Method for designing coil systems for generation of magnetic fields of desired geometry, a magnetic resonance imaging or magnetoencephalography apparatus with a coil assembly and a computer program

Abstract

The present invention introduces a method, apparatus and computer program for magnetic resonance imaging or magnetoencephalography applications in order to control currents of a coil assembly (20), and thus achieving desired magnetic fields precisely in the measuring volume (21). The approach is an algebraic method where a field vector is generated for the test currents of each coil (20). Vector and matrix algebra is applied and a linear set of equations is formed. Field components and their derivatives up to the desired order can be taken into account. Principal component analysis or independent component analysis can be applied for determination of the dominant external interference components. By checking the condition value for the matrix (33, 45), it is possible to investigate whether a reasonable solution of currents for desired magnetic fields is possible to achieve. Finally, solved currents can be installed into a current supply unit (29) feeding the coils of the assembly (20). The invention can be applied as an active compensation feature for different interference shapes in the MEG application (25), or for the precise creation of the fields and gradients in the MRI application (24).

Claims

1. A method of controlling a magnetic field of a geometrically fixed coil assembly to thereby create magnetic fields of a geometrically precise shape as required in medical magnetic imaging applications around a given origin, the method comprising: decomposing a field, created around the origin by a test current in each coil of the geometrically fixed coil assembly at a time, into desired and undesired components of the field, wherein the desired components correspond to components giving rise to the geometrically precise shape and the undesired components correspond to other components, forming a system of linear equations based on the decomposed components that gives the same decomposition of the field that results from simultaneous powering of the coils of the geometrically fixed coil assembly by a set of unknown currents, determining the set of unknown currents that result in the geometrically precise shape of the fields by solving the system of linear equations, and applying the set of unknown currents to the coils of the geometrically fixed coil assembly to thereby create magnetic fields that have the geometrically precise shape, wherein the decomposition of the field of each coil is obtained from a measurement of the magnetic field distribution around the origin caused by the test current in said coil, and the desired field components comprise at least one dominant external interference component, or one or several linear combinations of the dominant external interference components, determined from a separate measurement of interference, the linear combinations of the dominant external interference components being used as feedback field shapes in an active compensation system.

2. A method according to claim 1, wherein the decomposition of the field of each coil is calculated around the origin from the geometry of the coil assembly using equations that describe behaviour of the magnetic field in vacuum.

3. A method according to claim 1, wherein the desired field components and the undesired field components are constructed from three orthogonal components of the magnetic field and their independent Cartesian derivatives.

4. A method according to claim 1, wherein the desired field components are constructed from three orthogonal components of the magnetic field and their five independent Cartesian derivatives of the first order, and the undesired field components are seven independent Cartesian derivatives of the second order.

5. A method according to claim 1, wherein the unknown current vector is calculated by a product of a Moore-Penrose pseudo-inverse of a matrix comprising the field component vectors for each of the coils with the test current, and the summed field vector of the simultaneous powered coils at the origin.

6. A method according to claim 5, wherein the method further comprises the following steps: determining a degree of singularity of the said matrix by a condition number, and in case the condition number of the said matrix exceeds a desired threshold value, thus indicating a singular or substantially singular matrix, modifying the coil assembly, and when the redetermined condition number of the said matrix is below the desired threshold value, thus indicating a non-singular matrix, and calculating the set of unknown currents.

7. A method according to claim 1, wherein the dominant external interference components used as desired field components are determined from a principal component analysis or an independent component analysis of the separate measurement of interference.

8. A method according to claim 1, wherein the linear combinations forming the feedback field shapes, and the locations and orientations of the sensors, are chosen so that the coupling between simultaneously operating feedback loops is minimized.

9. A method according to claim 1, wherein the method further comprises switching between the magnetic resonance imaging functionality creating the magnetic fields with gradients, and the magnetoencephalography device functionality performing active compensation for the environmental interference.

