Enhanced inference of network structure from functional connectivity - PowerPoint PPT Presentation

Enhanced inference of network structure from functional connectivity Eugene Duff Eugene Duff, Steve Smith, Tamar Makin, Mark Woolrich

Brain connectivity in functional neuroimaging Cole, Nature Neuroscience, 2013

Brain connectivity in functional neuroimaging Correlation (network matrices) Power/frequency analysis PPI Mutual Information Coherence Partial correlation Dynamic Causal modelling Structural Equation modelling Granger Graph models

Brain connectivity in functional neuroimaging Correlation (network matrices) Pros: • Simple pairwise measures permit, Power/frequency analysis comprehensive characterisation. • Computationally efficient. PPI Mutual Information Cons: • Can be sensitive to a wide range of effects: Coherence ambiguous interpretation • Do not estimate neurophysiological parameters How to use FC to inform EC model structure? Pros: • Can estimate more biologically meaningful variables Partial correlation • Can model out uninteresting variables Dynamic Causal modelling Cons: • Often overparameterised, can only Structural Equation modelling compare limited set of model structures • Difficult to estimate for many nodes Granger • Strong assumptions for ROIs, connectivity patterns, signal dynamics, noise sources Graph models • All parameters/regions interdependent

What causes changes in correlations? Typical assumption is some sort of change in level of interaction between brain regions: • Strength of interaction • Extent of interaction 𝜍 x, y • Activity level of network With no model of signal, analyses will be sensitive to variations in noise: X • Increase in noise level 𝜍 x, y Y e.g. Differences in patient group, due to vascular tone. Healthy Patients • Reduction in signal X 𝜍 x, y e.g. Differences across activation Y states due to BOLD ceiling effect state 1 state 2 .

Aims To identify a simple approach to characterising functional connectivity: • that is less ambiguous • remains a bivariate function for mapping and flexible implementation • provides insight into effective connectivity network modelling methods (e.g. DCM, causal methods) .

Signal changes affecting correlations X 𝜍 x, y Region 2 Region 1 Y Increase in signal levels X Y 𝜍 x, y Increase in common activity in one of two regions y x BOLD signal 𝜍 x, y 𝜍 x, y Decrease in noise 𝜍 x, y Decrease in unrelated activity in one of two regions 𝜍 x, y Opposite changes in amplitude (combinations of above) 𝜍 x, y Synchronisation of signals across regions

Signal changes affecting correlations σ x X 𝜍 x, y σ y Region 2 Region 1 Y Increase in signal levels X Y σ x 𝜍 x, y σ y Increase in common activity in one of two regions y x BOLD signal σ x 𝜍 x, y 𝜍 x, y σ y Decrease in noise σ x σ y σ x 𝜍 x, y σ y Decrease in unrelated activity in one of two regions σ x 𝜍 x, y σ y Opposite changes in amplitude (combinations of above) σ x 𝜍 x, y σ y Synchronisation of signals across regions

Potential dynamics affecting connectivity By observing variances, we can eliminate the possibility of certain changes.. Condition 1 Condition 2 Increase in shared signal levels Increase in common activity in ? one of two regions Decrease in noise Decrease in unrelated activity in one of two regions 𝜍 x, y 𝜍 xb,b O pposite changes in amplitude σ x σ xb σ y σ yb Synchronisation of signals across regions But the necessary extent of a change required to explain a specific change in correlation is unclear. Can we determine if certain variance changes explain a particular observed change? 𝜍 x,y σ x, σ xb σ y, σ yb a < 𝜍 xb,yb < b

Shared/Unshared Signal Model Pairwise model linking regions X and Y. Model Formulation Shared signal BOLD signal for condition a as a function of S and Ux Uy. Condition a S proportion of shared signal y w 2 x a w 2 y a X Y U x U y Proportion of shared signal in each region is bounded by c orrelation Unshared signal (x) Unshared signal (y) y x BOLD signal 𝜍 xa,y a σ y a σ x a BOLD statistics (corr,var ) Condition b Shared signal S w 2 yb w 2 xb proportion of shared signal (y) Y U x X U y Unshared signal (y) Unshared signal (x) x y BOLD signal 𝜍 xb,yb BOLD statistics (corr,var) σ yb σ xb

