DE19726332A1 - Coil arrangement for generating predetermined target magnetic field in NMR tomography - Google Patents

Abstract

The device has conductors through which current flows arranged on the surface of a coil. The conductors run on tracks whose support points are determined. The points are determined by placing a network of grating meshes over the coil surface. Each mesh is covered with an elementary coil in the form of a closed winding. The magnetic field resulting from each elementary coil is calculated. On the basis of the target magnetic field, an ampere- winding number for each elementary coil is determined by minimising a given function. The current distribution is realised using discrete conductors. The current variation between adjacent elementary coils may be limited by selection of a matrix. Also the maximum deviation from the target magnetic field may be limited by selection of the matrix.

Description

Precisely defined target magnetic fields are e.g. B. in MRI tomography required. As is known, there is a spatial resolution of the nuclear magnetic resonance signals in magnetic resonance imaging because a magnetic field gradient is superimposed on a homogeneous, static basic field in the order of magnitude of 1 Tesla. The principles of imaging are explained, for example, in Bottomley's article "NMR Imaging Techniques and Applications: A Review" in Review of Scientific Instrumentation 53,9, 9/82, pages 1319 to 1337. For spatial resolution in three dimensions, magnetic field gradients must be generated in three directions that are preferably perpendicular to one another. In Figs. 1 and 2 are each a Koordi natenkreuz x, y, z shown, is supposed to represent the directions of each weiligen gradient. Fig. 1 shows the esterification of the problem Erläu schematically a simple Anord voltage of transverse gradient coils for generating magnetic field gradients G ei nes _y in the y direction. The Gradientenspu len 2 are designed as saddle coils, which are attached to a support tube 1 . A largely constant magnetic field gradient G _y in the y direction is generated by the conductor sections 2 a within a spherical examination volume 11 . Because of their size and distance from the examination volume 11 , the return conductors produce only small magnetic field components there, which are often neglected in the design of the gradient coil.

The gradient coils for the x magnetic field gradient are constructed identically to the gradient coils 2 for the y magnetic field gradient and are only rotated by 90 ° in the azimuthal direction on the support tube 1 . For the sake of clarity, they are therefore not shown in FIG. 1.

The (axial) gradient coils 3 for the magnetic field gradient in the z direction are shown schematically in FIG. 2. The coils are ring-shaped and arranged symmetrically to the center of the examination volume 11 . Since the two individual coils 3 a and 3 b in the current flowing through it in Fig. 2 the manner illustrated in the opposite direction, they Doomed things a magnetic field gradient in the z-direction.

In order to avoid image distortions, high demands are placed on the linearity of the gradient fields, which cannot be achieved with the schematically illustrated simple conductor structures according to FIGS. 1 and 2. In particular, the transverse gradient coils (G _x , G _y ) are complex to design.

There are basically two approaches to the design of gradient coils:

• - the analytical approach and
• - the numerical approach.

The analytical approach has the problem that the ge wanted linear field course in its strictly mathematical Form leads to technically not feasible solutions that the introduction of relaxing boundary conditions is necessary. The algorithm is in terms of degree, order and amplitude arbitrary error terms attached, which generally refer to is not the optimum in terms of what is physically and technically feasible put.

The numerical approach is an advantage here: With suitable ones mathematical optimization process (in the simplest case e.g. least-mean-square fit) result in addition to the desired  Field course deviations that are only in their amplitude, not but minimized in terms of their degree and order of disturbance are.

Because the approach already has the physical nature of the arrangement is taken into account, a "natural range of errors" surrender.

Due to the large parameter space are numerical methods however, generally on simple coil geometries limits (e.g. saddle coils).

A more complex coil geometry was described in US Pat. No. 4,456,881 (Technicare). The coil surface is in one Large number of surface elements divided. In each of these A current density vector is determined such that the resulting current density distribution the desired Target field with a maximum permissible error amplitude testifies. Because this procedure does not meet the continuity condition taken into account, the coils calculated in this way lack the respective against conductor returns. These are therefore without consideration considering their impact on the gradient field on the outside most end of the coil attached. However, this results in a Field error, which is a disadvantage of this method.

The disadvantages mentioned above are largely due to processes avoided as described in U.S. Patents 5,309,107 and 5,581,187. The desired coils mentally covered surface with a grid mesh, each grid mesh with an elementary coil in the form of egg a closed turn is occupied. By means of a fit Algorithm is based on a given target field distribution an ampere number of turns for each elementary coil telt. Subsequently, bases for conductor tracks will be Right.  

With this method, not only a conventional opti be carried out towards a target field, but by introducing suitable boundary conditions, other re properties of the gradient coil can be optimized. For this belongs to B. the minimization of the coil energy, the minimie eddy currents and minimizing global bending forces.

