Patent Publication Number: US-2021173024-A1

Title: Swaged component magnet assembly for magnetic resonance imaging

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
     This application claims priority under 35 U.S.C. § 119(e) to U.S. Provisional Patent Application Ser. No. 62/946,075, titled “SWAGED COMPONENT MAGNET ASSEMBLY FOR MAGNETIC RESONANCE IMAGING,” filed on Dec. 10, 2019, which is incorporated by reference in its entirety herein. 
    
    
     BACKGROUND 
     Magnetic resonance imaging (MRI) provides an important imaging modality for numerous applications and is widely utilized in clinical and research settings to produce images of the inside of the human body. As a generality, MRI is based on detecting magnetic resonance (MR) signals, which are electromagnetic waves emitted by atoms in response to state changes resulting from applied electromagnetic fields. For example, nuclear magnetic resonance (NMR) techniques involve detecting MR signals emitted from the nuclei of excited atoms upon the re-alignment or relaxation of the nuclear spin of atoms in an object being imaged (e.g., atoms in the tissue of the human body). Detected MR signals may be processed to produce images, which in the context of medical applications, allows for the investigation of internal structures and/or biological processes within the body for diagnostic, therapeutic and/or research purposes. 
     SUMMARY 
     Some embodiments are directed to an apparatus for providing a B 0  magnetic field for a magnetic resonance imaging (MRI) system. The apparatus comprises a cylindrical shell forming a bore extending along a common longitudinal direction. The cylindrical shell comprises a first plurality of ferromagnetic rings including a first ferromagnetic ring with an angularly varying magnetization orientation and a second plurality of rings. 
     Some embodiments are directed to a method of manufacturing an apparatus for providing a B 0  magnetic field for a magnetic resonance imaging (MRI) system. The method comprises manufacturing a ferromagnetic cylindrical shell at least in part by: placing a magnetic metal alloy powder in an annular volume between an outer cylindrical tube and an inner cylindrical tube; applying a magnetic field to the magnetic metal alloy powder while compressing the magnetic metal alloy powder; bonding the magnetic metal alloy powder to form at least a part of the ferromagnetic cylindrical shell; magnetizing the ferromagnetic cylindrical shell to have an angularly varying magnetization orientation; partitioning the ferromagnetic cylindrical shell into a first plurality of ferromagnetic rings; and assembling, from the first plurality of ferromagnetic rings and a second plurality of rings, a cylindrical shell forming a bore extending along a common longitudinal direction. 
     Some embodiments are directed to a method of manufacturing an apparatus for providing a B 0  magnetic field for a magnetic resonance imaging (MRI) system. The method comprises manufacturing a ferromagnetic cylindrical shell at least in part by: placing magnetic metal alloy powder and non-ferromagnetic powder in an annular volume between an outer cylindrical tube and an inner cylindrical tube; applying a magnetic field to the magnetic metal alloy powder while compressing the magnetic metal alloy powder; bonding the magnetic metal alloy powder and the non-ferromagnetic powder to form the ferromagnetic cylindrical shell; and magnetizing the ferromagnetic cylindrical shell to have an angularly varying magnetization orientation. 
     Some embodiments are directed to a method of manufacturing an apparatus for providing a B 0  magnetic field for a magnetic resonance imaging (MRI) system. The method comprises manufacturing a ferromagnetic cylindrical shell at least in part by: placing magnetic metal alloy powder in an annular volume between an outer cylindrical tube and an inner cylindrical tube; applying a magnetic field to the magnetic metal alloy powder while compressing the magnetic metal alloy powder; bonding the magnetic metal alloy powder and the non-ferromagnetic powder to form the ferromagnetic cylindrical shell; selectively magnetizing first ring regions of the ferromagnetic cylindrical shell to have a first angularly varying magnetization orientation; and selectively magnetizing second ring regions of the ferromagnetic cylindrical shell to have a second angularly varying magnetization orientation, the second angularly varying magnetization orientation varying in a direction opposing that of the first angularly varying magnetization orientation. 
