CN110433396B - Brain tissue electromagnetic field analysis method based on transcranial magnetic stimulation instrument - Google Patents

Brain tissue electromagnetic field analysis method based on transcranial magnetic stimulation instrument Download PDF

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CN110433396B
CN110433396B CN201910763444.3A CN201910763444A CN110433396B CN 110433396 B CN110433396 B CN 110433396B CN 201910763444 A CN201910763444 A CN 201910763444A CN 110433396 B CN110433396 B CN 110433396B
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王懿
李世俊
邹军
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Chinese PLA General Hospital
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    • A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
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    • A61B5/00—Measuring for diagnostic purposes; Identification of persons
    • A61B5/05—Detecting, measuring or recording for diagnosis by means of electric currents or magnetic fields; Measuring using microwaves or radio waves 
    • A61B5/0522—Magnetic induction tomography
    • A—HUMAN NECESSITIES
    • A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
    • A61B—DIAGNOSIS; SURGERY; IDENTIFICATION
    • A61B5/00—Measuring for diagnostic purposes; Identification of persons
    • A61B5/05—Detecting, measuring or recording for diagnosis by means of electric currents or magnetic fields; Measuring using microwaves or radio waves 
    • A61B5/055—Detecting, measuring or recording for diagnosis by means of electric currents or magnetic fields; Measuring using microwaves or radio waves  involving electronic [EMR] or nuclear [NMR] magnetic resonance, e.g. magnetic resonance imaging
    • A—HUMAN NECESSITIES
    • A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
    • A61N—ELECTROTHERAPY; MAGNETOTHERAPY; RADIATION THERAPY; ULTRASOUND THERAPY
    • A61N2/00—Magnetotherapy
    • A61N2/004—Magnetotherapy specially adapted for a specific therapy
    • A61N2/006—Magnetotherapy specially adapted for a specific therapy for magnetic stimulation of nerve tissue
    • A—HUMAN NECESSITIES
    • A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
    • A61N—ELECTROTHERAPY; MAGNETOTHERAPY; RADIATION THERAPY; ULTRASOUND THERAPY
    • A61N2/00—Magnetotherapy
    • A61N2/02—Magnetotherapy using magnetic fields produced by coils, including single turn loops or electromagnets

Abstract

The invention relates to the field of biomedical engineering, and discloses a brain tissue electromagnetic field analysis method based on a transcranial magnetic stimulator, which comprises the following steps: placing 8 coils of a transcranial magnetic stimulator on the top of the brain; setting brain tissue below the central part of the 8-shaped coil as a plane layered structure; and analyzing and obtaining the electromagnetic field distribution of each layer structure in the brain tissue according to the current introduced into the 8-shaped coil and the thickness and the conductivity of each layer structure in the brain tissue. The invention provides a brain structure electromagnetic field analysis method based on a transcranial magnetic stimulation instrument, which is characterized in that a plane layered model of a brain is established, the influence of layered structure eddy current is considered, and induced current and magnetic field distribution in various tissues are calculated and analyzed, so that the induced current and magnetic field distribution of different layers of the brain can be more accurately known when being magnetically stimulated, thus providing positioning guidance of current action points for clinic and improving the clinical use effect of the transcranial magnetic stimulation instrument.

Description

Brain tissue electromagnetic field analysis method based on transcranial magnetic stimulation instrument
Technical Field
The invention relates to the field of biomedical engineering, in particular to a brain tissue electromagnetic field analysis method based on a transcranial magnetic stimulator.
Background
The induced current density and Magnetic field intensity distribution generated by the brain tissue under the action of repeated Transcranial Magnetic Stimulation (rTMS) are key factors for determining the Stimulation curative effect, and how a clinician quickly understands the principles is the key for mastering the accurate positioning of rTMS and playing the efficacy. The coil stimulation safety range and the curative effect mechanism in the rTMS precise positioning operation are important contents of clinical teaching, but the traditional theoretical teaching cannot vividly illustrate the advantages of the noninvasive technology.
With the development of magnetic stimulation technology and the continuous deepening and expanding of research teaching and clinical application, the magnetic stimulation technology has developed into an important nerve modulation and nerve stimulation technology, and the application field is gradually expanded from the initial application of the magnetic stimulation technology in the examination and the evaluation of the functional integrity of central nerve conduction pathways to the treatment of various diseases, in particular to the clinical intervention research of autistic patients. In recent years, the physiological influence of rTMS on brain function has been more and more emphasized, and certain effects have been achieved in the treatment of neurological diseases such as paralysis, parkinson's disease, psychosis, and cerebrovascular disease.
