JPH05220124A - Biomagnetism measuring instrument - Google Patents

Abstract

PURPOSE:To determine the distribution of a current source with good accuracy with a relatively small number of pickup coils with the biomagnetism measuring instrument which measures the magnetic field generated from the inside of a living body by using a high-sensitive magnetic field sensor. CONSTITUTION:A current dipole estimating grid 2 to be placed in a scanning region 1 is constituted by providing a means for scanning this grid over an arbitrary region in the scanning region 1 at the time of calculating the intensity of the respective current sources on the grid points from the intensity of measured magnetic fields on assumption that the current sources are distributed on the virtual grid points placed in the scanning region 1 and obtaining the solution to minimize the difference between the magnetic fields based on the calculated values and the measured magnetic fields.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention, in a biomagnetism measuring apparatus for measuring a magnetic field generated in a living body using a highly sensitive magnetic field sensor, estimates the position of an active region in the living body which is a source of the magnetic field. For technology.

With the recent development of superconducting device technology,
SQUID (Superconducting QUantum Interference
A biomagnetic measuring device using a highly sensitive magnetic field sensor called Devices) is being put to practical use as one of medical diagnostic devices. The electric phenomenon occurring in the living body simultaneously generates a weak magnetic field. The device for measuring the weak magnetic field distribution is expected to be useful for diagnosing a diseased part.

However, in order to clarify the heart disease and the brain function, it is necessary to inversely estimate the position of the current source, which is the source of the magnetic field, from the measured magnetic field. For that purpose, it is necessary to solve the inverse problem of searching for a distribution of current dipoles in which the calculated magnetic field and the measured magnetic field are equal using a calculation model assuming a current dipole that is a short current element in a conductor. is there.

[0004]

2. Description of the Related Art A conventional biomagnetism measuring device operates according to a flow chart shown in FIG. In the drawings, reference numerals starting with the letter S indicate a processing number, and the conventional technique will be described below along with the processing number. First, as shape data, for example, a homogeneous infinite conductor is used when estimating the current source of the heart, and a homogeneous or multi-layered concentric circular conductor sphere is used when estimating the current source of the brain (S7).
0).

A virtual current dipole is set in this conductor (S71), and magnetic field calculation based on the setting is performed (S7).
2). On the other hand, the magnetic field generated by the living body is measured (S7
3), digitally convert the measurement data and import it into the computer (S74). This measurement data is compared with the calculated magnetic field (S75), and if they match (S76), the current source is displayed (S78). If they do not match, the set value is changed (S77).

The setting value of the virtual current dipole is changed so that the difference between the measured magnetic field and the calculated magnetic field becomes small. In this calculation model, the difference between the measured magnetic field and the calculated magnetic field is compared while moving one virtual current dipole. However, in this method, not only the calculation may not be converged in a finite number of times, but even if the calculation is converged, it takes a lot of time to obtain an accurate position of the current source.

Furthermore, it is difficult to accurately estimate the position of the current source because there is a possibility of falling into another solution, that is, a local minimum that produces a similar output distribution. Thus, the least-squares method of non-linear systems requires iterative operations. As a method for avoiding this, there is a method in which the current dipoles are set at a plurality of positions, the positions are fixed on the lattice points, and the problem is replaced with a linear system, which is presented in the following paper.

Brain Jeffs, Richard Leahy and Manb
ir Singh: "An Evaluation of Methods for Neuromagneti
c Image Reconstruction ", IEEE Transactions on Biomed
ical Engineering, Vol.BME-34, No.9, September 1987; Warren E. Smith, William J. Dallas, Walter H. K
ullmann and Heidi H. Schlitt: "Linear estimation t
heory applied to the reconstruction of a3-D vector
current distribution ", Applied Optics, Vol.29, N
o.5 (1990); Jukka Sarvas: "Basic mathematical and electromag
netic concepts of the biomagnetic inverse problem
m ".

Next, a method of expressing the measured magnetic field and the current intensity of the virtual current dipole by simultaneous linear equations and obtaining the least squares solution for the difference between the measured magnetic field and the calculated magnetic field will be described. In order to express the measured magnetic field picked up by the pickup coil and the current density of the virtual current dipole on each lattice point by a simultaneous linear equation, the distribution of the virtual current dipole is determined on a fixed three-dimensional lattice point.