A disadvantage of this known method, however, is that no real limits for certain physical parameters be introduced. For example, the optimization in result in a current density that leads to a difficult to achieve leading conductor density. This is especially true if the conductors are designed as wire coils. A high ladder density can also be too difficult to control local Lead to cooling problems. Furthermore, the field distribution in Hin view of the target magnetic field only globally optimized. For maxi There are no limits provided for local field deviations.

The object of the invention is to design a coil arrangement in this way shape that the disadvantages mentioned above avoided will.

This object is achieved by the features of the An spell 1 solved. Due to the claimed type of minimization can set fixed limit values for physi cal parameters are introduced.

By choosing a matrix, the maxima le deviation from the target magnetic field can be limited. So who in contrast to the exclusively global view of Field deviations according to the state of the art local field deviation considerations included.  

By selecting the matrix, it is advantageously possible to change the current Courses between adjacent elementary coils are limited. This will be used to implement the desired field course required conductor density is limited.

In the following, the design of a gradient coil according to the invention is explained by way of example with reference to FIGS. 3 and 4. It shows

Fig. 3 is a grid mesh.

Fig. 4 shows an example of the matrix.

The design is carried out in several steps, some of which are already known per se:

• 1st step (known):
  To design the coil, the planned coil surface is first broken down into a plurality of adjoining elementary surfaces, so that a grid mesh is formed. This is shown schematically in Fig. 3, wherein the individual elementary areas or meshes are numbered 1 to N. Each of these surfaces is thought to be surrounded by a conductor, so that a large number of "elemen tar coils" arise, each consisting of one turn. In the example shown, the individual stitches are quite angular in the general case (for example with curved coil surfaces) but other stitch shapes are also possible. The current distribution on the entire conductor structure is taken up in the optimization as the superposition of closed elementary circulating currents in the elementary coils, these are referred to below as mesh currents.
• Step 2 (known):
  Furthermore, a target field z _i (gradient field or shim characteristic) is predetermined in a number of points P _i , where (i = 1,..., M), M <N. The target field z _i = (z _t ,..., Z _M ) normally includes points on the surface of the homogeneity sphere and points on eddy current surfaces on which the target field should be zero.
• 3rd step (known):
  In each of the N meshes one thinks of a unit current flowing. So that for each mesh of the field f _ij generated by this unit in each of the M points.
  f _ij is the field contribution of a unit current in the jth mesh at the i-th point. The following field vector b _i = (b ₁ ,..., B _M ) is obtained for the current vector I _i = (I ₁ ,..., I _N ).
  There are a number of known methods for magnetic field calculation, the most common being the calculation based on spherical functions, as described, for example, in the article Magnet Field Profiling: Analysis and Correction Coil Design, Magnetic Resonance in Medicine 1, 44-65 (1984) by Romeo and Hoult is shown. A11 (i), A31 (i), A51 (i), A33 (i), A53 (i) are, for example, in the spherical function representation. . . the field spectrum of the i-th elementary saddle coil. For gradients one generally strives for a linear course so that the desired target field has the following spectrum:
  A11 = 1, A31 = A51 = A33 = 0.
• 4th step (known):
  For the sum of the quadratic deviations from the target field, you get:
  
• Step 5 (known):
  The field energy contained in the coil can be represented as follows, the L _{jk being} the coupling or self-inductances of the mesh network:
  If one assumes that the field energy is included in the function to be optimized with a certain weighting factor, then the function F to be minimized is obtained:
  where w _{e is} the weighting factor with which the minimization of field energy is included in the overall function.
• 5th step (new):
  An expanded least mean square fit method has so far been used to solve the optimization task at hand. However, no limit values can be specified for this. This results in the disadvantages already mentioned in the introduction to the description.
  According to the present invention, the function to be optimized (ie minimized in the specific case) is therefore defined as follows:
  The first summand represents the linear component, the second summand the quadratic component of the function. T stands for a transposed vector. The following linear boundary conditions are applied to this function:
  So 1 is a lower and u an upper limit.

For the optimization task described above, including the boundary conditions, a method was used by Gill et al in Report 50 L 82-7 "The design and implementation of a quadratic programming algo rithm" by the Department of Operations Research, Stanford University, California, 95305, 1982 described. Furthermore, a computer program for solving this optimization problem is available from NAG as part of the NAG Fortran Library under the name "EONNAF". The above functions with the following definitions can be applied to the problem for the coil design. The vector c is defined by:

It says
j for the index of the elementary coil (1 ≦ i ≦ N)
i for the index of the point
f _ij for the field contribution of a standard current in the j-th elementary coil at the i-th point
z _i for the target field at the i th point.

