Skip to main page content
Access keys NCBI Homepage MyNCBI Homepage Main Content Main Navigation
. 2017 Jun 22;12(6):e0178952.
doi: 10.1371/journal.pone.0178952. eCollection 2017.

How Much Detail Is Needed in Modeling a Transcranial Magnetic Stimulation figure-8 Coil: Measurements and Brain Simulations

Free PMC article

How Much Detail Is Needed in Modeling a Transcranial Magnetic Stimulation figure-8 Coil: Measurements and Brain Simulations

Petar I Petrov et al. PLoS One. .
Free PMC article


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.

Conflict of interest statement

Competing Interests: S.F.W. Neggers has, besides being employed at the UMC Utrecht as Associate Professor, 25% share in the spinoff company Brain Science Tools BV (BST). This company designs, develops, manufacturers and markets accessories for use with transcranial magnetic stimulation (TMS). Regarding this paper, BST contributed some expert advice on coregistration of TMS coil position with respect to an MR image. Otherwise, the involvement of SFW Neggers in this paper was purely scientific, and his co ownership of BST did not influence any decision related to the design, execution, data analysis of the studies or writing of the manuscript. This does not alter our adherence to PLOS ONE policies on sharing data and materials.


Fig 1
Fig 1. Coil current approximation.
On the left (Fig 1A) is shown the plot of the electric field of the coil, while on the right (Fig 1B) it is shown the resulting current profile. The DC approximation in red (shaded area) Fig 1B. Both subplots are idealized and given for 50% machine power.
Fig 2
Fig 2. Experimental and virtual setup.
On top (Fig 2A) photo of physical phantom; holder; MR flex coils. Fig 2Aa, top right, the actual TMS figure-of-8 coil with capsules visible in red. On bottom (Fig 2B) is shown a visualization of the phantom T2, coil model BSM-811 as well as a single slice of MR phase accumulation measurements.
Fig 3
Fig 3. Volumetric tetrahedral mesh of the human head (FEM) model.
On the left (Fig 3A) a mid-coronal slice with well conforming to anatomy boundaries for each tissue. On the right (Fig 3B) a closer view of 3A, the black sided rectangle in Fig 3A, where individual pyramidal shapes for each tetrahedron are easy to discern.
Fig 4
Fig 4. The three coil models and the empirical results.
From top to bottom BSM-811, BSM-819 and BSM-879: Fig 4A the 3D models of the three coils under investigation. Fig 4B shows the Bz results, coming from MR measurements (all slices are the same). Fig 4C shows the Bz results, coming from computer simulations. Finally, Fig 4D gives the AD (absolute difference) metric for each coil model, between MR measurements (Fig 4B) and numeric calculations (Fig 4C). The slice views (Fig 4B, C and D) correspond to the 1mm thick slice depicted in Fig 2B.
Fig 5
Fig 5. Plot of Bz field at distance 4cm away from the coil.
On top Fig 5A absolute value of the measured magnetic field in the MRI and the predicted values for all three coil models. On bottom Fig. 5B The value of BSM-811 used as a baseline; MRI measures, BSM-819 and BSM-879 prediction relative to the baseline.
Fig 6
Fig 6. Total electric field results from FEM.
On the left an overview image of the coil, the cortical gray matter sheet, semi-transparent skin rendering. On the right a close-up view (zoom-in) of the area just under the coil (M1 moto-cortex gyrus). Fig 6A coil model BSM-811 orthogonal to the M1 gyrus. Fig 6B coil model BSM-819 orthogonal to the M1 gyrus. Fig 6C coil model BSM-811 parallel to the M1 gyrus. Fig 6D coil model BSM-819 parallel to the M1 gyrus.
Fig 7
Fig 7. Results for the electric field(s) inside our ROI.

Similar articles

See all similar articles

Cited by 6 articles

See all "Cited by" articles


    1. Neggers SFW, Petrov PI, Mandija S, Sommer IEC, van den Berg C a. T. Understanding the biophysical effects of transcranial magnetic stimulation on brain tissue: The bridge between brain stimulation and cognition Prog Brain Res. 1st ed Elsevier B.V.; 2015; 1–31. doi: 10.1016/bs.pbr.2015.06.015 - DOI - PubMed
    1. Opitz A, Windhoff M, Heidemann RM, Turner R, Thielscher A. How the brain tissue shapes the electric field induced by transcranial magnetic stimulation Supplementary Material. Neuroimage. Elsevier Inc.; 2011;58: 849–59. doi: 10.1016/j.neuroimage.2011.06.069 - DOI - PubMed
    1. De Lucia M, Parker GJM, Embleton K, Newton JM, Walsh V. Diffusion tensor MRI-based estimation of the influence of brain tissue anisotropy on the effects of transcranial magnetic stimulation. Neuroimage. 2007;36: 1159–70. doi: 10.1016/j.neuroimage.2007.03.062 - DOI - PubMed
    1. Pu L, Liu Z, Yin T, An H, Li S. Simulation of induced electric field distribution based on five-sphere model used in rTMS. J Xray Sci Technol. 2010;18: 57–67. doi: 10.3233/XST-2010-0241 - DOI - PubMed
    1. Salinas FS, Lancaster JL, Fox PT. Detailed 3D models of the induced electric field of transcranial magnetic stimulation coils. Phys Med Biol. 2007;52: 2879–2892. doi: 10.1088/0031-9155/52/10/016 - DOI - PubMed

Grant support

This work was supported by the DeNeCor project being part of the ENIAC Joint Undertaking, Project number ENIAC131003, The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.