JP2611960B2 - Dipole estimation method - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to an equivalent dipole estimating method for measuring a potential on the surface of a living body and calculating a position and a vector component of an equivalent dipole assumed inside the living body from the measured value.

[0002]

2. Description of the Related Art Conventionally, an electroencephalograph, an electromyograph, an evoked potential adding device, and the like have been used as devices for measuring a potential appearing on the surface of a living body due to nerve activity of the living body. 2. Description of the Related Art Recently, an equivalent dipole has been proposed, which measures a potential or a magnetic field generated on the surface of a living body in accordance with a nerve activity of the living body, and estimates an active site in the living body. The principle of this method is as follows.
That is, for example, when cells in each active site of the brain are stimulated, an electromotive force is generated to generate a potential or a magnetic field on the scalp.
From these potentials or magnetic fields, each part in the brain is made to correspond with an electric dipole, and the position of this dipole and the vector component are calculated from the above potential or magnetic field to estimate the position of active brain cells. By doing so, the state of activity of the brain is tracked. In the equivalent dipole method for estimating such a dipole, initially, for example, the head is assumed to be a complete sphere and the skull is one-handed because of the repeated calculation of the potential or magnetic field generated by the dipole. The calculations were performed assuming that they were in such an infinite conductor. That is, a method of calculating a potential or a magnetic field by assuming a homogeneous conductive sphere having a homogeneous brain in the head and assuming a concentric or eccentric spherical shell has been proposed.

However, the method of approximating a non-spherical skull with a spherical model not only involves an error in the calculation of electric potential and magnetic field, but also makes it unclear where the estimated equivalent dipole position corresponds in the brain. . In view of this, a method for removing the influence of a cavity such as an eye hole or an ear hole that disturbs the homogeneity in the skull (Japanese Patent Application No. 62-285728, Japanese Patent Application No. 63-86464, etc.) and an influence of the head shape are removed. Method (Japanese Patent Application No. 62-2)
No. 85728, Japanese Patent Application No. 63-182163).

[0004]

In the conventional equivalent dipole method, for example, in the head, the influence of a cavity that causes disturbance of intracranial homogeneity can be removed to some extent. However, the influence of the skull cannot be neglected in calculating the position and vector component of the equivalent dipole. That is, the skull is different in conductivity from other tissue filling portions in the skull, and an error occurs when calculated as the same conductivity as the other tissue filling portions. The present invention has been made in order to solve such a drawback of the conventional equivalent dipole method, and takes into account the difference in the electrical conductivity in each part that causes an error, and the accurate position of the dipole. It is an object of the present invention to provide a dipole estimating method which can obtain a vector component relatively easily .