In order to stimulate brain cells accurately, the induced currents generated by the rTMS coil in the various tissues in the brain need to be analyzed computationally. However, the induced current generated by the rTMS coil in the brain has not been found by measurement.
Disclosure of Invention
Technical problem to be solved
The invention aims to provide a method for analyzing a brain tissue electromagnetic field based on a transcranial magnetic stimulator, which is used for solving or partially solving the problem that induced current generated by the transcranial magnetic stimulator in the brain cannot be obtained through actual measurement.
(II) technical scheme
In order to solve the technical problem, the invention provides a method for analyzing the electromagnetic field of brain tissue based on a transcranial magnetic stimulator, which comprises the following steps: placing 8 coils of a transcranial magnetic stimulator on the top of the brain; setting brain tissue below the central part of the 8-shaped coil as a plane layered structure; and analyzing and obtaining the electromagnetic field distribution of each layer structure in the brain tissue according to the current introduced into the 8-shaped coil and the thickness and the conductivity of each layer structure in the brain tissue.
On the basis of the scheme, the brain tissue below the central part of the 8-shaped coil is set to be a planar layered structure, and the planar layered structure specifically comprises the following steps: the brain tissue below the central part of the 8-shaped coil is set to sequentially comprise a skin layer, a fat layer, a skull layer, a hard brain membrane layer and a cerebrospinal layer from the surface of the brain to the bottom.
On the basis of the scheme, the thickness of each layer structure in the brain tissue is obtained through magnetic resonance imaging.
On the basis of the scheme, the method further comprises the following steps: arranging a magnetic field sensor on the surface of the brain corresponding to the central part of the 8-shaped coil; and verifying the brain tissue electromagnetic field analysis method according to the magnetic induction intensity of the brain surface detected by the magnetic field sensor and the magnetic induction intensity of the brain surface obtained by analysis.
On the basis of the scheme, currents with different frequencies are introduced into the 8-shaped coil through the waveform generator and the current power amplifier, so that the form of the current in the 8-shaped coil is as follows: (i) (t) Asin (2 pi ft); wherein A is the current amplitude determined by the power amplifier; f is the current frequency determined by the waveform generator; t is a time variable.
On the basis of the scheme, the magnetic induction intensity of the surface of the brain is as follows:
Figure GDA0002929794170000021
wherein λ is an integral variable; r1And R2The inner radius and the outer radius of one coil of the 8-coil respectively; a is the average value of the inner and outer radii of the coil; j. the design is a square0(λ a) is a Bessel function; r0(λ) is the reflection coefficient.
Based on the scheme, the reflection coefficient R0(λ) is: r0＝(N0-Y1)/(N0+Y1) (ii) a Wherein N is0Is the wave impedance of the air layer; y is1Is the wave admittance of the skin layer;
wherein N ism＝um/(jωμ0)，m＝0，1，2，3，4，5，6；
Figure GDA0002929794170000031
Figure GDA0002929794170000032
Wherein, mu0Is the permeability of the air layer; m is the number of layers from top to bottom in the brain tissue; u. ofmIs a variable related to an electromagnetic parameter of the tissue; sigmamIs the electrical conductivity of the mth layer in brain tissue; n is a radical ofmWave impedance of the mth layer in brain tissue; y ismIs the wave admittance of the mth layer in the brain tissue.
On the basis of the above scheme, the induced electric field in the brain tissue is:
Em(ω)＝jωI(ω)Mm(ω),m＝1,2,…,N
Figure GDA0002929794170000033
wherein E ism(ω) is the electric field in the mth layer of brain tissue generated by the coil current I (ω); n is the total number of layers of the brain tissue; omega is angular frequency; mm(ω) is the transfer impedance between the coil current and the electric field;
further, the air conditioner is provided with a fan,
Figure GDA0002929794170000034
im(t)＝σmem(t)m＝1,2,…,N
wherein e ism(t) is the induced electric field in the mth layer in the brain tissue; i (t) is a time domain expression of the current in the coil; mm(t) is a time domain expression of the transfer impedance between the coil current and the electric field;
Figure GDA0002929794170000035
are the convolution symbols.