10. A magnetic resonance imaging or magnetoencephalography apparatus with a geometrically fixed coil assembly for controlling a magnetic field of the geometrically fixed coil assembly to thereby create magnetic fields of a geometrically precise shape as required in medical magnetic imaging applications around a given origin, comprising: a sensor array comprising plurality of sensors for measuring multi-channel data, and control means for controlling the apparatus, wherein: the control means is configured to decompose a field, created around the origin by a test current in each coil of the geometrically fixed coil assembly at a time, into desired and undesired components of the field, wherein the desired components correspond to components giving rise to the geometrically precise shape and the undesired components correspond to other components, the control means is configured to form a system of linear equations based on the decomposed components that gives the same decomposition of the field that results from simultaneous powering of the coils of the geometrically fixed coil assembly by a set of unknown currents, the control means is configured to determine the set of unknown currents that result in the geometrically precise shape of the fields by solving the system of linear equations, the control means is configured to apply the set of unknown currents to the coils of the geometrically fixed coil assembly to thereby create magnetic fields that have the geometrically precise shape, the control means is configured to obtain the decomposition of the field of each coil from a measurement of the magnetic field distribution around the origin caused by the test current in said coil, and the desired field components comprise at least one dominant external interference component, or one or several linear combinations of the dominant external interference components, determined from a separate measurement of interference, and the control means is configured to use the linear combinations of the dominant external interference components as feedback field shapes in an active compensation system.

11. An apparatus according to claim 10, wherein the control means is configured to calculate decomposition of the field of each coil around the origin from the geometry of the coil assembly using equations that describe behaviour of the magnetic field in vacuum.

12. An apparatus according to claim 10, wherein the control means is configured to construct the desired field components and the undesired field components from three orthogonal components of the magnetic field and their independent Cartesian derivatives.

13. An apparatus according to claim 10, wherein the control means is configured to construct the desired field components from three orthogonal components of the magnetic field and their five independent Cartesian derivatives of the first order, and the undesired field components are seven independent Cartesian derivatives of the second order.

14. An apparatus according to claim 10, wherein the control means is configured to calculate the unknown current vector by a product of a Moore-Penrose pseudo-inverse of a matrix comprising the field component vectors for each of the coils with the test current, and the summed field vector of the simultaneous powered coils at the origin.

15. An apparatus according to claim 14, wherein the apparatus further comprises: the control means is configured to determine a degree of singularity of the said matrix by a condition number, and in case the condition number of the said matrix exceeds a desired threshold value, thus indicating a singular or substantially singular matrix, modifying means is configured to modify the coil assembly, and when the redetermined condition number of the said matrix is below the desired threshold value, thus indicating a non-singular matrix, and the control means is configured to calculate the set of unknown currents.

16. An apparatus according to claim 10, wherein the control means is configured to determine the dominant external interference components used as desired field components from a principal component analysis or an independent component analysis of the separate measurement of interference.

17. An apparatus according to claim 10, wherein the linear combinations forming the feedback field shapes, and the locations and orientations of the sensors, are chosen so that the coupling between simultaneously operating feedback loops is minimized.

18. An apparatus according to claim 10, wherein the apparatus further comprises switching means in order to choose between the magnetic resonance imaging functionality configured to create the magnetic fields with gradients, and the magnetoencephalography device functionality configured to perform active compensation for the environmental interference.

19. A non-transitory computer readable medium containing a computer program for controlling a magnetic field of a geometrically fixed coil assembly to thereby create magnetic fields of a geometrically precise shape as required in medical magnetic imaging applications around a given origin, the computer program comprises code adapted to perform the following steps when executed on a data-processing device: decomposing a field, created around the origin by a test current in each coil of the geometrically fixed coil assembly at a time, into desired and undesired components of the field, wherein the desired components correspond to components giving rise to the geometrically precise shape and the undesired components correspond to other components, forming a system of linear equations based on the decomposed components that gives the same decomposition of the field that results from simultaneous powering of the coils of the geometrically fixed coil assembly by a set of unknown currents, determining the set of unknown currents that result in the geometrically precise shape of the fields by solving the system of linear equations, and applying the set of unknown currents to the coils of the geometrically fixed coil assembly to thereby create magnetic fields that have the geometrically precise shape, wherein the decomposition of the field of each coil is obtained from a measurement of the magnetic field distribution around the origin caused by the test current in said coil, and the desired field components comprise at least one dominant external interference component, or one or several linear combinations of the dominant external interference components, determined from a separate measurement of interference, the linear combinations of the dominant external interference components being used as feedback field shapes in an active compensation system.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) FIG. 1 discloses an example of an assembly of square shaped field generating coils around a measurement volume,

(2) FIG. 2 discloses an embodiment of the electronics arrangement controlling the currents in the coil assembly to either provide the measuring field and gradients for the MRI device or the active compensation of the environmental interference of the MEG device,

(3) FIG. 3 discloses an embodiment of the method as a flow chart of the process of the coil assembly design for the MRI application, and

(4) FIG. 4 discloses an embodiment of the method as a flow chart of the process of the coil assembly design for the active interference cancellation in MEG.

