Network diffusion accurately models the relationship between structural and functional brain connectivity networks

Abstract

The relationship between anatomic connectivity of large-scale brain networks and their functional connectivity is of immense importance and an area of active research. Previous attempts have required complex simulations which model the dynamics of each cortical region, and explore the coupling between regions as derived by anatomic connections. While much insight is gained from these non-linear simulations, they can be computationally taxing tools for predicting functional from anatomic connectivities. Little attention has been paid to linear models. Here we show that a properly designed linear model appears to be superior to previous non-linear approaches in capturing the brain’s long-range second order correlation structure that governs the relationship between anatomic and functional connectivities. We derive a linear network of brain dynamics based on graph diffusion, whereby the diffusing quantity undergoes a random walk on a graph. We test our model using subjects who underwent diffusion MRI and resting state fMRI. The network diffusion model applied to the structural networks largely predicts the correlation structures derived from their fMRI data, to a greater extent than other approaches. The utility of the proposed approach is that it can routinely be used to infer functional correlation from anatomic connectivity. And since it is linear, anatomic connectivity can also be inferred from functional data. The success of our model confirms the linearity of ensemble average signals in the brain, and implies that their long-range correlation structure may percolate within the brain via purely mechanistic processes enacted on its structural connectivity pathways.

Cooperative and Competitive Spreading Dynamics on the Human Connectome

“…between association weight and empirical functional connectivity (r = 0.41). Overall, these correlations between predicted and empirical functional connectivity compare favorably to many other computational ''forward'' models, including neural mass models (Honey et al, 2009), random walk/diffusion models (Betzel et al, 2013;Abdelnour et al, 2014), and routing models (Goñ i et al, 2014). Similar to those models, the present spreading model is even better at predicting functional connectivity for single hemispheres (r = 0.47 for left, r = 0.49 for right), most likely due to the inherent limitations of computational tractography for inferring inter-hemispheric anatomical projections (see Methodological Considerations for more discussion).…”

Path ensembles and a tradeoff between communication efficiency and resilience in the human connectome

“…These measures assume that optimally short paths are highly privileged and are exclusively selected for signaling among remote node pairs. However, this presupposes that neural signals have access to information or ''knowledge'' about the global network topology (Boguña et al 2009;Goñi et al 2013;Abdelnour et al 2014) which is unlikely to be the case. Furthermore, it excludes from consideration numerous alternative paths that, while not optimally short, may represent near-optimal alternative routes.…”

Connectome Networks: From Cells to Systems

“…This connectome-based modeling framework can be extended to include anatomically detailed models of dynamic effects induced by focal brain lesions (Alstott et al 2009) or degeneration of brain connectivity (de Haan et al 2012). While biophysically based models can generate simulations of rich brain dynamics, simpler models that are based on structural graph measures (Goñi et al 2014) and/or models of diffusive processes (Abdelnour et al 2014) and routing (Mišić et al 2014) are gaining in importance due to their computational simplicity and analytic transparence.…”