On the basis of the scheme, the current i (t) in the coil is as follows:
Figure GDA0002929794170000036
Figure GDA0002929794170000037
wherein, R, L and C are equivalent resistance, inductance and capacitance of the discharge loop; u shape0Is the initial charge voltage on the capacitor.
On the basis of the above scheme, the impedance M is transferredmThe (t) is specifically:
get
Figure GDA0002929794170000038
When λ > T, there are
Figure GDA0002929794170000041
It is possible to obtain,
Figure GDA0002929794170000042
wherein the content of the first and second substances,
Figure GDA0002929794170000043
Figure GDA0002929794170000044
Figure GDA0002929794170000045
(III) advantageous effects
The invention provides a brain structure electromagnetic field analysis method based on a transcranial magnetic stimulation instrument, which is characterized in that a plane layered model of a brain is established, the influence of layered structure eddy current is considered, and induced current and magnetic field distribution in various tissues are calculated and analyzed, so that the induced current and magnetic field distribution of different layers of the brain can be more accurately known when being magnetically stimulated, thus providing positioning guidance of current action points for clinic and improving the clinical use effect of the transcranial magnetic stimulation instrument.
Drawings
FIG. 1 is a schematic diagram of a planar layered structure of brain tissue in an embodiment of the present invention;
fig. 2 is a schematic diagram of an 8-word coil arrangement in an embodiment of the present invention.
Detailed Description
The following detailed description of embodiments of the present invention is provided in connection with the accompanying drawings and examples. The following examples are intended to illustrate the invention but are not intended to limit the scope of the invention.
In the description of the present invention, it should be noted that, unless otherwise explicitly specified or limited, the terms "mounted," "connected," and "connected" are to be construed broadly, e.g., as meaning either a fixed connection, a removable connection, or an integral connection; can be mechanically or electrically connected; they may be connected directly or indirectly through intervening media, or they may be interconnected between two elements. The specific meanings of the above terms in the present invention can be understood in specific cases to those skilled in the art.
The embodiment of the invention provides a method for analyzing a brain tissue electromagnetic field based on a transcranial magnetic stimulation instrument, which comprises the following steps: placing 8 coils of a transcranial magnetic stimulator on the top of the brain; setting brain tissue below the central part of the 8-shaped coil as a plane layered structure; and analyzing and obtaining the electromagnetic field distribution of each layer structure in the brain tissue according to the current introduced into the 8-shaped coil and the thickness and the conductivity of each layer structure in the brain tissue.
The transcranial magnetic stimulation process mainly stimulates the area near the target point, and the embodiment provides that a layered plane brain model is selected when the stimulation process of the transcranial magnetic stimulation coil to the brain is researched. According to the sequence from outside to inside, the brain is divided into six layers of skin, fat, skull, dura mater, cerebrospinal fluid and brain in turn, each layer is characterized by electric conductivity and magnetic conductivity, and a plane model of the brain is shown in figure 1.
In the embodiment, a plane layering model of the brain is established, the influence of eddy currents of a layering structure is considered, and the distribution of the induced currents and the magnetic fields in different layers of the brain can be more accurately known through calculation and analysis of the distribution of the induced currents and the magnetic fields in various tissues, so that the positioning guidance of current action points is provided for clinic, and the clinical using effect of the transcranial magnetic stimulation instrument is improved.
On the basis of the above embodiment, further, the setting of the brain tissue below the central portion of the 8-word coil as a planar layered structure specifically includes: the brain tissue below the central part of the 8-shaped coil is set to sequentially comprise a skin layer, a fat layer, a skull layer, a hard brain membrane layer, a cerebrospinal layer and a brain layer from the surface of the brain to the bottom.
On the basis of the above embodiment, further, the thickness of each layer structure in the brain tissue is obtained by magnetic resonance imaging.
On the basis of the above embodiment, further, a method for analyzing an electromagnetic field of brain tissue based on a transcranial magnetic stimulator further includes: arranging a magnetic field sensor on the surface of the brain corresponding to the central part of the 8-shaped coil; and verifying the brain tissue electromagnetic field analysis method according to the magnetic induction intensity of the brain surface detected by the magnetic field sensor and the magnetic induction intensity of the brain surface obtained by analysis.
A coil of a transcranial magnetic stimulator 8 is placed on the top of the brain, a magnetic field sensor is placed below the center of the plane of the coil, and the sensor is small enough to view the layered structure of the brain near the sensor as a planar layered structure.