     Some embodiments are directed to an apparatus for providing a B 0  magnetic field for a magnetic resonance imaging (MRI) system. The apparatus comprises: at least one first B 0  magnet configured to produce a first magnetic field to contribute to the B 0  magnetic field for the MRI system, the at least one first B 0  magnet comprising ferromagnetic rings including a first ferromagnetic ring and a second ferromagnetic ring, the first ferromagnetic ring having a first magnetization and the second ferromagnetic ring having a second magnetization. The first magnetization and the second magnetization have first radial and axial components and second radial and axial components, respectively; and the first radial and axial components are different than the second radial and axial components. 
    
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
       Various aspects and embodiments will be described with reference to the following figures. It should be appreciated that the figures are not necessarily drawn to scale. In the drawings, each identical or nearly identical component that is illustrated in various figures is represented by a like numeral. For purposes of clarity, not every component may be labeled in every drawing. 
         FIG. 1  illustrates exemplary components of a magnetic resonance imaging (MRI) system, in accordance with some embodiments of the technology described herein; 
         FIG. 2  illustrates a schematic of a cross section of an ideal Halbach cylinder; 
         FIG. 3  illustrates an example of a cylindrical coordinate system; 
         FIG. 4  illustrates an example of a cylindrical magnet assembly for providing a B 0  magnetic field for an MRI system, in accordance with some embodiments of the technology described herein; 
         FIG. 5A  illustrates an example of a cylindrical magnet assembly including regions of differing magnetization for providing a B 0  magnetic field for an MRI system, in accordance with some embodiments of the technology described herein; 
         FIG. 5B  illustrates an example of another cylindrical magnet assembly including regions of differing magnetization for providing a B 0  magnetic field for an MRI system, in accordance with some embodiments of the technology described herein; 
         FIG. 6  illustrates an example of a bi-planar magnet assembly for providing a B 0  magnetic field for an MRI system, in accordance with some embodiments of the technology described herein; 
         FIG. 7  illustrates an example of magnetic orientations within the bi-planar magnet assembly of  FIG. 6 , in accordance with some embodiments of the technology described herein; 
         FIG. 8  illustrates an example of a C-shaped frame configured to support the bi-planar magnet assembly of  FIG. 6 , in accordance with some embodiments of the technology described herein; 
         FIGS. 9-11  illustrate examples of frames configured to support the bi-planar magnet assembly of  FIG. 6 , in accordance with some embodiments of the technology described herein; 
         FIG. 12  illustrates an MRI system including the magnet assembly of  FIG. 8 , in accordance with some embodiments of the technology described herein; 
         FIG. 13  illustrates the use of the MRI system of  FIG. 10  to image a patient&#39;s head, in accordance with some embodiments of the technology described herein; and 
         FIG. 14  depicts, schematically, an illustrative computing device on which aspects of the technology described herein may be implemented. 
     
    
    
     DETAILED DESCRIPTION 
     Conventional magnetic resonance imaging (MRI) systems are overwhelmingly high-field systems, particularly for medical or clinical MRI applications. The general trend in medical imaging has been to produce MRI scanners with increasingly greater field strengths, with the vast majority of clinical MRI scanners operating at 1.5 T or 3 T, with higher field strengths of 7 T and 9 T used in research settings. As used herein, “high-field” refers generally to MRI systems presently in use in a clinical setting and, more particularly, to MRI systems operating with a main magnetic field (i.e., a B 0  field) at or above 1.5 T, though clinical systems operating between 0.5 T and 1.5 T are often also characterized as “high-field.” By contrast, “low-field” refers generally to MRI systems operating with a B 0  field of less than or equal to approximately 0.2 T, though systems having a B 0  field of between 0.2 T and approximately 0.3 T have sometimes been characterized as low-field as a consequence of increased field strengths at the high end of the high-field regime. 
     Some conventional low-field MRI systems may produce the main magnetic B 0  field using one or more permanent magnets. A permanent magnet may be 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 and include, as non-limiting examples, iron, nickel, cobalt, neodymium alloys (e.g., NdFeB), samarium cobalt (SmCo) alloys, alnico (AlNiCo) alloys, strontium ferrite, barium ferrite, etc. 
