₀magnetic field adjustment is limited to the direction of the B₀magnetic field. Specifically, as discussed above, such passive shims are magnetized by B₀magnetic field and therefore produce a magnetic field in the same direction. Magnetic field contributions are generally not possible in other directions because, for example, if pre-magnetized shims of typical materials were provided to produce magnetic fields in other directions, the relatively high field strengths of conventional MRI systems generally provide sufficient coercive force to realign the magnetic fields of such passive shims in the direction of the B₀magnetic field. Accordingly, the technique of positioning ferromagnetic material proximate the B₀magnet in conventional MRI systems is generally limited to corrective fields oriented in the same direction as the main B₀magnetic field.

Furthermore, in addition to conventional passive shimming techniques being time consuming and expensive, there are further challenges for their use, particularly in the low-field context. In particular, at the low-fields characteristic of low-field MRI, frequently used material for passive shims (e.g., steel) may not be driven to saturation by the low field strengths of the target B₀magnetic field (e.g., field strength in the 10-50 mT range, as a non-limiting example), resulting in non-linear magnetic behavior that complicates the shimming process and/or makes it difficult (or potentially impossible) to employ satisfactorily. Thus, conventional passive shimming techniques may be unsuitable for low-field MRI for this additional reason.

The inventors have appreciated that permanent magnet shims may be utilized in many low-field contexts in any orientation, providing a measure of flexibility and precision in correcting the B₀magnetic field of a low-field MRI device. Such passive shimming techniques are generally not available in the high-field context due to the high magnetic field strengths produced by the B₀magnet that, for example, aligns the magnetization of magnetic material in the direction of the B₀magnetic field. A permanent magnet refers to any object or material that maintains its own persistent magnetic field once magnetized. Materials that can be magnetized to produce a permanent magnet are referred to herein as ferromagnetic, or simply magnetic, and include, as non-limiting examples, iron, nickel, cobalt, neodymium (NdFeB) alloys, samarium cobalt (SmCo) alloys, alnico (AlNiCo) alloys, strontium ferrite, barium ferrite, etc. Permanent magnet material (e.g., magnetizable material that has been driven to saturation by a magnetizing field) retains its magnetic field when the driving field is removed. The amount of magnetization retained by a particular material is referred to as the material's remanence. The strength of a magnetic field in the opposing direction needed to demagnetize material once it has been driven to saturation is referred to as the coercivity of the material.

Because the low field strengths characteristic of some exemplary low-field MRI systems are typically insufficient to exceed the coercivity of most commonly used magnetic material, permanent magnet shims can be arranged in orientations other than along the B0 magnetic field without being demagnetized or re-magnetized in alignment with the B₀magnetic field. For example, permanent magnet shims can be used to adjust the B₀magnetic field of a low-field MRI system in the direction of the B₀magnetic field, opposite the B₀magnetic field, parallel or transverse to the B₀magnetic field, or in directions or orientations between, significantly expanding the space of solutions for correcting the B₀magnetic field. According to some embodiments, at least one permanent magnet shim is arranged to produce a magnetic field that is not aligned with the B₀magnetic field to facilitate correction of the B₀magnetic field produced by a low-field MRI system. This technique is not limited to the low-field context to the extent that the strength of the B₀magnetic field remains insufficient to re-magnetize the shim in the direction of the B₀magnetic field.

As discussed above, many conventional shimming techniques require extensive manual involvement in assessing and correcting unsatisfactory magnetic field variation produced by the B0 magnet of an MRI system (e.g., an uncorrected B₀magnet post-production). The inventors have developed techniques to minimize the manual effort involved in correcting the B₀magnetic field produced by a B₀magnet, for example, correcting at least some field inhomogeneity resulting from imperfect manufacturing processes. In particular, the inventors have developed automated techniques for patterning magnetic material to provide field correction to the B₀magnetic field produced by a B₀magnet. The term automated or automatically refers to processes that perform the substance of a given act or function substantially without human involvement. While a human may be involved in an automated process, e.g., by having programmed a device to perform given act(s) or function(s), or by providing data to the device, instructing or engaging the device to perform the automated process, the substantive of the automated process, act or function is performed by the device and not by a human. A number of exemplary automated processes for automatically applying a magnetic pattern to magnetic material to produce, at least in part, a permanent magnetic shim are discussed in further detail below.

According to some embodiments, an un-magnetized sheet of material is magnetized in a pattern configured to improve the profile of a B₀magnetic field produced by an MRI system (e.g., a low-field MRI system). For example, the sheet of un-magnetized material may be magnetized by an automated magnetizing head that can be programmed to magnetize the material in a desired pattern to produce a magnetic field that improves the profile of a B₀magnetic field (e.g., improve B₀magnetic field homogeneity) produced by a B₀magnet of the MRI system. In some embodiments, the un-magnetized regions (i.e., regions outside the magnetization pattern) remain as-is and their magnetization in the B₀magnetic field, to the extent that it occurs, is taken into account when determining the magnetic pattern to apply to the material via the automated magnetizing head. In other embodiments, the un-magnetized regions are removed (e.g., via cutting) prior to incorporating the resulting shim into the system, for example, a low-field MRI system.

According to other embodiments, a desired pattern of magnetization is achieved by an automated magnetizing head that operates on a magnetized piece of material to orient the magnetic field at discrete locations so that the resulting magnetic pattern produces a magnetic field that improves the profile of a B₀magnetic field produced by a B0 magnet of an MRI system. For example, a piece of material may be initially magnetized with alternating polarization at a high spatial frequency so that the magnetic fields produced cancel out at short distances from the material. Thus, while maximally magnetized (e.g., saturated), the magnetized material will appear un-magnetized in the region of interest of the B₀magnetic field (e.g., within the field of view of an MRI system). To apply a desired magnetic pattern to the material, an automated magnetizing system may control a magnetizing head to magnetize the material in accordance with a desired pattern, while leaving the remaining material untouched so that the high spatial frequency polarization is retained in these regions. In this way, when the patterned shim is added to the system, these regions will not affect the magnetic field in the region of interest but, being magnetized, will be less susceptible to the influence of the B₀magnetic field of the MRI system.

According to some embodiments, a magnetic pattern is applied to magnetic material using an automated subtractive process. For example, magnetic material may be patterned using automated cutting techniques (e.g., using a computer numerical control (CNC) router, laser cutter, etc.) to produce a pattern of magnetized material that improves the profile of a B₀magnetic field produced by a B₀magnet of an MRI system. For example, instead of magnetizing permanent magnetic material according to a desired pattern, pre-magnetized material may be cut in accordance with the magnetic pattern so that remaining material produces a desired magnetic field to facilitate correction of the B₀magnetic field produced by a B0 magnet (e.g., a B0 magnet of a low-field MRI device). Alternatively, the magnetic material may be magnetized after the magnetic material has been patterned by cutting the magnetic material in accordance with the determined pattern configured to improve the profile of the B₀magnetic field produced by the B₀magnet. Other automated subtractive processes include any of various subtractive 3D printing process, etc.

In some circumstances, a magnetic pattern determined to improve the profile of a B0 magnetic field may be disconnected so that the resulting material, after cutting or otherwise removing material, has a plurality of separate unconnected regions. To address these circumstances, the magnetic material may first be bonded to a substrate layer that is not cut, or not fully cut, during the process of patterning the magnetic material such that unconnected regions maintain their relationship to each other so that the desired corrective magnetic field is produced. Alternatively, the same pattern to which the magnetic material is cut may be traced onto a substrate (e.g., an adhesive substrate) and the machined pieces may be affixed to the substrate at the position of the corresponding trace. Other techniques for allowing unconnected pieces of magnetic material to be arranged according to the determined pattern may also be used, as the aspects are not limited in this respect.

According to some embodiments, a magnetic pattern determined to improve the profile of a B₀magnetic field may be applied to magnetic material to produce a permanent magnet shim using one or more automated additive processes. For example, a magnetic pattern may be applied to magnetic material using any of various additive 3D printing techniques that apply magnetic material at locations and in amounts in accordance with the magnetic pattern. Another example of an automated additive process includes any number of spraying techniques such as cold spraying, thermal spraying (e.g., plasma spraying, arc spraying etc.), etc., that are capable of depositing magnetic material on a substrate in accordance with the desired magnetic pattern. For example, using cold spraying, also known as gas dynamic spraying, magnetic material (e.g., a ferromagnetic powder) may be deposited on a substrate via a gas jet to coat the substrate in accordance with the magnetic pattern. It should be appreciated that a combination of additive and subtractive techniques may be used as well, as the aspects are not limited in this respect.

According to some embodiments, a permanent magnet shim is produced for use with an ultra low-field MRI system having a B₀magnetic field less than 10 mT (e.g., greater than or equal to approximately 6.5 mT and less than or equal to approximately 10 mT). According to some embodiments, a permanent magnet shim is produced for use with a very low-field MRI system having a B₀magnetic field greater than or equal to approximately 10 mT and less than or equal to approximately 20 mT. According to some embodiments, a permanent magnet shim is produced for use with a very low-field MRI system having a B₀magnetic field greater than or equal to approximately 20 mT and less than or equal to approximately 50 mT. According to some embodiments, a permanent magnet shim is produced for use with a very low-field MRI system having a B₀magnetic field greater than or equal to approximately 50 mT and less than or equal to approximately 0.1 T. According to some embodiments, a permanent magnet shim is produced for use with a low-field MRI system having a B₀magnetic field greater than or equal to approximately 0.1 T and less than or equal to approximately 0.2 T. According to some embodiments, a permanent magnet shim is produced for use with an MRI system having a B₀magnetic field greater than or equal to approximately 0.2 T and less than or equal to approximately 0.3 T. According to some embodiments, a permanent magnet shim is produced for use with an MRI system having a B₀magnetic field greater than 0.3 T, for example, up to 0.5 T. According to some embodiments, a permanent magnet shim is produced for use with an MRI system having a B₀magnetic field greater than 0.5 T, for example, for a mid-field or high-field MRI system.

Following below are more detailed descriptions of various concepts related to, and embodiments of, shimming techniques for use in, for example, improving the profile of a B₀magnetic field of an MRI system. While some of the techniques described herein are well suited for low-field MRI, the techniques described herein are not limited for use in the low-field context. It should be appreciated that various aspects described herein may be implemented in any of numerous ways. Examples of specific implementations are provided herein for illustrative purposes only. In addition, the various aspects described in the embodiments below may be used alone or in any combination, and are not limited to the combinations explicitly described herein.

