Conditions for numerically accurate TMS electric field simulation

Gomez, Luis J.; Dannhauer, Moritz; Koponen, Lari M.

doi:10.1016/j.brs.2019.09.015

Cited by 85 publications

(84 citation statements)

References 59 publications

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“…The added error due to ignoring the separation of white and gray matter is of the same order with some model differences presented in [10,26] and smaller than the approximation errors in the fast solution of [8]. That said, the choice between a 5-C and 4-C model is not just a question of accuracy under ideal simulation conditions: taking an experimental point of view and admitting that MR images, segmentations and meshings are not perfect, conductivity parameters are poorly known, and also the 5-C model is an approximation of reality, the 4-C model provides an accessible solution for experimenters, who wish to upgrade from spherical models but have no resources or skills for making fast 5-C models.…”

Section: Discussionmentioning

confidence: 93%

“…In addition to our reciprocal approach, the surface-integral solution for TMSinduced E-field can be formulated in direct way via induced surface charges [9,10,26]. Both approaches follow from quasi-static Maxwell equations without further approximations and are hence physically equivalent.…”

Section: Computational Approachmentioning

confidence: 99%

“…With the same meshing and matching discretization and integration techniques, the E-fields should thus be nearly identical, apart from small numerical differences. We implemented the direct approach following [9,26], using the same linear discretization and integration techniques as in our approach, and computed the cortical E-field for 251 coil positions in a 4-C model. The mean relative difference between the approaches was 0.28%.…”

Section: Computational Approachmentioning

confidence: 99%

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Real-time computation of the TMS-induced electric field in a realistic head model

Stenroos

Koponen

2019

Preprint

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Transcranial magnetic stimulation (TMS) is often targeted using a model of TMS-induced electric field (E). In such navigated TMS, the E-field models have been based on spherical approximation of the head. Such models omit the effects of cerebrospinal fluid (CSF) and gyral folding, leading to potentially large errors in the computed E-field. So far, realistic models have been too slow for interactive TMS navigation. We present computational methods that enable real-time solving of the E-field in a realistic five-compartment (5-C) head model that contains isotropic white matter, gray matter, CSF, skull and scalp.Using reciprocity and Geselowitz integral equation, we separate the computations to coil-dependent and -independent parts. For the Geselowitz integrals, we present a fast numerical quadrature. Further, we present a moment-matching approach for optimizing dipole-based coil models.We verified and benchmarked the new methods using simulations with over 100 coil locations. The new quadrature introduced a relative error (RE) of 0.3-0.6%. For a coil model with 42 dipoles, the total RE of the quadrature and coil model was 0.44-0.72%. Taking also other model errors into account, the contribution of the new approximations to the RE was 0.1%. For comparison, the RE due to omitting the separation of white and gray matter was >11%, and the RE due to omitting also the CSF was >23%.Using a standard PC and basic GPU, our solver computed the full E-field in a 5-C model in 9000 points on the cortex in 27 coil positions per second (cps). When the separation of white and gray matter was omitted, the speed was 43-65 cps. Solving only one component of the E-field tripled the speed.The presented methods enable real-time solving of the TMS-induced E-field in a realistic head model that contains the CSF and gyral folding. The new methodology allows more accurate targeting and precise adjustment of stimulation intensity during experimental or clinical TMS mapping. (Matti Stenroos) 2. Theory Reciprocity relationLet there be a system of conductors. Let primary current distribution J p 1 give rise to electric field E 1 . Correspondingly, J p 2 gives rise to E 2 . Then, assuming the head electrically resistive and small compared to the wavelength of electromagnetic waves, we get the reciprocity relation [10]Letting J p 1 be a dipolar current element Q at r Q , i.e. J p 1 ( r ) = Qδ( r − r Q ), and J p 2 a current loop (coil) with current I flowing in a thin wire c, we get [11]

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Section: Discussionmentioning

confidence: 93%

Section: Computational Approachmentioning

confidence: 99%

Section: Computational Approachmentioning

confidence: 99%

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Real-time computation of the TMS-induced electric field in a realistic head model

