JPH03280934A - Estimating system for magnetic field-generarting source - Google Patents

Abstract

(57) [Summary] This bulletin contains application data before electronic filing, so abstract data is not recorded.

Description

[Detailed description of the invention] [Industrial application field]

The present invention relates to a method for estimating the source of a magnetic field, and in particular, a method for estimating the source of a brain magnetic field, that is, the active site of the cranial nervous system.

[Conventional technology]

In order to elucidate the functions of the nervous system and muscle fiber system of living things, it is effective to investigate the magnetic fields generated by these systems. The fundamental problem with this method is how to accurately estimate the source of the magnetic field. The generation of brain magnetic fields is caused by active currents in the cranial nervous system, and it is known that a distinct magnetic field is generated when cranial nerve bundles that are relatively aligned in direction are simultaneously excited. Moreover, as a model of the above-mentioned magnetic field generation source, a current dipole model in which a current flows through a conductor is most often adopted. Conventional current dipole estimation methods are divided into those that assume a single current dipole and those that assume a plurality of current dipoles. Among the methods for estimating a single current dipole, the most basic and long-used method is to estimate the current dipole when the distance between the maximum and minimum magnetic field strength points is Δ, and the current dipole is located at the measurement surface. If it is parallel to , it is the depth Δ/J between the two points
It is estimated that it is located at No. 2. By extending this to a current dipole in any direction, we create a model with the position 2 strength and direction of the current dipole as parameters.
Some methods determine parameters to minimize the squared error between the magnetic field on the model and the measured magnetic field. This method can also be extended to current dipole estimation when there are multiple sources. On the other hand, methods for estimating multiple current dipoles include algebraic reconstruction method, Fourier transform method, maximum end

[There is a P method 0
In the algebraic reconstruction method, the correction amount of the current X-pole distribution is derived from the difference between the estimated magnetic field and the measured magnetic field of each current X-pole distribution, and this is added to each current dipole distribution to solve iteratively. That's what I do. The Fourier transform method assumes that the current dipole and the measurement angle are in parallel planes, performs Fourier transform on the Maskra-Elk equation, obtains a linear equation related to the current and the magnetic field, and solves the linear equation. Furthermore, the maximum entropy method uses as a solution the one with the least information structure among the stagnation distributions of current dipoles. Regarding the above situation, see IE Transactions on Biomedical Engineering, B.M.E. 34, 9 (1987), pp. 713 to 723 (IE E E, Trans.
, on Biomedical Engineer
ing, BME-34, 9 (1987) pp713-
723). [Problem to be Solved by the Invention 1] However, the conventional method described above has the following problems. For example, in the brain, many nervous systems are active at the same time, so it is desirable to be able to estimate a plurality of magnetic fields at different positions, except for applications such as epilepsy where the magnetic field source is highly localized. The method of estimating the magnetic field source based on the minimum square error condition between the model magnetic field and the actually measured magnetic field can be expanded to cases where there are multiple sources, but it requires a large amount of calculation to solve the nonlinear equation obtained during estimation. The disadvantage is that the amount of magnetic field increases dramatically compared to the case of a single magnetic field source. The algebraic reconstruction method has the disadvantage that it is strongly influenced by noise contained in the measured magnetic field and has extremely poor convergence. Furthermore, the Fourier transform method has the problem that the positional relationship between the current dipole and the measurement surface is limited, and the maximum entropy method also raises questions about whether the principle of minimum information structure really holds true in brain nerve activity. In this way, conventional methods can only make estimates that are insufficient to explain the actual nervous system, and on the other hand, when trying to estimate multiple sources like the actual nervous system, the amount of calculation increases and convergence increases. There is a problem that deterioration of An object of the present invention is to provide a method for efficiently estimating the distribution of one or more sources of brain magnetic fields based on measurement results of brain magnetic field distribution without increasing the amount of calculation. [Means for Solving the Problems] In order to achieve the above object, the present invention provides information on the distribution of brain magnetic fields obtained by measuring at a finite number of locations. The brain magnetic field can be generated by setting the neuron coupling coefficient of the network and by correlating the state of the neurons when the change in the energy function of the neural network reaches an extreme value or takes a predetermined transition with the distribution of the magnetic field source. The feature is that the source is estimated.

[Effect]

According to the present invention, for example, by setting a coupling coefficient easily calculated from the brain magnetic field distribution to neurons of a Hopfield type neural network, from short-term changes in the spontaneous energy function of the neural network, It becomes possible to associate the state of neurons with the distribution estimation of magnetic field generation sources.