FIGS. 1A and 1B illustrate side and top views, respectively, of an automated system for magnetizing material in a desired pattern, in accordance with some embodiments. System 100 may be used, for example, to produce a permanent magnet shim to correct the B₀magnetic field produced by an MRI system, for example, a low-field MRI system. In FIGS. 1A and 1B, system 100 includes a magnetizing head 150 magnetically coupled to magnetic coils 110, each configured to produce a magnetic field that is channeled through magnetizing head 150 to magnetize material 105 (e.g., a sheet of permanent magnet material such as hard ferrite, rare earth magnets or other suitable material that is initially not magnetized, or pre-magnetized with high spatial frequency, as discussed in further detail below) at locations between the tips (also referred to herein as “poles”) of magnetizing head 150. Magnetization of material 105 should be localized to the gap between the tips of the magnetizing head 150 to avoid magnetizing unintended portions of the material 105. To achieve this, frame 140, constructed of any suitable magnetic material, forms a magnetic circuit to provide a return path for the magnetic flux and operates to confine the magnetic fields generated by coils 110. The magnetic circuit includes the magnetizing head 150, formed with a pole gap, that focuses the magnetic fields to provide enhanced flux density between the poles of the magnetizing head 150 sufficient to magnetize the material in the localized region provided there between.

To magnetize a material, it is generally recommended to apply a magnetizing field at least three times the coercive field for the particular material used. The inventors have recognized that the low field strengths involved in some exemplary low-field MRI system facilitate the use of materials needing a weaker magnetic field to magnetize, thus eliminating constraints on the types of material that can be used. For example, material such as neodymium (NdFeB) may be used, though such material usually require fields in excess of 3 T. Additionally, hard ferrites such as strontium or barium ferrites, which can be magnetized at field strengths of ˜1 T (which are more easily generated), may be utilized in the low-field context. These materials are widely available, relatively inexpensive and can be produced in various forms, including flexible sheets that are relatively easy to cut and form into desired geometries, making them attractive permanent magnet material in this respect. However, any suitable material may be used, as the techniques described herein are not limited for use with any particular type or types of magnetic material.

According to some embodiments, to facilitate the use of stronger magnetic materials (e.g., materials with higher coercivity and remanence values), the material may be heated to reduce the strength of the magnetic field needed to magnetize the material. For example, the material may be heated locally (e.g., via laser or induction heating) so that the magnetizing head can magnetize the material in the heated region using a reduce strength magnetic field. Alternatively, the entire sheet of material may be heated, as the aspects are not limited in this respect. As a result, materials that may not be suitable at regular temperatures due to the high magnetic field strengths required, may be utilized via heat assisted magnetizing techniques.

The magnetizing head 150 may be movably coupled to the frame 140 so that the head can be translated over the surface of material 105 as desired (see e.g., the direction arrows illustrated in FIG. 1B). For example, magnetizing head 150 may be translated using one or more linear stages so that control of the magnetizing head can be automated. According to some embodiments, a desired pattern for the magnetizing head can be input to the system and a control program can control the one or more linear stages to translate the magnetizing head so that it traces the desired pattern over the surface of material 105. Magnetizing head 150 may also be controlled in the vertical direction to increase the distance between the poles (e.g., to move the poles away from material 105) to prevent magnetization of material 105 at certain locations as the magnetizing head is translated. This allows for desired locations to be skipped over, permitting the magnetization of patterns that are not continuous. Alternatively, the magnetization process may also be ceased at desired locations by controlling the coils 110 so that they do not generate magnetic fields when the magnetizing head is positioned at locations where no magnetization is desired. According to some embodiments, none, one or both of these techniques may be used to produce a desired pattern of magnetization on material 105.

FIG. 2 illustrates another configuration for an automated magnetization system, in accordance with some embodiments. System 200 includes a magnetizing head 250 having a single tip. Magnetizing head 250 is coupled to and/or integral with an extended portion 240. A plate 260 of ferromagnetic material, such as steel, is provided to support material 205. Coils 210 provide a magnetic field whose flux is provided through material 205 at the location underneath the tip, with plate 260 and extended portion 240 providing a return path for the magnetic flux. Using this geometry, the flux density at the tip of the magnetizing head is strong enough to magnetize material 205, but spreads out sufficiently along the return path via plate 260 such that the flux density is insufficient to magnetize material 205 elsewhere. As a result, material 205 is magnetized only at locations underneath the tip of the magnetizing head 205. Magnetizing head 250 and extended portion 240 may be mounted to linear stages to allow the magnetizing head to be moved over the surface of material 205 to magnetize the material in a desired pattern. As discussed in connection with FIGS. 1A and 1B, to skip over locations on material 205, the magnetizing head 250 may be moveable in the vertical direction (Z-direction) to lift the head away from material 205, and/or the magnetic coils 210 may be cycled on and off, so that desired locations of material 205 remain un-magnetized.

Alternatively (or additionally), plate 260 and/or material 205 may be translated in the XY plane (i.e., the plane of material 205) so that the tip of magnetizing head 205 remains fixed and magnetizes desired portions of material 205 as material 205 passes underneath the pole of the magnetizing head 250. For example, plate 260 may be place on, or may itself be, a translation table capable of being moved in the XY plane.

FIG. 3 illustrates yet another exemplary configuration for an automated magnetization system, in accordance with some embodiments. In the configuration of FIG. 3, material 305 is supported by a rotatable component, illustrated schematically as rotatable component 360 that can be caused to rotate about a central axis 315 (e.g., via one or more motors), thus causing material 305 to rotate or spin about this same axis. According to some embodiments, the rate at which the rotatable component spins may also be controlled. It should be appreciated that the rotatable component may be a platform on which material 305 generally sits and can be secured, or a piece to which material 305 can be otherwise attached or affixed so that rotation of component 360 causes a corresponding rotation of material 305. Any component suitable for this purpose may be used, as the aspects are not limited in this respect.

Magnetization head 350 and coils 310 (if present) are configured to translate in the X-direction as indicated by arrows 325 (e.g., via one or more linear stages). A control component may be coupled so as to coordinate rotation of material 305 (e.g., via rotatable component 360) and translation of the magnetizing head so as to magnetize desired regions of material 305. In particular, based on the magnetic field correction determined for a given B₀magnetic field produced by a B0 magnet after manufacture and assembly, a control program can be provided to rotate material 305 while magnetization head 350 is translated in the X-direction (i.e., in a radial direction with respect to material 305) to magnetize material 305 in a pattern that produces a corrective magnetic field. In this way, the magnetization head 350 may be simplified as it need only be moveable along a single access.

It should be appreciated that any combination of translation and/or rotation of any one or combination of the magnetizing head, magnetic material and/or component provided to support the magnetic material may be employed to allow the magnetic material to be magnetized at desired locations to produce a magnetic pattern configured to improve the profile of the B₀magnetic field of a B₀magnet (e.g., a B0 magnet for use by a low-field MRI device, though not limited to such devices), as the techniques are not limited for use in this respect.

According to some embodiments, the magnetizing head (e.g., magnetizing head 150, 250, 350) is formed by a permanent magnet. Accordingly, in some implementations using a permanent magnet head, the magnetic coils (e.g., magnetic coils 110, 210, 310) may be unnecessary. In particular, the magnetizing head may be constructed of magnetic material capable of producing a magnetic field sufficient to magnetize regions of the magnetic material to which a magnetic pattern is to be applied. In embodiments that utilize permanent magnets for the magnetizing head, it may be beneficial to provide two permanent magnetizing heads, each magnetized in the opposite direction as the other so that regions of the magnetic material may be magnetized in either direction. However, the use of permanent magnetizing heads is not limited in this respect.

According to some embodiments, magnetic coils may be used in combination with a permanent magnet magnetizing head to facilitate providing increased magnetizing field strengths at the same power levels as using magnetic coils alone, or less power can be used to provide the same magnetizing field strengths. It should be appreciated that magnetic coils and/or a permanent magnet magnetizing head can be used alone or in any combination to achieve an automated magnetizing system having desired operating characteristics capable of suitably magnetizing magnetic material of interest to produce permanent magnet shims. It should be further appreciated that the magnetizing head, when fixed at a given location, can be configured to magnetize a region of any desired volume. For example, the magnetization head may be chosen so that a volume of 1 cm³is magnetized when the magnetization head is positioned at a given location. However, it should be appreciated that any size magnetization head may be used, as the aspects are not limited in this respect. Use of a smaller magnetization head allows for a magnetization pattern having finer features to be applied to the magnetic material. Use of a larger magnetization head allows for a given magnetization pattern to be magnetized in less time.

FIG. 4 illustrates a further configuration of a device for magnetizing a permanent magnet shim in directions parallel or transverse to the B₀magnetic field for which correction is desired, in accordance with some embodiments. Magnetizing device 400 comprises coils 410a and 410b for producing a magnetic field to magnetize desired regions of magnetic material 405. The magnetic flux is channeled through magnetizing head 450 in the direction indicated by the arrows, which can be produced in the opposing direction by driving coils 410a and 410b with current flowing in the opposite direction. Magnetic flux 455 across gap 453 magnetizes material 405 in the region below the gap in a direction that is substantially in the plane of material 405. In this manner, material 405 can be magnetized in directions substantially parallel to the plane of material 405. For a B0 magnet having a bi-planar or single-sided geometry, material 405 can be magnetized in directions transverse (e.g., substantially perpendicular) to the B₀magnetic field for which correction is desired. For a B0 magnet having a cylindrical geometry (e.g., a solenoid or Halbach-type magnet), material 405 can be magnetized in directions substantially parallel (e.g., aligned and/or anti-aligned) with the B₀magnetic field.

Magnetizing head 450 may be coupled to frame 400 via one or more linear stages that allow the magnetizing head 450 to be moved in the X-direction and/or Z-direction so that that the magnetizing head 450 can be positioned above desired regions of magnetic material 405 to apply a magnetic pattern to material 405 to produce a magnetic field that improves the profile of a B₀magnetic field of a B₀magnet, for example, a B₀magnet configured for use in a low-field MRI device. As one example, magnetizing head 450 may be coupled via linear stages that allow the magnetizing head to be controlled in the X-direction and Z-direction so that the magnetizing head can be moved to desired locations in the XZ plane of material 405. Alternatively, magnetizing head 450 may be coupled to allow for control in along the X-axis (i.e., in the X and −X directions) while material 405 is rotated (e.g., via a rotatable component as described in connection with FIG. 3) so that the magnetizing head can be positioned over desired regions of material 405. Other ways of positioning magnetizing head 450 may also be used, as the aspects are not limited in this respect.

According to some embodiments, magnetizing head 450 may be rotatably coupled to frame 400 to allow the magnetizing head to be swiveled about axis 415. In this way, regions of material 405 can be magnetized in any desired direction in the plane of magnetic material 405. It should be appreciated, however, that the ability to rotate magnetizing head 450 is not a requirement and the magnetizing head 450 may be fixed in orientation in some embodiments.

