Neural Field Theory

Neural field theory propagators

Propagator formalism of neural field theory. Feynman diagrams showing (a) direct propagation, (b) propagation via one intermediate node, and (c) propagation via two intermediate nodes. The dressed propagator is a sum of these, and all higher-order, bare propagators. Taken from reference [5]

Neural activity in the brain has been observed for over a century and is widely used to probe brain function and disorders, through the electroencephalogram (EEG), electrocorticogram, depth electrodes, functional MRI, and many other measures. However, the connections between stimuli, physiology, processing, and measurements have been chiefly qualitative until recently, and most links between stimuli, activity, function, and measurements have been based on phenomenological correlations.

We have developed a quantitative multiscale model of brain stimulus-activity-measurement dynamics that includes key physiology and anatomy from synapses to the whole brain and from milliseconds up in timescale. With the inclusion of measurement effects, the model successfully predicts a wide range of linear and nonlinear phenomena at many scales. These include time series, spectra, evoked responses to stimuli, seizure dynamics, visual phenomena during perception, arousal (sleep-wake) dynamics, and influences of pharmacology and aging. Fitting to experimental data enables physiological parameters to be inferred in normal and abnormal conditions.

Such multiscale modeling thus provides a framework within which to interrelate, predict, and interpret diverse phenomena and measurements. The physiological basis of the model enables it to predict experimental observables such as electroencephalographic and functional MRI measurements, and the results have given rise to commercial applications. Numerous areas exist for PhD, MSc, or Honors projects, which could include theoretical, computational, and experimental components in cooperation with our international and local collaborators.


  1. Robinson, P. A., Rennie, C. J., and Wright, J. J. (1997). Propagation and Stability of Waves of Electrical Activity in the Cerebral Cortex, Physical Review E, 56, 826-840.
  2. Robinson, P. A., Rennie, C. J., Rowe, D. L., and O'Connor, S. C. (2004). Estimation of Multiscale Neurophysiological Parameters by EEG Means: Consistency and Complementarity vs. Independent Measures, Human Brain Mapping, 23, 53-72.
  3. Robinson, P. A. (2006): "Patchy propagators, brain dynamics, and the generation of spatially structured gamma oscillations." Physical Review E 73.4 041904.
  4. Breakspear, M., Roberts, J. A., Terry, J. R., Rodrigues, S., Mahant, N., & Robinson, P. A. (2006). A unifying explanation of primary generalized seizures through nonlinear brain modeling and bifurcation analysis. Cerebral Cortex, 16(9), 1296-1313.
  5. Robinson, P. A. (2012) "Interrelating anatomical, effective, and functional brain connectivity using propagators and neural field theory." Physical Review E 85.1 : 011912.
  6. Abeysuriya, R., Rennie, C., Robinson, P. (2014). Prediction and verification of nonlinear sleep spindle harmonic oscillations. Journal of Theoretical Biology, 344, 70-77-70-77.
  7. Fung, P., Robinson, P. (2014). Neural field theory of synaptic metaplasticity with applications to theta burst stimulation. Journal of Theoretical Biology, 340, 164-176.
  8. Zhao, X., Kim, J., Robinson, P., Rennie, C. (2014). Low dimensional model of bursting neurons. Journal of computational neuroscience, 36(1), 81-95.