The matrix is defined for all j (j = 1.. .N) and k (k = 1.. .N) by:

The above-mentioned linear boundary conditions are used to limit the currents that actually flow. By defining the matrix appropriately, you can also limit various parameters. By means of a matrix in the form shown in FIG . B. limit the differential currents between each two adjacent stitches according to FIG. 3 be, the matrix shown namely delivers after multiplication with the mesh flows I ₁ . . . I _N the difference currents

This possibility of limitation offers z. B. the advantage that you ultimately limit the conductor density in the coil design can. On the one hand, this can prevent the process provides a coil design with a conductor density that the Winding is no longer possible. On the other hand too high conductor densities can lead to cooling problems.

But you can z. B. also limit the maximum field deviation by inserting the matrix defined above into the matrix. The following applies:. I = B.

The lower limit l and the upper limit u are then set as follows:
l = z - Δa target field - maximum deviation
u = z + Δa target field + maximum deviation.

In contrast to the known method, this not only optimizes the global field deviation, it can also be used to ensure that the local field deviation from the target field does not exceed a specified value. Examples of other possibilities for limiting coil properties include:

• - Limitation of the normal components of the field strength to adj bearded conductor surfaces to a predetermined value,
• - Limitation of field disturbances caused by eddy currents neighboring metallic parts are caused on a predetermined value,
• - in the case of asymmetrical gradient coils or an asymmetry of the basic field exposed conductor arrangements:
  Limiting the torque acting on the coil to a predetermined value.
• Step 6 (known):
  The given current distribution is formed by means of discrete conductors through which a constant target current flows. Various approaches are known for this. For example, each mesh branch can first be assigned a defined area (mesh width, mesh length) in which the calculated current should flow. A surface current density distribution is then calculated from the global current distribution in the lateral surface and, after a further division by the desired current, a winding density distribution in the given lateral surface. The spatial curve of the respective conductor can be determined from this by integrating along suitable integration paths (e.g. projecting a tuft of straight lines through the stagnation point of the winding density distribution onto the outer surface). To do this, the winding density function is integrated along the path until the integral value becomes an integer. Within the integral limits determined in this way, the position of the conductor is determined in such a way that the turns are equally large on both sides.

For more details on the process, a wrap It will still be necessary to determine design based on a mesh network sometimes referred to U.S. Patent 5,309,107.

The method described cannot only be applied to gradients Apply tensile coils, but to any problem where with ladders a given target field on a given area to be fathered. As further examples of this, shim Coils, shielding coils and basic field coils called.

Claims (6)

1. Coil arrangement for generating a target magnetic field specified in M points, wherein current-carrying conductors are arranged on a coil surface and run on tracks whose bases are determined according to the following method:

• a) a grid mesh is placed over the surface of the coil;
• b) each grid mesh is covered with an elementary coil in the form of a closed turn;
• c) the magnetic field resulting from each elementary coil is calculated;
• d) due to the target magnetic field by minimizing the function
  with the boundary condition
  an ampere number of turns is defined for each elementary coil, whereby the following applies:
  I = current vector, which indicates the currents in the individual elementary coils 1 ≦ j ≦ N
  C ^T = transposed vector C
  C = vector defined by
  j = index for the elementary coil (1 ≦ i ≦ N)
  i = index for the point of impact (1 ≦ i ≦ M)
  f _ij = field contribution of a standard current in the j-th elementary coil at the i-th point
  z _i = target field at the i-th point
  L _jk = coupling or self-inductance of each elementary coil
  w _e = weighting factor with which the minimization of field energy is included in the overall function
  = Matrix with which physical parameters are limited
  l , u = fixed lower or upper limit values for the currents in the individual elementary coils
• e) the current distribution determined on the basis of steps a) to d) is realized with the aid of discrete conductors.

2. Coil arrangement according to claim 1, wherein by choosing the Ma trix the current changes between neighboring elementals coils are limited. 3. Coil arrangement according to claim 2, wherein by choice of Matrix limits the maximum deviation from the target magnetic field becomes. 4. Coil arrangement according to one of claims 1 to 3, wherein the design as a shielding coil to reduce eddies flow in a metallic surrounding the coil arrangement Structure takes place.   5. Coil arrangement according to one of claims 1 to 3, wherein the design as a shim coil to reduce field errors of a magnet, the field errors of Magnets can be determined in the unshimmed state and then the target magnetic field is determined to be this field error compensated. 6. Coil arrangement according to claim 5, wherein the field errors in Spherical function terms are shown and the target Magnetic field corresponds to a spherical function term.