In some circumstances, it may be desirable to have the ability to apply a magnetic pattern wherein regions can be magnetized substantially in alignment, substantially in anti-alignment and/or substantially in directions transverse to the B₀magnetic field being corrected. Thus, according to some embodiments, an automated device for applying a magnetic pattern to produce a permanent magnet shim may be provided with dual magnetizing heads, allowing for regions of the permanent magnet shim to be magnetized in directions substantially parallel and substantially perpendicular to the B₀magnetic field. According to some embodiments, a first magnetizing head is provided to magnetize regions of the permanent magnet shim in directions substantially parallel to the B₀magnetic field (e.g., in alignment or anti-alignment with the B₀magnetic field), and a second magnetizing head is provided to magnetize regions of the permanent magnet shim in directions substantially perpendicular to the B₀magnetic field (e.g., in directions transverse to the B₀magnetic field). According to some embodiments, the dual magnetizing heads are provided in close proximity (e.g., side-by-side).

To magnetize a region in a desired direction, the respective magnetizing head may be operated (e.g., by providing current to operate coil(s) coupled to the selected magnetizing head) while the other magnetizing head remains non-operational (e.g., by not providing current to respective coil(s) and/or by moving the magnetizing head away from the magnetic material being magnetized). According to some embodiments, a first pass over the permanent magnet shim is performed using the first magnetizing head and a second pass over the permanent magnet shim is performed using the second magnetizing head, or vice versa, to reduce the amount of switching between operating the respective magnetizing heads.

FIGS. 5A and 5B illustrate a device for applying a magnetic pattern to a permanent magnet shim having dual magnetizing heads, in accordance with some embodiments. Device 500 comprises a first magnetizing head 550a configured to magnetize regions of magnetic material 505 in the Y and −Y directions (e.g., in directions substantially parallel to the B₀magnetic field of a bi-planar or single-sided B0 magnet), and a second magnetizing head 550b configured to magnetize regions of magnetic material 505 in directions in the XZ plane (e.g., in directions substantially perpendicular to the B₀magnetic field of a bi-planar or single-sided B0 magnet). For example, magnetizing head 550a may be similar to the magnetizing heads illustrated in FIGS. 1 and 3, or may be any other suitable magnetizing head, and magnetizing head 550b may be similar to the magnetizing head illustrated in FIG. 4 or any other suitable magnetizing head. The dual magnetizing heads may be constructed using electromagnet coils (not shown in FIG. 5) as described in connection with FIGS. 1-4, using permanent magnet material, or a combination of both, as the aspects are not limited in this respect.

Magnetizing head 550a (upper) and magnetizing head 550b are coupled to a rotatable component 580 that allows the respective magnetizing heads to be selectively rotated into place depending on the direction of magnetization desired, as illustrated by the two positions shown in FIGS. 5a and 5b, respectively. The dual magnetizing heads can be positioned at desired locations relative to magnetic material using any of the techniques described herein (e.g., linear stages, motors, rotating tables, etc.) to apply a desired magnetic pattern to magnetic material 505. As discussed above, magnetizing a permanent magnet shim in accordance with a desired pattern may be performed in two passes, or may be performed in a single pass. Switching between magnetizing head 550a and 550b may be controlled in an automated way (e.g., under control of the device using motors or other automated means), may be manually switched, or both. Lower magnetizing head 550a may also be coupled to a component that allows the head to be rotated (e.g., as illustrated in FIG. 5B) or otherwise positioned away (e.g., to be raised and lowered) from magnetic material 505 when the magnetizing head is not being operated. As with magnetizing head 450 illustrated in FIG. 4, wherein the magnetization head may be rotatably coupled to frame 400 to allow the magnetizing head to be swiveled about axis 415 to magnetize regions of magnetic material in any desired direction in the plane of magnetic material, magnetizing head 550b may be rotatably coupled to rotatable component 580 to allow regions of magnetic material 505 to be magnetized in any desired orientation with respect to a planar surface of the magnetic material.

FIGS. 23A and 23B illustrate a device for magnetizing a permanent magnet shim according to a magnetic pattern, in accordance with some embodiments. As illustrated in the portion of device 2300 illustrated in FIGS. 23A and 23B, a magnetization head 2350 comprises a pair of coils 2350a and 2350b configured to generate a magnetic field sufficient to selectively magnetize regions of magnetic material 2305. Coils 2350a and 2350b may be copper or another suitable conductive material arranged in a number of turns about respective center portions 2385a and 2385b, respectively. Coils 2350a and 2350b may be formed of conductive ribbon (e.g., copper), or sheets, disks or plates of conductive material manufactured in a generally helical geometry. To magnetize a region of magnetic material 2305, a current pulse is applied to coils 2350a and 2350b. For example, a relatively high amperage (e.g., 10,000 amps) current is applied for a relatively brief interval of time (e.g., approximately 1 ms) to produce a strong magnetic field at the center.

Due to the geometry of the coils, a relatively strong magnetic field is produced through centers 2385a and 2385b in either direction indicated by arrow 2355 depending on which direction the current pulse is applied. Each turn of the conductor has a relatively wide surface of conductive material in the radial direction (e.g., a relatively large radial width w) that provides a measure of shielding that substantially limits magnetic field production to the diameter of the center portions of the coils (e.g., center portions of approximately 5 mm in diameter). Specifically, a strong magnetic field is generated at the center where most of the current pulse circulates while eddy currents generated at increasing distances from the center resist magnetic field production outside or in the close vicinity of the boundary of center portions 2385a and 2385b, providing improved spot magnetization of magnetic material 2305. That is, when a current pulse is applied, eddy currents generated at increasing radial distances from the center prevent the magnetic fields from diffusing outwards, confining magnetic fields of sufficient strength to magnetize the magnetic material 2305 substantially to the diameter of center portions 2385a and 2385b. If the duration of the current pulse is chosen appropriately, each current pulse applied to magnetize a given region of magnetic material 2305 subsides before the eddy currents have dissipated enough to permit production of a magnetic field strong enough to magnetize the magnetic material outside the center portion. As a result, magnetization of magnetic material 2305 is localized substantially to the boundary of the center portions. In this manner, a localized magnetizing field can be produced by magnetization head 2350 to magnetize magnetic material 2305 in accordance with a desired magnetic pattern to produce a permanent magnet shim.

It should be appreciated that magnetization head 2350 may be produced without using steel or other ferromagnetic materials. Magnetization head 2350 may be controlled to traverse magnetic material 2305 using any of the example linear stage and/or radial techniques discussed in the foregoing, or using any other suitable means to control magnetization head 2350. It should be appreciated that magnetization head 2350 may be used to produce a single polarity or a dual polarity magnetic pattern.

FIG. 6 illustrates a method of producing a permanent magnet shim, in accordance with some embodiments. Method 600 may be performed to improve the profile of the B₀magnetic field produced by any type of B₀magnet, including a permanent B₀magnet, a B₀electromagnet or any combination thereof. For example, method 600 may be performed to correct non-uniformities and/or offsets in the field strength of the B₀magnetic field produced by the exemplary electromagnets and exemplary permanent magnets discussed in further detail below (e.g., in connection with FIGS. 17-19), and/or any of the exemplary B0 magnets described in U.S. patent application Ser. No. 14/845,652 ('652 application), titled “Low Field Magnetic Resonance Imaging Methods and Apparatus,” and filed Sep. 4, 2015 and/or U.S. patent application Ser. No. 14/846,255 ('255 application), titled “Ferromagnetic Augmentation for Magnetic Resonance Imaging,” and filed on Sep. 4, 2015.

According to some embodiments, method 600 may be performed to produce generally planar permanent magnet shims that can be arranged proximate one or both of the bi-planar B₀magnets in open magnet arrangements. In this respect, a permanent magnet shim may be produced and arranged on both sides of the field of view of a bi-planar B₀magnet, or on a single side of a bi-planar B₀magnet. In embodiments where multiple permanent magnet shims are used (e.g., a pair of permanent magnet shims associated with respective sides of a bi-planar B0 magnet), the permanent magnet shims may be produced having different or the same magnetic pattern provided thereon. According to some embodiments, method 600 may be used to produce a permanent magnet shim for other geometries (e.g., cylindrical geometries), for example, by applying a magnetic pattern to flexible material that can be shaped or otherwise formed to a particular geometry, as discussed in further detail below.

Multiple permanent magnet shims may also be used to provide different corrective magnetic fields to improve the profile of the B0 magnet. For example, one or more permanent magnet shims may correct for non-uniformities resulting from manufacturing tolerances (e.g., variability in production processes) and/or non-uniformities resulting from a ferromagnetic yoke used to increase the magnetic flux density in the field of view of a B₀magnet (e.g., an asymmetric yoke as discussed in further detail below). One or more permanent magnet shims may be used to raise or lower the field strength of the B₀magnetic field produced by the B₀magnet to correct for a B₀offset. It should be appreciated that multiple types of corrections (e.g., improved homogeneity, B₀offset, etc.) may be provided by a single permanent magnet shim, or using a combination of permanent magnet shims produced either independently or concurrently, as the aspects are not limited in this respect.

In act 610, deviation of a B₀magnetic field from a desired B₀magnetic field of a B₀magnet is obtained. In particular, B₀magnets are designed to produce a uniform B₀magnetic field at a specific field strength. Deviation of a B₀magnetic field from uniform, referred to herein as non-uniformities or inhomogeneity, degrades the performance of an MRI system incorporating the B0 magnet (e.g., by causing a proportional reduction in the signal-to-noise ratio (SNR) for the system by degrading MR signal excitation and/or detection performance, causing image distortion, etc.). Deviation of a B₀magnetic field from the desired field strength, referred herein to as a B₀offset, shifts the Larmor frequency of the B₀magnet, causing a mismatch between the Larmor frequency and the intended operating frequency of the MRI system that, if not corrected, also degrades the performance. Thus, in act 610, deviation of the B₀magnetic field, either non-uniformities and/or B₀offsets are determined. The determined deviation may be represented in any suitable way. For example, spherical harmonics (or any other suitable series of basis functions) may be used to provide a representation of magnetic field variation to limit the number of parameters needed to characterize the magnetic field and/or to improve numerical stability.

Practical B₀magnet designs are not able to achieve perfect uniformity at exactly a desired field strength. Thus, some deviation of a B₀magnetic field from a desired profile is inherent in the design of the system. In addition, variability in manufacturing processes cause further deviation of a B₀magnetic field produced by a B₀magnet from its desired uniformity and/or field strength, which typically varies in extend for each production of a B₀magnet. Further, the design of the B₀magnet itself may introduce deviations of the B₀magnetic field from a desired profile. For example, a ferromagnetic yoke designed to increase the magnetic flux in the region of interest may in some circumstances introduce non-uniformities in the B₀magnetic field, as discussed in further detail below. Deviation of a B₀magnetic field inherent in or introduced by the design of the B₀magnet and/or introduced by the manufacturing processes may be determined by performing act 610.

Deviation from a desired B₀magnetic field may be obtained in a number of ways. For example, in act 610, the B₀magnetic field produced by a B₀magnet configured for use in MRI system may be measured in a region of interest. To measure the B₀magnetic field, magnetic field sensors may be arranged spatially to measure or map the magnetic field generated by the B0 magnet within the relevant field of view of a the MRI device. Alternatively, a sensor or an array of sensors can be moved about a region of interest to measure the magnetic field produced by the B0 magnet. Any number or type of sensors may be utilized that allow the profile of the B₀magnetic field to be suitably characterized. For example, Hall probes, NMR probes, fluxgate sensors, solid state magnetometers or any other sensor capable of detecting magnetic fields to capture relatively small variations may be utilized.