Now, the current intensities of the n virtual current dipoles in each of the three directions are (q _1x , q _1y , q _1z ) ,.
(Q _nx , q _ny , q _nz ) and the position is (x _{1 ′} , y _{1 ′} ,
z _{1 ′} ), ..., (x _{n ′} , y _{n ′} , z _{n ′} ). Also,
The magnetic field strengths at the installation locations of the m pickup coils are (b _1x , b _1y , b _1z ), ..., (b _mx , b _my ,
b _mz ), and the position is (x ₁ , y ₁ , z ₁ ), ...,
_{(X m, y m, z} m) to.

At this time, according to the Biot-Savart law, the measurement magnetic field b is calculated by using the current intensity q of the virtual current dipole: b ₁ = a ₁₁ q ₁ + a ₁₂ q ₂ + a ₁₃ q ₃ + ... + a _1n q _n b ₂ = a ₂₁ q ₁ + a ₂₂ q ₂ + a ₂₃ q ₃ + ... + a _2n q _n ··· · · b _m = a _m1 q ₁ + a _m2 q ₂ + a _m3 q It can be expressed as ₃ + ... + a _mn q _n . However,

[0012]

[Equation 1]

[0013] Here, a column vector {q ₁ , q ₂ , ..., Q having the current intensity of the virtual current dipole as a component is used.
_{Let n} } ^T be Q. Also, let B be the column vector {b ₁ , b ₂ , ..., B _m } ^T having the measured magnetic field as a component, and let A be the coefficient matrix [a _ij ] of the simultaneous linear equations described above. At this time,
B = AQ holds.

This equation is obtained by setting the virtual current dipole setting positions (x _{1 '} , y _1' , z _{1 '} ), ..., (x _n' , y _{n '} , z _n' ).
And the installation location of the pickup coil (x ₁ , y ₁ ,
z _1), ···, a linear equation which is determined out with _{(x m, y m, z} m). By solving this equation, the density distribution Q of the virtual current dipole can be obtained. Hereinafter, how to obtain it will be described.

If the coefficient matrix A is a square matrix and its column vectors are regular matrices independent of each other,
The coefficient matrix A has an inverse matrix A ⁻¹ . Therefore, the current dipole Q can be directly solved from Q = A ^-1 B <equation 50>.

However, since the coefficient matrix A is generally not a square matrix, the inverse matrix cannot be directly obtained. That is, there is no unique solution. However, since the product of the coefficient matrix A and its transposed matrix ^AT is a square matrix, the coefficient matrix A
If the column vectors of are independent of each other, the matrix A ^T A has an inverse matrix (A ^T A) ^-1 .

At this time, according to the normal equation Q = (A ^T A) ^-1 A ^T B <equation 60>, the sum of squares of the difference between the measured value B _m and the calculated value B _c = AQ _c Σ (B _m -B _c ) We can find a least-squares solution that minimizes ² (Gil
bert Strang: LinearAlgebra and its Application
s).

Further, when the rank vector "rank (A) <n" in which the column vector of A is not independent, the inverse matrix of A ^T A does not exist. In this case, a unique solution cannot be obtained. However, in such a case, a method called singular value decomposition can be used.

An arbitrary m × n matrix A can be decomposed into A = UΛV ^T by an m × m orthogonal matrix U, an m × n diagonal matrix Λ, and an n × n orthogonal matrix V. It is possible.

[0020] Incidentally, lambda is a AA ^T and A ^T A of the eigenvalues of the square root lambda (singular value called) diagonal matrix arranged in descending order in pairs on the corner of. U is composed of eigenvectors of AA ^T, V
Is composed of the eigenvectors of A ^T A (George E, Fo
rsythe, Michael A. Macolmand Cleave B. Moler: Com
puter Methods for Mathematical Computations, Prenti
ce-Hall, New Jersey, 1978).

[0021] In this case, the supra least squares minimum norm solution Q ⁺ <expression ^{50>, Q + = VΛ +} U T B m = A + B m can be determined from the <Equation 70>.

Where Λ ⁺ is a diagonal matrix whose diagonal component is the reciprocal λ ⁺ = 1 / λ of the diagonal component λ of Λ. A ⁺ is an inverse matrix A ^-1 expanded from a square matrix of n × n to a matrix of arbitrary order of m × n, and is called a pseudo-inverse matrix (the aforementioned paper).

