JP2993725B2 - Signal processing method in magnetic field measurement - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION [Industrial Application Field] The present invention measures the magnetic field distribution on the surface of the brain, estimates the distribution of the magnetic field sources inside the brain from the data, and displays the magnetic field generation in a magnetoencephalograph. The source estimation method.

[Conventional technology]

FIG. 1 shows a coordinate system for measuring the magnetic field distribution on the brain surface. In FIG. 1, 1 represents a magnetometer and 2 represents a pickup coil. Usually, this pickup coil detects the normal component of the magnetic field with respect to the coil surface. 3 indicates a measurement point. This measurement point is represented by r _m {m = 1, 2,..., M}. Figure it is shown that current represented by a vector q _n to the position of r _n is present. In the field of magnetoencephalography, such an isolated current vector can be assumed, and this is called a current dipole. Therefore, the position of the nth current dipole is r
_{n {n = 1,2, ...,} N} and represents the current vector q _n.

Estimation of the current distribution in the brain from the measured value of the magnetic field on the brain surface is usually performed as follows.

As described above, if there are N current dipoles in the brain, the magnetic flux density vector B _m at the position of r _m Is represented by

You can observe a normal magnetometer is normal component, the actual measurement data in terms of r _m ▲ B ^a _m ▼ to.

On the other hand, the current vector of each current dipole, and virtually appropriately determined its coordinates, which _{1, 2,} ..., _N, and _{1, 2,} ..., expressed as _N. Normal component of the magnetic field these estimated magnetic source is made in the r _m points (m = 1,2,3, ...), i.e. it is possible to calculate the virtual measurements. This is ▲
^{If a} _m ▼ is set, the cost function shown in the equation (2) indicates the degree of coincidence between the estimated data and the actual measurement data.

Therefore, if the estimated values ₁ ,..., _N , ₁ ,..., _N that minimize the cost function of the equation (2) are found by sequential calculation, these estimated values are the actual distribution of the magnetic field source in the brain,
That is, it can be adopted as a signal indicating the current distribution.

[Problems to be solved by the invention]

Now, in the conventional method, area and structure of the pickup coil is ignored, the point r _m of the center of each pickup coil
Then, the normal component ▲ ^a _m ▼ of the magnetic field generated by the estimated magnetic field source was calculated, and this was used as a virtual measurement value and compared with the actual measurement value. That (2) used to calculate the formula ▲ ^a _m ▼ was determined by equation (3).

In practice, however, has an area of the pickup coil is also because sometimes a differential structure was determined as described above ▲ ^a _m ▼ and measurements ▲ B ^a _m ▼ and exactly the Do not correspond. It has been found that this causes an error in current distribution estimation.

Accordingly, an object of the present invention is to provide an estimation method capable of preventing occurrence of an estimation error due to the structure of a pickup coil and performing highly accurate current distribution estimation.

[Means for solving the problem]

The object is to calculate a normal component of a magnetic field generated by the estimated magnetic field source at a plurality of points in each pickup coil when calculating a virtual measurement value from a virtually determined estimated magnetic field source. This is achieved by making the average value of the calculated magnetic field a virtual measurement value. In other words, the comparison between the virtual measurement value and the actual measurement value of each pickup coil obtained on average in this manner is performed by calculating the cost function, and the coordinates of the estimated magnetic field generating source at which the cost function is minimized. The present invention is characterized in that the current distribution is estimated by finding each current vector.

According to one of the more specific aspects of the present invention, the pickup coils arranged at each measurement point are axial primary differential coils, and each pickup coil is used as a virtual measurement value calculated from an estimated magnetic field generation source. Calculation of the normal component of the magnetic field at one or more points in the coil far from the living body from the average of the calculated values of the normal components of the magnetic field at one or more points in the coil closer to the living body Use the value obtained by subtracting the average value of the values. Regardless of whether it is a planar differential coil or a multi-order differential coil, there is an appropriate virtual measurement calculation method according to the type of the pickup coil.

Furthermore, a method of minimizing the estimation error is to perform a virtual integration of a value obtained by linearly integrating a vector potential generated by an estimated magnetic field generation source in a micro element on each pickup coil arranged at each measurement point along the pickup coil. The measured value is compared with the actual measured value.

[Action]

According to the method of the present invention as described above, when calculating the magnetic field distribution near the surface of the living body from the virtual estimated magnetic field source inside the living body, the pickup coil used for measurement is more accurate as the magnetic field to be detected. Therefore, the accuracy of estimating the coordinates of the magnetic field source and the current vector by comparing the virtual measurement value and the actual measurement value can be improved.