DETAILED DESCRIPTION OF THE INVENTION

(5) Reference will now be made in detail to the embodiments of the present invention.

(6) The present invention formulates a method for solving the generalized Helmholz/Maxwell design problem described in the background section. The method can be extended in a straightforward manner beyond the Helmholz and Maxwell design problems, that is, for designing coil assemblies that create magnetic fields with vanishing derivatives up to any required order. For simplicity, the derivatives are cut to second order in the examples below. However, in a situation where the coils are located close to the measured object and where very smooth and homogenous magnetic fields are desired, we might use derivatives of even higher order than two. The orders of the derivatives taken into the calculations can be chosen according to the accuracy requirements in the used application. Of course, the greater amount of the derivatives taken into account increases the complexity of the calculations (the dimensions of the vectors and matrices), but the main principle of the algebraic operations remain the same.

(7) Three different conditions in which the method can be applied, for instance, are described in the following. The design conditions are presented in the order of increasing complexity.

(8) First we describe the first condition where the method according to the invention can be applied.

(9) In this simplest case the coil assembly is located in an environment that contains no magnetic materials, and the goal is to generate, at a given point inside the coil assembly (the origin), strictly uniform fields in the three Cartesian directions (B.sub.x, B.sub.y, B.sub.z), and constant first derivatives of these three components.

(10) In a volume that is free of magnetic sources (magnetic materials or electric currents) the divergence and curl of magnetic field are zero. Therefore, out of the nine possible first derivatives (dB.sub.x/dx, dB.sub.x/dy, dB.sub.x/dz, dB.sub.y/dx, dB.sub.y/dy, dB.sub.y/dz, dB.sub.z/dx, dB.sub.z/dy, dB.sub.zz/dz) only five are independent, for example dB.sub.x/dx, dB.sub.x/dy, dB.sub.x/dz, dB.sub.y/dy, and dB.sub.y/dz. Similarly, for a divergence and curl free vector field in three dimensional space, out of the 27 second derivatives only seven are independent, for example d.sup.2B.sub.x/dx.sup.2, d.sup.2B.sub.x/dxdy, d.sup.2B.sub.x/dxdz, d.sup.2B.sub.y/dxdy, d.sup.2B.sub.x/dx.sup.2, d.sup.2B.sub.y/dy.sup.2, d.sup.2B.sub.y/dydz and d.sup.2B.sub.x/dydz.

(11) A set of n.sub.c coils is specified and the three magnetic field components, the five first derivatives, and the seven second derivatives of the fields arising from the current running in each one of the coils are calculated at the origin. In an environment free of magnetic materials this can be done by using simple, well known mathematical expressions. In this way for each of the n.sub.c coils a field-vector, B.sub.c, is obtained with fifteen components, which are B.sub.x, B.sub.y, B.sub.z, dB.sub.x/dx, dB.sub.x/dy, dB.sub.x/dz, dB.sub.y/dy, dB.sub.y/dz, d.sup.2B.sub.x/dx.sup.2, d.sup.2B/dxdy, d.sup.2B.sub.x/dxdz, d.sup.2B.sub.y/dxdy, d.sup.2B.sub.y/dx.sup.2, d.sup.2B.sub.y/dy.sup.2, d.sup.2B.sub.y/dydz, and d.sup.2B.sub.x/dydz.

(12) Using these n.sub.c field-vectors as column vectors, a 15n.sub.c matrix M is formed. If the n.sub.c coils are simultaneously powered with currents I.sub.1, I.sub.2, . . . I.sub.nc, the resulting field vector for the whole assembly, at the origin, is given by the matrix equation
B=MI(1)

(13) where I is a column vector with components I.sub.1, I.sub.2, . . . I.sub.nc, which are the currents in the individual coils. Thus, the current vector needed to create any field vector B is obtained from the equation
I=inv(M)B.(2)

(14) Here inv (M) is inverse matrix of M if the number of coils is the same as the number of components in the field vector B, 15 in this example. If the number of coils is smaller or larger than the number of components in the field vector, then inv (M) is the Moore-Penrose pseudo-inverse of M.