The embodiment is a method for non-invasively acquiring the conductivity parameters of the brain in vivo tissues. Alternating current is introduced into a coil through a skull magnetic stimulator 8 to generate an excitation magnetic field, the normal components of the magnetic field on the surface of the brain under different frequencies are measured, and the conductivity parameters of the brain tissue are obtained through an inversion method. The existing transcranial magnetic stimulator 8 coils are used for generating an excitation magnetic field, the magnetic field on the surface of the brain is measured through a high-precision magnetic field sensor, and the in-vivo conductivity of the brain conductivity can be obtained noninvasively by means of a mature inversion method.
The magnetic field value measured by the magnetic field sensor is the result of superposition of the excitation field and the eddy current field of the layered structure in the brain, and therefore, the measurement field contains the conductivity and thickness information of the layered structure of the brain. The thickness of the layered structure can be known by using the nuclear magnetic resonance imaging technology, and the conductivity value can be obtained by a proper optimization algorithm through the difference between the magnetic field measured at different frequencies and the value of an analytical formula.
Because the magnetic induction intensity of the surface of the brain can be measured by using the magnetic field sensor, the actual magnetic induction intensity of the surface of the brain obtained by measurement and the magnetic induction intensity of the surface of the brain obtained by calculation and analysis can be used for carrying out comparative analysis to verify whether the calculation and analysis method is accurate or not.
On the basis of the above embodiment, further, currents with different frequencies are introduced into the 8-word coil through the waveform generator and the current power amplifier, so that the form of the current in the 8-word coil is as follows:
i(t)＝Asin(2πft)；
wherein A is the current amplitude determined by the power amplifier; f is the current frequency determined by the waveform generator; t is a time variable.
By means of a waveform generator, the frequency of the current is varied, N frequency samples are taken, and the current is measured at a given frequency fi1, 2, …, N, the normal magnetic induction B at the top of the brain is measured using a magnetic field sensormea，i. Obtaining brain layered structure by magnetic resonance imaging, and determining thickness h of skin, fat, skull, dura mater and cerebrospinalm，m＝1，2，3，4，5。
In the case of a brain horizontal layered structure, the magnetic induction at different frequencies at the surface of the brain can be calculated as follows:
Bana,i＝F(fi,σ1,h1,σ2,h2,σ3,h3,σ4,h4,σ5,h5,σ6)，i＝1，2，…，N
in the formula, σ1，σ2，σ3，σ4，σ5And σ6Is the conductivity of skin, fat, skull, dura, cerebrospinal fluid and white brain matter.
On the basis of the above embodiment, further, the magnetic induction on the surface of the brain is:
Figure GDA0002929794170000071
wherein λ is an integral variable; r1And R2The inner radius and the outer radius of one coil of the 8-coil respectively; a is the average value of the inner and outer radii of the coil; j. the design is a square0(λ a) is a Bessel function; r0(λ) is the reflection coefficient.
On the basis of the above embodiment, further, the reflection coefficient R0(λ) is:
R0＝(N0-Y1)/(N0+Y1) (ii) a Wherein N is0Is the wave impedance of the air layer; y is1Is the wave admittance of the skin layer;
wherein N ism＝um/(jωμ0)，m＝0，1，2，3，4，5，6；
Figure GDA0002929794170000072
Figure GDA0002929794170000073
Wherein, mu0Is the permeability of the air layer; m is the number of layers from top to bottom in the brain tissue; u. ofmIs a variable related to an electromagnetic parameter of the tissue; sigmamIs the electrical conductivity of the mth layer in brain tissue; n is a radical ofmWave impedance of the mth layer in brain tissue; y ismIs the wave admittance of the mth layer in the brain tissue.
The magnetic induction intensity of the surface of the brain can be obtained through the calculation; and then according to the formula, the magnetic induction intensity in each layer of the structure of the brain tissue can be calculated and obtained by substituting different parameters. The conductivity of the brain layered structure can also be inferred by measuring the magnetic induction.
Further, at σ1，σ2，σ3，σ4，σ5And σ6In the case of positive real numbers, the following problem is calculated: i Bana,i-Bmea,iI | → min, i ═ 1, 2, …, N; the solution to the optimization problem is the in vivo conductivity of each layer of brain tissue. The optimization algorithm is calculated by adopting the existing functions in the optimization tool box in Matlab software.
