Real-Time Computation of E-Field for Transcranial Magnetic Stimulation

Transcranial Magnetic Stimulation (TMS) is a non-invasive brain stimulation technique employing coils to induce electric fields (E-fields) in the brain, influencing its activity. Accurately determining the dosage of E-field induced in targeted brain areas during TMS is crucial for evaluating its effects and optimizing parameters such as coil current amplitude and placement. We present a method capable of computing induced E-fields for arbitrary coil positions in real-time (within 4 milliseconds) within the brain. Initially, white noise currents, defined on a surface delineating the head and its surrounding medium, are employed to generate a comprehensive basis set of mode field patterns representing TMS-induced brain E-fields. Subsequently, electromagnetic reciprocity and Huygens' principles are leveraged to establish the relationship between expansion coefficients for these modes and TMS-induced electric fields in free space. Our real-time TMS solver predicts E-fields with comparable accuracy to existing solvers using fewer than 400 modes, rendering it suitable for neuronavigation systems and real-time adjustment of coil dosing parameters.