Accurate simulations on detailed realistic head models are necessary to gain a better understanding of the response to transcranial magnetic stimulation (TMS). Hitherto, head models with simplified geometries and constant isotropic material properties are often used, whereas some biological tissues have anisotropic characteristics which vary naturally with frequency. Moreover, most computational methods do not take the tissue permittivity into account. Therefore, we calculate the electromagnetic behaviour due to TMS in a head model with realistic geometry and where realistic dispersive anisotropic tissue properties are incorporated, based on T1-weighted and diffusion-weighted magnetic resonance images. This paper studies the impact of tissue anisotropy, permittivity and frequency dependence, using the anisotropic independent impedance method. The results show that anisotropy yields differences up to 32% and 19% of the maximum induced currents and electric field, respectively. Neglecting the permittivity values leads to a decrease of about 72% and 24% of the maximum currents and field, respectively. Implementing the dispersive effects of biological tissues results in a difference of 6% of the maximum currents. The cerebral voxels show limited sensitivity of the induced electric field to changes in conductivity and permittivity, whereas the field varies approximately linearly with frequency. These findings illustrate the importance of including each of the above parameters in the model and confirm the need for accuracy in the applied patient-specific method, which can be used in computer-assisted TMS.

In transcranial magnetic stimulation (TMS), an applied alternating magnetic field induces an electric field in the brain that can interact with the neural system. It is generally assumed that this induced electric field is the crucial effect exciting a certain region of the brain. More specifically, it is the component of this field parallel to the neuron's local orientation, the so-called effective electric field, that can initiate neuronal stimulation. Deeper insights on the stimulation mechanisms can be acquired through extensive TMS modelling. Most models study simple representations of neurons with assumed geometries, whereas we embed realistic neural trajectories computed using tractography based on diffusion tensor images. This way of modelling ensures a more accurate spatial distribution of the effective electric field that is in addition patient and case specific. The case study of this paper focuses on the single pulse stimulation of the left primary motor cortex with a standard figure-of-eight coil. Including realistic neural geometry in the model demonstrates the strong and localized variations of the effective electric field between the tracts themselves and along them due to the interplay of factors such as the tract's position and orientation in relation to the TMS coil, the neural trajectory and its course along the white and grey matter interface. Furthermore, the influence of changes in the coil orientation is studied. Investigating the impact of tissue anisotropy confirms that its contribution is not negligible. Moreover, assuming isotropic tissues lead to errors of the same size as rotating or tilting the coil with 10 degrees. In contrast, the model proves to be less sensitive towards the not well-known tissue conductivity values.

In many important bioelectromagnetic problem settings, eddy-current simulations are required. Examples are the reduction of eddy-current artifacts in magnetic resonance imaging and techniques, whereby the eddy currents interact with the biological system, like the alteration of the neurophysiology due to transcranial magnetic stimulation (TMS). TMS has become an important tool for the diagnosis and treatment of neurological diseases and psychiatric disorders. A widely applied method for simulating the eddy currents is the impedance method (IM). However, this method has to contend with an ill conditioned problem and consequently a long convergence time. When dealing with optimal design problems and sensitivity control, the convergence rate becomes even more crucial since the eddy-current solver needs to be evaluated in an iterative loop. Therefore, we introduce an independent IM (IIM), which improves the conditionality and speeds up the numerical convergence. This paper shows how IIM is based on IM and what are the advantages. Moreover, the method is applied to the efficient simulation of TMS. The proposed IIM achieves superior convergence properties with high time efficiency, compared to the traditional IM and is therefore a useful tool for accurate and fast TMS simulations.

Objective. Transcranial magnetic stimulation (TMS) is a promising non-invasive tool for modulating the brain activity. Despite the widespread therapeutic and diagnostic use of TMS in neurology and psychiatry, its observed response remains hard to predict, limiting its further development and applications. Although the stimulation intensity is always maximum at the cortical surface near the coil, experiments reveal that TMS can affect deeper brain regions as well. Approach. The explanation of this spread might be found in the white matter fiber tracts, connecting cortical and subcortical structures. When applying an electric field on neurons, their membrane potential is altered. If this change is significant, more likely near the TMS coil, action potentials might be initiated and propagated along the fiber tracts towards deeper regions. In order to understand and apply TMS more effectively, it is important to capture and account for this interaction as accurately as possible. Therefore, we compute, next to the induced electric fields in the brain, the spatial distribution of the membrane potentials along the fiber tracts and its temporal dynamics. Main results. This paper introduces a computational TMS model in which electromagnetism and neurophysiology are combined. Realistic geometry and tissue anisotropy are included using magnetic resonance imaging and targeted white matter fiber tracts are traced using tractography based on diffusion tensor imaging. The position and orientation of the coil can directly be retrieved from the neuronavigation system. Incorporating these features warrants both patient-and case-specific results. Significance. The presented model gives insight in the activity propagation through the brain and can therefore explain the observed clinical responses to TMS and their inter-and/or intra-subject variability. We aspire to advance towards an accurate, flexible and personalized TMS model that helps to understand stimulation in the connected brain and to target more focused and deeper brain regions.S Online supplementary data available from stacks.iop.org/jne/13/026028/mmedia

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