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

## TL;DR

This paper introduces a new computational model to simulate how transcranial magnetic stimulation affects neural activity in the brain, improving understanding of its effects for research and treatment.

## Contribution

A biophysically motivated coupling model that translates TMS-induced electric fields into neural state variables for cortical circuit simulations.

## Key findings

- TMS induces directionally sensitive synaptic outputs in different cell types.
- The model captures how TMS affects dendritic currents in downstream neurons.
- The approach can be generalized to other brain regions with different cell morphologies and circuits.

## Abstract

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.

Transcranial magnetic stimulation is a powerful technique to interfere with the brain’s function in a non-invasive way. It does so by magnetically inducing an electric field in the brain that influences the state of neurons. It has widespread medical application for diagnostics and treatment of diseases, such as depression. Moreover, it is valuable for fundamental brain research as it allows stimulating the brain and then observing its response. In order to optimize its utility in medicine and drawing more well-founded conclusions from scientific experiments, it is important to precisely describe its working mechanisms. In this work, we introduce a computational technique to simulate a crucial ingredient of these mechanisms, namely the precise way the induced electric field excites populations of interconnected neurons. We exemplify the technique for the case of stimulating the motor areas of the cortex, causing muscle activity. However, it can be generalized to a wide variety of use cases, thus forming an important tool that helps researchers to devise accurate mechanistic links between transcranial magnetic stimulation and its observed effects. In consequence, it supports future research aiming at the development of better diagnostics and treatment of brain diseases, as well as better understanding of brain function.