     Permanent magnets are conventionally manufactured using powder metallurgy methods. In this process, a suitable permanent magnet material is pulverized into a fine powder, compacted, and heated to sinter the powder into a solid piece. Conventionally, such sintered magnets are compacted in a hydraulic or mechanical press, which can limit the shape of the resulting sintered magnets to simple cross-sections that can be pushed out of the die cavity. 
     Recently, demonstrations of sintered magnets formed using a swaging manufacturing process have been made. As used herein, a swaging manufacturing process refers to any process for manufacturing a permanent magnet that involves forming the permanent magnet by swaging its constituent material (e.g., metallic powder) while applying a magnetic field to the constituent material. In some embodiments, the swaged and magnetized materials may then be sintered to form a solid component. In other embodiments, the constituent material may include a bonding agent so that a separate sintering step is not needed. In such embodiments, the bonding agent may be used to programmably reduce a net magnetization of a region of the resulting solid component. After the swaged material is cooled, it may be further magnetized (e.g., using an electromagnet, an array of permanent magnets) to have a desired magnetization direction or directions. Examples of swaging manufacturing processes are described in U.S. Patent Application Publication No. 2019/0122818, filed Sep. 28, 2018, and titled “Method of Manufacturing Permanent Magnets,” and U.S. Patent Application Publication No. 2018/0226190, filed Mar. 30, 2018, and titled “Single-Step Manufacturing of Flux-Directed Permanent Magnet Assemblies,” each of which is incorporated by reference herein in its entirety. Such swaging manufacturing processes enable the production of long lengths of magnet block in a rapid and efficient manner. 
     Additionally, such swaging manufacturing processes enable the production of hollow magnetic structures integrally formed as a single component. In particular, these hollow magnetic structures may be magnetized during the manufacturing process to form continuous flux Halbach cylinders. These continuous flux Halbach cylinders have been implemented in electric propulsion motor applications, as described in the &#39;818 and &#39;190 patent application publications identified in the foregoing paragraph. 
     Although these swaging manufacturing processes have been implemented for producing components for electric propulsion motors, the inventors have recognized that these swaging manufacturing processes may be adapted for manufacturing permanent magnets for MRI applications. For example, MRI applications may rely on substantially homogenous B 0  magnetic fields to produce high-resolution and/or otherwise clinically useful magnetic resonance (MR) images. However, the finite length of such hollow magnetic structures may create non-homogenous magnetic fields. The inventors have recognized that such non-homogeneity may be compensated for, by way of example, by splitting the permanent magnet into multiple rings of tailored length, separated by gaps and/or permanent magnets of opposing polarity. The inventors have recognized that such rings could be manufactured using a swaging manufacturing process. 
     Accordingly, the inventors have developed methods and systems for providing a B 0  magnetic fields within an MRI system using one or more permanent magnets and/or permanent magnetic assemblies formed using a swaging manufacturing process. In some embodiments, the apparatus for providing a B 0  magnetic field for an MRI system may include a cylindrical shell forming a bore extending along a common longitudinal direction. The cylindrical shell may include a first plurality of ferromagnetic rings including a first ferromagnetic ring with an angularly varying magnetization orientation. The cylindrical shell may also include a second plurality of rings. In some embodiments, the first ferromagnetic ring may be manufactured by swaging. In some embodiments, at least one (e.g., one, some or all) of the first plurality of ferromagnetic rings may be manufacturing by swaging. 
     In some embodiments, the second plurality of rings also includes ferromagnetic rings. The ferromagnetic rings may include a second ferromagnetic ring having an angularly varying magnetization orientation. In some embodiments, the angularly varying magnetization of the first ferromagnetic ring and that of the second ferromagnetic rings angularly vary in opposing directions. In other embodiments, the second plurality of rings includes non-ferromagnetic rings (e.g., spacers made from non-ferrous material such as plastic, fiberglass, etc.). 
     In some embodiments, the first plurality of ferromagnetic rings may be interspersed with the second plurality of rings (e.g., the first plurality of ferromagnetic rings may be alternatingly arranged between rings of the second plurality of rings). 