Deviation from a desired B₀magnetic field may also be obtained in act 610 by computing the deviation based on properties of the design. In particular, deviation inherent in the design of the B₀magnet may be evaluated based on the known design specification. For example, non-uniformities introduced by a yoke can be determined from the known properties of the yoke and the known relationship between the yoke and the B₀magnet. Performance of act 610 should be able to sufficiently characterize deviation of the B₀magnetic field so that unsatisfactory degrees of inhomogeneity and/or B₀offset can be detected and corrected via one or more permanent magnet shims. Deviation from a desired B₀magnetic field may also be obtained by retrieving and/or receiving a previously determined deviation, for example, a deviation determined from a previous measurement or a deviation determined from a previous computation. As such, according to some embodiments, act 610 may be performed without necessarily determining the deviation.

In act 620, a magnetic pattern configured to produce a corrective magnetic field based on the determined deviation to improve the profile of the B₀magnetic field is determined. The magnetic pattern may be determined in a number of ways. According to some embodiments, a model of a permanent magnet shim is generated, for example, a computer generated model configured to simulate properties of the permanent magnet shim. A magnet pattern that, when applied to magnetic material, provides the corrective magnetic field may be determined, for example, via an optimization scheme, examples of which are described in further detail below. For example, an optimization may be used to determine a magnetic pattern that indicates which regions of magnetic material to which the magnetic pattern is applied are to be magnetized, in what direction and/or at what field strength. Additional techniques for determining a magnetic pattern are also discussed in further detail below.

In act 630, the determined magnetic pattern is applied to magnetic material to produce one or more permanent magnet shims that contribute to and improve the B0 magnetic field produced by a B0 magnet. Applying a magnetic pattern to magnetic material refers to any technique that transfers, provides or otherwise produces magnetized material in accordance with the determined magnetic pattern, including, but not limited to using a magnetizing head to traverse and magnetize magnetic material in accordance with the magnetic pattern, cutting or removing magnetic material to produce magnetized material in accordance with the magnetic pattern, additive techniques such as 3D printing, spraying, etc. that produce or provide magnetic material in accordance with the magnetic pattern, etc.

According to some embodiments, a ferromagnetic sheet of material, initially not magnetized, or pre-magnetized at high spatial frequency, may have a determined magnetic pattern applied using an automated magnetizing system, such as those described in connection with FIG. 1A, 1B or 2. In particular, the determined magnetic pattern may be provided to a control system of the automated magnetizing system to control the magnetizing head to traverse the pattern over the surface of the magnetic material (e.g., a ferromagnetic sheet of initially un-magnetized material) to apply the magnetic pattern to the material to produce a permanent magnet shim. The permanent magnet shim may then be arranged proximate the field of view to produce, via the magnetic pattern, a magnetic field that contributes to the B₀magnetic field produced by the MRI device (e.g., a low-field MRI device) to improve the field profile (e.g., by increasing the homogeneity of the B₀magnetic field).

According to some embodiments, a determined magnetic pattern may be applied to magnetic material by cutting the magnetic material in accordance with the determined magnetic pattern. For example, a sheet of magnetic material may be magnetized and then subsequently patterned via cutting or removal of magnetic material (e.g., via a CNC router, laser cutter or any suitable machining process, subtractive 3D printing techniques, etc.) in accordance with the magnetic pattern. That is, regions of the magnetic material determined as not contributing to the corrective magnetic field may be removed using any suitable technique, leaving only regions corresponding to the magnetic pattern that contribute to the corrective magnetic field. Alternatively, the magnetic material may be initially un-magnetized when the magnetic material is patterned in accordance with the magnetic pattern, after which the patterned magnetic material is subsequently magnetized to produce the permanent magnet shim. The technique of cutting or removing magnetic material to apply the determined magnetic pattern may provide a simpler approach by eliminating the automated magnetizing head apparatus (e.g., eliminating the exemplary apparatus illustrated in FIGS. 1-4), reducing the cost and complexity of producing a permanent magnet shim in some circumstances. For example, magnetizing the magnetic material all at once, either before or after it has been patterned, eliminates the need for the relatively time consuming and complex process of controlling a magnetizing head to traverse and magnetize each region of the magnetic material corresponding to the determined magnetic pattern.

As discussed above, when a magnetic pattern is applied using subtractive process (e.g., cutting, subtractive 3D printing), the patterned magnetic material may be affixed or adhered to a substrate, either prior or subsequent to cutting, so that unconnected pieces of magnetic material are positioned and maintained in the correct locations relative to one another so that the determined magnetic patterned is preserved. It should be appreciated that the magnetized regions or pieces of magnetic material may be attached to the substrate in any suitable manner. In some embodiments, the substrate provides a measure of stability for the patterned magnetized material forming the permanent magnet shim. According to some embodiments, a determined magnetic pattern is applied using suitable additive processes such as additive 3D printing techniques, cold spray techniques, etc. Any other suitable techniques for applying a determined magnetic pattern may be used, as the aspects are not limited in this respect.

As discussed above, to determine a deviation of the B₀magnetic field produced by a B₀magnet subject to correction (e.g., to perform act 610 in method 600 illustrated in FIG. 6) the B₀magnetic field may be measured to characterize its profile so that shimming techniques described herein can be applied. FIGS. 7A-7D illustrate exemplary approaches to measuring the B₀magnetic field produced by a B0 magnetic so as to characterize the profile (e.g., the strength and/or variation) of the B₀magnetic field to facilitate correction and/or improvement thereof. FIG. 7A illustrates a bi-planar B0 magnet 775 in which a sensor 755 is placed within the field produced by B0 magnet 775 and its location varied in three-dimensions so as to measure the B₀magnetic field at desired locations in space. The sensor may be of any type suitable for measuring the local magnetic field produced by B₀magnet, some exemplary sensors of which were discussed above in connection with method 600 illustrated in FIG. 6. The sensor may be moved to as many locations as desired to suitably characterize the magnetic field so that a correction can be computed. FIG. 7B illustrates the same technique as shown in FIG. 7A in the context of a cylindrical geometry B₀magnet. It should be appreciated that measuring the magnetic field using a sensor 755 may be used with any geometry, as the technique is not limited in this respect.

To facilitate a faster more cost effective means to measure the B₀magnetic field of a subject B₀magnet, an array of sensors 765 may be used as illustrated in FIGS. 7C and 7D. Sensor array 765 may include any number of sensors of any type suitable for measuring magnetic fields. Similar to the techniques described in connection with sensor 755, sensor array 765 may be moved in three dimensions to measure the B₀magnetic field produced by B₀magnet 775 at desired locations in space. In the schematic drawings in FIGS. 7C and 7D, the sensor array is illustrated as a rectangular array of sensors. However, the sensors in an array may be configured in any way, for example, spherically (e.g., arranged as if on the surface of a sphere and/or within a sphere), within or substantially within a plane, or in any other desired configuration or geometry, as the aspects are not limited in this respect.

The inventors have recognized that the relatively small magnetic fields generated in many low field contexts facilitates the use of relatively inexpensive solid state sensors. For example, solid state sensors may be used to form sensor array 765 illustrated in FIGS. 7C and 7D. According to some embodiments, sensor array 765 may comprise a number of solid state sensors sufficient to measure the entirety of the region of interest of a B₀magnetic field in a single measurement. For example, hundreds or thousands (or more) sensors may be integrated in a sensor array capable of capturing sufficient information about the B₀magnetic field in a region of interest (e.g., the entirety or substantially the entirety of the useful field of view of the B₀magnet in the context of a low-field MRI device) via a single measurement by the sensors in the array (or in a relatively small number of measurements). In this manner, a B₀magnetic field can be quickly and effectively characterized. It should be appreciated that a “one-shot” sensor array can be produced to measure a desired region of interest of a B₀magnetic field at any desired resolution by appropriately choosing the number of sensors and spatial arrangement (e.g., spacing between sensors). It should be further appreciated that any type of sensor may be used to form a sensor array, including a one-shot sensor array, though costs associated with many sensors may render such implementations less desirable from a cost perspective.

FIG. 8 illustrates a further sensor arrangement that may be suitable for characterizing the B₀magnetic field produced by a B₀magnet, in accordance with some embodiments. In FIG. 8 a sensor 865, comprising a plurality of coils 867, is provided within the region of interest of B₀magnet 875. Sensor 865 is rotated as indicated by the arrow (either about an axis along the edge of the sensor or an axis through the center of the sensor) and the flux-induced voltages from each of the coils as it rotates can be used to infer the magnetic field produced by B₀magnet 875. In this manner, the magnetic field produced by a B₀magnet can be measured in three dimensions via a rotating array of coils.

To assist in both determining the magnetic pattern that provides a correction to the B₀magnetic field of a given B₀magnet and in applying a desired magnetic pattern to magnetic material (e.g., to assist in performing acts 620 and 630 of method 600 illustrated in FIG. 6), the magnetic material that will form a permanent magnet shim may be magnetized can be logically partitioned into a plurality of regions. For example, a model of the magnetic material may be logically partitioned to spatially divide the model into the plurality of regions. According to some embodiments, the process of determining a magnetic pattern (e.g., by performing act 620 in method 600 illustrated in FIG. 6) includes determining which of the plurality of regions will be magnetized to contribute to the corrective magnetic field to be produced by the permanent magnet shim when the magnetic pattern is applied (e.g., by performing act 630 in method 600 illustrated in FIG. 6).

According to some embodiments, the process of determining a magnetic pattern includes determining the direction (e.g., polarity) of the magnetization applied to each of a plurality of regions to provide a desired corrective magnetic field to be produced by the permanent magnet shim when the magnetic pattern is applied. A magnetic pattern may indicate which regions of a logical partitioning are to be magnetized, in which direction and/or and at what field strength. According to some embodiments, a magnetic pattern indicates that at least one region is to have a magnetization oriented in a first direction (e.g., aligned with the B₀magnetic field, aligned with the normal to a planar surface of the magnetic material to which the magnetic pattern is to be applied, etc.), and indicates that at least one region is to have a magnetization oriented in a second direction (e.g., anti-aligned or opposite the B₀magnetic field, anti-aligned or opposite the normal to the planar surface of the magnetic material to which the magnetic pattern is to be applied, etc.). While the first and second directions may be opposite or supplementary each other (e.g., opposing polarities), the first and second directions may have other relationships to one another, such as complementary or orthogonal relationships, etc., as the aspects are not limited in this respect.

