attention V1 V5

  3. Effective Connectivity: linear regression methods Testing Psycho-Physiological Interactions V5 = (V1 x U) bPPI + [V1 U] bM + e U = attention bilinear term (PPI) main effects (V1 x U) bilinear term (PPI)

  4. Effective Connectivity: linear regression methods Testing Psycho-Physiological Interactions V5 = (V1 x U) bPPI + [V1 U] bM + e U = attention bilinear term (PPI) main effects e Null hypothesis: bPPI = 0

  5. Effective Connectivity: linear regression methods Structural Equation Modelling Multivariate tool used to test hypotheses regarding the influences among interacting variables. b12 z1 y2 y1 z2 y3 b13 b32 z3 0 b12b13 y1 y2 y3 = y1 y2 y30 0 0 + z1 z2 z3 0 b320 y – time series b - path coefficients z – white noise inputs (independent) NB. Not stimuli inputs b = coupling matrix contains connection strengths for paths of interest

  6. Effective Connectivity: linear regression methods Structural Equation Modelling Possible to make statistical comparison of different models Compare parameters using c2 A A bV5-PPC bV1-V5 PPC V5 V1 NA NA bV5-PPC bV1-V5 PPC V5 V1 H0: bV1-V5A = bV1-V5NA , bV5-PPCA = bV5-PPCNA See Büchel & Friston, 1997 for example.

  7. Effective Connectivity: linear regression methods Structural Equation Modelling Also possible to include bilinear interaction terms in SEMs. bV5-PPC bV1-V5 bPFC-PPC PPC PFC V5 V1 b Nonlinear SEM models are constructed by adding a bilinear term as an extra node. A significant connection from a bilinear term represents a modulatory effect. b b PPIV5xPFC b Attentional Set See Büchel & Friston, 1997 for example.

  8. Effective Connectivity: linear regression methods Problem: Temporal information is discounted. i.e. assumes interactions are instantaneous But interactions within the brain take time and are not instantaneous. Furthermore the state of any brain system that conforms to a dynamical system will depend on the history of its input. Solution: Use DYNAMIC models to investigate connectivity

  9. x1 ……. xt-1 xt-2 xt-p ……. y1 yt-1 yt-2 yt-p Effective Connectivity: dynamic models • Advantages: • Accommodate non-linear and dynamic aspects of neuronal interactions • Uses the temporal information present in the data • Possible to use information about experimental manipulations and stimuli as inputs into particular nodes and/or connections within the model.

  10. Effective Connectivity: linear regression methods Structural Equation Modelling Multivariate tool used to test hypotheses regarding the influences among interacting variables. b12 z1 y2 y1 z2 y3 b13 b32 z3 0 b12b13 y1 y2 y3 = y1 y2 y30 0 0 + z1 z2 z3 0 b320 y – time series b - path coefficients z – white noise inputs (independent) NB. Not stimuli inputs b = coupling matrix contains connection strengths for paths of interest

  11. Input u1 Input u2 c11 c22 a21 region z1 region z2 a22 a11 a12 Effective Connectivity: dynamic models linear time-invariant system e.g. state of region z1: z1 = a11z1 + a21z2 + c11u1 . . z1 z1 A – intrinsic connectivity C – inputs . z2 z2 z = Az + Cu • Linear behaviour – inputs cannot influence intrinsic connection strengths

  12. Input u1 Input u2 b212 c11 c22 region z1 region z2 a21 a22 a11 a12 Effective Connectivity: dynamic models Bilinear effects to approximate non-linear behaviour state of region z1: z1 = a11z1 + a21z2 + b212u2z2 + c11u1 . . z1 z1 A – intrinsic connectivity B – induced connectivity C – driving inputs . z2 z2 . z = Az + Bzu + Cu • Bilinear term – product of two variables (regional activity and input)

  13. Input u1 Input u2 b212 c11 c22 region z1 region z2 a21 a22 a11 a12 Effective Connectivity: Dynamic Causal Modelling • DCM allows to model a cognitive system at the neuronal level (which is not directly accessible for fMRI). • The modelled neuronal dynamics (z) 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 BOLD signals are maximally similar to the experimentally measured BOLD signals. Change in state of region z1: z1 = a11z1 + a21z2 + b212u2z2 + c11u1 . The states (z) refer to the neuronal activity, not the BOLD response. λ z y

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