Shared/Unshared Signal Model Pairwise model linking regions X and Y. Shared signal Condition a S proportion of shared signal y w 2 x a w 2 y a X Y U x U y Unshared signal (x) Unshared signal (y) Condition b produces some change in levels of shared and unshared signals - w xb = c x w x, w yb = c y w y. , matching the total change in variance: y x BOLD signal 𝜍 xb,y b σ y a σ x a BOLD statistics (corr,var ) New observed variance can be expressed: Condition b Shared signal S w 2 yb w 2 xb proportion of shared signal (y) And correlation: Y U x X U y Unshared signal (y) Unshared signal (x) x y BOLD signal 𝜍 xb,yb BOLD statistics (corr,var) σ yb σ xb

Shared/Unshared Signal Model Pairwise model linking regions X and Y. Shared signal Condition a S proportion of shared signal y w 2 x a w 2 y a X Y U x U y Unshared signal (x) Unshared signal (y) y x BOLD signal 𝜍 xb,y b σ y a σ x a BOLD statistics (corr,var ) Given the limits on w ay , the effects of particular changes in signal Condition b and noise on 𝜍 xb,yb can be determined based on variance Shared signal S changes. w 2 yb w 2 xb proportion of shared signal (y) E.g. if there was no change in signal levels (variance was associated with unshared signal): Y U x X U y Unshared signal (y) Unshared signal (x) x y BOLD signal 𝜍 xb,yb BOLD statistics (corr,var) σ yb σ xb

Identifying bounds on correlation c x >1 (u x =1) σ x 𝜍 x, y σ y (u y =1) c y >1 Increase in signal levels c x >1 (u x =1) σ x 𝜍 x, y σ y c y =1 (u y =1) Increase in common activity in one of two regions c x =1 (u x <1) σ x 𝜍 x, y σ y (u y <1) c y =1 Decrease in noise σ x c x =1 (u x =1) 𝜍 x, y σ y (u y <1) c y =1 Decrease in unrelated activity in one of two regions σ x c x >1 (u x =1) 𝜍 x, y σ y c y <1 (u y= 1) Opposite changes in amplitude (combinations of above) σ x c x >1 (u x <1) 𝜍 x, y σ y c y >1 (u y <1) Synchronisation of signals across regions

Potential dynamics affecting connectivity c x >1 (u x =1) σ x 𝜍 x, y σ y (u y =1) c y >1 Increase in signal levels c x >1 (u x =1) σ x 𝜍 x, y σ y c y =1 (u y =1) Increase in common activity in one of two regions c x =1 (u x >1) σ x 𝜍 x, y σ y (u y >1) c y =1 Decrease in noise σ x c x= 1 (u x >1) 𝜍 x, y σ y (u y =1) c y= 1 Decrease in unrelated activity in one of two regions σ x c x <1 (u x =1) 𝜍 x, y σ y c y >1 (u y= 1) Opposite changes in amplitude (combinations of above) c x >1 (u x <1) σ x 𝜍 x, y σ y c y >1 (u y <1) Synchronisation of signals across regions

Active-state experiment 16 Subjects Multiband-6 TR: 1.3, 2x2x2mm voxels Five active-state conditions produce robust changes in ongoing dynamics providing a good testing set for connectivity measures.

Active-state experiment Are changes in connectivity across associated with variance changes? Do these changes correspond to particular types of changes in connectivity - are they predicted by model?

Activation, variance, and correlation changes Visual task activation Motor task activation Connectivity change from rest for visual condition (V1 seed ) Connectivity change from rest for visual condition (V1 seed ) Variance changes from rest for visual condition Variance changes from rest for motor condition

Activation, variance, and correlation changes Variance changes from rest for visual Variance changes from rest for motor Proportion Proportion of edges with at least one region changing in variance Number of edges Change in correlation (z-score)