When applying a determined magnetic pattern includes using a magnetizing head that traverses magnetic material to magnetize the material in accordance with the magnetic pattern, the determined magnetic pattern may indicate which of the plurality of regions are to be magnetized and/or in what direction (e.g., either in alignment with the B₀magnetic field or opposite or anti-alignment with the B₀magnetic field), and/or which of the plurality of regions should be left alone (either in a magnetized or de-magnetized state depending on the implementation). For example, each region may be magnetized according to a given polarization, magnetized according to the opposite polarization or passed over by the magnetizing head. When applying a determined magnetic pattern includes using subtractive processes (e.g., cutting or subtractive 3D printing), the determined magnetic pattern may indicate which of the plurality of regions contribute to the corrective magnetic field and which of the plurality of regions are to be cut away or removed. When applying a determined magnetic pattern includes using additive processes, the determined magnetic pattern may indicate which regions magnetic material are to be added.

As shown in FIG. 3 and FIG. 9A, a logical partitioning is formed via intersecting concentric ellipses and radial lines extending from the center of the material to points on the perimeter to form a plurality of regions 307 and 907, respectively. This logical partitioning may be particularly suitable for implementations that include an automated magnetizing head. For example, in the context of the exemplary system in FIG. 3, when applying a magnetic pattern to magnetic material to produce a corrective magnetic field to improve the profile of a B₀magnetic field of a given B0 magnet, the automated magnetization system may control the magnetizing head while the material is rotated via rotatable component 360 to magnetize selected regions 307 to achieve a magnetization pattern configured to improve the profile of the B₀magnetic field produced by the given B₀magnet. The pattern of partitioning illustrated in FIGS. 3 and 9A results in regions that are smaller towards the center of material 305/905 and larger towards the periphery. In some B₀magnet geometries (e.g., in bi-planar configuration), the influence of magnetized regions on the region of interest of the B₀magnetic field (e.g., the field of view of a resulting low-field MRI system) decreases the farther the region is from the center due to the corresponding increased distance from the region of interest due to the magnetic field strength decreasing as a cube of the distance. As such, differing region sizes may make sense in such implementations, providing higher levels of granularity (e.g., higher “resolution”) towards the center where magnetized regions will have the greatest impact, and less granularity towards the periphery. In embodiments in which applying the magnetic pattern includes subtractive processes (e.g., laser cutting or subtractive 3D printing), the logical partitions may form the borders along which the magnetic material is cut or removed. In embodiments in which applying the magnetic pattern includes additive processes, the logical partitions may form the boundaries of where magnetic material is added.

It should be appreciated that other logical partitions, as well as other shapes for the magnetic material are suitable and may be desirable for certain implementations. For example, FIG. 9B illustrates circular-shaped magnetic material 905 with a square logical partitioning, which according to some embodiments, are uniform in size, though this is not a limitation as the sizes of the partitions can be varied as desired to provide a plurality of regions 907′. FIG. 9C illustrates circular-shaped magnetic material 905 that is logically partitioned by tessellation. For example, the magnetic material 905 may be logically partitioned using a triangulated mesh to form a plurality of regions 907″. It should be appreciated that magnetic material may be tessellated using polygons having any number of sides, as this technique is not limited to any specific tessellated geometry.

According to some embodiments, a tessellated mesh used to logically partition the magnetic material may be iteratively refined during an optimization process formulated to determine a magnetic pattern to be applied to produce a permanent magnet shim, examples of which are described in further detail below. FIGS. 10A-C illustrate rectangular-shaped magnetic material 1005 logically partitioned in the manner illustrated in FIGS. 9A-C, respectively, providing a plurality of regions 1007, 1007′ and 1007″ on a rectangular sheet of magnetic material. FIG. 20 illustrates concentric rings that constrain the region where magnetic material can provided, aligning the permanent magnet shim with, for example, permanent magnet rings of a B0 magnet, as discussed in further detail below. It should be appreciated that any size and shape may be used for the magnetic material, as well as for the logical partitioning of the material, as the techniques described herein are not limited for use in this respect.

Partitioning may also assist in the process of determining the magnetic pattern needed to provide a desired correction. According to some embodiments, a magnetic pattern is determined using a “library” of magnetic contributions or effects compiled by magnetizing regions of material and measuring the magnetic field that results. A library may be compiled in this manner for the various, shapes, sizes and materials used for magnetic shims as well as for any desired partitioning scheme. Using the exemplary magnetic material 305 illustrated in FIG. 3, for each type of material used, a single region 307 may be magnetized and the resulting magnetic field recorded. This may be repeated for each region to which the material has been partitioned so that the individual magnetic contribution or effect resulting from magnetizing each respective region is known and recorded in a corresponding library. When the deviation of a subject B₀magnetic field from a desired profile is determined (e.g., by performing act 610 in method 600 illustrated in FIG. 6), the library corresponding to the type, shape and partitioning scheme of the shim being produced may be searched to locate a pattern of regions that, when magnetized, will produce the desired magnetic pattern.

Alternatively, instead of actually magnetizing regions of material and measuring the magnetic field produced, the magnetic contribution of regions of a given size and shape (i.e., according to a given partitioning scheme) for material of given type and shape may be modeled. A model may be produced for any of various desired shapes, sizes and types of materials to be used, as well as for different partitioning schemes. Thus, when the deviation from a desired profile is determined for a given B₀magnetic field, the model corresponding to the type and shape of material and the partitioning scheme of the shim being produced may be used to identify a pattern of regions that will produce the desired magnetic pattern. Examples of employing a model to determine a magnetic pattern are discussed in further detail below. It should be appreciated that other techniques may be used to determine a magnetic pattern, as the aspects are not limited in this respect.

The search for a magnetic pattern that produces a desired corrective magnetic field may be performed using any technique and/or optimization scheme, in connection with either of the techniques described above (e.g., using a library, model, etc.). According to some embodiments, an optimization scheme to locate or identify a magnetic pattern suitable for generating a desired corrective magnetic field includes minimizing the total volume of material that needs to be magnetized to produce the corrective magnetic field. In this manner, a magnetic pattern may be determined that reduces or minimizes the amount of magnetization to be applied to the material, reducing the time required to produce a shim that produces the desired corrective magnetic field.

FIG. 11 is a flowchart depicting a method of determining a magnetic pattern to be applied to magnetic material, in accordance with some embodiments. Method 1100 may be performed, for example, as act 620 of method 600 illustrated in FIG. 6. In particular, once the deviation of the subject B₀magnetic field from a desired profile is (e.g., by performing act 610 of method 600), method 1100 may be performed to determine a magnetic pattern to be applied to magnetic material that is adapted to provide a corrective magnetic field to compensate for the determined deviation to improve the profile of the B₀magnetic field produced by a B₀magnet. A magnetic pattern produced using method 1100 may be applied in any manner, including using any one or combination of a magnetizing head, subtractive processes, additive processes, etc.

In act 1132, a model of the magnetic material (e.g., a mathematical or geometric representation of relevant properties of the magnetic material to which a magnetic pattern is to be applied) is generated. A model may include the geometry of the magnetic material (size, shape, boundaries, etc.), one or more magnetic properties of the magnetic material and/or any other parameters or properties that facilitate determining a magnetic pattern that improves the profile of a B₀magnetic field. Numerous software tools are available that facilitate the generation, manipulation and/or simulation of a model. According to some embodiments, the model generated in act 1132 allows for the magnetic field generated by the magnetic material to be simulated for different magnetic patterns.

In act 1132a, the magnetic material is tessellated to incorporate a logical partition into the model of the magnetic material. For example, the magnetic material may be tessellated using a triangular mesh as shown in FIG. 9C or FIG. 12A. These exemplary tessellations include regions in which the logical partition is not permitted to provide a region that can be indicated as contributing to a magnetic field correction. For example, the circular regions in the mesh may designate areas that must remain free of magnetic material either to allow the resulting permanent magnet shim to be affixed to the B0 magnet, another shim, and/or to ensure that the permanent magnet shim does not interfere with other aspects of the B0 magnet design, though in some embodiments, no such regions need to be designated. It should be appreciated that magnetic material may be logically partitioned by applying any suitable partitioning of the model and may be partitioned at any desired resolution. For example, the model of the magnetic material may be tessellated at a desired resolution by selecting the number of control points (vertices) used in tessellating the model of the magnetic material. As an example, the model may be tessellated to provide 40 mm, 20 mm, 10 mm, 5 mm, 1 mm or less resolution. The higher the resolution (e.g., the smaller the tessellated partitions), the more computationally intensive the process of determining a magnetic pattern becomes, as discussed in further detail below.

In act 1134, a magnetic pattern is determined that, when applied to magnetic material, produces a corrective magnetic field that improves the profile of a B0 magnetic field. In particular, using the logical partition applied in act 1132a to partition the magnetic material into a plurality of regions (e.g., polygons), an optimization may be performed to determine which of the regions should be magnetized, in what polarity/direction and/or at what field strength to produce a corrective magnetic field that corrects, at least in part, the deviation of the B₀magnetic field (e.g., as determined in act 610 of method 600). According to some embodiments, a dual state solution is utilized to produce a magnetic pattern. As one example of a dual state solution, the optimization determines a magnetic pattern that indicates whether each of the plurality of partitioned regions is to be magnetized in a given polarity or not magnetized. As another example of a dual state solution, the optimization determines whether each of the plurality of partitioned regions is to be magnetized in a given polarity or the opposite polarity.

According to some embodiments, a tri-state solution is utilized to produce a magnetic pattern. As one example of a tri-state solution, the optimization determines a magnetic pattern that indicates whether each of the plurality of partitioned regions is to be magnetized in a given polarity, magnetized in the opposite polarity, or not magnetized. According to some embodiments, additional states may be utilized in determining a magnetic pattern. For example, the optimization may determine a magnetic pattern that indicates whether each of the plurality partitioned regions is to be magnetized and in what direction, not magnetized and/or the strength of the magnetization for the respective magnetized region (i.e., different regions may be assigned different magnetic field strengths), or any combination thereof. It should be appreciated that determining a magnetic pattern is not limited for use with any particular type of solution, and any suitable method of producing a magnetic pattern that compensates for a determined deviation of a B₀magnetic field may be used.

FIG. 12B illustrates an exemplary magnetic pattern 1215 determined using an optimization that seeks to minimize the volume of the magnetized regions. In the exemplary magnetic pattern 1215 illustrated in FIG. 12B, the darker shaded regions indicate the portions of the magnetic material that are to be magnetized (i.e., portions of the magnetic material that contribute to the corrective magnetic field produced by the permanent magnet shim to which the magnetic pattern is applied), exemplary magnetized regions 1227 of which are labeled on the magnetic pattern 1215. The lighter shaded regions 1217 indicate portions that do not contribute to the corrective magnetic field. As discussed above, magnetic pattern 1215 may be applied to the magnetic material in any number of ways (e.g., by performing act 640 in method 600 illustrated in FIG. 6), including but not limited to using an automated magnetizing head (either on pre-magnetized or un-magnetized magnetic material), subtractive processes such as cutting away or removing portions determined as not contributing to the corrective magnetic field (either before or after magnetizing the magnetic material), additive processes such as additive 3D printing, cold spray techniques, etc. The resulting permanent magnet shim may then be arranged or positioned proximate the B₀magnet to assist in correcting the B₀magnetic field.