By using the coil with the 8-shaped structure, a global coordinate system as shown in fig. 2 is established for conveniently calculating the electromagnetic field generated by the coil in the brain. The origin of the coordinate system is set on the skin surface, the direction of the external normal of the skin surface is set as the positive direction of the coordinate axis, and the part under the skin is the brain tissue, which is layered according to the structure shown in fig. 1. The distance between the plane of the coil and the skin is h, the coil generally has a plurality of turns in the height direction, and the total height is c. Fig. 2 is a sectional view of the two coils at the top and a plan view of the two coils at the bottom. The current passing through the coil is generated by an RLC circuit, and the current of the two coils is equal in magnitude and opposite in direction.
The electromagnetic fields generated by the two coils in fig. 2 are independent of each other, and therefore the electromagnetic fields in the tissues of the brain of a single coil need to be calculated. Taking point P on the z-axis in fig. 2 as an example of an induced electric field along the x-direction, the electric field in each layer of tissue can be expressed as follows: the induced electric field in brain tissue is:
Em(ω)＝jωI(ω)Mm(ω),m＝1,2,…,N
Figure GDA0002929794170000081
wherein E ism(ω) is the electric field in the mth layer of brain tissue generated by the coil current I (ω); n is the total number of layers of the brain tissue; omega is angular frequency; mmAnd (ω) is the transfer impedance between the coil current and the electric field. a represents the average radius of the coil; u. ofmIs a variable related to an electromagnetic parameter of the tissue; the definition of rho and z and the definition of F (lambda) are referred to the calculation process of the coil induced electric field in the horizontal layered medium in the existing cylindrical coordinate system.
Further, from Fourier transform properties, it is easy to know that:
Figure GDA0002929794170000082
wherein e ism(t) is the induced electric field in the mth layer in the brain tissue; i (t) is a time domain expression of the current in the coil; mm(t) is a time domain expression of the transfer impedance between the coil current and the electric field, obtained by numerical inverse Fourier transform;
Figure GDA0002929794170000083
are the convolution symbols.
The induced current in brain tissue can be calculated as follows:
im(t)＝σmem(t)m＝1,2,…,N。
on the basis of the above embodiment, further, the current i (t) in the coil is:
Figure GDA0002929794170000084
Figure GDA0002929794170000085
wherein, R, L and C are equivalent resistance, inductance and capacitance of the discharge loop; u shape0The initial charging voltage on the capacitor; the above parameters are known quantities.
To obtain Mm(t), calculating values at different frequencies. Because the integral kernel contains the product of two Bessel functions and the brain tissue is millimeter scale, the whole integral is high-oscillation and slow-convergence, and the numerical calculation is difficult.
On the basis of the above embodiment, further, the transfer impedance M is considered in consideration of the approximate function characteristic of the Bessel functionmThe (t) is specifically:
get
Figure GDA0002929794170000091
When λ > T, there are
Figure GDA0002929794170000092
It is possible to obtain,
Figure GDA0002929794170000093
wherein the content of the first and second substances,
Figure GDA0002929794170000094
Figure GDA0002929794170000095
Figure GDA0002929794170000096
the first formula is a fixed integral with two Bessel functions at [0, T]The number of zero points in the interval is limited, so that the problem of numerical oscillation does not exist, and the interval can be divided into intervals for calculation according to the zero points on the real axis by adopting a conventional numerical integration method according to the Bessel function. The second and third formulas have expressed MmThe product of the double Bessel functions in (omega) is converted into the integral problem of a single sine function or a single cosine function, and the oscillation property of an integral kernel is effectively weakened. The integral of the two functions can be calculated by adopting a steepest descent method for changing an integral path. Therefore, the induced current can be obtained by calculation.
In the embodiment, a fast frequency domain calculation method is provided for infinite generalized integral with a Bessel function; according to the time domain induced current and magnetic field distribution of different layers of the brain, clinical learners can be guided to quickly complete the accurate positioning of the transcranial magnetic stimulation instrument.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents, improvements and the like that fall within the spirit and principle of the present invention are intended to be included therein.