[Explanation of principle]

First, the basic principle of the present invention will be explained. Currently proposed engineering models of neural networks are classified into interconnected models and hierarchical models depending on the connection form of neurons. The mutually connected model is a circuit in which all neurons can be mutually connected on one plane, and is also called a Hopfield circuit. On the other hand, the hierarchical model creates synaptic connections between the eyebrows and allows information to be transmitted between layers. In the case of Hopfield circuits, it is known that the computational principle of interconnected neural networks is one method for solving optimization problems, and the basic principle of the present invention is also based on this. That is, when focusing on the energy function that represents the characteristics of the entire circuit system of the neural network, each neuron has the property of spontaneously changing its state so as to always minimize the energy function. Therefore, an optimization problem whose objective function can be expressed in the same quadratic form as the energy function of the neural network can be programmed on the neural network using the energy minimization principle. In this case, the energy function of the network must correspond to the objective function and constraints to be minimized, and the states of neurons must correspond to variables. If the distribution of n current dipoles in the brain is represented by a vector Q, and the magnetic field distribution of m measurement points is represented by a vector B, by discretizing the Biot-Savoir equation, it can be expressed as WQ=B... (1) Ru. Here, W is a constant (array of functions) determined by the measurement point and the position of the current dipole. If the estimate of the current dipole distribution is Q', then the estimated magnetic field distribution B obtained from Q' is
' becomes WQ'. Therefore. If we choose the square of the difference between the measured magnetic field and the estimated magnetic field as the objective function E, we get
E is E=1/2・IB-B' 12=1/2・IIB-WQII2...(2) =1/2-Wv/rQQ"-BWQ+1/2-BBT・
...(3) becomes. Here, BB" is a value unrelated to the estimation method, so if it is omitted, E=1/2・WW"QQ"-BWQ (4) The energy form of the neural network is the state of the neuron as v
l, the synaptic load is TIJ, and the bias signal of the neuron is E, then E= 1/2 ・X: TIJVIVJ−ΣItV+・
...(5) Represented by: Comparing Equation (4) and Equation (5) above, it can be seen that it is sufficient to make the current dipole distribution correspond to the neuron distribution. In other words, a current dipole is located at each coordinate point in the space where a current dipole may exist, the presence or absence of neuron firing corresponds to the presence or absence of a current dipole, and each dimension is used to represent the direction of the current dipole. Assign a neuron to each component. Also. The magnitude of the current dipole is expressed by the number of excited neurons. The state variable V of the neuron varies from 0 to 1 depending on the degree of excitement.
If the input to the i-th neuron at time t is U+(t), then the following relationship holds true. dUt(t)/dt=XTtjVJ+It
-(6) Furthermore, the state Vi(t) taken by the i-th neuron in response to the above input is as follows: Vt(t)=g[U□(t)] (7). Here g is a sigmoid function. When T i i = T Ji, the energy minimization principle is established in which the neural network spontaneously lowers the energy. By comparing the energy expressions of both, the correspondence between T and engineering is determined. If we add AaΣ (1-2Vi)2 to the energy function so that the neuron will eventually take either 1 or 0. E=1/2・ΣTIJV1■4-ΣI IV 5-Aa
Σ(12Vz)2 (8) From the above, the following relational expression can be obtained. T m J knee ΣWkIWkj (9) T eye=-ΣWh+” +4 A a (10) In”ΣB hWkI2 A a ・=
(11) Therefore, by setting the neuron coupling coefficient using equations (9) to (11) and changing the state of the neuron using equations (6) and (7), the energy function of equation (8) becomes the minimum. By determining the state of neurons,
Current dipole distribution can be estimated. A Boltzmann machine is known as a stochastic version of the operation of Equation 1 (6). Although this method requires more calculation time than the Hopfield neural network, it is expected to provide higher estimation accuracy. As described above, the present invention has been explained using an example in which the neural activity factor of the brain is represented by a current dipole.2 The present invention also applies to the activities of other living organs such as the heart and muscles, and magnetic field generation phenomena other than living bodies. It can also be applied to estimating the source of magnetic fields generated by chemical currents caused by metal corrosion.

