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Related Concept Videos

Magnetostatic Boundary Conditions01:28

Magnetostatic Boundary Conditions

An electric field suffers a discontinuity at a surface charge. Similarly, a magnetic field is discontinuous at a surface current. The perpendicular component of a magnetic field is continuous across the interface of two magnetic mediums. In contrast, its parallel component, perpendicular to the current, is discontinuous by the amount equal to the product of the vacuum permeability and the surface current. Like the scalar potential in electrostatics, the vector potential is also continuous...
Boundary Conditions for Current Density01:25

Boundary Conditions for Current Density

Current density becomes discontinuous across an interface of materials with different electrical conductivities. The normal component of the current density is continuous across the boundary.
Electrostatic Boundary Conditions01:16

Electrostatic Boundary Conditions

Consider an external electric field propagating through a homogeneous medium. When the electric field crosses the surface boundary of the medium, it undergoes a discontinuity. The electric field can be resolved into normal and tangential components. The amount by which the field changes at any boundary is given by the difference between the field components above and below the surface boundary.
The surface integral of an electric field is given by Gauss's law in integral form and is related to...
Electrostatic Boundary Conditions in Dielectrics01:27

Electrostatic Boundary Conditions in Dielectrics

When an electric field passes from one homogeneous medium to another, crossing the boundary between the two mediums imparts a discontinuity in the electric field. This results in electrostatic boundary conditions that depend on the type of mediums the field propagates through.
Consider a case where both the mediums across a boundary are two different dielectric materials. Recall that the electric field and electric displacement are proportional and related through the material's permittivity.
Induced Electric Fields: Applications01:27

Induced Electric Fields: Applications

An important distinction exists between the electric field induced by a changing magnetic field and the electrostatic field produced by a fixed charge distribution. Specifically, the induced electric field is nonconservative because it does not work in moving a charge over a closed path. In contrast, the electrostatic field is conservative and does no net work over a closed path. Hence, electric potential can be associated with the electrostatic field but not the induced field. The following...
Torque On A Current Loop In A Magnetic Field01:13

Torque On A Current Loop In A Magnetic Field

The most common application of magnetic force on current-carrying wires is in electric motors. These consist of loops of wire, which are placed between the magnets with a magnetic field. When current flows through the loops, the magnetic field applies torque, which causes the shaft to rotate, thus converting electrical energy to mechanical energy.
Consider a rectangular current-carrying loop containing N turns of wire, placed in a uniform magnetic field. The net force on a current-carrying loop...

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How to Use the H1 Deep Transcranial Magnetic Stimulation Coil for Conditions Other than Depression
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Published on: January 23, 2017

Novel TMS coils designed using an inverse boundary element method.

Clemente Cobos Sánchez1, Jose María Guerrero Rodriguez1, Ángel Quirós Olozábal1

  • 1Depto. Ingeniería de Sistemas y Electrónica, E-11519, Puerto Real (Cádiz), Spain.

Physics in Medicine and Biology
|July 1, 2026
PubMed
Summary

A novel method designs transcranial magnetic stimulation (TMS) coils using electric current stream functions and boundary element methods. This versatile approach allows for custom coil shapes and performance optimization for various applications, including concurrent TMS and fMRI.

Keywords:
TMSboundary element methodcoil design

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Area of Science:

  • Electromagnetism and Applied Physics
  • Biomedical Engineering
  • Computational Modeling

Background:

  • Transcranial magnetic stimulation (TMS) requires precisely designed coils for effective and safe neural stimulation.
  • Existing TMS coil design methods may lack versatility in accommodating diverse performance requirements and arbitrary shapes.
  • Integrating quasi-static electric current concepts offers a new avenue for advanced coil design.

Purpose of the Study:

  • To introduce a new computational method for designing transcranial magnetic stimulation (TMS) coils.
  • To demonstrate the versatility of the proposed method for arbitrary coil shapes and performance constraints.
  • To investigate the feasibility of using designed TMS coils for concurrent TMS and functional magnetic resonance imaging (fMRI).

Main Methods:

  • Incorporation of the stream function of quasi-static electric current into a boundary element method (BEM).
  • Application of the BEM-based method to design TMS coils on rectangular, spherical, and hemispherical surfaces.
  • Analysis of coil performance under constraints like minimum stored magnetic energy and power dissipation.
  • Theoretical calculation of torque on TMS coils in a static magnetic field for fMRI compatibility.

Main Results:

  • The developed method successfully designed TMS coils with various geometries (flat, spherical, hemispherical).
  • Coil designs met specific performance constraints, including energy efficiency and power management.
  • Torque analysis indicated potential for concurrent TMS and fMRI applications.
  • The method proved efficient for a wide range of coil geometries and performance requirements.

Conclusions:

  • The presented stream function-based boundary element method is an efficient tool for TMS coil design.
  • The approach offers significant versatility for prototyping coils with diverse shapes and performance specifications.
  • The designed coils show promise for advanced neuroimaging techniques, including simultaneous TMS and fMRI.