〔Example〕

FIG. 1 shows a coordinate system for measuring the magnetic field distribution on the brain surface. In FIG. 1, 1 represents a magnetometer and 2 represents a pickup coil. Usually, this pickup coil detects the normal component of the magnetic field. 3 indicates a measurement point. This measurement point
r _m {m = 1, 2,..., M}, the position of the n-th dipole is r _n {n = 1, 2,..., N}, and the current vector is represented by q _n . When the estimated values of the dipole position and the current vector are represented by _{n 1} and _n , the optimum estimated value is obtained by the following procedure.

x _1, x _2, ..., the function E (x _1, x _2, ..., x _N) of the variables x _N gives the minimum value and the minimum value of {x _1, x _2, ..., x _N} value of Is called optimization. In particular, E (x ₁ , x ₂ , ..., x _N ) is ｛x ₁ , x ₂ ,
.., X _N } is called nonlinear optimization if it is nonlinear.
Conventionally, various methods have been proposed for nonlinear optimization, and the present invention can be applied to current dipole estimation using these nonlinear optimization techniques.

However, many nonlinear optimization methods have a disadvantage that when the function E has a local minimum, the solution is trapped at a local minimum, and the true minimum of the function E cannot be obtained. On the other hand, an optimization technique called simulated annealing recently proposed can overcome this drawback.
Thus, the present embodiment uses simulated annealing as a method for estimating a current dipole in the brain.

First, explaining the summed-up annealing, a function E (x ₁ , x ₂ ,..., X _N ) to be minimized is called a cost function. The goal is a variable ｛x ₁ , which minimizes E (x ₁ , x ₂ , ..., x _N )
x ₂ , ..., x _N ｝. First, one variable x _i
Gives the displacement [Delta] x _{i to, E (x 1, x 2} , ..., x N) to calculate the change ΔE in. If ΔE <0 replace the Δx _i to x _i + _{Δx i,}
When the ΔE> 0 according to the Boltzmann distribution exp (-ΔE / T), the probability to replace the x _i and x _i + Δx _i. The reason why the displacement in the direction of increasing the cost function is stochastically accepted is to prevent the solution from trapping at a local minimum. Here, T is a multiplier that determines scaling, and is called a virtual temperature.

As described above, applying the displacement to the parameters {x ₁ , x ₂ ,..., X _N } and changing the parameter values according to the above rule is repeated for all the parameters until the state of thermal equilibrium is reached. . Here, the thermal equilibrium state refers to a state in which the probability of accepting a change that increases the cost function is equal to the probability of accepting a change that decreases the cost function. After reaching the thermal equilibrium state, T is further reduced slightly according to a predetermined formula, and the above process is repeated at T.

Using the above-described simulated annealign, the current distribution in the brain is estimated as follows from the measured value of the magnetic field on the surface of the brain in the present embodiment.

The coordinate system is defined as shown in FIG. In this coordinate system, assume that _{r n {n = 1,2,3, ...} N} is the current vector q _n exists called current dipole at each position.

On the other hand, the SQUID located at the measurement point r _m (m = 1,2,…, M)
The method of calculating a virtual measurement value for estimating the current distribution differs depending on the type of pickup coil of the magnetometer, and thus each type of pickup coil will be described below.

FIG. 2 shows an example of a pickup coil of the magnetometer.
This pickup coil 2-1 does not have a differential configuration. The area of the pickup coil S, and the area segment and Delta] s, when N in the pickup coil 2-1 is located at the position r _m, the magnetic flux density B _m of the pickup coil 2-1 is observed Is represented by Therefore, when using such a coil, virtual measurement data calculated from the estimated current dipole
_m And the cost function to be minimized in order to find the optimal estimated current dipole in the nonlinear optimization method described above And R _mi in equation (5) is an arbitrary point in the pickup coil disposed in a position of r _m. That is, the calculation of the virtual measurement value _m of the pickup coil arranged at each measurement point r _m (m = 1, 2,..., M) is performed by calculating a plurality of points r _mi (i = 1 , 2, ..., carried out by taking the average of the values of the normal component to the coil surface of the magnetic field assumed estimated magnetic source make ^{_{▲ B a m ▼ (r mi}} ) in I). Calculation of ^{_{▲ B a m ▼ (r mi}} ) shall be indicated by the following equation.

Next, a case where a SQUID magnetometer having another type of pickup coil is used for measurement will be described with reference to FIG.