(15) For example, the currents needed in the coils of the assembly to create a uniform field of one Tesla in the x-direction, B.sub.x, are obtained from equation (2) by using the column vector B=[1, 0, 0, . . . 0]. The field generated by the resulting I-vector is in the x-direction, that is B.sub.y, B.sub.z=0. In addition, all of its first, and second order derivatives are zero at the origin. It should be noted that the field derivatives up to second order vanish in the origin only because they are included the model (B.sub.c-vector) for each coil. Derivatives left out from the B.sub.c-vectors are not controlled in the algorithm defined by equations (1) and (2).

(16) The only design problem left after equation (2) is that the overall geometry of the coil assembly must be so chosen that the matrix M is not singular, and thus inv (M) exists. This is not difficult because M is strictly singular only for highly symmetric assemblies. From practical point of view it also matters how close to singular M is. If M is close to singular, creation of some field components or their derivatives may require very high currents in some of the coils. Therefore, the condition number of matrix M, which is a measure of how close to singular M is, is a good measure of the quality of geometric design of the coil assembly also. In case we have a coil assembly located e.g. on a single plane or in otherwise symmetrical mutual locations, it usually occurs that at least one of the resulting currents in the compensating coil assembly needs to be notably high in order to work properly. This is not feasible or economical. Therefore, a good measure for indicating this kind of behaviour is the condition number which in that uneconomical case would be big (e.g. over 100). In order to minimize the condition number, we must relocate the coil assembly e.g. in a less symmetrical fashion, and then we will achieve an optimal coil assembly where with relatively small currents it is possible to accomplish a well-functioning system for creation of smooth measuring field in MRI or effective active compensation in MEG.

(17) The cases where the number of coils in the assembly is 1) equal to, 2) larger than, or 3) smaller than the number of components in the field vector B differ in principle from, each other.

(18) Case 1) is the simplest. Here the number of coils (available degrees of freedom) is the same as the number of quantities to control (the three field components and their 5+7 independent derivatives at the origin). In this case M is a 1515 square matrix and equation (2) has a unique solution. The current vector I needed to create a uniform field in the z-direction, B.sub.z, for example, is obtained from equation (2) by using the column vector B={0, 0, 1, 0, . . . , 0}. The resulting field is precisely (with numerical accuracy) along the z-axis and all its derivatives up to the second derivatives vanish at the origin.

(19) In case 2) the system defined by equation (1) is underdetermined. The number of coils is larger than the number of quantities to be controlled. In this case equation (1) has an infinite number of solutions I. The solution given by the Moore-Penrose pseudo-inverse is the one that has the smallest Euclidian norm, that is, the smallest length of the vector I. In this case another optimal solution I can also be chosen: the shortest vector I among those solutions that have nonzero currents only in 15 of the n.sub.c coils. This is a way to find out which ones of the n.sub.c coils are least useful for creation of the uniform fields and constant first derivatives, and could possibly be left out from the assembly. This latter solution usually requires higher maximal currents than the Moore-Penrose pseudo-inverse solution.

(20) In the overdetermined case 3) an exact solution I for equation (1) does not exist. Here the number of the available degrees of freedom (number of coils) is smaller than the number of quantities to be controlled. In this case the Moore-Penrose pseudo-inverse gives a vector I that is optimal in the sense that it minimizes the Euclidian norm of the deviation I-MB. This current vector I is a least squares solution to the overdetermined problem.

(21) The number of components in vector B, and in all the B.sub.c's can be increased to include derivative orders higher than two. This may be needed if uniform fields and precise first gradients are needed over a relatively large volume, like in the MRI application. Or this may be needed in the active shielding application if the interference contains components expressing complicated geometry, that is, higher derivatives. To achieve a satisfactory result in this case the number of coils in the assembly must also be increased.

(22) A second condition where the method according to the invention can be applied, is described in the following.

(23) In reality the coil assembly will be installed in a building environment that has magnetic materials and structures. Specifically, in the case of MEG, the magnetically shielding room with its high permeability walls will be quite close to the coils, resulting in a considerable scattered field. The geometry and magnetic properties of these materials are usually complicated and impossible to characterize in detail. Therefore, obtaining the B.sub.c vectors for each coil by calculation may be inaccurate or impossible. In this case, the assembly of coils must be made and installed first, and then the field vectors B.sub.c must be measured one at a time by feeding current into each coil in the assembly. For example, in the case of MEGand in devices possibly combining MEG and MRI in the same instrumentmeasuring the field and its derivatives is straightforward because the MEG device itself contains an array of a large number of magnetic sensors. From the response, a signal vector, of the MEG sensor array to the current excitation fed into each one of the coils, the field components and their derivatives needed for B.sub.c are easily derived. If an MEG sensor array is not available, the measurement of the field and its derivatives can be made with some other accurately calibrated sensor array, or with one sensor that can be accurately moved around the origin.