     In some embodiments, each of the first plurality of ferromagnetic rings and each of the second plurality of rings may have the same diameter to provide a bore having a constant diameter along the common longitudinal direction. In other embodiments, at least two of the plurality of ferromagnetic rings may have different inner diameters (e.g., to provide a bore with a changing diameter along its length). For example, rings of the first plurality of ferromagnetic rings and second plurality of rings may have differing diameters along the length of the bore so that bore&#39;s diameter is larger at one end of the bore than at another end of the bore. 
     In some embodiments, the B 0  magnetic field has a field strength that is greater than 0.02 T and less than 0.2 T. In some embodiments, the B 0  magnetic field has a field strength that is greater than 0.05 T and less than 0.1 T. In some embodiments, the B 0  magnetic field has a field strength that is greater than 0.06 T and less than 0.07 T. 
     In some embodiments, the B 0  magnetic field has a homogeneity less than or equal to substantially 1000 ppm within an imaging region disposed within the bore. In some embodiments, the B 0  magnetic field has a homogeneity less than or equal to substantially 500 ppm, less than or equal to substantially 250 ppm, less than or equal to substantially 100 ppm, or less than or equal to substantially 50 ppm within an imaging region disposed within the bore. In other embodiments, the B 0  magnetic field has a homogeneity of substantially 10 ppm within an imaging region disposed within the bore. Alternatively, in some embodiments, the B 0  magnetic field has a homogeneity in a range from 100 ppm to 1000 ppm, from 500 ppm to 1000 ppm, 100 ppm to 500 ppm, from 5 ppm to 100 ppm, or any other suitable range within these ranges within an imaging region disposed within the bore 
     In some embodiments, the apparatus includes less than 400 kg of permanent magnet material. In some embodiments, the apparatus includes less than 300 kg of permanent magnet material, less than 200 kg of permanent magnet material, less than 100 kg of permanent magnetic material, or less than 40 kg of permanent magnet material. In other embodiments, the apparatus includes between 300 kg to 500 kg of permanent magnet material, between 100 kg to 400 kg of permanent magnet material, between 10 kg and 100 kg of permanent magnet material, or any other suitable range within these ranges. 
     The inventors have also developed an MRI system including an apparatus for providing a B 0  magnet field using one or more permanent magnets formed using a swaging manufacturing process. In some embodiments, the apparatus may include a cylindrical shell forming a bore extending along a common longitudinal direction. The cylindrical shell may include a first plurality of ferromagnetic rings including a first ferromagnetic ring with an angularly varying magnetization orientation. The cylindrical shell may also include a second plurality of rings. In some embodiments, the MRI system may also include gradient coils configured to, when operated, generate magnetic fields to provide spatial encoding of emitted magnetic resonance signals, at least one radio frequency (RF) transmit coil, and a power system configured to provide power to the gradient coils and the at least one RF transmit coil. 
     The inventors have further developed methods of manufacturing an apparatus for providing a B 0  magnet field within an MRI system using one or more permanent magnets formed using a swaging manufacturing process. In some embodiments, the method may include manufacturing a ferromagnetic cylinder at least in part by placing a magnetic metal alloy powder in an annular volume between an outer cylindrical tube and an inner cylindrical tube and applying a magnetic field to the magnetic metal alloy powder while compressing the magnetic metal alloy powder. The method may include bonding (e.g., sintering, using a binding compound, etc.) the magnetic metal alloy powder to form at least a part of the ferromagnetic cylinder and magnetizing the ferromagnetic cylinder to have an angularly varying magnetization orientation. 
     In some embodiments, the method may include partitioning the ferromagnetic cylinder into a first plurality of ferromagnetic rings and assembling, from the first plurality of ferromagnetic rings and a second plurality of rings, a cylindrical shell forming a bore extending along a common longitudinal direction. In some embodiments, the second plurality of ferromagnetic rings may include one or more ferromagnetic rings with an angularly varying magnetization orientation. In some such embodiments, the first plurality of ferromagnetic rings may include a first ferromagnetic ring with an angularly varying magnetization orientation, and the second plurality of rings may include a second ferromagnetic ring with an angularly varying magnetization orientation. The magnetization orientations of the first and second ferromagnetic rings may angularly vary in opposing directions. In other embodiments, the second plurality of rings comprises one or more non-ferromagnetic rings. 