Numerous optimization methodologies may be used to determine a magnetic pattern and the aspects are not limited for use with any particular optimization scheme. According to some embodiments, an optimization scheme may be configured to minimize the volume of magnetized regions. According to some embodiments, an optimization scheme may be configured to maximize the volume of magnetized regions. One exemplary technique of which may be formulated as follows. The effect of all of the regions resulting from the logical partitioning (e.g., the triangulated mesh illustrated in FIG. 12A) are evaluated based on the model (e.g., based on the size, shape, magnetic properties, etc., of the magnetic material being modeled). The optimization problem to be solved can be expressed as follows.

$\begin{matrix} minimize & \sum_{i} w_{i} ❘ x_{i} ❘ \\ subject to & 𝒞_{l} \leq AX \leq 𝒞_{u} \\ B_{l} \leq X \leq B_{u} \end{matrix}$

In this formulation, the optimization seeks to minimize the volume of magnetic material that is magnetized (i.e., that contributes to the magnetic field correction) in the magnetic pattern. It should be appreciated that the volume of magnetic material that is magnetized may be maximized (e.g., by maximizing the summation in the above formulation), which may have some benefits in some circumstances, as discussed in further detail below. The variables x_irepresent the values that are assigned to the i regions of the logical partition of the model of the magnetic material, which are allowed to take on values between a lower bound B_land an upper bound B_u. For example, the values x_imay be allowed to take on values from a lower bound of zero, indicating that the corresponding region does not contribute a magnetic field correction, to an upper bound of one, indicating that the corresponding region produces a maximum magnetic field contribution. The weights w; correspond to any one or combination of weights that may be applied to the variables x_i, for example, area, volume, etc. For example, the normalized contribution of each region i may be weighted according to the area or volume of the region according to the logical partition. The weights w_imay also be used to, for example, favor one or more other properties of each region, for example, the location of the region, connectedness of the region with other regions, etc. Thus, X represents a magnetic pattern indicating, inter alia, which of the plurality of regions contribute to the magnetic field correction. Matrix A is a magnetic model of the magnetic material that, when applied to X, produces a representation of a corrective magnetic field that would be produced if the magnetic pattern X were applied to the magnetic material. Accordingly, the exemplary optimization determines a magnetic field correction AX that sufficiently compensates for the determined deviation of the subject B₀magnetic field from a desired profile using a minimum number of contributing regions. As with the determined deviation, matrix A may represent the magnetic field using an appropriate set of basis functions, such as spherical harmonics, or any other suitable representation.

Stated differently, the exemplary optimization determines a magnetic field correction AX that, when applied to the magnetic material, produces a corrective magnetic field that satisfactorily counteracts the determined deviation, thus bringing the B₀magnetic field nearer the desired profile. Provided there are sufficient degrees of freedom and, more particularly, that the logical partitioning is at a high enough resolution to provide a sufficient number of regions, the minimization will drive the values x_ito the bounds B_l, B_u. For example, in the exemplary formulation where Bl=0 and Bu=1, provided the optimization is performed at a high enough resolution, the minimization constraint will drive the values x_ito the bounds of 0 or 1. Thus, the resulting magnetic pattern will indicate which of the regions of the logical partition contribute to the magnetic field correction and which regions do not, thereby providing a dual state solution.

As another example, Bl=−1 and Bu=1 so that the optimization determines a magnetic pattern that indicates which of the regions are to have a magnetization of a first polarity and which of the regions are to have a magnetization of the opposite polarity, providing another example of a dual state solution. This formulation may have the advantage that each region of the logical partition contributes to the magnetic field correction, either via a magnetization of a given polarity or via a magnetization of the opposite polarity, thus facilitating the elimination of the step of cutting away or otherwise removing regions of magnetic material that do not contribute to the corrective magnetic field. According to some embodiments, an optimization may be configured so that the resulting magnetic pattern indicates which regions contribute to the magnetic field correction and at which polarity and also indicates which regions do not contribute to the magnetic field correction (e.g., regions may be assigned a −1, 0 or −1), thus provide a tri-state solution. It should be appreciated that numerous other formulations may be used to determine a magnetic pattern that, when applied to magnetic material, produces a corrective magnetic field that improves the profile of a B0 magnetic field, as the aspects are not limited in this respect. Any suitable technique may be used to solve the optimization problem (e.g., the minimization or maximization problem) discussed above, including, but not limited to gradient descent, simulated annealing, Monte Carlo, linear programming, etc., as the aspects are not limited in this respect.

As discussed above, a magnetic pattern may be determined at a resolution to produce a suitable or desired magnetic field correction (e.g., a correction that improves homogeneity, produces a B₀offset, etc.). However, increasing the resolution of the magnetic pattern also increases the time and complexity needed to compute the magnetic pattern. The inventors have developed an iterative approach that begins with a relatively low resolution optimization process followed by one or more subsequent iterations at increasingly higher resolutions. The magnetic pattern from each iteration can be used to refine the logical partitioning for the subsequent iteration primarily at or limited to locations where further resolution is needed or desired, thereby reducing the computational burden while achieving desired resolution. FIG. 13 is a flowchart illustrating a method 1300 of iteratively determining a magnetic pattern to apply to magnetic material to produce a permanent magnet shim, in accordance with some embodiments.

In act 1332, a model of the magnetic material to which the determined magnetic pattern is to be applied is obtained (e.g., in a manner similar to act 1132 of method 1100 illustrated in FIG. 11). In act 1332a, the magnetic material is logically partitioned by, for example, incorporating a tessellation of the magnetic material into the model as described in connection with act 1132a above. According to some embodiments, the partitioning is performed at a lower resolution than the target resolution for the final magnetic pattern to be applied to produce a permanent magnet shim. For example, the model may be triangulated at a resolution of approximately 40 mm, which is schematically illustrated in FIG. 14A. By initially partitioning the magnetic material at a relatively low resolution, the computation time to produce an initial magnetic pattern can be significantly reduced.

In act 1334, a magnetic pattern is determined, for example, by performing an optimization that determines a magnetic pattern that, when applied to magnetic material, produces a corrective magnetic field that improves the profile of the B₀magnetic field (e.g., a magnetic pattern that corrects for the deviation computed in act 610 of method 600 illustrated in FIG. 6). For example, the optimization discussed above may be used to determine a magnetic pattern using the logical partition provided in act 1332a. FIG. 14B illustrates an example of a magnetic pattern determined by performing act 1334. In this exemplary embodiment, the optimization permits each region to take on any value between 0 and 1, though other bounds and ranges may be used. As discussed in connection with the exemplary optimization above, when sufficient variables are present (e.g., sufficient control points), the values assigned to the plurality of regions will be driven to the boundaries (0 or 1) because the optimization can be formulated to prefer the boundary values. However, due to the relatively low resolution at which the first iteration is performed, many of the regions are assigned values in between 0 and 1.

It should be appreciated that the magnetic pattern generated in the first iteration may operate as the final magnetic pattern depending on how the magnetic pattern is applied to the magnetic material. For example, 3D printing techniques allow for differing amounts of magnetic material to be applied at different locations, allowing the magnetic field contribution to vary from region to region in accordance with the values between zero and one assigned to corresponding regions of the logical partition. However, for a permanent magnet shim having a uniform thickness, further refinement of the magnetic pattern may be required.

In act 1336, the logical partitioning of the magnetic material is refined. For example, the logical partitioning may be refined by increasing the resolution (e.g., by increasing the number of control points) in regions where the optimization assigned non-zero values, or alternatively, increasing the resolution in regions assigned relatively significant values in the previous iteration (e.g., values above a predetermined threshold). In this manner, the resolution may be increased only in areas where the magnetic pattern contributes to the corrective magnetic field, reducing computation time while achieving greater resolution. According to some embodiments, the logical partitioning is refined by adding control points along the boundaries of regions contributing to the magnetic field correction. For example, additional control points may be provided along the boundary of each region that was assigned a non-zero value, as illustrated in FIG. 14C.

FIG. 14C illustrates an magnified view of portion 1425 of the magnetic pattern illustrated in FIG. 14B showing two partitioned regions 1427a and 1427b that were assigned non-zero values by the optimization. To refine the logical partition, a control point may be added at the mid-point of each edge forming the boundary between zero and non-zero regions. As shown in FIG. 14C, the result of tessellating the model of the magnetic material with the additional control points produces smaller partitioned regions in the area proximate to regions 1427a and 1427b than the regions produced using the initial tessellation, as illustrated in FIG. 14B. According to some embodiments, instead of refining the logical partition about each region assigned a non-zero value by the optimization, the partitioned regions may first be re-assigned either a zero or one value based on a comparison to a threshold value to further reduce the area that undergoes refinement. For example, all regions assigned a value less than 0.5 by the optimization may be assigned a zero and all regions assigned a value greater than or equal to 0.5 may be assigned a value of one. After thresholding using any desired threshold value, refinement of the logical partition may be implemented by adding control points to the boundary between zero-valued and one-valued regions in the manner discussed above. By reducing the number of regions that are refined (e.g., by adding control points to boundary edges), the resolution may be increased in these areas without unsatisfactorily increasing the computation time. It should be appreciated that the above techniques are merely exemplary and a logical partition may be refined in any suitable way, as the aspects are not limited in this respect.

FIG. 14D illustrates a refined logical partition of the magnetic material determined by performing act 1336. As shown, the partitioned regions at a boundary between regions that contribute to the magnetic field correction and regions that do not contribute to the magnetic field correction in the magnetic pattern determined in the first iteration are of a higher resolution (e.g., approximately 20 mm), while partitioned regions that are not at boundaries between contributing and non-contributing regions remain substantially at the lower resolution (e.g., approximately 40 mm). A magnetic pattern may then be determined using the refined logical partitioning determined in act 1336, for example, by again performing act 1334 on the refined logical partitioning. This iterative process (repeating acts 1334 and 1336) of determining a magnetic pattern at increasingly higher resolutions may be repeated any number times to achieve a suitable magnetic pattern to apply, using any suitable technique, to produce a permanent magnet shim.

FIGS. 15A-E illustrate respective magnetic patterns produced over the course of five iterations, wherein the logical partition is refined on each iteration to improve the resolution (e.g., approximately 40 mm resolution in FIG. 15A, approximately 20 mm resolution in FIG. 15B, approximately 10 mm resolution in FIG. 15C, approximately 5 mm resolution in FIG. 15D and approximately 1 mm resolution in the final magnetic pattern illustrated in FIG. 15E). As shown, as the logical partitioning is refined, the optimization has increased degrees of freedom (e.g., by virtue of added control points in contributing areas) on each iteration and is therefore capable of finding a solution that assigns a boundary value (e.g., zero or one value) to most, if not all, partitioned regions. Thus, the resulting magnetic pattern is suitable for single polarity solutions capable of being applied to magnetic material having generally uniform thickness.

