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

Abstract

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 Ca(2+) 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.

Figure 1. Results of a simple model that accounts for the different long lasting effects of cTBS, imTBS and iTBS

The model has three stages, represented by the three rows of graphs. The after effects in stage 3 are superimposed with the experimental results from our previous work. In stage 3, the left Y axis is the arbitrary units for the simulated results, while the right Y axis is the % of change of the MEP size for the experimental results.

Figure 2. Simulated results of cTBS with and without prior muscle contraction

cTBS300 with prior muscle activity shows a suppressive effect (A), while the effect of cTBS300 without prior contraction becomes slightly facilitatory (B). cTBS600 still has an inhibitory effect even there is no muscle contraction beforehand. The after effects in stage 3 are superimposed with the experimental results from our previous work and those from the study of Gentner et al. (Gentner et al., 2008) with permission. The left Y axis is the arbitrary units for the simulated results, while the right Y axis is the % of change of the MEP size for the experimental results.

Figure 3. Simulated results of cTBS300 and iTBS followed by 1-min contraction

The effect of cTBS300 (with precontraction due to measurement of active motor threshold) was reversed from inhibition to facilitation (A), while the facilitatory effect of iTBS was enhanced by the 1-min contraction (B). The after effects in stage 3 are superimposed with the experimental results from our previous work. The left Y axis is the arbitrary units for the simulated results, while the right Y axis is the % of change of the MEP size for the experimental results.