Self-shielded gradient coils for nuclear magnetic resonance imaging

Abstract: A two coil system is described which produces a linear gradient field inside and an arbitrarily low field outside the two coil set. By eliminating the field outside the gradient coils, interaction between the gradient coils and external structure can be eliminated. A reduction in eddy current ef­ fects of greater than a factor 100 are readily obtained. Two coils are required for each gradient axis instead of one so that some increase in power supply capability may be required.

Description: The present invention relates in general to a coil system for producing a gradient magnetic field used in magnetic resonance imaging and spectroscopy, and more specifically to a coil system for producing a magnetic field having a linear gradient in the interior of the coil system and having a substantially zero value exterior of the coil system. Magnetic resonance (MR) imaging systems are currently employed in forming tomographic images of the internal human anatomy. In such systems, a patient is placed in a static magnetic field and is subjected to radio-frequency electromagnetic pulses. The magnetic resonance of the atomic nuclei of the patient are detected . with an antenna to provide information from which an image of that portion of the patient containing these nuclei may be formed. The magnetic field possesses linear gradients in each of the three spatial dimensions so that the position of resonating nuclei can be determined. These same phenomena are employed in magnetic resonance spectroscopy for analyzing properties of nuclei. Typically, a main magnet establishes a uniform magnetic field of high strength and the linear gradients are superimposed on that magnetic field by gradient coils located within the main magnet interior. The main magnet may be comprised of a superconducting coil, a resistive coil, or a set of permanent magnets. A gradient coil may be comprised of windings etched on a flexible printed circuit board which is curved to form a cylinder or may be comprised of conductors held by a frame in their proper locations. Bringing the inner bore of the main magnet close to the imaging volume, and thus close to the gradient coils, enhances the efficiency of the magnet in terms of amount of material, cost and, except for permanent magnets, power consumption. However, the close proximity of the magnet to the gradient coils leads to undesirable interactions between them. For instance, where the main magnet includes electrically conductive material (e.g. neodymium permanent magnets or the cryostat of a superconducting magnet), the changing magnetic fields of the gradient coils induce currents in the conductive material. These currents distort the magnetic field in the imaging volume in both time and space. Furthermore, when permanent magnets are used, the eddy currents dissipate power which appears as heat, distorting the magnetic field even more. The solution of placing a conducting shield between the gradient coils and the magnets merely shifts the eddy currents to the shield . and so the distortions of the gradient fields persist. Magnetic interaction between the main magnet and the gradient coils also results in attractive and repulsive forces which create annoying audible sound. Structural supports having high strength and rigidity have been employed in attempts to reduce audible sound from the gradient coils, but with limited success. From EP-A-0 167 243 magnetic shielding of a magnet such as a first set of superconducting coils as used in nuclear magnetic resonance applications is known which includes a second set of coils around and spaced from the first set of coils. The magnetic flux of the second set of coils opposes and offsets the magnetic flux of the first set of coils in the region outside of the second set of coils, but is less than the magnetic flux of the first set of coils in the region within the first set of coils. The uniformity of magnetic flux within the first set of coils is not adversely effected by the magnetic flux produced by the second set of coils. The use of the external field cancelling method can allow the gradient fields to be produced in NMR imaging with greatly reduced problems to the eddy currents. US-A-3 466 499 related to a particle accelerator discloses a coil system for producing a gradient magnetic field in the volume enclosed by a first coil provided on a first cylindrical surface, wherein the first coil is surrounded by a second coil on a second cylindrical surface and wherein the current distributions are such that the magnetic field outside of the second coil is substantially zero. Hereby, the magnetic field in the inner volume is oriented vertically to the axial direction. In the older. non-prepublished EP-A-0 216 590, a coil system with a gradient magnetic field coil and two outer screen coils is disclosed. Accordingly, it is a principal object of the present invention to reduce interaction between the main magnet and the gradient coils of an MR imaging system. It is another object of the present invention to provide a coil system for producing a magnetic field having a substantially linear gradient in the interior of the coil system and having a substantially zero value exterior of