The exemplary optimization discussed above to produce the magnetic pattern illustrated in FIGS. 15A-15E is formulated to minimize the volume of magnetic material contributing to the corrective magnetic field. This may be particularly suitable for certain techniques of applying the magnetic pattern to magnetic material such as an automated magnetizing head or 3D printing, as it minimizes the number of regions that the head needs to traverse and magnetize in the former and reduces the amount of material additively applied in the latter. While the magnetic pattern illustrated in FIG. 15E is suitable for application using other techniques, such as by cutting or removing magnetic material in accordance with the magnetic pattern (e.g., via laser cutting, subtractive 3D printing techniques), it may be advantageous to use an optimization that seeks to maximize the volume of magnetized material. For example, a maximization optimization may reduce or eliminate isolated regions in the resulting magnetic pattern that complicate application of the magnetic pattern using some techniques, may reduce the amount of cutting required, etc. Additionally, a maximization approach may also facilitate providing certain types and/or combinations of corrections, as discussed in further detail below.

FIG. 16 illustrates a magnetic pattern resulting from an optimization that seeks to maximize the volume of magnetized material. As shown in FIG. 16, the majority of the partitioned regions in magnetic pattern 1615 contribute to the magnetic field correction, as exemplified by magnetized regions 1627. Significantly fewer partitioned regions do not contribute to the magnetic field correction, as exemplified by non-magnetized regions 1617. Magnetic pattern 1615 may provide a simpler pattern to apply to magnetic material to produce a permanent magnet shim, for example, when the technique used to apply the magnetic pattern involves cutting away or removing the regions that do not contribute to the magnetic field correction. Magnetic pattern 1615 may produce substantially the same magnetic field correction as the magnetic pattern illustrated in FIG. 15E from a uniformity perspective, but with the addition of a B₀offset that can be used to raise the field strength of the B₀magnetic field, as discussed in further detail below. As a result, magnetic pattern 1615, when applied to magnetic material, may produce a magnetic field that corrects for at least some non-uniformity in the B₀magnetic field produced by a B₀magnetic field as well as correcting for a B₀offset error. It should be appreciated that any combination of optimization to produce a magnetic pattern and any technique for applying the magnet pattern to magnetic material to produce a permanent magnet shim may be used, as the aspects are not limited in this respect.

As discussed above, permanent magnet shims provided using the techniques described herein can be used to correct the B₀magnetic field produced by any type of B₀magnet, including, but not limited to electromagnets, permanent magnets and/or combinations of both, some examples of which are described in further detail below. For example, FIGS. 17A and 17B illustrate a B₀magnet formed using an electromagnet and a ferromagnetic yoke. In particular, B₀magnet 1700 is formed in part by an electromagnet 1710 arranged in a bi-planar geometry comprising electromagnetic coils 1712a and 1712b on an upper side and electromagnetic coils 1714a and 1714b on a lower side of B₀magnet 1700. According to some embodiments, the coils forming electromagnet 1710 may be formed from a number of turns of a conductor 1713 (e.g., a copper wire or copper ribbon, or any other conductive material) suitable for producing a magnetic field when operated (e.g., when electrical current is driven through the conductor windings). While the exemplary electromagnet illustrated in FIGS. 17A and 17B comprises two pairs of coils, an electromagnet may be formed using any number of coils in any configuration, as the aspects are not limited in this respect. Conductor 1713 (e.g., a copper ribbon, wire, paint, etc. with suitable insulation to electrically isolate the multiple windings of the coil) may be wound about a fiberglass ring 1717 and a connector 1719 may be provided to allow for a power connection to provide current to operate coils 1714a and 1714b in series. A similar connector on the upper side of the electromagnet (not visible in FIGS. 17A and 17B) may be provided to operate coils 1712a and 1712b. It should be appreciated that the electromagnetic coils may be formed from any suitable material and dimensioned in any suitable way so as to produce or contribute to a desired B₀magnetic field, as the aspects are not limited for use with any particular type of electromagnet.

In the exemplary B₀magnet illustrated in FIGS. 17A and 17B, each coil pair 1712 and 1714 is separated by thermal management components 1730a and 1730b, respectively, to transfer heat produced by the electromagnetic coils and gradient coils (not illustrated in FIGS. 17A and 17B) away from the magnets to provide thermal management for the MRI device. In particular, thermal management components 1730a and 1730b may comprise a cooling plate having conduits that allow coolant to be circulated through the cooling plate to transfer heat away from the magnets. The cooling plate 1730a, 1730b may be constructed to reduce or eliminate eddy currents induced by operating the gradient coils that can produce electromagnetic fields that disrupt the B₀magnetic field produced by the B₀magnet 1700.

B₀magnet 1700 further comprises a yoke 1720 that is magnetically coupled to the electromagnet to capture magnetic flux that, in the absence of yoke 1720, would be lost and not contribute to the flux density in the region of interest between the upper and lower electromagnetic coils. In particular, yoke 1720 forms a “magnetic circuit” connecting the coils on the upper and lower side of the electromagnet so as to increase the flux density in the region between the coils, thus increasing the field strength within the field of view of the B₀magnet (i.e., the region between the coils where the B₀magnetic field is suitable for imaging). Yoke 1720 comprises frame 1722 and plates 1724a, 1724b, which may be formed using any suitable ferromagnetic material (e.g., iron, steel, etc.). Plates 1724a, 1724b collect magnetic flux generated by the coil pairs of electromagnet 1710 and directs it to frame 1722 which, in turn, returns the flux back to the opposing coil pair, thereby increasing, by up to a factor of two, the magnetic flux density in the imaging region between the coil pairs (e.g., coil pair 1712a, 1712b and coil pair 1714a, 1714b) for the same amount of operating current provided to the coils. The imaging region, or field of view, refers to the volume of space wherein the profile of the B₀magnetic field has sufficient field homogeneity and satisfactory field strength that detectable MR signals can be produced. Thus, yoke 1720 can be used to produce a higher B₀magnetic field (resulting in higher SNR) without a corresponding increase in power requirements, or yoke 1720 can be used to lower the power requirements of B₀magnet 1700 for a given B₀magnetic field. It should be appreciated that the yoke 1720 may be made of any suitable material (e.g., low-carbon steel, silicon steel, cobalt steel, etc.) and may be dimensioned to provide desired magnetic flux capture while satisfying other design constraints such as weight, cost, magnetic properties, etc.

B₀magnet 1710 further comprises shim rings 1740a, 1740b and shim disks 1742a, 1742b configured to augment the generated B₀magnetic field to improve homogeneity in the field of view (e.g., in the region between the upper and lower coils of the electromagnet where the B₀magnetic field is suitable for sufficient MR signal production), as best seen in FIG. 17B in which the lower coils have been removed. In particular, shim rings 1740 and shim disk 1742 are dimensioned and arranged to increase the uniformity of the magnetic field generated by the electromagnet at least within the field of view of the B₀magnet. In particular, the height, thickness and material of shim rings 1740a, 1740b and the diameter, thickness and material of shim disks 1742a, 1742b may be chosen as appropriate.

Despite the use of shim rings, manufacturing tolerances and/or other errors in production of a B₀electromagnet (e.g., B₀magnet 1710) result in non-uniformities in the B₀magnetic field. To correct for at least some non-uniformities in the B₀magnetic field (e.g., post-production non-uniformities), a permanent magnet shim produced using any of the techniques described herein may be used. For example, method 600 illustrated in FIG. 6 may be performed to produce a permanent magnet shim that can be arranged proximate electromagnet 1712a and/or 1712b to improve the profile of the B₀magnetic field. It should be appreciated that the techniques described herein may be used to improve the profile of a B₀magnetic field produced by any B₀electromagnet, and are not limited for use with the exemplary B₀magnet described in FIGS. 17A and 17B.

Permanent magnet shims may also be used to improve the profile of a B₀magnetic field produced by a permanent B0 magnet. For example, FIG. 18 illustrates a permanent B₀magnet for which the shimming techniques described herein may be applied. B₀magnet 1800 is formed by permanent magnets 1810a and 1810b arranged in a bi-planar geometry and a yoke 1820 that captures electromagnetic flux produced by the permanent magnets and transfers the flux to the opposing permanent magnet to increase the flux density between permanent magnets 1810a and 1810b. Each of permanent magnets 1810a and 1810b are formed from a plurality of concentric permanent magnets. In particular, as visible in FIG. 18, permanent magnetic 1810b comprises an outer ring of permanent magnets 1814a, a middle ring of permanent magnets 1814b, an inner ring of permanent magnets 1814c, and a permanent magnet disk 1814d at the center. Permanent magnet 1810a may comprise the same set of permanent magnet elements as permanent magnet 1810b. The permanent magnet rings are sized and arranged to produce a relatively homogenous field of a desired strength in the central region (field of view) between permanent magnets 1810a and 1810b. In the exemplary embodiment illustrated in FIG. 18, each permanent magnet ring comprises a plurality segments, each segment formed using a plurality of blocks that are stacked in the radial direction and positioned adjacent to one another about the periphery to form the respective ring.

B₀magnet 1800 further comprises yoke 1820 configured and arranged to capture magnetic flux generated by permanent magnets 1810a and 1810b and direct it to the opposing side of the B₀magnet to increase the flux density in between permanent magnets 1810a and 1810b, increasing the field strength within the field of view of the B₀magnet. By capturing magnetic flux and directing it to the region between permanent magnets 1810a and 1810b, less permanent magnet material can be used to achieve a desired field strength, thus reducing the size, weight and cost of the B₀magnet. Yoke 1820 comprises a frame 1822 and plates 1824a and 1824b that capture magnetic flux generated by permanent magnets 1810a and 1810b and direct it to frame 1822 to be circulated via the magnetic return path of the yoke to increase the flux density in the field of view of the B₀magnet. Exemplary frame 1822 comprises arms 1823a and 1823b that attach to plates 1824a and 1824b, respectively, and supports 1825a and 1825b providing the magnetic return path for the flux generated by the permanent magnets.

As another example of a permanent magnet, FIG. 19 illustrates a B₀magnet 1900 to which shimming techniques described herein may be applied. B₀magnet 1900 may share design components with B₀magnet 1800 illustrated in FIG. 18. In particular, B₀magnet 1900 is formed by permanent magnets 1910a and 1910b arranged in a bi-planar geometry with a yoke 1920 coupled thereto to capture electromagnetic flux produced by the permanent magnets and transfer the flux to the opposing permanent magnet to increase the flux density between permanent magnets 1910a and 1910b. Each of permanent magnets 1910a and 1910b are formed from a plurality of concentric permanent magnets, as shown by permanent magnet 1910b comprising an outer ring of permanent magnets 1914a, a middle ring of permanent magnets 1914b, an inner ring of permanent magnets 1914c, and a permanent magnet disk 1914d at the center. Permanent magnet 1910a may comprise the same set of permanent magnet elements as permanent magnet 1910b. The permanent magnet material used may be selected depending on the design requirements of the system (e.g., NdFEB, SmCo, etc. depending on the properties desired).