That is, according to the present invention, the inside has a different conductivity σ.
Multiple triangles on the surface of a living body
Arrange them in a mesh without gaps, and join these triangles together.
To approximately form a polyhedron,
An electrode is attached to the vertex of the
The potential u on the surface of the living body is measured, and a predetermined value is determined using the measured value.
And the position r _opt of the dipole d inside the living body and
A bi <br/> pole estimation method for estimating a vector component _{d opt (d x, d y} , d z), the internal biological, each unique conductive
The regions Ω1, Ω2, Ω3 where the electric powers σ _a , σ _b , σ _c are distributed
Dipole d to be obtained
A virtual existence position of (d _x , d _y , d _z ) is defined as a temporary position r.
And a plurality of dipoles d are set in advance.
Based on the provisional position r of (d _x , d _y , d _z ),
Each component (a ₁ , a ₂ , a ₃ ) of the potential distribution on the surface is
Computed by the boundary element method and based on these computed values
The transfer matrix A (r) is determined, and the transfer matrix A (r) is determined.
From the following equation using (r), u _cal = A (r) d,
Calculate each potential u _cal generated at each electrode point of
Each life and potential u _meas at each position r on the surface of the living body
When there is a dipole d at each temporary position r inside the body,
Calculated by calculation expected to be generated from dipole d
Each square error between each potential u _cal at the same position and
Given square error function S (r, d) = | u _meas −u _cal |
² and the square error formed by the position r and the potential distribution d
Regarding the difference function, each of these three changes of the position r and the potential distribution d
Of the numbers, three variables d regarding the potential distribution are converted into the following conversion formulas, d
^{_{opt = (A (r) t}} A (r)) -1 A (r) t u meas,
(Where A (r) ^t is the transposed matrix of matrix A (r))
Squared error only for dipole position r
Difference function ^{_{S (r) = u t meas}} {E M -A (r) (A (r)
^t A (r)) ^-1 A (r) ^t ｝ u _meas , (where, u
^t _meas is the transposed matrix of matrix u _meas , and E _M is the identity matrix.
In other words, regarding these square error functions S (r),
Simplify the temporary position r of the dipole d when giving a small error
Corrected by the Rex method, the obtained hypothesis of dipole d
The location r and the true position r _opt true dipole d _opt in vivo
And the estimated true dipole position r
_{From opt} , the conversion equation d _opt = (A (r) ^t A (r)) ^-1
Calculated vector components of the dipole d using A (r) ^t u _meas
Because, the obtained vector components of the dipole d twin pole true
It is estimated as a vector component d _opt .

[0006]

In the equivalent dipole measuring apparatus according to the present invention, a potential generated on the surface of a living body is measured by a dipole power supply inside the living body. On the other hand, a dipole is set at a specific position in advance, and the inside of the living body is divided into regions according to the magnitude of the electric conductivity, and the potential distribution on the surface is calculated for each of the regions. The potential is calculated, and the position and vector component of the set dipole are corrected so as to minimize the square error between the calculated value and the actually measured value, and the true position and vector component of the dipole are estimated. be able to.

[0007]

An embodiment of the present invention will be described below with reference to the accompanying drawings. FIG. 1 shows a method of estimating a dipole in the skull (in the brain) according to the present invention.
The dipole estimating method includes first to seventh steps S1 to S7.

[0008]

(Equation 1)

[0009]

(Equation 2)

[0010]

(Equation 3)

[0011]

(Equation 4)

[0012]

(Equation 5)

[0013]

(Equation 6)

[0014]

(Equation 7)

[0015]

(Equation 8)

[0016]

(Equation 9)

[0017]

(Equation 10)

[0018]

[Equation 11]

[0019]

(Equation 12)

[0020]

(Equation 13)

[0021]

[Equation 14]

[0022]

(Equation 15)

[0023]

As described above, according to the present invention, the inside of a living body is divided into a plurality of parts in accordance with the distribution region of the same conductivity, and the virtual position and vector component of the dipole to be obtained are determined. The potential distribution on the surface is calculated for each region based on the calculated values, the potential on the surface of the living body is calculated based on these calculated values, and the potential measured on the surface of the living body and the potential at the same position calculated by the calculation are calculated. thin to minimize the square error between
The position and vector components of the dipole are corrected using the plex method, and the true position and vector component of the dipole in the living body are estimated. Estimation of the dipole position or vector component of the present invention can be performed with much higher accuracy than conventional methods, thereby providing a powerful means for pathological and clinical studies on the brain. .

[Brief description of the drawings]

FIG. 1 is a flowchart showing a dipole estimation method according to the present invention.

FIG. 2 is an explanatory diagram showing triangles formed on the surface of each region in the dipole estimation method according to the present invention.

FIG. 3 is a schematic diagram showing an intracranial three-layer model to which the dipole estimation method according to the present invention is applied;

FIG. 4 is a schematic diagram showing another three-layer model to which the dipole estimation method according to the present invention is applied.

FIG. 5 is an explanatory diagram showing a distribution of conductivity in first and second layer regions according to the present invention.

