A coupling model of transcranial magnetic stimulation induced electric fields to neural state variables

Transcranial magnetic stimulation (TMS) is a non-invasive brain stimulation technique used to modulate neural activity, with applications in clinical treatment, diagnostics, and neuroscientific research. TMS targeting the human primary motor cortex (M1) is well studied, aided by experimental readouts from the cerebral cortex, the spinal cord, and activated muscle targets. One key readout is a series of pulses that descend the spinal cord following TMS, called DI-waves. These reflect the output of M1 to the spinal cord and are influenced by TMS parameters such as orientation, strength, and waveform. Previous modeling studies have deployed numerous strategies to explain DI-wave generation, but generally approximate TMS inputs as semi-arbitrary current or synaptic inputs. A consistent missing piece to these models is a biophysically motivated coupling between TMS and the neural states of cells and cell populations. This study aims to leverage cable simulations of realistic neuron morphologies to couple TMS induced electric fields to average state variables of cortical cell populations. This coupling model quantifies the spatial-temporal activation function of directly stimulated axonal fibers and the average input current that downstream cells receive due to synaptic inputs from directly stimulated cells. An example M1 cortical circuit is studied, in which TMS stimulates layer 2/3 excitatory and inhibitory neurons that project synapses onto layer 5 corticospinal neurons. Results indicate that TMS induces unique directionally sensitive distributions of synaptic outputs in time and space for each cell type. Directional and dosage sensitivity carries forward to the dendritic current flowing into layer 5 cells. Ultimately, the coupling model provides a novel architecture to translate electric fields from TMS into activation functions that alter neural states and serve as inputs to cortical circuit modeling. The study of other brain regions is achievable through an alternate choice of cell morphologies, cell locations, and circuit design.