(24) After the B.sub.c-vectors for each coil have been determined by measurement, the procedure for obtaining the I-vectors corresponding to the different components of B is applied exactly as in the first condition above.

(25) A third condition where the method according to the invention can be applied, is described in the following.

(26) This third case applies to the MEG application of the present method. The goal in the MRI application is to use the coils to get uniform field components and constant gradients (first derivatives) over the measurement volume, whereas in the MEG application the goal is to be able to counteract the environmental magnetic interference as precisely as possible. This is not necessarily optimally done by cancelling the uniform fields and the spatially constant first derivatives only, because the dominant interference field shapes inside an MSR may contain higher derivatives. Therefore, to achieve optimal cancellation one must determine the current distributions I that accurately reproduce the actual dominant interference field patterns, but exclude the unwanted higher derivative field shapes.

(27) The actual dominant interference patterns can be determined by recording the interference signal with the MEG system (no subject in the helmet) and making for example a principal component analysis (PCA) on the multichannel MEG signal. Another embodiment; is to make an independent component analysis (ICA) on the multichannel MEG signal. After this the present method can be applied so that the first n.sub.c components of the B.sub.c-vectors are the projections of the coil signal along the dominant n.sub.p principal components of the previously recorded interference. To prevent the appearance of the unwanted higher derivatives in the cancellation fields, the rest of the components in the B.sub.c-vectors are chosen among these higher derivatives.

(28) In principle, in the third condition exactly the same procedure is applied as in the second condition. In the B.sub.c-vectors the first few components (B.sub.x, B.sub.y, B.sub.z, . . . ) are only replaced by the dominant PCA components of the actual, measured interference.

(29) In the active compensation application in MEG the interference cancellation runs as a feedback system. Magnetometer sensors on different sides of the MEG helmet are used as zero detectors in feedback loops that control the currents in the compensating coil assembly (PCT/FI2005/000090). Several of such feedback loops run in parallel to compensate for the rip dominant PCA components of the environmental interference. It is advantageous for the stable functioning of such a system of parallel feedback loops to maximally decouple the loops from each other. The coil combination driven by one loop should create a minimal signal in the zero detectors of the other loops. This prevents the counteractions from circulating among the different control loops and therefore makes the entire control system faster and stable over a wider bandwidth.

(30) This orthogonalization of the control system, is built, in the first and second conditions above. This is because in these conditions the controlled field shapes are orthogonal Cartesian components; it is natural to choose the zero detector sensor for the B.sub.x-feedback loop strictly in x-direction so that it does not see the B.sub.y and B.sub.x components etc.

(31) This, however, is not automatically the case if the third condition is used to achieve maximal interference compensation. The n.sub.p dominant PCA-components are not pure magnetic field components precisely orthogonal in space. Even if the first three of them are nearly uniform fields and define principal interference directions in three dimensions, these directions are often rotated with respect to the principal directions of the measuring device and the coil assembly. In this case the parallel feedback loops can be optimally decoupled by mixing the dominant n.sub.p PCA components of the interference with a proper linear transformation within the signal subspace defined by these PCA components. The optimal linear transformation is constructed so that it rotates the coordinate system defined by the PCA components along the principal axes of the device and mixes the interference field shapes so that the zero detector of any feedback loop does not see the counteraction fields related to the other control loops.

(32) To construct the mathematical formalism, let us first denote the n.sub.chn.sub.p and n.sub.chn.sub.c dimensional PGA and coil signal subspaces by matrices P and C, respectively. Here n.sub.ch is the number of measurement channels. Also, let us denote the actual signal vector containing measurement, values from all channels by f. Now, the task is to produce a counteracting signal as precise to f as possible, given the set of coil signals C.