Continuation of the front page (72) Inventor Yoshio Nakajima 4-3 Asahimachi, Chuo-ku, Chiba-shi, Chiba Prefecture (72) Inventor Yoshio Okamoto 227-7 Shimosakunobu, Takatsu-ku, Kawasaki-shi, Kanagawa-ken (72) Inventor Hitoda Nakamura Hachioji-shi, Tokyo 1-9-9 Moto-Honcho Chuo Denshi Co., Ltd. (72) Inventor Hiromoto Watanabe 1-9-9 Moto-Hongocho, Hachioji-shi, Tokyo Chuo Denshi Co., Ltd. (72) Inventor Keiichi Miyamoto Hachioji, Tokyo 1-9-9 Motomotocho, Ichimoto Chuo Denshi Co., Ltd. (72) Inventor Nobuo Nakagawa 1-9-9 Motohongocho, Hachioji City, Tokyo Inside Chuo Denshi Co., Ltd. (72) Inventor Masafumi Kikuchi Hachioji, Tokyo 1-9-9 Hongocho, Ichimoto Inside Chuo Denshi Co., Ltd. (56) References JP-A-5-49607 (JP, A)

Claims (1)

(57) [Claims] 1. The inside of a plurality of layers having different conductivity σ
On the surface of a living body consisting of multiple triangles in a mesh without gaps
Arrange them and join these triangles together to approximate polyhedral
And electrodes on the vertices of each triangle.
And the potential on the surface of the living body is determined by the plurality of M electrodes.
u is measured, and a predetermined calculation is performed by using the measured value.
Position r _opt and vector component d of dipole d inside living body
_This is a dipole estimating method for estimating _opt (d _x , d _y , d _z ), in which a specific conductivity σ _a , σ _b , σ _c is set inside a living body.
The virtual region of the dipole d (d _x , d _y , d _z ) to be obtained is divided into a plurality of distribution regions Ω 1, Ω 2 and Ω 3.
Advance configure several Do presence position as the temporary position r, the set dipoles _{d (d x, d y,} d z) temporary position of
Each component of the potential distribution on the surface for each region based on r
(A ₁ , a ₂ , a ₃ ) is calculated by the boundary element method, and a transfer matrix A (r) is determined based on these calculated values.
And the following equation using this transfer matrix A (r): u _cal
= A (r) d generated at each of the electrode points on the body surface from A (r) d
Calculating the potential u _cal, potential u _meas and that in each position r on the measured biometric surface
When there is a dipole d at each temporary position r inside the living body,
By the operation expected to be generated from the dipole d,
Each square error between the calculated potential u _cal at the same position and the calculated potential u _cal
Square error function S (r, d) = | u _meas −u giving the difference
_cal | ² is calculated, and a square error function composed of the position r and the potential distribution d is calculated.
Out of the three variables of the position r and the potential distribution d.
The three variables d for the rank distribution are converted into the following conversion formula, d _opt = (A
(R) ^t A (r)) ^-1 A (r) ^t u _meas , (however,
Where A (r) ^t is the inverse of the matrix A (r).
Leaving the squared error function S only for dipole position r
^{_{(R) = u t meas {}} E M -A (r) (A (r) t A
(R)) ⁻¹ A (r) ^t ｝ u _meas , (where, u ^t
_meas is the transpose of the matrix u _meas , E _M is the identity matrix
And the least squared error function S (r)
Simplex the provisional position r of the double-pole d at the time of giving the error
The tentative position r of the obtained dipole d is determined by the correction method using the true dipole in vivo.
Estimate as the true position r _opt of d _opt and its
From the estimated true dipole position r _opt , the conversion formula d _opt =
^{(A (r) t A (} r)) using the ^-1 A (r) ^t u _meas bi
The vector component of the dipole d is obtained, and the obtained vector component of the dipole d is calculated as the true vector of the dipole.
A method for estimating a dipole, comprising estimating as a tor component d _opt .