Stenroos

Koponen

2019

Preprint

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“…We use the boundary element method formulated in terms of induced surface charge density ( ) residing at the conductivity interfaces and naturally coupled with the fast multipole method [30], [31] or BEM-FMM, originally described in [32], [33]. The method possesses high numerical accuracy, which was recently shown to exceed that of the comparable finite element method of the first order [34]. Once the solution for the induced surface charge density is obtained, the normal electric field at any interface is found precisely and without postprocessing (cf.…”

Section: Tms Forward Problem Solutionboundary Element Fast Multipole mentioning

confidence: 99%

A Note about the Individualized TMS Focality

Makarov

Wartman

Daneshzand

et al. 2020

Preprint

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A particular yet computationally successful solution of an inverse transcranial magnetic stimulation (TMS) problem is reported. The goal has been focusing the normal unsigned electric field at the inner cortical surface and its vicinity (the D wave activation site) given a unique highresolution gyral pattern of a subject and a precise coil model.For 16 subjects and 32 arbitrary target points, the solution decreases the mean deviation of the maximum-field domain from the target by a factor of 2 on average. The reduction in the maximum-field area is expected to quadruple. The average final deviation is 6 mm.Rotation about the coil axis is the most significantly altered parameter, and the coil moves 10 mm on average during optimization. The maximum electric field magnitude decreases by 16% on average. Stability of the solution is enforced. The relative average de-focalization is below 1.2 when position/orientation accuracies are within 3 mm/6 degrees, respectively. The solution for the maximum normal field may also maximize the total field and its gradient for neighboring cortical layers III-V (I wave activation).

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“…The total E-field induced in cortical ROIs can be determined by using MRI-derived subject-specific volume conductor models and finite element method (FEM) or boundary element method (BEM) [23,[27][28][29][30][31][32][33]. Evaluating the TMS induced E-field for a single coil position using a standard resolution head model currently requires 35 seconds using FEM [34] or 104 seconds using a fastmultipole method accelerated BEM [35].…”

Section: Introductionmentioning

confidence: 99%

Fast computational optimization of TMS coil placement for individualized electric field targeting

Gomez

Dannhauer

Peterchev

2020

Preprint

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Highlights• Auxiliary dipole method (ADM) optimizes TMS coil placement in under 8 minutes • Optimum orientations are near normal to the sulcal wall • TMS induced E-field is less sensitive to orientation than position errors Abstract Background: During transcranial magnetic stimulation (TMS) a coil placed on the scalp is used to non-invasively modulate activity of targeted brain networks via a magnetically induced electric field (E-field). Ideally, the E-field induced during TMS is concentrated on a targeted cortical region of interest (ROI).Objective: To improve the accuracy of TMS we have developed a fast computational auxiliary dipole method (ADM) for determining the optimum coil position and orientation. The optimum coil placement maximizes the E-field along a predetermined direction or the overall E-field magnitude in the targeted ROI. Furthermore, ADM can assess E-field uncertainty resulting from precision limitations of TMS coil placement protocols, enabling minimization and statistical analysis of E-field dose variability.Method: ADM leverages the reciprocity principle to rapidly compute the TMS induced E-field in the ROI by using the E-field generated by a virtual constant current source residing in the ROI. The framework starts by solving for the conduction currents resulting from this ROI current source. Then, it rapidly determines the average E-field induced in the ROI for each coil position by using the conduction currents and a fast-multipole method. To further speed-up the computations, the coil is approximated using auxiliary dipoles enabling it to represent all coil orientations for a given coil position with less than 600 dipoles.Results: Using ADM, the E-fields generated in an MRI-derived head model when the coil is placed at 5,900 different scalp positions and 360 coil orientations per position can be determined in under 15 minutes on a standard laptop computer. This enables rapid extraction of the optimum coil position and orientation as well as the E-field uncertainty resulting from coil positioning uncertainty.Conclusion: ADM enables the rapid determination of coil placement that maximizes E-field delivery to a specific brain target. This method can find the optimum coil placement in under 15 minutes enabling its routine use for TMS. Furthermore, it enables the fast quantification of uncertainty in the induced E-field due to limited precision of TMS coil placement protocols.

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Conditions for numerically accurate TMS electric field simulation

Cited by 85 publications

References 59 publications

Real-time computation of the TMS-induced electric field in a realistic head model

Real-time computation of the TMS-induced electric field in a realistic head model

A Note about the Individualized TMS Focality

Fast computational optimization of TMS coil placement for individualized electric field targeting

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