A revised calcium-dependent model of transcranial magnetic theta-burst stimulation

•The paper corrects discrepancies in the difference equations of the previously suggested model of theta-burst stimulation.•The corrected stages are consistently calibrated to experimental data to serve for quantitative analysis.•This work improves the model accuracy in various conditions and secures the model that underlies a rich body of research. Calcium dependency is presently an essential assumption in modelling the neuromodulatory effects of transcranial magnetic stimulation. Y.Z.Huang et al.developed the first neuromodulation model to explain the bidirectional effects of theta-burst stimulation (TBS) based on the postsynaptic intracellular calcium concentration elevation. However, we discover that the published computer code is not consistent with the model formulation, neither do the parameters and derived plots consequently match the formulations. Here we intend to fix the computer code and re-calibrate the model. We corrected the affected difference equations and re-calibrated the revised model with experimental data using non-convex optimisation based on a L2 penalty. The revised model outperforms the initial model in characterising the relative motor-evoked potential levels of TBS-induced after-effects in various conditions. We corrected the inconsistencies in the previous model and computer code and provided a complete calibration to support the research that is based on it. This work improves the accuracy and secures the scope of the model, which is necessary to retain a rich body of research resulting from the model. Furthermore, this model provides both a quantitative model for several parameters of TBS and a basic model foundation for future refinement.