A method using a general inverse matrix using such a normal equation or a method using singular value decomposition assumes a plurality of current dipoles. Therefore, it is an effective method for obtaining the density distribution of a plurality of current dipoles. Once the coefficient of the inverse matrix is obtained by the normal equation or the singular value decomposition, the measured value B can be calculated from <Equation 60> and <Equation 70>.
The density distribution Q _c of the current source can be obtained only by multiplying _m by the coefficient matrix A ⁺ .

The method based on the calculation model assuming such a plurality of current dipoles is compared with the method of solving the nonlinear least squares method for estimating the position while moving one virtual current dipole as shown in FIG. , It is possible to obtain the density distribution of the current dipole at high speed.

However, in order to accurately obtain the current intensity distribution of the current dipole from the least squares solution of such simultaneous linear equations, the number m of magnetic field sensors is equal to or more than the set number n of virtual current dipoles. Must be the number of.

[0026]

Therefore, in order to estimate the position of the current dipole with an accuracy of several millimeters necessary for medical diagnosis, a huge number of pick-up coils and their magnetic field strengths must be measured. A SQUID magnetometer is required. For the above reasons, there has been a problem in the related art that it is difficult to realize a diagnostic device that displays changes in the magnetic field distribution in a living body in real time.

In view of such conventional problems, the present invention utilizes a method for obtaining a least squares solution of simultaneous linear equations by using a normal equation or a singular value decomposition method as a current source estimation method, and a comparison is made. An object of the present invention is to provide a biomagnetism measuring device having a function of accurately obtaining the distribution of a current source with a relatively small number of pickup coils and enlarging and displaying the distribution range to an arbitrary size.

[0028]

According to the present invention, the above object is achieved by means as set forth in the claims.

That is, the invention according to claim 1 uses one of a plurality of current sources existing in the living body by measuring the magnetism emitted by the living body by using a highly sensitive magnetometer having a plurality of pickup coils. It is a device that estimates the position and displays the result.Assuming that the current source is distributed on a virtual grid point placed in the measurement region, the strength of each current source on the grid point is measured and the strength of the magnetic field is measured. Calculated from the above, the biomagnetism that operates so as to output a solution that minimizes the difference between the magnetic field based on the calculated value and the measured magnetic field, and that scans the grid placed in the measurement region over an arbitrary region. It is a measuring device.

Further, in the invention of claim 2, the relation between the strength of each current source on the lattice point and the strength of the measurement magnetic field detected by each pickup coil is represented by simultaneous linear equations based on the physical law, and It is a biomagnetism measuring device provided with means for calculating the intensity distribution of a current source by solving a normal equation of a coefficient matrix.

Further, in the invention of claim 3, the relationship between the strength of each current source on the lattice point and the strength of the measurement magnetic field detected by each pickup coil is expressed by simultaneous linear equations based on the physical law, and The biomagnetism measuring device is provided with a means for performing singular value decomposition on a coefficient matrix and calculating an intensity distribution of a current source from a least square least norm solution.

Further, the invention of claim 4 comprises means for setting the cumulative number of singular values in the case of performing the singular value decomposition to obtain the least squares minimum norm solution to be small in the initial position estimation and gradually increasing. This is a biomagnetism measuring device.

The invention according to claim 5 further comprises a means for independently setting, for each grid point, the cumulative number of singular values when performing singular value decomposition to obtain a least squares minimum norm solution. It is a magnetic measuring device.

Further, the invention of claim 6 is a biomagnetism measuring device, comprising means for integrating intensity distributions of a plurality of current sources obtained by scanning a grid and reconstructing the entire intensity distribution.

Further, the invention of claim 7 comprises means for multiplying the intensity distribution of each current source by a predetermined weighting coefficient based on known medical information, and integrating the multiplication result. This is a biomagnetism measuring device.

[0036]

In the present invention, as shown in FIG. 1, the current dipole estimation grid 2 is set in a part of the scanning area 1 where the current dipole may exist.
Then, in the current dipole existence possible region, the general inverse matrix A ⁺ is obtained by normal equation or singular value decomposition while moving the current dipole estimation grid 2. Then, the general inverse matrix A ⁺ is multiplied by the measurement magnetic field B _m obtained first.

After the distribution of the current dipole at each lattice position is obtained in this way, the distribution of the current dipole Q _{c of the} entire existing possible region is reconstructed from the superposition of the distributions. By performing the estimation of the current source while moving the small grid on which a small number of current dipoles are mounted, it is possible to perform the reverse estimation with higher resolution with a relatively small number of pickup coils.

