# Theoretical Analysis and Design of an Innovative Coil Structure for Transcranial Magnetic Stimulation

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## Abstract

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## Featured Application

**Since magnetic stimulation can activate brain tissue with optimum intensity and frequency, it demonstrates great potential for many medical applications, procedures, and treatments. For example, it makes it easier to reach a deeper region beneath the skin without causing any trauma or pain. In addition, magnetic stimulation does not leave any residues in the operated tissues. However, the magnetic fields generated by typical and conventional coils are uniform around their targets, and their magnetic stimulation performance still needs improvement. Thus, an innovative coil that has a quad coil form was proposed for transcranial magnetic stimulation, which makes it possible to shrink the irritative zone and strengthen the stimulation intensity, thus achieving higher magnetic stimulation performance.**

## Abstract

## 1. Introduction

## 2. Transcranial Magnetic Stimulation

#### 2.1. Principle of the Transcranial Magnetic Stimulation

#### 2.2. Design of the Signal Generator

_{c}is the voltage of the charging capacitor.

## 3. The Design of an Innovative Coil for Magnetic Stimulation

#### 3.1. Calculation of the Electromagnetic Fields

_{0}is the permeability, d

**l**is a vector along the path C whose magnitude is the length of the differential element of the wire in the direction of current, l is a point on path C, and

**r**′ =

**r**−

**l**is the full displacement vector from the wire element d

**l**at point

**l**to the point at which the field is being calculated (

**r**).

**A**is the magnetic vector potential, φ is the scalar potential, and

**E**is the induced electric field strength.

**A**= 0.

#### 3.2. Measurement of the Field Distribution

#### 3.3. Design of the Stimulation Coil

## 4. Theoretical Analysis and Field Distribution

#### 4.1. Analysis of the Field Distribution and Verifications

#### 4.2. Comparison of the Typical Performances

#### 4.3. The Simulation of the Influential Factors

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 6.**(

**a**) Front view of the proposed coil, (

**b**) top view of the proposed coil, and (

**c**) the location of the compared plane (8 cm beyond the coil plane).

**Figure 9.**Comparison of the measurements and the simulated calculations of the magnetic flux density.

**Figure 10.**Comparison of the magnetic flux density distribution between the proposed coil and the typical coils. (

**a**) The proposed coil, (

**b**) figure-8 quad coil, (

**c**) figure-8 coil, and (

**d**) round coil.

Big-Coils | Little-Coils | |
---|---|---|

Turns | 12 | 10 |

Coil diameter | 15.6 cm | 10 cm |

Wire radius | 0.3 cm | 0.3 cm |

Conductivity (S/m) | Permittivity (F/m) | Permeability (H/m) | Depth (mm) | |
---|---|---|---|---|

Skin | 0.465 | 1.2 × 10^{4} | 1 | 3 |

Skull | 0.01 | 0.8 × 10^{4} | 1 | 10 |

Cerebrospinal Fluid | 1.654 | 0.6 × 10^{4} | 1 | 2 |

Brain | 0.126 | 1.2 × 10^{4} | 1 | 30 |

**Table 3.**The comparison of the four types of the coil at the same depth (8 cm beyond the coil plane).

Electrical Field (V/m) | Magnetic Flux Density (mT) | FWHM (cm) | |
---|---|---|---|

Proposed coil | 120.6 | 26.1 | 11.7 |

Figure-8 quad coil | 97.9 | 20.4 | 12.3 |

Figure-8 coil | 58.7 | 13.0 | 11.9 |

Round coil | 3.3 | 13.9 | 14.7 |

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**MDPI and ACS Style**

Zhang, N.; Wang, Z.; Shi, J.; Ning, S.; Zhang, Y.; Wang, S.; Qiu, H.
Theoretical Analysis and Design of an Innovative Coil Structure for Transcranial Magnetic Stimulation. *Appl. Sci.* **2021**, *11*, 1960.
https://doi.org/10.3390/app11041960

**AMA Style**

Zhang N, Wang Z, Shi J, Ning S, Zhang Y, Wang S, Qiu H.
Theoretical Analysis and Design of an Innovative Coil Structure for Transcranial Magnetic Stimulation. *Applied Sciences*. 2021; 11(4):1960.
https://doi.org/10.3390/app11041960

**Chicago/Turabian Style**

Zhang, Naming, Ziang Wang, Jinhua Shi, Shuya Ning, Yukuo Zhang, Shuhong Wang, and Hao Qiu.
2021. "Theoretical Analysis and Design of an Innovative Coil Structure for Transcranial Magnetic Stimulation" *Applied Sciences* 11, no. 4: 1960.
https://doi.org/10.3390/app11041960