【Example】

Embodiments of the present invention will be described below with reference to the drawings. FIG. 1 shows an example of a system for carrying out the method of the invention. Reference numeral 40 denotes a neuron circuit section consisting of a plurality of neurons 41 corresponding to lattice points in a space in which a dipole can exist, and each neuron 41 is made of an amplifier having a sigmoid characteristic shown in equation (7). The coupling coefficients of the neuron 41 are generated by a coupling matrix 42. The outputs B1 to Bn of the magnetic field measuring device 43 are read into the data holding device 44, and the value of the neuron bias signal is determined by processing these input data in the bias signal determining circuit 45. Each part of the above device is controlled by a timing signal T and a reset signal R1 output from a timing controller 46. First, the state of the n neurons 41 is reset to a specific value by the reset signal R1.
Set the observation signal from. As a result, the bias signal processing, ~ processing, and coupling coefficient of each neuron are determined, and the two neurons spontaneously minimize their energy. The outputs V~vn of each neuron are led to a coupling matrix 42 and an output device 47. When the energy of each neuron is sufficiently reduced, the timing signal T2 is output and the output of each neuron is output! Take it out to 47. As a result, a distribution of sources corresponding to the magnetic field measurement pattern can be obtained. FIG. 2 shows an example of the configuration of the coupling matrix 42. As shown in FIG. ■
1 to vn are the output feedbacks of the neuron 41, signal engineering, ~ engineering. is the output of the bias signal determining circuit. These signals (Vt and r+) form a matrix, each grid point being coupled by a resistor. For example, 工, and V
The lattice points of J are connected by a resistor having a resistance value T I J. The coupling resistance value of each lattice point is expressed by formulas (9) and (10)
corresponds to FIG. 3 is a diagram showing one embodiment of the bias determining circuit 45, and particularly shows the configuration of a circuit section 45-1 that determines the i-th bias signal generator 1. Data holding device output B
B to B are input to multipliers 61-1 to 61-n, multiplied by constants Wzit to Wfil, respectively, and then input to the first adder 62. The first adder 6
The output value of 2 (total sum of multiplication values) is input to the second adder 63 and added to a constant (-2Aa). The signal thus obtained has a value corresponding to equation (11). Next, with reference to FIGS. 4 to 7, the effects of magnetic field estimation according to the present invention using the aforementioned Hopfield neural network will be explained using computer simulation results for simple examples. In actual applications, the magnetic field generation surface and the M measurement surface are non-planar, but here the IR measurement surface 10 of the magnetic field is a plane divided into areas like a mesh, and the I2 measurement point is at each mesh point. shall be taken as a thing. Also, current dipole (dipole)
The position where D can exist is assumed to be a mesh point on the plane 11 that is a distance 1 d away from the fR measurement surface 10, and to simplify the explanation, the components of each dipole consist of only x and y components. 2 equations are zero, and the intensity of each component of X+3' is l or 0
Assume that In this case, the observed amount B for the unknown Q is 1/2 from equation (1), but Q is normalized to 1 or O. Assuming that all dipoles in the neural network take the initial state of 0, when d = 2, the estimation method according to the present invention can calculate the positions of up to four parallel dipoles within an error range of 1 mesh. I was able to estimate correctly. FIG. 5 shows the positions of the four parallel dipoles D1 to D4 used in the computer simulation and the intensity distribution of the magnetic field generated by these parallel dipoles. This corresponds to the magnetic field observed at observation plane 10 in Fig. 4, and is
This corresponds to the input of the magnetic field measuring device 43 in the figure. FIG. 6 shows the relationship between the value E of energy trapped in the neural network and the number N of calculations (learning) repeated to minimize the energy. In this example, the energy almost reaches its minimum value at N=4,
After that, it can be seen that even if the number of repetitions increases, the change in energy is small. FIG. 7(B) shows the positions of the signal sources D1' to D4' whose positions are estimated from the observed magnetic field when N=7. Figure 7 (
B) shows the probability of the existence of a signal source (current dipole) on the dipole existence surface 11 of FIG. 4 using contour lines, which is expressed three-dimensionally as shown in FIG. 7(A). Comparing Figure 7 (B) with Figure 5, the positions of the three dipoles other than D1 (Dz~D4) can be estimated correctly, and D□ is also estimated with a position error within 1 mesh. I understand that. In the above example, the directions of the dipoles are parallel to each other, but according to the present invention, when two orthogonal dipoles whose directions of generated magnetic fields are orthogonal to each other are separated by 3V/2 mesh or more , we were able to correctly estimate the positions of these dipoles from the observed magnetic fields. In the above estimation, if the initial value of the dipole is O<Q≦1, each dipole is estimated at multiple positions, but the variation range is narrow, and practical estimation results can be obtained by adopting the center of gravity position, for example. be able to. Note that when observing the magnetic field generated by a dipole located at a deep position, the degree of adverse conditions increases and the estimation accuracy deteriorates. For example, when d=4, the plurality of dipoles that could be identified when d=2 are estimated as one dipole having the magnetic field of their combined vector.

【Effect of the invention】

As explained above, according to the present invention, the solution is obtained from spontaneous energy changes using the massively parallel operation of the neural network, so the calculation time is more than an order of magnitude faster than the conventional method. In addition, the positions, sizes, and directions of multiple magnetic field sources can be identified with high accuracy.

[Brief explanation of drawings]

FIG. 1 is a diagram showing one embodiment of an estimation system implementing the present invention, FIG. 2 is a diagram showing details of the coupling matrix 42 in FIG. 1, and FIG. 3 is a diagram showing the main components of the bias signal determination circuit 45 in the first embodiment. Figures 4 to 7 (A), (B
) is a diagram for explaining computer simulation results of the method of the present invention. 41...Neuron, 42...Connection matrix,
43... Magnetic field measuring device, 45... Bias determination circuit.

Claims (1)

[Claims] 1. When the magnetic field distribution is measured at a finite number of points, the coupling coefficients of the neurons in the neural network are set from the results, and the energy function of the neural network is spontaneously changed to take the extreme value. , a magnetic field source estimation method characterized in that the distribution of the source of the brain magnetic field is estimated as the distribution of current dipoles from the state taken by the neuron.