As shown in FIG. 3, the pickup coil 2-2 of the present embodiment is an axial primary differential coil, that is, a primary differential coil. At this time, virtual measurement data _m calculated from the estimated current dipole is Then, an optimum estimated current dipole that minimizes the coil function shown in Expression (6) is obtained. In the formula (8), r _mi and r _mj indicate arbitrary points in the coils 2a and 2b constituting the pickup coil 2, respectively. That is, when the axial primary differential coil is used, the coil 2a closer to the living body is used.
From the average value of the normal component of the magnetic field generated by the estimated magnetic field generation source at a plurality of points _rmi in the differential coil 2b farther from the living body
Virtual values obtained by subtracting the average value of the normal component of the magnetic field generated by the estimated magnetic field source at multiple points r _mj in
_m . ▲ B ^a _m ▼ formulas for calculating the (r _mj) is omitted so the description (7) a formula the same form.

FIG. 4 shows still another pickup coil, and this pickup coil 2-3 is a planar primary differential coil. Also in this case, since the other coil 2b is differentially connected to the one coil 2a, the average value of the calculated values of the normal component of the magnetic field at a plurality of points in the coil 2a is calculated by using the equation (8). A virtual measurement value _m is obtained by subtracting the average value of the calculated values of the magnetic field normal components at a plurality of points in the coil 2b.

FIG. 5 shows the case of another pickup coil. The pickup coil 2-4 is of a secondary differential type, that is, a secondary differential type. At this time, _m is Then, an optimum estimated current dipole that minimizes the cost function shown in Expression (6) is obtained. R _mi , r _mj , in equation (9)
And _rmk denote arbitrary points in the coils 2a, 2b and 2c constituting the pickup coil 2, respectively. That is, in accordance with the principle of operation of the axial type secondary differential coil, the average value of the calculated values of the magnetic field normal components at a plurality of points in the coil closest to the living body,
From the sum of the average of the calculated values of the magnetic field normal components at multiple points in the coil farthest from the living body and twice the average of the calculated values of the magnetic field normal components at multiple points in the middle coil The value is assumed to be a virtual measurement value _m .

In the above description of FIGS. 3, 4 and 5, for each unit coil constituting the differential coil, the difference is calculated after calculating the average value of the magnetic field normal component at a plurality of points in the unit coil. However, in the case of such a differential coil, it is also possible to calculate a magnetic field normal component at least at one point at the center of each unit coil and take the respective differences as described above to obtain a more accurate virtual And a highly accurate measurement of the magnetic field source can be achieved.

Another embodiment of the present invention will be described with reference to FIG.
The pickup coil 2-1 does not have a differential configuration as in FIG. The line elements on the coil is d, the vector potential in the position of d caused by the estimated current dipole q _n and A _n. In this embodiment, virtual measurement data _m calculated from the estimated current dipole is Then, an optimum estimated current dipole that minimizes the cost function shown in Expression (6) is obtained. That is, the vector potential of the magnetic field generated by the estimated magnetic field generation source in the minute element on the pickup coil is linearly integrated along the pickup coil to be _m .

Another embodiment of the present invention will be described with reference to FIG.
Pickup coil 2-2 is the line elements on the coil 2a constituting the pickup coil 2 is an axial-type first-order differential coil d _a, the line elements on the coil 2b and d _b, d _a and generated by a current dipole q _n the vector potential in the position of d _b, respectively a _an,, and a _bn. In this embodiment, virtual measurement data _m calculated from the estimated current dipole Then, an optimum estimated current dipole that minimizes the cost function shown in Expression (6) is obtained. It should be noted that the configuration of the pickup coil is a planar primary differential coil 2-2 as shown in FIG.
In the case of 3, _m is calculated using equation (11), and equation (6) is obtained.
An optimal estimated current dipole that minimizes the cost function shown in (1) is obtained.

When the pickup coil is the axial type secondary differential coil 2-4 as shown in FIG. 9, the line element on the coil 2a constituting the pickup coil 2-4 is d _a ,
Line elements on 2b and d _b, the line elements on the coil 2c and d _c, current dipole q _n caused by d _a, d _b and d _c, respectively A _an, a vector potential in the position of, A _bn, and A _cn I do. At this time, in this embodiment, _m
To Then, an optimum estimated current dipole that minimizes the cost function shown in Expression (6) is obtained.

〔The invention's effect〕

According to the present invention, the measurement data and the magnetic field distribution obtained from the current dipole estimated in the nonlinear optimization method can be matched with high accuracy, so that the accuracy of the estimated value of the position and size of the current dipole is improved. effective.

BRIEF DESCRIPTION OF THE DRAWINGS FIG. 1 is a view showing a coordinate system in biomagnetic field measurement, and FIGS. 2 to 9 are pickup coils in different embodiments of the present invention and calculation of a magnetic field measured by the coils. It is a figure showing a method. Explanation of reference numerals 1 ... magnetic flux meter, 2 ... pickup coil, 2a, 2b, 2c ...
… Coil constituting differential pickup coil, 3 ……
Measurement point.