the coil system. It is a further object of the invention to practically eliminate currents in the main magnet induced by the magnetic fields of the gradients coils. It is yet another object of the invention to reduce audible sound from the gradient coils of a nuclear magnetic resonance imaging system. These and other objects are achieved in a coil system and in a method for providing a coil system for producing a time changing substantially linear gradient magnetic field in as NMR apparatus as defined in claims 1 and 10. Advantegeous embodiments of the coil system are claimed in dependent claims 2 to 9. The invention, as to organization and method of operation, together with further objects and advantages thereof, may best be understood by reference to the following description taken in conjunction with the accompanying drawing, in which: Figure 1A is a perspective view of a single coil on a printed circuit board for producing a gradient field. Figure 1B is a diagram of the coil of Figure 1A unrolled to show the configuration of the windings. Figure 2A is a cross-sectional view of the coil of Figure 1A. Figure 2B is a cross-sectional view of a coil system in accordance with the present invention. Figure 3 is a winding pattern for a conventional gradient coil. Figure 4 is a diagram of an exemplary winding configuration of a portion of the inner coil of Figure 23. Figure 5 is a diagram of the winding configuration of a portion of the outer coil of Figure 2B such that the outside field is zero when used with the winding configuration of Figure 4. Figure 6 is a cross-sectional view of a magnetic resonance system employing the invention. Figure 7 is a streamline plot for an inner coil of a z-gradient coil set. Figure 8 is a streamline plot for an outer coil corresponding to the inner coil plot of Figure 7. Figures 9-11 are magnetic field plots for gradient coils which show the improvement achieved by use of shielding coils. Referring now to the drawings, Figure 1A shows a cylindrical gradient coil 10 with length L and central axis A, for producing a gradient magnetic field in its interior. The three spatial directions x, y and z are shown extending from an origin O and with the z coordinate extending parallel to axis A, the x coordinate extending horizontally and the y coordinate extending verticully. Also shown are cylindrical coordinates r,  and z which may be defined from x, y and z as follows: z = z, r = (x 2 + y 2 ) ½ and  = arc tan (y/x). The coordinate systems define points on cylindrical coil 10, in its interior and in its exterior. The windings of coil 10 may be formed on a flexible printed circuit board 11, as shown in Figure 1B. Windings 12a-12d (also referred to as fingerprints) are etched on board 11 and have a configuration which provides the desired gradient magnetic field when board 11 is rolled into a cylinder and current is applied to windings 12a-12d. The winding pattern (i.e. surface currents) shown in figure 1B_is in accordance with a gradient coil described in EP-A-140259. The etching of flexible circuit boards is described in EP-A-140259. Cylindrical coil 10 is shown in cross section in Figure 2A. In this case, surface currents are restricted to a cylinder having radius r 1 . Specification of a desired "gradient magnetic field inside coil 10 in region I uniquely determines the required surface current distribution of coil 10 as well as a non-zero magnetic field outside of coil 10 in region II. Thus, any structure in region II (0.7. the main magnet) will be subjected to a time changing magnetic field from coil 10, thus inducing eddy currents which in turn distort the gradient in region I. The coil set of the present invention is shown in cross section in Figure 2B. A first coil 20 with a radius r i is coaxial with a second coil 30 with a radius r o . Coils 20 and 30 are preferably connected in series so that a single power supply can supply equal current to each coil. A first surface current J 1 may flow in coil 20 and a second surface current J 2 may flow in coil 30. In this case, specification of a desired gradient magnetic field in region I does not uniquely determine the two current distributions. It is possible to impose the further condition that the magnetic field be equal to zero everywhere in region III, in which case fixing one surface current and the radii of the coils determines the other surface current. An exemplary method for finding a pair of cylindrical surface currents which result in the desired gradient in region I and a zero field in region III will be described below. A convenient method for describing the surface currents of a gradient coil is by means of stream functions. A stream function S describes a flow in which every region of the flow is free from any sources or sinks (i.e. points where flow is produced or disappears). Lines of constant S are parallel to the flow (e.g. flow of surface current J ). Surface current J (z,) is related to the stream function S(z,) derivatives and the z and and  and unit vectors as follows: J (z,) = -(∂S/∂z)  + (l/ r)(∂s/∂) z . The streamlines (i.e. lines of constant S) yielded by the stream functions are a series of concentric closed curves which are an idealized representation of surface current J . The actual surface current