In FIG. 1, pickup coils 3 to 7
Measures the magnetic field emitted by a current dipole 9 in the region of the heart 8. In this way, in the method of expressing the relationship between the magnetic field strength and the current dipole with simultaneous linear equations and obtaining the general inverse matrix from the normal equation,
A method of further subdividing a portion having a large current dipole strength based on the initial estimated value is known in the following paper.

(YCOkada, JCHuang: "Current De
nsity Imaging as a method of visualizing neuronal a
ctivity of the brain ", Society for NeuroscienceAbs
tructs, 509.16 (1990) p1241) However, in this known example, the set point of the current dipole is increased by subdivision, so that there is a drawback that the number of pickup coils is limited during subdivision.

[0040]

FIG. 2 is a view showing an embodiment of the present invention,
The structural example of the biomagnetism measuring device in the case of estimating the position of the current source from the brain magnetic field is shown. In FIG. 2, the pickup coil 15 captures the magnetic field generated from the human head 10.
The SQUID array 16 contained in the dewar 17 converts the magnetic field signal into an electrical signal proportional to its strength. SQ
The UID chip control circuit 18 converts an analog signal into a digital signal.

The computer 19 takes in this digital signal and inversely estimates the magnetic field distribution of the human head 11. At the same time, the computer 19 obtains the image data from the MRI data image input device 21 together with the measurement data. Then, the distribution of the current dipole and the tomographic image of the human head 10 are output to the display device 20. The radio wave vector sensor 14 is used for the transmitter 1.
Receives the radio wave transmitted in 3.

FIG. 3 shows an example of a hardware configuration for obtaining the magnetic field distribution over the entire region where the current dipole can exist. In FIG. 3, each matrix multiplication circuit 31 to 34
Is multiplied by the measurement data output from the SQUID magnetometer 30 and the inverse matrix A ⁻¹ _(i) of the coefficient matrix at each scanning position.
Thus, the density distribution Q _(i) of the current dipole at each lattice position is obtained.

The multipliers 35 to 38 hold weighting coefficients that are predetermined for each grid point based on the MRI image data and medical information. When multiplying the current distribution Q _(i) by this weighting coefficient, the multipliers 35 to 38 are processed in advance so that the error due to superposition is minimized.

The adder circuit 39 distributes the data Q _(i) distributed on each grid so as to become the data of the distribution over the entire estimable region. In this way it is possible to reconstruct the whole distribution. Note that the calculation corresponding to such a circuit configuration can also be implemented by software using a computer.

FIG. 4 is a flowchart showing an example of an algorithm for inverse estimation. In FIG. 4, first, the magnetic field in the region of interest is measured (S40). Next, the region of interest is divided into small grids, and a coefficient matrix for the grids is obtained from the installation position of the magnetic field sensor and the grid setting position (S4).
1). Then, the general inverse matrix A ⁺ _(i) on each lattice is obtained by normal equation or singular value decomposition (S42).

The magnetic field distribution B measured in the process S40 is multiplied by a general inverse matrix to obtain each estimated distribution Q _{(i )} (S4 _).
3). Each of these estimated values Q _(i) is multiplied by a weighting coefficient (S44), and the multiplication result is integrated while being expanded on all grids to obtain the distribution of the entire region of interest (S45).
Finally, the distribution of the current dipole is converted into image data with a change in color and brightness, and the image data is output together with the MRI data to the display device (S46).

FIG. 5 is a diagram showing another embodiment of the present invention. In FIG. 1 described above, the current dipole estimation grid 2
Was placed on a flat surface. On the other hand, in FIG. 5, the shape of the current dipole estimation grid 51 is a three-dimensional rectangular parallelepiped. Scanning area 5 where current dipole can exist
Since 0 spreads in three dimensions, the resolution can be improved by performing position estimation with a three-dimensional distribution.

In this case, it is desired to expand the array of magnetic field sensors to a two-dimensional plane. In FIG. 5, the illustration of the pickup coil 52 is partially omitted. Actually, the pickup coil 52 is provided so as to be enlarged over the two-dimensional plane and measures the magnetic field of the entire scanning region 50.

FIG. 6 is a diagram showing another embodiment of the present invention. In FIG. 1 described above, the grid to be scanned is made smaller than the possible area, but in FIG. 6, the current dipole estimation grids 61 and 63 are roughly set in the entire possible area. By limiting the movement of the current dipole estimation grids 61 and 63 to a narrow range of the scanning ranges 60 and 62,
It is possible to perform highly accurate inverse estimation in a wide range including grids.