Claims (8)

1. A method for analyzing a brain tissue electromagnetic field based on a transcranial magnetic stimulator is characterized by comprising the following steps:
placing 8 coils of a transcranial magnetic stimulator on the top of the brain;
setting brain tissue below the central part of the 8-shaped coil as a plane layered structure;
analyzing and obtaining the electromagnetic field distribution of each layer structure in the brain tissue according to the current introduced into the 8-shaped coil and the thickness and the conductivity of each layer structure in the brain tissue;
the induced electric field in brain tissue is:
Em(ω)＝jωI(ω)Mm(ω),m＝1,2,…,N
Figure FDA0002929794160000011
wherein E ism(ω) is the electric field in the mth layer of brain tissue generated by the coil current I (ω); n is the total number of layers of the brain tissue; omega is angular frequency; mm(ω) is the transfer impedance between the coil current and the electric field;
further, the air conditioner is provided with a fan,
Figure FDA0002929794160000012
im(t)＝σmem(t) m＝1,2,…,N
wherein e ism(t) is the induced electric field in the mth layer in the brain tissue; i (t) is a time domain expression of the current in the coil; mm(t) is a time domain expression of the transfer impedance between the coil current and the electric field;
Figure FDA0002929794160000013
is a convolution symbol;
transfer impedance MmThe (t) is specifically:
get
Figure FDA0002929794160000014
When λ > T, there are
Figure FDA0002929794160000015
It is possible to obtain,
Figure FDA0002929794160000016
wherein the content of the first and second substances,
Figure FDA0002929794160000017
Figure FDA0002929794160000018
Figure FDA0002929794160000021
2. the method for analyzing the electromagnetic field of the brain tissue based on the transcranial magnetic stimulation device as claimed in claim 1, wherein the brain tissue below the central part of the 8-shaped coil is set to be a planar layered structure, and specifically:
the brain tissue below the central part of the 8-shaped coil is set to sequentially comprise a skin layer, a fat layer, a skull layer, a hard brain membrane layer and a cerebrospinal layer from the surface of the brain to the bottom.
3. The method of claim 1, wherein the thickness of each layer in the brain tissue is obtained by magnetic resonance imaging.
4. The method for analyzing the electromagnetic field of brain tissue based on transcranial magnetic stimulation apparatus according to claim 1, further comprising:
arranging a magnetic field sensor on the surface of the brain corresponding to the central part of the 8-shaped coil;
and verifying the brain tissue electromagnetic field analysis method according to the magnetic induction intensity of the brain surface detected by the magnetic field sensor and the magnetic induction intensity of the brain surface obtained by analysis.
5. The method for analyzing the electromagnetic field of the brain tissue based on the transcranial magnetic stimulation device according to any one of claims 1 to 4, wherein currents with different frequencies are introduced into the 8-shaped coil through the waveform generator and the current power amplifier, so that the current in the 8-shaped coil is in the form of:
i(t)＝Asin(2πft)；
wherein A is the current amplitude determined by the power amplifier; f is the current frequency determined by the waveform generator; t is a time variable.
6. The method for analyzing the electromagnetic field of the brain tissue based on the transcranial magnetic stimulation apparatus according to claim 5, wherein the magnetic induction intensity of the surface of the brain is as follows:
Figure FDA0002929794160000022
wherein λ is an integral variable; r1And R2The inner radius and the outer radius of one coil of the 8-coil respectively; a is the average value of the inner and outer radii of the coil; j. the design is a square0(λ a) is a Bessel function; r0(λ) is the reflection coefficient.
7. The method for analyzing electromagnetic field of brain tissue based on transcranial magnetic stimulation apparatus according to claim 6, wherein reflection coefficient R0(λ) is:
R0＝(N0-Y1)/(N0+Y1) (ii) a Wherein N is0Is the wave impedance of the air layer; y is1Is the wave admittance of the skin layer;
wherein N ism＝um/(jωμ0)，m＝0，1，2，3，4，5，6；
Figure FDA0002929794160000031
m＝1，2，3，4，5；
Figure FDA0002929794160000032
m＝1，2，3，4，5；
Wherein, mu0Is the permeability of the air layer; m is from top to bottom in the brain tissueThe number of layers; u. ofmIs a variable related to an electromagnetic parameter of the tissue; sigmamIs the electrical conductivity of the mth layer in brain tissue; n is a radical ofmWave impedance of the mth layer in brain tissue; y ismIs the wave admittance of the mth layer in the brain tissue.
8. The method for analyzing the electromagnetic field of brain tissue based on transcranial magnetic stimulation apparatus according to claim 1, wherein the current i (t) in the coil is:
Figure FDA0002929794160000033
Figure FDA0002929794160000034
wherein, R, L and C are equivalent resistance, inductance and capacitance of the discharge loop; u shape0Is the initial charge voltage on the capacitor.
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