(33) Mathematically, this can be formulated as
fCKf.sub.0,(3)

(34) wherein in the simplest case K is an n.sub.cn.sub.c dimensional identity matrix so that, the coil signals are used without any kind of mixing, and the n.sub.c1 dimensional vector f.sub.0 contains feedback information from the zero detectors. However, K may not provide the optimal compensation result as an identity matrix. This can be seen easily by first expressing the signal vector f as a combination of the dominating interference as f=Px and by extracting the contribution of the zero detectors from f and P as f.sub.0=P.sub.0x, so that
x=pinv(P.sub.0)*f.sub.c(4)

(35) Here pinv (P.sub.0) denotes pseudo inverse of P.sub.0. By setting f=Px and solving for K in such a way that (3) holds true as accurately as possible, we have
K=pinv(C)*P*pinv(P.sub.0)(5)

(36) This is the optimal coil mixing matrix. As a final step, we can remove the cross-talk between the zero detectors by rotating the matrix K. First, set C.sub.2=CK. The rotation K.sub.orth=KR will be done so that in the rotated set C.sub.3=C.sub.2R=CKR the zero detectors will be orthogonal, i.e., C.sub.20R=I is a n.sub.zn.sub.z dimensional identity matrix, where n.sub.z is the number of zero detectors and C.sub.20 only contains the contribution of the zero detectors. Thus, we have R=pinv(C.sub.23) and the rotated mixing matrix is
K.sub.orth=K*pinv(C.sub.20)(6)

(37) By utilizing an embodiment according to the method of the present invention, one and the same coil assembly can be used for MRI field and gradient generation, and for MEG active cancellation of interference in a combined MEG/MRI instrument. In these cases and in one embodiment of the invention, the MRI electronics controlling magnetic resonance imaging measurement fields can function as a host device. In that case the MEG device can act as a slave device for the MRI electronics, the MEG device being the measuring instrument, for the magnetic resonance signal.

(38) The same coil system can also be used for different measurement locations (origins) within the coil assembly, like seated and supine measurement positions in MEG. The vectors B.sub.c for each coil in the assembly only need to be determined for each measurement location separately, either by calculation or measurement. The same applies to the environmental interference field PCA analysis in the third condition. After this the current distributions I for each of the measurement locations will be obtained from equation (2). Because the B.sub.c-vectors and thus the M-matrices are different for the two measurement positions, the resulting I-vectors will also differ. But there is no need to use different coil assemblies, or move or geometrically change the coil assembly when changing from one measurement position to the other. Also, possible repositioning of the measuring device with respect to the coil assembly only requires determination of a new M-matrix, and then calculation of new current vectors I using equation (2).

(39) Reference is now made to the additional examples, which are illustrated in the accompanying drawings.

(40) FIG. 1 shows one possible assembly of square shaped field generating coils around the measurement volume, in an embodiment of the present invention. The twenty-four coils 10 are arranged in groups of three coils in each of the eight corners of a rectangular frame 11. The three coils 10 in each corner are orthogonal to each other. If the measuring device is placed in a magnetically shielding room the frame 11 can be the inside wall of the room. Two possible locations for the origin, centers of the measuring volume, are indicated as 12.

(41) FIG. 2 shows the electronics arrangement controlling the currents in the coil assembly 20 to provide either the measuring field and gradients for an MRI device, or the active compensation of the environmental interference of the MEG device, in an embodiment of the present invention. The measuring volume (e.g. a MSR) is depicted as 21 where the patient is located in the vicinity of the measuring sensors 22. The setting up the system begins with determination of the field vectors B.sub.c for the coils 20 of the assembly in its environment. The data acquisition electronics 23 commands the current supply 29 having n.sub.c outputs 29 to feed current into the coils 20 in the assembly, each one at a time. The resulting coil signals are recorded by the magnetometer channel array 22 and stored in the acquisition system 23.

(42) For setting up the MRI-function 24, these coil signals are decomposed into the Cartesian field components and their derivatives, which are the components of the B.sub.c-vectors for the MRI application. After this the M-matrix is formed from these B.sub.c-vectors, and the current vectors I.sub.MRI are determined by taking the inverse of M. Each one of these I.sub.MRI-vectors, when fed as input to the current supply 29, will result in a pure Cartesian measuring field or a pure gradient field. These vectors are stored in the MRI control unit 24. In the MRI function this unit controls the timing of the MRI sequence, and the recording field geometries by sending the proper I.sub.MRI-vectorsof both the uniform field and the gradientvia the link 26a to the n.sub.c-channel current supply 29.