     In some embodiments, assembling of the ferromagnetic cylinder may include using the second plurality of rings as spacers among rings in the first plurality of ferromagnetic rings so that the first plurality of ferromagnetic rings are interspersed with the second plurality of rings (e.g., so that rings of the first plurality of ferromagnetic rings alternate with rings of the second plurality of rings along the length of the ferromagnetic cylinder). 
     In other embodiments, the method of manufacturing the apparatus may include manufacturing a ferromagnetic cylindrical shell at least in part by placing magnetic metal alloy powder and non-ferromagnetic powder in an annular volume between an outer cylindrical tube and an inner cylindrical tube. The method may include applying a magnetic field to the magnetic metal alloy powder while compressing the magnetic metal alloy powder and bonding the magnetic metal alloy powder and the non-ferromagnetic powder to form the ferromagnetic cylindrical shell. The method may further include magnetizing the ferromagnetic cylindrical shell to have an angularly varying magnetization orientation. In such embodiments, placing the non-magnetic powder between the two cylindrical tubes may include interspersing the non-magnetic powder with the magnetic metal alloy powder. The method may further include removing the two cylindrical tubes from the ferromagnetic cylindrical shell. 
     In other embodiments, the method of manufacturing the apparatus may include manufacturing a ferromagnetic cylindrical shell at least in part by placing magnetic metal alloy powder in an annular volume between an outer cylindrical tube and an inner cylindrical tube and applying a magnetic field to the magnetic metal alloy powder while compressing the magnetic metal alloy powder. The method may further include bonding the magnetic metal alloy powder and the non-ferromagnetic powder to form the ferromagnetic cylindrical shell and selectively magnetizing first ring regions of the ferromagnetic cylinder to have a first angularly varying magnetization orientation. Second ring regions of the ferromagnetic cylindrical shell may be selectively magnetized to have a second angularly varying magnetization orientation. The second angularly varying magnetization orientation may vary in a direction opposing that of the first angularly varying magnetization orientation. In some embodiments, the first ring regions may be interspersed with the second ring regions. In some embodiments, the method may further include removing the two cylindrical tubes from the cylindrical shell. 
     Alternatively, the inventors have recognized that permanent magnets formed using a swaging manufacturing process may be used in place of conventional permanent magnet blocks to form planar permanent magnet assemblies. The inventors have accordingly developed an apparatus for providing a B 0  magnetic field for a magnetic resonance imaging (MRI) system, the apparatus may include at least one first B 0  magnet configured to produce a first magnetic field to contribute to the B 0  magnetic field for the MRI system. 
     In some embodiments, the at least one first B 0  magnet may include ferromagnetic rings, the ferromagnetic rings including a first ferromagnetic ring and a second ferromagnetic ring. The first ferromagnetic ring may have a first magnetization, and the second ferromagnetic ring may have a second magnetization, and the first magnetization and the second magnetization may have first radial and axial components and second radial and axial components, respectively. In some embodiments, the first radial and axial components may be different than the second radial and axial components. 
     In some embodiments, the first ferromagnetic ring may be integrally formed as a single monolithic component. For example, the first ferromagnetic ring may be manufactured at least in part by swaging. 
     In some embodiments, the ferromagnetic rings may have different heights. In some embodiments, the ferromagnetic rings may be concentric rings having different diameters. 
     Following below are more detailed descriptions of various concepts related to, and embodiments of swaged magnet assemblies. 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. 
       FIG. 1  is a block diagram of components of a MRI system  100 . In the illustrative example of  FIG. 1 , MRI system  100  comprises computing device  104 , controller  106 , pulse sequences store  108 , power management system  110 , and magnetics components  120 . It should be appreciated that system  100  is illustrative and that an MRI system may have one or more other components of any suitable type in addition to or instead of the components illustrated in  FIG. 1 . However, an MRI system will generally include these high level components, though the implementation of these components for a particular MRI system may differ. 