The permanent magnet rings are sized and arranged to produce a relatively homogenous field of a desired strength in the central region (field of view) between permanent magnets 1910a and 1910b. In particular, in the exemplary embodiment illustrated in FIG. 19, each permanent magnet ring comprises a plurality of circular arc segments sized and positioned to produce a desired B₀magnetic field, as discussed in further detail below. In a similar manner to yoke 1820 illustrated in FIG. 18, yoke 1920 is configured and arranged to capture magnetic flux generated by permanent magnets 1910a and 1910b and direct it to the opposing side of the B₀magnet to increase the flux density in between permanent magnets 1910a and 1910b. Yoke 1920 thereby increases the field strength within the field of view of the B₀magnet with less permanent magnet material, reducing the size, weight and cost of the B₀magnet. Yoke 1920 also comprises a frame 1922 and plates 1924a and 1924b that, in a manner similar to that described above in connection with yoke 1920, captures and circulates magnetic flux generated by the permanent magnets 1910a and via the magnetic return path of the yoke to increase the flux density in the field of view of the B₀magnet. The structure of yoke 1920 may be similar to that described above to provide sufficient material to accommodate the magnetic flux generated by the permanent magnets and providing sufficient stability, while minimizing the amount of material used to, for example, reduce the cost and weight of the B₀magnet.

The B₀magnets illustrated in FIGS. 18 and 19 includes yokes that are asymmetric (e.g., yokes 1820 and 1920), as opposed to the symmetric yoke 1720 of the B₀magnet illustrated in FIG. 17. An asymmetric yoke will cause the magnetic field produced by the corresponding B0 magnet for which it captures and focuses magnetic flux to be likewise asymmetric, negatively impacting the uniformity of the B₀magnetic field. For example, in FIGS. 18 and 19, the position of frame 1822/1922 (in particular, legs 1825a/1925a and 1825b/1925b) relative to the permanent magnets 1810a/1910a and 1810b/1910b results in magnetic flux being drawn away from regions proximate the frame, reducing the flux density in these regions. While the effect of the yoke on the magnetic field can be compensated for by varying the dimensions (e.g., the height) of selected permanent magnet circular arc segments, requiring the permanent magnet circular arc segments to be machine or produced at different heights is expensive, significantly increasing the cost of the B₀magnet.

The inventors recognized that the techniques for producing a permanent magnet shim discussed herein may be used to produce a permanent magnet shim to compensate for the effects of the B₀magnetic field by an asymmetric yoke. For example, method 600 illustrated in FIG. 6 and described in the foregoing may be performed to determine a magnet pattern that mitigates and/or substantially eliminates the non-uniformity in the B₀magnet resulting from the yoke. It should be appreciated that correcting for magnetic field non-uniformities resulting from an asymmetric yoke and other non-uniformities, such as those resulting from manufacturing tolerances, may be compensated by the same permanent magnet shim. Specifically, characterizing the B₀magnetic field produced by a B₀magnet with an asymmetric yoke to determine deviation from a desired profile (e.g., performing act 610 of method 600 illustrated in FIG. 6) allows for a magnetic pattern to be determined that, when applied to produce one or more permanent magnet shims, can compensate for non-uniformities in the B₀magnetic field whatever the source. Accordingly, compensating for yoke effects by manufacturing the permanent magnet segments at different heights can be eliminated, thereby reducing the cost and complexity of manufacturing a B₀magnet.

According to some embodiments, one or more permanent magnet shims to compensate for the effects of an asymmetric yoke is produced independent from one or more permanent magnetic shims adapted to compensate for other non-uniformities, such as those resulting from manufacturing tolerances. A magnetic pattern that, when applied to a permanent magnet shim, that compensates for the effect of the yoke may be determined using techniques described above (e.g., by performing method 600). As discussed above, the deviation of the B₀magnetic field from a desired profile may be computed by measuring the B₀magnetic field produced by the B₀magnet or by computing the deviation from the design specification of the B₀magnet and yoke. The inventors have appreciated that there may be some advantages in positioning a permanent magnet shim directly over and on top of the permanent magnets of the B₀coil. For example, for B0 magnets 1800 and 1900, a permanent magnet shim may be placed directly over the permanent magnet rings forming one or both of permanent magnets 1810a/1910a and 1810b/1910b.

FIG. 20 illustrates a magnet pattern 2015 determined for a permanent magnet shim to compensate for the effects of the yoke on the B₀magnetic field. As shown, by tessellating a model having a geometry that corresponds to the permanent magnet rings, a magnetic pattern can be determined that is constrained to area of the underlying permanent magnets. It should be appreciated that this technique can be used to determine a magnetic pattern that is constrained to any desired geometry. Magnetic pattern 2015 includes regions 2027 that contribute to the magnetic field correction and regions 2017 that do not contribute to the magnetic field correction. A potential advantage to independently producing a permanent magnet shim to compensate for yoke effects is that for a given B₀magnet design, the yoke effect will be substantially the same for each manufactured B₀magnet. As a result, permanent magnet shims to compensate for the yoke effect can be pre-made and placed onto the permanent magnetic shim at the manufacturing stage, resulting in cost savings efficiencies.

FIG. 21 illustrates a permanent magnet shim 2125 produced by applying magnetic pattern 2015 and positioned over permanent magnet rings of B₀magnet 2100 to compensate for non-uniformities resulting from asymmetric yoke 2120. As shown, permanent magnetic shim 2125 aligns with the permanent magnet rings of permanent magnet 2110a. Depending on how the magnetic pattern is determined, a permanent magnet shim may be positioned over permanent magnet 2110b in the manner illustrated. As discussed above, permanent magnet shim 2125 may be pre-made (but need not be) and installed as part of the manufacturing process. Post-manufacturing non-uniformities, which typically vary from magnet to magnet, may then be corrected by producing one or more further permanent magnet shims using the techniques described herein. For example, FIG. 22 illustrates permanent magnet shim 2225a adapted to compensate for yoke effects and permanent magnet shim 2225b adapted to correct for post-manufacturing non-uniformities. Permanent magnet shims 2225a and 2225b are positioned proximate permanent magnets 2210a and 2210b of B0 magnet 2200 to improve the profile of the B₀magnetic field produced.

In addition to non-uniformity in the B₀magnetic field produced by a B₀magnet, manufacturing variability can also result in an offset in the field strength of the B₀magnetic field. For example, the B₀magnetic field may deviate from the desired field strength by being either too low or too high, resulting in a corresponding shift in the Larmor frequency. Accordingly, significant B₀offsets resulting from variability in manufacturing need compensation so that the Larmor frequency better matches the intended operating frequency of the MRI device incorporating the B₀magnet. Conventionally, B₀offsets were frequently corrected using shim coils, typically one or more coils that, when operated, contributed to the B₀magnetic field to either raise or lower the field strength. However, operating shims coils requires power, a disadvantage particularly for portable MRI systems that may be operating on a very limited power budget. The inventors appreciated that B₀offsets may be corrected using one or more permanent magnet shims produced using the techniques described herein. Such permanent magnet shims may be used alone, together and/or in conjunction with, or in replacement of one or more shim coils.

According to some embodiments, method 600 may be performed on a B₀magnet post-production to compensate for a B₀offset in the B₀magnetic field produced by the manufactured B₀magnet. For example, the B₀magnetic field produced by the B₀magnet after manufacturing is characterized to determine a deviation from a desired profile (e.g., by performing act 610 of method 600 illustrated in FIG. 6). A magnetic pattern may be determined based on the determined deviation and the determined magnetic pattern may be applied to produce one or more permanent magnet shims (e.g., by performing acts 620 and 630 in method 600 of FIG. 6.).

It should be appreciated that when the B₀magnetic field is characterized after manufacture and prior to performing other shimming techniques (compensating for yoke effects, B₀offset shim coils, etc.), the magnetic pattern that is determined by performing method 600 may compensate for multiple deficiencies in the profile of a B₀magnetic field. That is, when the B₀magnetic field is characterized will, according to some embodiments, dictate what deviations the determined magnetic pattern provides compensation for. For example, if the B₀magnetic field is characterized prior to other compensation measures, the determined magnetic field may compensate, at least in part, for B₀offset, non-uniformities inherent in or introduced by the design of the B₀magnet (e.g., yoke effects), and non-uniformities arising from the manufacturing process. If the B₀magnetic field is characterized after certain non-uniformities inherent in and/or introduced by the design of the B₀magnet (e.g., yoke effects) have been corrected, but prior to other compensation measures, the determined magnetic pattern may compensate, at least in part, for B₀offset, certain other non-uniformities inherent in or introduced by the design of the B₀magnet, and non-uniformities resulting from manufacturing tolerances. If the B₀magnetic field is characterized after the B₀offset is compensated for (e.g., by measuring the B₀magnetic field while operating one or more shim coils), the determined magnetic pattern may compensate, at least in part, non-uniformities inherent or introduced by the design of the B₀magnet (e.g., yoke effects) and/or non-uniformities caused by manufacturing variability. Accordingly, any one or combination of B₀magnetic field deviations may be at least partially compensated for using the techniques described herein, either separately (by determining separate magnetic patterns for each correction made) or together (e.g., by determining a magnetic pattern that compensates for a combination of deviations).

According to some embodiments, multiple sheets of material are magnetized to produce a desired corrective magnetic field. The inventors have appreciated that magnetizing multiple sheets facilitates producing a magnetic pattern at increased granularity. For example, a given material will have a corresponding remanence that governs the strength of the magnetic field that persists after the material is magnetized. As a result, when a region having a unit volume is magnetized, the resulting magnetic field strength will correspond to the material's remanence. Each additional unit volume will add a discrete amount of additional field strength in relation to the material's remanence. As discussed above, a region of material may be magnetized either positively or negatively or not at all, so that each magnetized region will provide a certain positive or negative magnetic field. By magnetizing multiple sheets and then stacking them on top of one another, finer control of the magnetic field generated may be provided. That is, regions can be magnetized on the multiple sheets such that the effect at a given location can be a desired fraction of the contribution resulting from magnetizing a single sheet. Multiple sheets may also be used to improve the magnetic field correction that results by iteratively magnetizing respective sheets of the multiple sheets to correct for the field produced by the one or more sheets patterned on previous iterations.

Additionally, when multiple layers are utilized, one or more layers (e.g., one or more sheets of magnetic material) may be produced wherein magnetized regions are either magnetized substantially in alignment or substantially in anti-alignment with the B₀magnetic field, and one or more layers may be produced wherein magnetized regions are magnetized substantially in transverse direction(s) to the B₀magnetic field. In this manner, greater and more granular control of the corrective field may be achieved. It should be appreciated that one or more layers (or a single layer in embodiments that utilize a single layer) may be magnetized such that magnetized regions include region(s) magnetized substantially in alignment, substantially in anti-alignment and substantially transverse to the B