# Tractography-based priors for dynamic causal models

Stephan, K E; Tittgemeyer, M; Knösche, T R; Moran, R J; Friston, K J (2009). Tractography-based priors for dynamic causal models. NeuroImage, 47(4):1628-1638.

## Abstract

Functional integration in the brain rests on anatomical connectivity (the presence of axonal connections) and effective connectivity (the causal influences mediated by these connections). The deployment of anatomical connections provides important constraints on effective connectivity, but does not fully determine it, because synaptic connections can be expressed functionally in a dynamic and context-dependent fashion. Although it is generally assumed that anatomical connectivity data is important to guide the construction of neurobiologically realistic models of effective connectivity; the degree to which these models actually profit from anatomical constraints has not yet been formally investigated. Here, we use diffusion weighted imaging and probabilistic tractography to specify anatomically informed priors for dynamic causal models (DCMs) of fMRI data. We constructed 64 alternative DCMs, which embodied different mappings between the probability of an anatomical connection and the prior variance of the corresponding of effective connectivity, and fitted them to empirical fMRI data from 12 healthy subjects. Using Bayesian model selection, we show that the best model is one in which anatomical probability increases the prior variance of effective connectivity parameters in a nonlinear and monotonic (sigmoidal) fashion. This means that the higher the likelihood that a given connection exists anatomically, the larger one should set the prior variance of the corresponding coupling parameter; hence making it easier for the parameter to deviate from zero and represent a strong effective connection. To our knowledge, this study provides the first formal evidence that probabilistic knowledge of anatomical connectivity can improve models of functional integration.

## Abstract

Functional integration in the brain rests on anatomical connectivity (the presence of axonal connections) and effective connectivity (the causal influences mediated by these connections). The deployment of anatomical connections provides important constraints on effective connectivity, but does not fully determine it, because synaptic connections can be expressed functionally in a dynamic and context-dependent fashion. Although it is generally assumed that anatomical connectivity data is important to guide the construction of neurobiologically realistic models of effective connectivity; the degree to which these models actually profit from anatomical constraints has not yet been formally investigated. Here, we use diffusion weighted imaging and probabilistic tractography to specify anatomically informed priors for dynamic causal models (DCMs) of fMRI data. We constructed 64 alternative DCMs, which embodied different mappings between the probability of an anatomical connection and the prior variance of the corresponding of effective connectivity, and fitted them to empirical fMRI data from 12 healthy subjects. Using Bayesian model selection, we show that the best model is one in which anatomical probability increases the prior variance of effective connectivity parameters in a nonlinear and monotonic (sigmoidal) fashion. This means that the higher the likelihood that a given connection exists anatomically, the larger one should set the prior variance of the corresponding coupling parameter; hence making it easier for the parameter to deviate from zero and represent a strong effective connection. To our knowledge, this study provides the first formal evidence that probabilistic knowledge of anatomical connectivity can improve models of functional integration.

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