     As illustrated in  FIG. 1 , magnetics components  120  comprise B 0  magnet  122 , shim coils  124 , RF transmit and receive coils  126 , and gradient coils  128 . Magnet  122  may be used to generate the main magnetic field B 0 . Magnet  122  may be any suitable type or combination of magnetics components that can generate a desired main magnetic B 0  field. In some embodiments, magnet  122  may be a permanent magnet, an electromagnet, a superconducting magnet, or a hybrid magnet comprising one or more permanent magnets and one or more electromagnets and/or one or more superconducting magnets. In some embodiments, magnet  122  may be a bi-planar permanent magnet and, in some embodiments, may include multiple sets of concentric permanent magnet rings. In some embodiments, magnet  122  may include one or more permanent magnets manufactured using swaging techniques, as described herein. 
     Gradient coils  128  may be arranged to provide gradient fields and, for example, may be arranged to generate gradients in the B 0  field in three substantially orthogonal directions (X, Y, and Z). Gradient coils  128  may be configured to encode emitted MR signals by systematically varying the B 0  field (the B 0  field generated by magnet  122  and/or shim coils  124 ) to encode the spatial location of received MR signals as a function of frequency or phase. For example, gradient coils  128  may be configured to vary frequency or phase as a linear function of spatial location along a particular direction, although more complex spatial encoding profiles may also be provided by using nonlinear gradient coils. 
     MRI is performed by exciting and detecting emitted MR signals using transmit and receive coils, respectively (often referred to as radio frequency (RF) coils). Transmit/receive coils may include separate coils for transmitting and receiving, multiple coils for transmitting and/or receiving, or the same coils for transmitting and receiving. Thus, a transmit/receive component may include one or more coils for transmitting, one or more coils for receiving and/or one or more coils for transmitting and receiving. Transmit/receive coils are also often referred to as Tx/Rx or Tx/Rx coils to generically refer to the various configurations for the transmit and receive magnetics component of an MRI system. These terms are used interchangeably herein. In  FIG. 1 , RF transmit and receive coils  126  comprise one or more transmit coils that may be used to generate RF pulses to induce an oscillating magnetic field B 1 . The transmit coil(s) may be configured to generate any suitable types of RF pulses. 
     Power management system  110  includes electronics to provide operating power to one or more components of the low-field MRI system  100 . For example, power management system  110  may include one or more power supplies, gradient power components, transmit coil components, and/or any other suitable power electronics needed to provide suitable operating power to energize and operate components of MRI system  100 . As illustrated in  FIG. 1 , power management system  110  comprises power supply  112 , power component(s)  114 , transmit/receive switch  116 , and thermal management components  118  (e.g., cryogenic cooling equipment for superconducting magnets). Power supply  112  includes electronics to provide operating power to magnetic components  120  of the MRI system  100 . For example, power supply  112  may include electronics to provide operating power to one or more B 0  coils (e.g., B 0  magnet  122 ) to produce the main magnetic field for the low-field MRI system. Transmit/receive switch  116  may be used to select whether RF transmit coils or RF receive coils are being operated. 
     Power component(s)  114  may include one or more RF receive (Rx) pre-amplifiers that amplify MR signals detected by one or more RF receive coils (e.g., coils  126 ), one or more RF transmit (Tx) power components configured to provide power to one or more RF transmit coils (e.g., coils  126 ), one or more gradient power components configured to provide power to one or more gradient coils (e.g., gradient coils  128 ), and one or more shim power components configured to provide power to one or more shim coils (e.g., shim coils  124 ). 
     As illustrated in  FIG. 1 , MRI system  100  includes controller  106  (also referred to as a console) having control electronics to send instructions to and receive information from power management system  110 . Controller  106  may be configured to implement one or more pulse sequences, which are used to determine the instructions sent to power management system  110  to operate the magnetic components  120  in a desired sequence (e.g., parameters for operating the RF transmit and receive coils  126 , parameters for operating gradient coils  128 , etc.). As illustrated in  FIG. 1 , controller  106  also interacts with computing device  104  programmed to process received MR data. For example, computing device  104  may process received MR data to generate one or more MR images using any suitable image reconstruction process(es). Controller  106  may provide information about one or more pulse sequences to computing device  104  for the processing of data by the computing device. For example, controller  106  may provide information about one or more pulse sequences to computing device  104  and the computing device may perform an image reconstruction process based, at least in part, on the provided information. 
