Neural field theory of synaptic metaplasticity with applications to theta burst stimulation

J Theor Biol. 2014 Jan 7;340:164-76. doi: 10.1016/j.jtbi.2013.09.021. Epub 2013 Sep 21.


Transcranial magnetic stimulation (TMS) is characterized by strong nonlinear plasticity effects. Experimental results that highlight such nonlinearity include continuous and intermittent theta-burst stimulations (cTBS and iTBS, respectively), where depression is induced in the continuous case, but insertion of an off period of around 8s for every 2s of stimulation changes the induced plasticity to potentiation in the intermittent case. Another nonlinearity is that cTBS and iTBS exhibit dosage dependency, where doubling of the stimulation duration changes the direction of induced plasticity. Guided by previous experimental results, this study postulates on the characteristics of metaplasticity and formulates a physiological system-level plasticity theory to predict TMS experiments. In this theory, plasticity signaling induces plasticity in NMDA receptors to modulate further plasticity signals, and is followed by a signal transduction delayed plasticity expression. Since this plasticity in NMDA receptor affects subsequent plasticity induction, it is a form of metaplasticity. Incorporating this metaplasticity into a recent neural field theory of calcium dependent plasticity gives a physiological basis for the theory of Bienenstock, Cooper, Munro (1982), where postsynaptic intracellular calcium level becomes the measure of temporal averaged postsynaptic activity, and converges to the plasticity threshold to give homeostatic effects. Simulations of TMS protocol responses show that intracellular calcium oscillations around the threshold predicts the aforementioned nonlinearities in TMS-induced plasticity, as well as the interpersonal TBS response polarity found experimentally, where the same protocol may induce opposite plasticity effect for different subjects. Thereby, recommendations for future experiments and TMS protocol optimizations are made. Input selectivity via spatially extended, mean field neural dynamics is also explored.

Keywords: BCM theory; Calcium dependent plasticity; Homeostasis; Synaptic plasticity; Transcranial magnetic stimulation.

Publication types

  • Research Support, Non-U.S. Gov't

MeSH terms

  • Animals
  • Calcium / metabolism
  • Homeostasis
  • Humans
  • Models, Neurological
  • Neural Inhibition / physiology*
  • Neuronal Plasticity / physiology*
  • Oscillometry
  • Receptors, N-Methyl-D-Aspartate / metabolism
  • Transcranial Magnetic Stimulation / methods*


  • Receptors, N-Methyl-D-Aspartate
  • Calcium