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

Objective: Theta 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. Methods: The 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. Results: The 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. Conclusions: The pattern-dependent after-effects and interactions with voluntary contraction can be successfully modelled by using reasonable assumptions about known cellular mechanisms of plasticity. Significance: The model could provide insight into development of new plasticity induction protocols using TMS.