Further, FIGS. 2 and 3 show the case where the current dipole exists on each estimation grid. However, when reconstructing a non-lattice current dipole using all singular values Λ = {λ ₁ , λ ₂ , ..., λ _r } of the coefficient matrix A up to the rank r, The position cannot be estimated because the influence of the current dipole, which is not found in the above, becomes large.

Therefore, there is a method in which the cumulative number of singular values is manipulated to sequentially add from the largest singular value by q _i = Σλ _i v _i u _i b, and the integration is stopped when the position can be estimated to some extent. Conceivable. Although the resolution is slightly degraded by this method, a reconstructed image capable of estimating the distribution range of the current dipole can be obtained.

[0052]

As described above, according to the present invention,
It is possible to accurately estimate the position of the current source from the magnetic field generated from the living body with a relatively small number of pickup coils. Therefore, it is very useful for diagnosis of heart disease and brain disease, and it greatly contributes to improvement of the performance of the biomagnetism measuring device.

[Brief description of drawings]

FIG. 1 is a diagram illustrating the principle of the present invention.

FIG. 2 is a diagram showing an embodiment of the present invention.

FIG. 3 is a diagram illustrating a configuration example of an arithmetic circuit.

FIG. 4 is a flowchart showing an example of an algorithm for inverse estimation.

FIG. 5 is a diagram showing another embodiment of the present invention.

FIG. 6 is a diagram showing another embodiment of the present invention.

FIG. 7 is a diagram illustrating a conventional technique.

[Explanation of symbols]

 1, 50, 60, 62 Scanning area 2, 51, 61, 63 Current dipole estimation grid 3 to 7, 15, 52 Pickup coil 8 Heart 9, 12 Current dipole 11 Human head 13 Oscillator 14 Radio wave vector sensor 16 SQUID array 17 Dewar 18 SQUID chip control circuit 19 Calculator 20 Display device 21 MRI data image input device 30 SQUID magnetometer 31-34 Matrix multiplication operation circuit 35-38 Multiplier 39 Adder circuit

Claims (8)

[Claims] 1. A high-sensitivity magnetometer having a plurality of pickup coils is used to measure the magnetism emitted by a living body to estimate the position of one or a plurality of current sources existing in the living body. Is a device that displays the current source, and assumes that the current source is distributed on a virtual grid point placed in the measurement area, and operates to calculate the strength of each current source on the grid point from the strength of the measured magnetic field. A biomagnetism measuring device comprising means for scanning the grid placed in the measurement region over an arbitrary region. 2. A magnetic field based on the calculated value is calculated by calculating the strength of each current source on the grid point from the strength of the measured magnetic field, assuming that the current source is distributed on a virtual grid point placed in the measurement area. Operates to output the solution that minimizes the difference between the
The biomagnetism measuring device according to claim 1, further comprising means for scanning the grid placed in the measurement region over an arbitrary region. 3. The relationship between the strength of each current source on the grid point and the strength of the measurement magnetic field detected by each pickup coil is represented by simultaneous linear equations based on the physical law, and the normal equation of the coefficient matrix is solved. The biomagnetism measuring device according to claim 1, further comprising means for calculating the intensity distribution of the current source. 4. The relationship between the strength of each current source on the grid point and the strength of the measurement magnetic field detected by each pickup coil is represented by simultaneous linear equations based on physical laws, and the coefficient matrix is decomposed into singular values. 2. The biomagnetism measuring apparatus according to claim 1, further comprising means for calculating the intensity distribution of the current source from the least-squares least-norm solution. 5. The living body according to claim 3, further comprising means for setting the cumulative number of singular values in the case of obtaining the least squares minimum norm solution by performing singular value decomposition to be small in initial position estimation and gradually increasing. Magnetic measuring device. 6. The biomagnetic measurement according to claim 3, further comprising means for independently setting, for each grid point, the cumulative number of singular values when the least squares minimum norm solution is obtained by performing singular value decomposition. apparatus. 7. The biomagnetism measuring apparatus according to claim 1, further comprising means for integrating intensity distributions of a plurality of current sources obtained by scanning the grid to reconstruct the entire intensity distribution. 8. A means for multiplying an intensity distribution of each current source by a predetermined weighting coefficient based on known medical information, and integrating the multiplication result.
The biomagnetism measuring device described.