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Highlights• Neural Field Theory (NFT) can yield effective connectivity from functional connectivity.• Effective and functional connectivity are related to cortical geometry.• Norm-minimization is a useful method to infer effective connectivity. *Highlights (for review)Page 3 of 44 A c c e p t e d M a n u s c r i p t N ew method : A method is presented to calculate the direct effective connection matrix (deCM), which embodies direct connection strengths between brain regions, from functional CMs (fCMs) by minimizing the difference between an experimental fCM and one calculated via neural field theory from an ansatz deCM based on an experimental anatomical CM.Results : The best match between fCMs occurs close to a critical point, consistent with independent published stability estimates. Residual mismatch between fCMs is identified to be largely due to interhemispheric connections that are poorly estimated in an initial ansatz deCM due to experimental limitations; improved ansatzes substantially reduce the mismatch and enable inter- Comparison with existing methods : This method gives insight into direct and multistep effective connectivity from fCMs and relating to physiology and brain geometry. This contrasts with other methods, which progressively adjust connections without an overarching physiologically based framework to deal with multistep or poorly estimated connections.Conclusions : deCMs can be usefully estimated using this method and the results enable multistep connections to be investigated systematically.

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