A computational model for real-time calculation of electric field due to transcranial magnetic stimulation in clinics

The aim of this paper is to propose an approach for an accurate and fast (real-time) computation of the electric field induced inside the whole brain volume during a transcranial magnetic stimulation (TMS) procedure. The numerical solution implements the admittance method for a discretized realistic brain model derived from Magnetic Resonance Imaging (MRI). Results are in a good agreement with those obtained using commercial codes and require much less computational time. An integration of the developed codewith neuronavigation toolswill permit real-time evaluation of the stimulated brain regions during the TMSdelivery, thus improving the efficacy of clinical applications

Computational Electromagnetic Methods for Transcranial Magnetic Stimulation.

Transcranial magnetic stimulation (TMS) is a noninvasive technique used both as a research tool for cognitive neuroscience and as a FDA approved treatment for depression. During TMS, coils positioned near the scalp generate electric fields and activate targeted brain regions. In this thesis, several computational electromagnetics methods that improve the analysis, design, and uncertainty quantification of TMS systems were developed. Analysis: A new fast direct technique for solving the large and sparse linear system of equations (LSEs) arising from the finite difference (FD) discretization of Maxwell’s quasi-static equations was developed. Following a factorization step, the solver permits computation of TMS fields inside realistic brain models in seconds, allowing for patient-specific real-time usage during TMS. The solver is an alternative to iterative methods for solving FD LSEs, often requiring run-times of minutes. A new integral equation (IE) method for analyzing TMS fields was developed. The human head is highly-heterogeneous and characterized by high-relative permittivities (10^7). IE techniques for analyzing electromagnetic interactions with such media suffer from high-contrast and low-frequency breakdowns. The novel high-permittivity and low-frequency stable internally combined volume-surface IE method developed. The method not only applies to the analysis of high-permittivity objects, but it is also the first IE tool that is stable when analyzing highly-inhomogeneous negative permittivity plasmas. Design: TMS applications call for electric fields to be sharply focused on regions that lie deep inside the brain. Unfortunately, fields generated by present-day Figure-8 coils stimulate relatively large regions near the brain surface. An optimization method for designing single feed TMS coil-arrays capable of producing more localized and deeper stimulation was developed. Results show that the coil-arrays stimulate 2.4 cm into the head while stimulating 3.0 times less volume than Figure-8 coils. Uncertainty quantification (UQ): The location/volume/depth of the stimulated region during TMS is often strongly affected by variability in the position and orientation of TMS coils, as well as anatomical differences between patients. A surrogate model-assisted UQ framework was developed and used to statistically characterize TMS depression therapy. The framework identifies key parameters that strongly affect TMS fields, and partially explains variations in TMS treatment responses.PhDElectrical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/111459/1/luisgo_1.pd

Numerical modelling of plasticity induced by transcranial magnetic stimulation

We use neural field theory and spike-timing dependent plasticity to make a simple but biophysically reasonable model of long-term plasticity changes in the cortex due to transcranial magnetic stimulation (TMS). We show how common TMS protocols can be captured and studied within existing neural field theory. Specifically, we look at repetitive TMS protocols such as theta burst stimulation and paired-pulse protocols. Continuous repetitive protocols result mostly in depression, but intermittent repetitive protocols in potentiation. A paired pulse protocol results in depression at short (∼ 100 ms) interstimulus intervals, but potentiation for mid-range intervals. The model is sensitive to the choice of neural populations that are driven by the TMS pulses, and to the parameters that describe plasticity, which may aid interpretation of the high variability in existing experimental results. Driving excitatory populations results in greater plasticity changes than driving inhibitory populations. Modelling also shows the merit in optimizing a TMS protocol based on an individual’s electroencephalogram. Moreover, the model can be used to make predictions about protocols that may lead to improvements in repetitive TMS outcomes