is derived by plotting a number of streamlines separated by a predetermined step-size in S, breaking each closed curve at a point and joining each curve with the adjacent curves to form a spiral winding pattern. The breaking points are preferably substantially colinear so that a lead brought in from outside the coil to join the innermost portion of the spiral winding pattern can be placed in a parallel arrangement which substantially cancels the effects of breaking the streamlines. Figure 3 is a winding pattern similar to a gradient coil winding pattern which is presently used in commercial NMR systems for providing an x-directed or a y-directed gradient. The plot corresponds to a fingerprint which is repeated four times in the gradient coil. The gradient coil has a length L and a radius r i . Each fingerprint carries a current I, has N turns, has a length in z of L/2 and has a height in  of π radians. In an aspect of the invention, the winding patterns of the inner and outer roils may be concurrently designed by selecting other stream functions for describing the surface currents. An exemplary stream function S 1 for an x-gradient or a y-gradient inner coil is: where coefficients A n are optimization parameters and z i is one-half of the length of the coil. Similarly, the outer coil stream function S 2 is: where B m are the optimization coefficients and z o is one-half the truncated length of the outer coil. With these stream functions of more general form, we can proceed to find the stream function coefficients that describe surface currents which produce the desired magnetic fielda. A series of points in space is chosen as a representation of the gradient magnetic field in the imaging volume near the origin. After selecting an initial inner coil length 2 • z i and an initial set of coefficients to work with, the field is calculated at each point in the imaging volume for each coefficient. The coefficients are then modified to minimize the sum of the squares of the difference between the desired gradient and the calculated gradient and to provide shielding such that the magnetic field outside the coil set is substantially zero. Iterations are made by increasing or decreasing the length of the inner coil and by including fewer or greater number of coefficients until a reasonable combination of linearity, current density, power requirements and overall length is obtained. In general it is desirable to use as small a set of coefficients as possible and as short a length as possible. A shorter length upsets the linearity but lowers the stored energy in the magnetic field. A larger set of coefficients results in improved Linearity but also increases the stored energy and creates large variations in current density. Figures 4 and 5 show winding patterns derived by this method and used to etch the inner and outer coil windings, respectively, for an x-gradient or a y-gradient coil system. Coils for a z-gradient may also be employed in a similar manner and have a shape which can be derived according to the above methods by changing the order of the Bessel functions used in the solutions to a zero order. Exemplary streamline plats for the inner and outer coils of such a z-gradient coil system are shown in Figures 7 and 8, respectively. The streamlines would be joined to form a continuous path as in the previous examples to form the desired winding pattern. Figures 9-11 are plots of lines of constant magnetic field magnitude produced by the various gradient coils previously described when they are provided with current. The plots show the effectiveness of the coil set of the invention in providing magnetic shielding. Figure plots the magnetic field of a single x-gradient or y-gradient coil having the winding pattern of Figure 3. It is apparent that a significant magnetic field extends to over twice the coil radius of 0.33 meters. Figures 10 and 11 show similar results for a z-gradient coil system. A single z-gradient coil with a winding pattern of the prior art and a radius of 0.33 meters produces the magnetic field plotted in Figure 10. Figure 11 plots the magnetic field resulting when inner and outer 2-gradient coils having winding patterns derived from the streamline plots of Figures 7 and 8 radii of 0.33 and 0.44 meters, respectively, are used. Figure 6 is a cross-sectional view of a magnetic resonance system with a main magnet 40. A gradient coil set 41 according to the invention is located within main magnet 40. An RF coil 42 creates electromagnetic pulses for stimulating resonance of a subject 44 located in an imaging volume 45. The magnetic resonance of subject 44 is detected by an antenna 43. The signal from antenna 43 is used to construct an image of the subject. The foregoing has described a gradient coil system having reduced interaction with the main magnet. The coil system produces a magnetic field having a linear gradient in the interior of the coil system and having a substantially zero value exterior of the coil system. The elimination of induced eddy currents improves the stability of the gradient field. With the inner and outer coils of the gradient coil set securely fastened together, forces between the gradient coil set and the main magnet substantially cancel so that audible sound is reduced.

