Dynamic Causal Models

Brain Mapping identifies regions where experimental effect sizes are significantly non-zero (orange). Brain connectivity then explains activity in a set of regions using (eg. differential equation) models with directed connections. For Brain Mapping the parameters of interest are regional activities and for Brain Connectivity they are directed pathways (blue). Both approaches can be applied to data from fMRI or M/EEG. For fMRI this requires Bayesian inversion of a forward model describing a temporal convolution, and for M/EEG a forward model describing a spatial mapping.

  • N. Ramnani, T.E.J. Behrens, W.D. Penny, and P.M. Matthews. New approaches for exploring anatomic and functional connectivity in the human brain. Biological Psychiatry, 2004, 56(9), 613-619.


  • W.D. Penny, K.E. Stephan, A. Mechelli, and K.J. Friston. Modelling Functional Integration: A Comparison of Structural Equation and Dynamic Causal and Models. NeuroImage, 23:264-274, 2004. Note: Supplement 1

Dynamic Causal Modeling (DCM) is a Bayesian estimation framework for fitting differential equation models of neuronal activity to brain imaging data. Model comparison in this context allows researchers to formally compare different theories about the architectures of the large-scale neural networks that mediate human perception, cognition and action, using non-invasive brain imaging data. In the figure below the red traces indicate time series of neuronal activity that result when the modulatory connection from u2 is activated. This is a mathematical model of gain control effects mediated eg. by neuromodulators.

These methodological developments are in collaboration with Karl Friston, Klaas Stephan, Jean Daunizeau and Rosalyn Moran among others.


  • W. Penny (2011). Comparing Dynamic Causal Models using AIC, BIC and Free Energy. Neuroimage 59(1):319-330. PDF


  • W Penny, K Stephan, J. Daunizeau, M. Rosa, K. Friston, T. Schofield and A Leff. Comparing Families of Dynamic Causal Models. PLoS Computational Biology, Mar 2010, 6(3), e1000709. PDF


  • K Stephan, W Penny, R Moran, H den Ouden, J Daunizeau and K Friston. Ten simple rules for dynamic causal modeling. Neuroimage, Feb 15 2010, 49(4):3099-109. PDF


  • K Stephan, W Penny, J Daunizeau, R Moran and K Friston. Bayesian model selection for group studies. Neuroimage, 46(4):1004-17. PDF


  • W Penny, V Litvak, L Fuentemilla, E Duzel, and K Friston. Dynamic Causal Models for Phase Coupling. J Neurosci Methods, 183(1):19-30, 2009. PDF


  • K.E. Stephan, L.M. Harrison, S.J. Kiebel, O. David, W.D. Penny, and K.J. Friston. Dynamic causal models of neural system dynamics: current state and future extensions. Journal of Biosciences, 32:411-416, 2007. PDF


  • K.E. Stephan, J.C. Marshall, W.D. Penny, K.J. Friston, and G.R. Fink. Interhemispheric integration of visual processing during task-driven lateralization. Journal of Neuroscience, 27:3512-3522, 2007.


  • K.E. Stephan, W.D. Penny, J.C. Marshall, G.R. Fink, and K.J. Friston. Investigating the functional role of Callosal connections with Dynamic Causal Models. Ann. N.Y. Acad. Sci., 1064:16-36, 2005.


  • W.D. Penny, K.E. Stephan, A. Mechelli, and K.J. Friston. Comparing Dynamic Causal Models. NeuroImage, 22(3):1157-1172, 2004. PDF


  • K.E. Stephan, L. Harrison, W.D. Penny, and K.J. Friston. Biophysical models of fMRI responses. Current Opinion in Neurobiology, 14(5):629-635, 2004. PDF


  • K.J. Friston, L. Harrison, and W.D. Penny. Dynamic Causal Modelling. NeuroImage, 19(4):1273-1302, 2003. PDF



Clinical Applications


Collaborations with Alex Leff's group have involved the application of Dynamic Causal Models (for MEG/EEG) in studying recovery of language function after brain injury (eg. due to stroke). Work with Klaas Stephan's group aims to fractionate schizophrenic groups into sub-categories with distinct brain connectivity fingerprints.

  • S. Kerry, O. Aguilar, W Penny, J . Crinion, A. Leff and Z. Woodhead (2019). How Does iReadMore Therapy Change the Reading Network of Patients with Central Alexia? Journal of Neuroscience 17 July 2019, 39 (29) 5719-5727. PDF
  • Z. Woodhead, J Crinion, S Teki, W. Penny, C. Price and A. Leff (2017). Auditory training changes temporal lobe connectivity in "Wernicke's aphasia": a randomised trial. Journal of Neurology, Neurosurgery and Psychiatry. Published Online First: 04 March 2017. PDF


  • Z. Woodhead, W. Penny, G. Barnes, H. Crewes, R. Wise, C. Price and A. Leff (2013). Reading therapy strengthens top-down connectivity in patients with pure alexia. Brain. 136, 2579-2591. PDF


  • S. Teki, G. Barnes, W. Penny, P. Iverson, Z. Woodhead, T. Griffiths and A. Leff (2013). The right hemisphere supports but does not replace left hemisphere auditory function in patients with persisting aphasia. Brain. 136, 1901-12. PDF


  • K. Brodersen, L. Deserno, F. Schlagenhauf, Z. Lin, W. Penny, J. Buhmann and K. Stephan (2014). Dissecting psychiatric spectrum disorders by generative embedding. Neuroimage: Clinical, 4, 98-111. PDF


  • W. Penny, J Iglesias-Fuster, Y Quiroz, F Lopera and A Bobes (2018). Dynamic causal modelling of preclinical autosomal-dominant Alzheimer's disease. Journal of Alzheimer's Disease. 65(3), 697-711. PDF