Solving an IBEM with supporting vector analysis to design quiet TMS coils

Transcranial magnetic stimulation is a promising tool in neuroscience of which successful development is affected by the loud click noise originated when the stimulating coil is energized. This undesired sound is produced by the coil winding deformations generated by the Lorentz self-forces in the TMS device. Addressing the need for TMS systems that produce less noise, a quiet coil design technique is proposed in this work, where instead of minimizing directly the coil deflection, the Lorentz self-force is optimized in order to reduce the acoustic noise. The presented method is based on a stream function IBEM for TMS coil design in which new computational models have been incorporated into the optimization problem, which is efficiently solved by using supporting vector analysis. Several examples of coils of different geometries were designed and simulated to demonstrate the efficiency of the suggested IBEM approach to produce TMS devices that experience minimum Lorentz self-forces. In order to evaluate the acoustic response of the designed TMS coils, the commercial MSC/NASTRAN was used to find the coil deflection. The obtained results show that significant noise reduction can be achieved by minimizing the Lorentz self-force over the TMS coil surface

Unification of optimal targeting methods in transcranial electrical stimulation

One of the major questions in high-density transcranial electrical stimulation (TES) is: given a region of interest (ROI) and electric current limits for safety, how much current should be delivered by each electrode for optimal targeting of the ROI? Several solutions, apparently unrelated, have been independently proposed depending on how ?optimality? is defined and on how this optimization problem is stated mathematically. The least squares (LS), weighted LS (WLS), or reciprocity-based approaches are the simplest ones and have closed-form solutions. An extended optimization problem can be stated as follows: maximize the directional intensity at the ROI, limit the electric fields at the non-ROI, and constrain total injected current and current per electrode for safety. This problem requires iterative convex or linear optimization solvers. We theoretically prove in this work that the LS, WLS and reciprocity-based closed-form solutions are specific solutions to the extended directional maximization optimization problem. Moreover, the LS/WLS and reciprocity-based solutions are the two extreme cases of the intensity-focality trade-off, emerging under variation of a unique parameter of the extended directional maximization problem, the imposed constraint to the electric fields at the non-ROI. We validate and illustrate these findings with simulations on an atlas head model. The unified approach we present here allows a better understanding of the nature of the TES optimization problem and helps in the development of advanced and more effective targeting strategies.Fil: Fernandez Corazza, Mariano. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Investigaciones en Electrónica, Control y Procesamiento de Señales. Universidad Nacional de La Plata. Instituto de Investigaciones en Electrónica, Control y Procesamiento de Señales; ArgentinaFil: Turovets, Sergei. University of Oregon; Estados UnidosFil: Muravchik, Carlos Horacio. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Investigaciones en Electrónica, Control y Procesamiento de Señales. Universidad Nacional de La Plata. Instituto de Investigaciones en Electrónica, Control y Procesamiento de Señales; Argentina. Provincia de Buenos Aires. Gobernación. Comisión de Investigaciones Científicas; Argentin

Numerical modelling in transcranial magnetic stimulation

Tese de doutoramento, Engenharia Biomédica e Biofísica, Universidade de Lisboa, Faculdade de Ciências, 2009In this work powerful numerical methods were used to study several problems that still remain unsolved in TMS.The first problem that was studied is related to the difficulties that arise when stimulating sub-cortical deep regions with TMS, due to the fact that the induced field rapidly decays and loses focality with depth. This study's approach to overcome this difficulty was to combine ferromagnetic cores with a coil designed to induce an electric field that decays slowly. The efficacy of this approach was tested by using the FEM to calculate the field induced by this coil / core design in a realistically shaped head model. The results show that the core might make this coil even more suited for deep brain stimulation.The second problem that was tackled is related to the lack of knowledge about the dominant mechanisms through which the induced electric field excites neurons in TMS. In this work the electric field along lines, representing trajectories of actual cortical neurons, was calculated using the FEM. The neurons were embedded in a realistically shaped sulcus model, with a figure-8 coil placed above the model. The electric field was then incorporated into the cable equation. The solution of the latter allowed the determination of the site and threshold of activation of the neurons. The results highlight the importance of axonal terminations and bends and tissue heterogeneities on stimulation of neurons.The third problem that was studied concerns TMS of small animals and the lack of knowledge about the optimal geometry, size and orientation of the used coils. This was studied by using the FEM to calculate the electric field induced in a realistically shaped mouse model by several commercially available coils. The results showed that the smaller coils induced fields with higher magnitude, better focality, and smaller decay than the bigger coils.These results highlight the importance of numerical modelling in TMS, either in coil design, determination of basic neurophysiologic mechanisms or optimization of experimental procedures

Fast and Efficient Formulations for Electroencephalography-Based Neuroimaging Strategies

L'abstract è presente nell'allegato / the abstract is in the attachmen