Transcranial Magnetic Stimulation: An Automated Procedure to Obtain Coil-specific Models for Field Calculations

Design and Validation of Miniaturized Repetitive Transcranial Magnetic Stimulation (rTMS) Head Coils

Repetitive transcranial magnetic stimulation (rTMS) is a rapidly developing therapeutic modality for the safe and effective treatment of neuropsychiatric disorders. However, clinical rTMS driving systems and head coils are large, heavy, and expensive, so miniaturized, affordable rTMS devices may facilitate treatment access for patients at home, in underserved areas, in field and mobile hospitals, on ships and submarines, and in space. The central component of a portable rTMS system is a miniaturized, lightweight coil. Such a coil, when mated to lightweight driving circuits, must be able to induce B and E fields of sufficient intensity for medical use. This paper newly identifies and validates salient theoretical considerations specific to the dimensional scaling and miniaturization of coil geometries, particularly figure-8 coils, and delineates novel, key design criteria. In this context, the essential requirement of matching coil inductance with the characteristic resistance of the driver switches is highlighted. Computer simulations predicted E- and B-fields which were validated via benchtop experiments. Using a miniaturized coil with dimensions of 76 mm × 38 mm and weighing only 12.6 g, the peak E-field was 87 V/m at a distance of 1.5 cm. Practical considerations limited the maximum voltage and current to 350 V and 3.1 kA, respectively; nonetheless, this peak E-field value was well within the intensity range, 60-120 V/m, generally held to be therapeutically relevant. The presented parameters and results delineate coil and circuit guidelines for a future miniaturized, power-scalable rTMS system able to generate pulsed E-fields of sufficient amplitude for potential clinical use.

Focality of the Induced E-Field Is a Contributing Factor in the Choice of TMS Parameters: Evidence from a 3D Computational Model of the Human Brain

Transcranial magnetic stimulation (TMS) is a promising, non-invasive approach in the diagnosis and treatment of several neurological conditions. However, the specific results in the cortex of the magnitude and spatial distribution of the secondary electrical field (E-field) resulting from TMS at different stimulation sites/orientations and varied TMS parameters are not clearly understood. The objective of this study is to identify the impact of TMS stimulation site and coil orientation on the induced E-field, including spatial distribution and the volume of activation in the cortex across brain areas, and hence demonstrate the need for customized optimization, using a three-dimensional finite element model (FEM). A considerable difference was noted in E-field values and distribution at different brain areas. We observed that the volume of activated cortex varied from 3000 to 7000 mm3 between the selected nine clinically relevant coil locations. Coil orientation also changed the induced E-field by a maximum of 10%, and we noted the least optimal values at the standard coil orientation pointing to the nose. The volume of gray matter activated varied by 10% on average between stimulation sites in homologous brain areas in the two hemispheres of the brain. This FEM simulation model clearly demonstrates the importance of TMS parameters for optimal results in clinically relevant brain areas. The results show that TMS parameters cannot be interchangeably used between individuals, hemispheres, and brain areas. The focality of the TMS induced E-field along with its optimal magnitude should be considered as critical TMS parameters that should be individually optimized.

Accurate TMS Head Modeling: Interfacing SimNIBS and BEM-FMM in a MATLAB-Based Module

We interface the head modelling, coil models, Graphical User Interface (GUI), and post-processing capabilities of the SimNIBS package with the boundary element fast multipole method (BEM-FMM), implemented in a MATLAB-based module. The resulting pipeline combines the best of both worlds: the individualized head modelling and ease-of-use of SimNIBS with the numerical accuracy of BEM-FMM. The corresponding TMS (transcranial magnetic stimulation) modeling package is developed and made available online. It imports a SimNIBS surface segmentation and a coil field, and then exports electric-field values in selected surfaces or volumes. Additional information is also made available, such as discontinuous compartment surface electric fields and associated surface electric charge distributions.

Obtaining accurate and calibrated coil models for transcranial magnetic stimulation using magnetic field measurements

Currently, simulations of the induced currents in the brain produced by transcranial magnetic stimulation (TMS) are used to elucidate the regions reached by stimuli. However, models commonly found in the literature are too general and neglect imperfections in the windings. Aiming to predict the stimulation sites in patients requires precise modeling of the electric field (E-field), and a proper calibration to adequate to the empirical data of the particular coil employed. Furthermore, most fabricators do not provide precise information about the coil geometries, and even using X-ray images may lead to subjective interpretations. We measured the three components of the vector magnetic field induced by a TMS figure-8 coil with spatial resolutions of up to 1 mm. Starting from a computerized tomography-based coil model, we applied a multivariate optimization algorithm to automatically modify the original model and obtain one that optimally fits the measurements. Differences between models were assessed in a human brain mesh using the finite-elements method showing up to 6% variations in the E-field magnitude. Our calibrated model could increase the precision of the estimated E-field induced in the brain during TMS, enhance the accuracy of delivered stimulation during functional brain mapping, and improve dosimetry for repetitive TMS. Graphical Abstract Geometrical model of TMS coil based on TAC images is optimally deformed to match magnetic field measurements. The calibrated model's induced electric field in the brain differs from the original.

