The theoretical model of theta burst form of repetitive transcranial magnetic stimulation

ObjectiveTheta burst stimulation, a form of repetitive transcranial magnetic stimulation, can induce lasting changes in corticospinal excitability that are thought to involve long-term potentiation/depression (LTD/LTD)-like effects on cortical synapses. The pattern of delivery of TBS is crucial in determining the direction of change in synaptic efficiency. Previously we explained this by postulating (1) that a single burst of stimulation induces a mixture of excitatory and inhibitory effects and (2) those effects may cascade to produce long-lasting effects. Here we formalise those ideas into a simple mathematical model.MethodsThe model is based on a simplified description of the glutamatergic synapse in which post-synaptic Ca2+ entry initiates processes leading to different amount of potentiation and depression of synaptic transmission. The final effect on the synapse results from summation of the two effects.ResultsThe model using these assumptions can fit reported data. Metaplastic effects of voluntary contraction on the response to TBS can be incorporated by changing time constants in the model.ConclusionsThe pattern-dependent after-effects and interactions with voluntary contraction can be successfully modelled by using reasonable assumptions about known cellular mechanisms of plasticity.SignificanceThe model could provide insight into development of new plasticity induction protocols using TMS.

► A simple mathematical model is built to explain why the pattern of delivery of TBS is crucial in determining the direction of change in synaptic efficiency.
► The pattern-dependent after-effects and interactions with voluntary contraction can be successfully modelled by using reasonable assumptions about known cellular mechanisms of plasticity.
► The model provides insight into development of new plasticity induction protocols using TMS, and it may be possible to develop new protocols of TBS by manipulating parameters in the model.