Numerical Investigation of Biconical Transcranial Magnetic Stimulation Coil

Abstract

Transcranial magnetic stimulation, also known as TMS, is rapidly developed as a no-invasive, non-painful and safe tool for studying the physiology of human brain and brain therapy [1, 2]. TMS is based on the principle of electro-magnetic induction of an electric field in the brain, which is of sufficient magnitude and density to depolarize neurons. Depending on the parameters of stimulation, TMS pulses can decrease or increase the cortical excitability even beyond the duration of the train of stimulation, and this produces behavioral consequences and prospect therapeutic potential [2–4]. Since electric field induced is an important parameter in stimulation process, this work investigates the 3-dimensional electric field distribution in human brain using the finite element method. Fig 1 shows the cross section of two-layer human head model and the investigated biconical TMS coils. The human head is modeled with harnpan and tissue fluid, and TMS coils consisted of two separated cones. The model is located in a solution region, in which the solution is generated and the mesh is refined, with proper boundary condition applied to determine the unique solution of the electromagnetic field. The magnitude of the induced electric field in the head is used for evaluating the stimulation effect. By investigating the influences of the distance between two cones, included angle, current frequency and the location of the coils, the optimized TMS coil sep-up for deep stimulation and good stimulation accuracy has been obtained. Fig 1. TMS model of biconical coil model Simulation result shows that high current frequency is beneficial for effectively deep stimulation, with 0.2V/m as threshold for effective electric field. Since the distribution of electric field is determined by the projection of TMS coil on the human head, decreasing the distance between two cones of biconical TMS coil can increase the magnitude of electric field along the symmetric axis, which is directing to the human head. The higher electric field means that the deeper tissue in the human head can be stimulated, as shown in Fig 2 a). Electric field in tissue fluid is decaying in an exponential form, which leads to a slightly improved stimulation depth by decreasing the distance between two cones. On the other hand, the decreasing the distance can also stimulate the human brain with a shaper peak of the magnitude of electric field, as shown in Fig 2 b) shows, which gives a better stimulation accuracy. The included angle between two cones has also been investigated, and the smaller angle generally leads to the larger electric field induced along the symmetric axis directing to the human head. In addition, to get good stimulation, TMS coil should be as close to the head as possible in the desired stimulation region. Fig 2. Influences of distance between coils on the magnitude of electric field on the distribution of the magnitude of electric field along symmetric axis directing to human head (a) and distribution of the magnitude of electric field in tissue fluid parallel to the connection of the center of the two cones (b).