(43) If the active interference compensation function is operated following the second condition above then these I.sub.MRI current vectors can be used for active compensation as well. But if the third condition is applied, then information from the PCA analysis of the interference must be used for defining the B.sub.c-vectors. The recorded coil signals are now decomposed in a coordinate system comprising of the first n.sub.p PCA components of the interference and then higher derivatives of the B-field components (see also FIG. 4). This leads to B.sub.c-vectors and M-matrix slightly different from the MRI case, and to current vectors I.sub.AC that differ from the vectors I.sub.MRI. When active compensation 25 is on, the n.sub.p first ones of these I.sub.AC vectors are multiplied by the error signals received from the sensors 22 used as zero detectors for the compensation feedback loops, and then transmitted via the link 26b through adders 27b and 27c and switch 28b to the current supply 29. By the two switches 28a-b on the links 26a-b one can choose between the MRI 24 and MEG (active compensation) 25 functions. In the MRI mode, the adder unit 27a adds the two vectors I.sub.MRI that correspond to the MRI measuring field and the chosen gradient. Whereas, in the MEG mode during active compensation, the adder unit 27b adds the I.sub.AC-vectors (weighted by the n.sub.p error signals) to form an n.sub.c-component current vector that counteracts the dominant interference components (the n.sub.p PCA components of it). Both these signals are fed to the current supply 29 through the adder unit 27c, with the chosen mode switched on (28a or 28b). In one embodiment, as disclosed earlier regarding the MRI measurements, the MRI electronics 24 can function as a host device to the MEG measurement unit 23 which can be set as a slave device working as measuring instrument for the magnetic resonance signals. This is expressed in FIG. 2 as a two-way arrow between the two units 23, 24.

(44) FIG. 3 shows an embodiment of the method according to the invention, as a flow chart of the process of designing coil assembly for the MRI application. This chart is kind of a summary of the steps already handled in the previous paragraphs. In the first step in the procedure, the magnetic field produced by each coil in the assembly is calculated or measured at origin 30. After this we determine a field vector B.sub.c (column vector comprising elements B.sub.x, B.sub.y, B.sub.z, dB.sub.x/dx, . . . ) for all the coils in the assembly 31. Then we are ready to construct the matrix M 32 from the field vectors for all coils. After this we can determine the condition number of M 33, which tells how close to singular the matrix M actually is. If the condition number is more than a hundred (or any other desired threshold value), we have to modify the coil assembly 34. Depending on the situation, this means relocating or reorienting the individual coils, or decreasing or increasing the number of coils in the assembly. In that case, we have to start from the beginning of the procedure, and calculate or measure the fields for each coil of the modified assembly again 30.

(45) When we result in the condition number less than a hundred, we may decide that the coil assembly is feasible, and we may calculate 35 the current vectors I.sub.MRI according to equation (2). Finally, in the last step 36, we can install the I.sub.MRI-vectors in the MRI unit which correspond to the measuring fields and gradients.

(46) FIG. 4 shows an example as a flow chart of the process of coil assembly design for another application, the active interference cancellation in MEG. At first, we set up the assembly of compensating coils 40 into the measuring volume, e.g. inside a MSR. Then we can measure the background interference 41 without any object present, and decompose this interfering field into components B.sub.1, B.sub.2, . . . , B.sub.np (n.sub.p means the number of dominant PCA components of the interference). After this we may measure the magnetic fields originating from each coil at the origin 42. Then we can determine the field vectors B.sub.c (B.sub.1, B.sub.2, . . . , B.sub.np, d.sup.2B.sub.x/dx.sup.2, . . . ).sup.7 for all the coils 43. When we have the B.sub.c's, we can construct the matrix M 44. Similarly as in the embodiment of FIG. 3, we can check the condition number of the matrix M 45, that is, check whether the matrix M is singular, close to singular or far from singular. We have to modify the assembly of coils 46 and remeasure the background interference until we achieve a matrix M which can be inverted (condition number less than 100, or any other desired threshold value). In that case we can calculate the current vectors I.sub.AC 47 by using the equation (2). Finally, we can install the vectors I.sub.AC to the active compensation unit of the MEG device 46.

(47) The presented method can be implemented by a computer program which can control a data-processing device to execute the applicable method steps. The computer program can be stored in a medium applicable by the processor or other control means.

(48) It is obvious to a person skilled in the art that with the advancement of technology, the basic idea of the invention may be implemented in various ways. Thus, the invention and its embodiments are not limited to the examples described above; instead, they may vary within the scope of the claims.