Claims: A coil system for producing a time changing substantially lincar gradient magnetic field in an NMR apparatus comprising: a first coil (20) adapted to be coupled to a source of current for providing a first surface current distribution on the surface of a first cylinder having a radius r i and an axial length 2z i ; and a second coil (30) adapted to be coupled to a source of current for providing a second surface current distribution on the surface of a second cylinder substantially coaxial with said first cylinder and having a radius r 0 greater than r i and an axial length 2z 0 ; said first and second surface current distributions being concurrently designed and mutually providing a magnetic field having said gradient in a predetermined direction and a substantially constant value across the other two directions within the volume enclosed by said first coil and having a substantially zero value in the volume outside of said second coil, whereby a) a series of points is chosen as a representation of the desired gradient magnetic field in the imaging volume enclosed by the first coil near the origin and the further condition is imposed that the magnetic field is equal to zero outside the second coil, b) an initial inner coil length and an initial set of stream function coefficients to work with is selected, said stream function coefficients being defined as optimization parameters of the stream function of the first and second coil and describing the surface current distribution of the first and second coil, c) the magnetic field is calculated outside the second coil and at each selected point in the imaging volume enclosed: by the first coil for each coefficient, and d) the coefficients are then modified to minimize the sum of the squares of the difference between the desired gradient magnetic field and the calculated gradient magnetic field in the volume enclosed by the first coil and to minimize the sum of the squares of the difference between the desired zero magnetic field and the calculated magnetic field outside the second coil to provide shielding such that the magnetic field in the volume outside the second coil has a substantially zero value. The coil system of claim 1, wherein said coils (20, 30) are connected in series. The coil system of claim 1, wherein said first and second coils (20, 30) are comprised of windings etched on first and second printed circuit boards, respectively, each of said printed circuit boards being curved to form said cylinders. The coil system of claim 1, wherein said coils (20, 30) arcefingerprints. The coil system of claim 1, wherein said coils (20, 30) are conductors. The coil system of claim 1, wherein said coils (20, 30) are connected to a single current supply. The coil system of claim 1 wherein said inner first coil (20) is adapted to be coupled to a source of current and having a radius r i and an axial length 2 z i for providing an inner surface current distribution substantially equal to the derivative of a first stream function, said first stream function is defined over variables z and Θ where z is the axial coordinate which varies from -z i to +z i and where Θ is the circumferential coordinate which varies from 0 to 2 Π , said first stream; function including a plurality of coefficients A n where n is a whole number from 1 to a predetermined number N, said first stream function is defined by the equation and said outer second coil (30) is adapted to be coupled to a source of current and is substantially coaxial with said inner first coil and having a radius r 0 and an axial length 2.z 0 for providing an outer surface current distribution substantially equal to the derivative of a second stream function where z varies from -z 0 to +z 0 , said second stream function including a plurality of coefficients B m where m is a whole number from 1 to a predetermined number M, said second stream function is defined by the equation said coefficients having values which minimize within predetermined limits the sum of squares difference between the desired gradient of said magnetic field and said gradient produced. A magnetic resonance system comprising: a main magnet (40) for establishing a uniform magnetic field in an imaging volume in the interior of said main magnet; radio-frequency means (42) for pulsing said imaging volume with electromagnetic energy for stimulating nuclear magnetic resonance of nuclei within said imaging volume; detecting means (43) for sensing the nuclear magnetic resonance of nuclei within said imaging volume; and a coil system as defined in one of claims 1 to 7. The magnetic resonance system of claim 8 further comprising second and third gradient coil systems for establishing magnetic fields having gradients in each of the two remaining dimensions, respectively, within the respective coil sets and having substantially zero values outside the respective coil sets. A method for providing a coil system for producing a time changing substantially linear gradient magnetic field in an NMR apparatus comprising the steps of: providing a first coil (20) adapted to be coupled to a source of current for providing a first surface current distribution on the surface of a first cylinder having a radius r i and an axial length 2z i ; and providing a second coil (30) adapted to be coupled to a source of current for providing a second surface current distribution on the surface of a second cylinder substantially coaxial with said first cylinder and having a radius r 0 greater than r, and an axial length 2z 0 ; determining said first and second surface current distributions by concurrently designing and mutually providing a magnetic field having said gradient in a predetermined direction and a substantially constant value across the other two directions within the volume enclosed by said first coil and having a substantially zero value in the volume outside of said second coil, by a) choosing a series of points as a representation of the desired gradient magnetic field in the imaging volume enclosed by the first coil near the origin and imposing the further condition that the magnetic field is equal to zero outside the second coil, b) selecting an initial inner coil length and an initial set of stream function coefficients to work with said stream function coefficients being defined as optimization parameters of the stream function of the first and second coil and describing the surface current distribution of the first and second coil, c) calculating the magnetic field outside the second coil and at each selected point in the imaging volume enclosed by the first coil for each coefficient, and d) modifying the coefficients to minimize the sum of the squares of the difference between the desired gradient magnetic field and the calculated gradient magnetic field in the volume enclosed by the first coil and to minimize the sum of the squares of the difference between the desired zero magnetic field and the calculated magnetic field outside the second coil to provide shielding such that the magnetic field in the volume outside the second coil has a substantially zero value.

Inventors: HICKEY JOHN SMITH, ROEMER PETER BERNARD, HICKEY, JOHN SMITH, ROEMER, PETER BERNARD
Applicants: GEN ELECTRIC, GENERAL ELECTRIC COMPANY
Application year: 1987
Main classification: G01R33
IPC codes: A61B5, A61B10, G01R33, H01F7, G01N33, A61B6