Claims (8)

(57) [Claims] An SQUID magnetometer including a pickup coil detects a normal component of a biomagnetic field detected at each of a plurality of fixed points on the surface of a living body and a magnetic field generated by an estimated magnetic field generating source in the living body at each of the measurement points. In the signal processing method in the magnetic field measurement to obtain the estimated value of the coordinates of the estimated magnetic field source and the current vector so as to minimize the cost function representing the degree of coincidence with the virtual measurement value that is the normal component, A signal in magnetic field measurement, wherein an average value of normal components of a magnetic field generated by the estimated magnetic field generation source at a plurality of points in the pickup coil arranged at each measurement point is used as the virtual measurement value. Processing method. 2. The pickup coil is an axial primary differential coil having a first coil closer to the surface of the living body and a second coil farther from the surface of the living body. A value obtained by subtracting the average value of the normal component of the magnetic field generated by the estimated magnetic field source at a plurality of points in the second coil from the average value of the normal component of the magnetic field generated by the estimated magnetic field source at a plurality of points. The signal processing method in the magnetic field measurement according to claim 1, wherein? 3. The pickup coil is located between the first coil closest to the living body surface, the second coil farthest from the living body surface, and between the first coil and the second coil. An axial second derivative coil having a third coil, an average value of a normal component of a magnetic field generated by the estimated magnetic field source at a plurality of points in the first coil, and a plurality of points in the second coil. From the sum of the point and the average value of the normal component of the magnetic field generated by the estimated magnetic field source, the average value of the average value of the normal component of the magnetic field generated by the estimated magnetic field source at a plurality of points in the third coil is calculated.
2. The signal processing method in magnetic field measurement according to claim 1, wherein a value obtained by subtracting the value is used as the virtual measurement value. 4. The pickup coil is a planar primary differential coil having a first coil and a second coil, and a normal of a magnetic field generated by the estimated magnetic field generation source at a plurality of points in the first coil. A value obtained by subtracting the average value of the normal component of the magnetic field generated by the estimated magnetic field source from a plurality of points in the second coil from the average value of the components is defined as the virtual measurement value. A signal processing method in magnetic field measurement according to claim 1. 5. A normal component of a biomagnetic field detected at each of a plurality of measurement points on a surface of a living body by a SQUID magnetometer including a pickup coil, and a magnetic field generated by an estimated magnetic field generation source in the living body at each of the measurement points. In the signal processing method in the magnetic field measurement to obtain the estimated value of the coordinates of the estimated magnetic field source and the current vector so as to minimize the cost function representing the degree of coincidence with the virtual measurement value that is the normal component, A value obtained by linearly integrating the vector potential of the magnetic field generated by the estimated magnetic field generation source along the pickup coil at the position of the minute element on the pickup coil arranged at each measurement point as the virtual measurement value. Characteristic signal processing method in magnetic field measurement. 6. The primary coil according to claim 1, wherein the pickup coil is an axial primary differential coil having a first coil closer to the surface of the living body and a second coil farther from the surface of the living body. The vector potential of the magnetic field generated by the estimated magnetic field source at the position of the microelement is linearly integrated along the first coil, and the value of the magnetic field generated by the estimated magnetic field source at the position of the microelement on the second coil is calculated. The signal processing method according to claim 5, wherein a value obtained by subtracting a value obtained by linearly integrating the vector potential along the second coil is set as the virtual measurement value. 7. The pickup coil is located between the first coil closest to the living body surface, the second coil farthest from the living body surface, and between the first coil and the second coil. A second derivative coil having a third coil and a value obtained by linearly integrating a vector potential of a magnetic field generated by the estimated magnetic field generation source at a position of a microelement on the first coil along the first coil; The position of the microelement on the third coil from the sum of the vector potential of the magnetic field generated by the estimated magnetic field source at the position of the microelement on the second coil and the value obtained by linearly integrating the vector potential along the second coil. The value obtained by subtracting a value obtained by linearly integrating a vector potential of a magnetic field generated by the estimated magnetic field generation source along the third coil in step 5, wherein the value is set as the virtual measurement value. The signal processing technique in field measurement of loading. 8. The pickup coil is a planar primary differential coil having a first coil and a second coil, and a vector of a magnetic field generated by the estimated magnetic field generation source at a position of a minute element on the first coil. From the value obtained by linearly integrating the potential along the first coil, a value obtained by linearly integrating the vector potential of the magnetic field generated by the estimated magnetic field generation source at the position of the minute element on the second coil along the second coil is given by The signal processing method in magnetic field measurement according to claim 5, wherein the subtracted value is used as the virtual measurement value.