Electric field simulations for transcranial brain stimulation using FEM: an efficient implementation and error analysis

OBJECTIVE

Transcranial magnetic stimulation (TMS) and transcranial electric stimulation (TES) modulate brain activity non-invasively by generating electric fields either by electromagnetic induction or by injecting currents via skin electrodes. Numerical simulations based on anatomically detailed head models of the TMS and TES electric fields can help us to understand and optimize the spatial stimulation pattern in the brain. However, most realistic simulations are still slow, and the role of anatomical fidelity on simulation accuracy has not been evaluated in detail so far.

APPROACH

We present and validate a new implementation of the finite element method (FEM) for TMS and TES that is based on modern algorithms and libraries. We also evaluate the convergence of the simulations and estimate errors stemming from numerical and modelling aspects.

MAIN RESULTS

Comparisons with analytical solutions for spherical phantoms validate our new FEM implementation, which is three to six times faster than previous implementations. The convergence results suggest that accurately capturing the tissue geometry in addition to choosing a sufficiently accurate numerical method is of fundamental importance for accurate simulations.

SIGNIFICANCE

The new implementation allows for a substantial increase in computational efficiency of FEM TMS and TES simulations. This is especially relevant for applications such as the systematic assessment of model uncertainty and the optimization of multi-electrode TES montages. The results of our systematic error analysis allow the user to select the best tradeoff between model resolution and simulation speed for a specific application. The new FEM code is openly available as a part of our open-source software SimNIBS 3.0.

The non-transcranial TMS-evoked potential is an inherent source of ambiguity in TMS-EEG studies

Transcranial Magnetic Stimulation (TMS) excites populations of neurons in the stimulated cortex, and the resulting activation may spread to connected brain regions. The distributed cortical response can be recorded with electroencephalography (EEG). Since TMS also stimulates peripheral sensory and motor axons and generates a loud "click" sound, the TMS-evoked EEG potentials (TEPs) reflect not only neural activity induced by transcranial neuronal excitation but also neural activity due to somatosensory and auditory processing. In 17 healthy young individuals, we systematically assessed the contribution of multisensory peripheral stimulation to TEPs using a TMS-compatible EEG system. Real TMS was delivered with a figure-of-eight coil over the left para-median posterior parietal cortex or superior frontal gyrus with the coil being oriented perpendicularly or in parallel to the target gyrus. We also recorded the EEG responses evoked by realistic sham stimulation over the posterior parietal and superior frontal cortex, mimicking the auditory and somatosensory sensations evoked by real TMS. We applied state-of-the-art procedures to attenuate somatosensory and auditory confounds during real TMS, including the placement of a foam layer underneath the coil and auditory noise masking. Despite these precautions, the temporal and spatial features of the cortical potentials evoked by real TMS at the prefrontal and parietal site closely resembled the cortical potentials evoked by realistic sham TMS, both for early and late TEP components. Our findings stress the need to include a peripheral multisensory control stimulation in the design of TMS-EEG studies to enable a dissociation between truly transcranial and non-transcranial components of TEPs.

Modelling of induced electric fields based on incompletely known magnetic fields

Determining the induced electric fields in the human body is a fundamental problem in bioelectromagnetics that is important for both evaluation of safety of electromagnetic fields and medical applications. However, existing techniques for numerical modelling of induced electric fields require detailed information about the sources of the magnetic field, which may be unknown or difficult to model in realistic scenarios. Here, we show how induced electric fields can accurately be determined in the case where the magnetic fields are known only approximately, e.g. based on field measurements. The robustness of our approach is shown in numerical simulations for both idealized and realistic scenarios featuring a personalized MRI-based head model. The approach allows for modelling of the induced electric fields in biological bodies directly based on real-world magnetic field measurements.

How much detail is needed in modeling a transcranial magnetic stimulation figure-8 coil: Measurements and brain simulations

Background

Despite TMS wide adoption, its spatial and temporal patterns of neuronal effects are not well understood. Although progress has been made in predicting induced currents in the brain using realistic finite element models (FEM), there is little consensus on how a magnetic field of a typical TMS coil should be modeled. Empirical validation of such models is limited and subject to several limitations.

Methods

We evaluate and empirically validate models of a figure-of-eight TMS coil that are commonly used in published modeling studies, of increasing complexity: simple circular coil model; coil with in-plane spiral winding turns; and finally one with stacked spiral winding turns. We will assess the electric fields induced by all 3 coil models in the motor cortex using a computer FEM model. Biot-Savart models of discretized wires were used to approximate the 3 coil models of increasing complexity. We use a tailored MR based phase mapping technique to get a full 3D validation of the incident magnetic field induced in a cylindrical phantom by our TMS coil. FEM based simulations on a meshed 3D brain model consisting of five tissues types were performed, using two orthogonal coil orientations.

Results

Substantial differences in the induced currents are observed, both theoretically and empirically, between highly idealized coils and coils with correctly modeled spiral winding turns. Thickness of the coil winding turns affect minimally the induced electric field, and it does not influence the predicted activation.

Conclusion

TMS coil models used in FEM simulations should include in-plane coil geometry in order to make reliable predictions of the incident field. Modeling the in-plane coil geometry is important to correctly simulate the induced electric field and to correctly make reliable predictions of neuronal activation