       FIG. 2  illustrates a schematic of a cross section of an ideal Halbach cylinder  200 . In such an ideal Halbach cylinder  200 , the permanent magnet material forms a cylindrical structure in which the magnetization, M, rotates twice as fast as the position rotates around the cylinder (e.g., the magnetization makes two complete rotations around the circumference of the cylinder). In the ideal two-dimensional case, the cylinder is infinitely long and the magnetization rotates continuously around the cylinder, creating a uniform magnetic field, B, within its cavity and generating zero field outside the cylinder. Although these characteristics are highly desirable, they are difficult to achieve in practice. Indeed, in practice, the cylinder has finite length and a continuous variation of magnetization orientation around the cylinder is difficult to achieve in manufacturing. Rather, conventional Halbach arrays are manufactured by: (1) discretizing the cylinder in the azimuthal direction and/or along the axis of the cylinder into multiple blocks, each of which is easier to manufacture; and (2) assembling the Halbach array out of the multiple blocks. However, the inventors have recognized that a swaging manufacturing process may be used to form cylindrical shells with continuous or nearly-continuous variation of magnetization orientation which may be used for MRI applications. 
       FIG. 3  illustrates an example of a cylindrical shell  300  within a cylindrical coordinate system. The cylindrical shell  300  has a cross section which is parallel to the x-y plane, while the cylindrical shell extends along a common longitudinal direction parallel to the z-direction (e.g., out of the page). The angular position within the cylindrical shell  300  is defined by an angle, θ, relative to the x-axis. The cylindrical shell  300  also has a thickness defined by a difference between an inner radius, R i , and an outer radius, R o . 
       FIG. 4  illustrates an example of a cylindrical magnet assembly  400  for providing a B 0  magnetic field for an MRI system, in accordance with some embodiments of the technology described herein. The cylindrical magnet assembly  400  includes ferromagnetic rings  410  and non-ferromagnetic regions  420 . The ferromagnetic rings  410  and non-ferromagnetic regions  420  may be tailored in length and spacing to provide a substantially homogenous magnetic field in a central region (e.g., imaging region) of the cylindrical magnet assembly  400 . The length, spacing, and arrangement of ferromagnetic rings  410  and non-ferromagnetic regions  420  may be determined using computational optimization methods, as described herein. 
     In some embodiments, the ferromagnetic rings  410  may be formed of any suitable permanent magnet material, examples of which are described herein. The ferromagnetic rings  410  may be formed by a swaging manufacturing process. For example, the ferromagnetic rings  410  may be individually manufactured by a swaging manufacturing process. Alternatively, the ferromagnetic rings  410  may be cut from a larger, integrally-formed piece of cylindrical stock formed by a swaging manufacturing process. 
     The swaging manufacturing process may use metallic tubes to form the ferromagnetic cylindrical shells, in some embodiments. Such metallic tubes, if left on the ferromagnetic rings  410  after manufacturing, may provide a conduction path for eddy currents caused by gradient field pulses within the MRI system. Accordingly, in some embodiments, such tubing is removed or partially removed (e.g., by abrasion, etching, or other techniques) prior to assembly of magnet assembly  400  to reduce eddy currents along the surfaces of the ferromagnetic rings  410 . Alternatively, using non-metallic tubes (e.g., plastic) or poorly conducting metal tubes (e.g., tungsten) may eliminate or reduce the effect of eddy currents in a final MRI system including magnet assembly  400 . 
     In some embodiments, the ferromagnetic rings  410  may have a continuously rotating magnetic orientation. The magnetic orientation may vary with angular position, θ, within the ferromagnetic rings  410 . For example, the ferromagnetic rings may have a continuously rotating magnetic orientation similar to that of the ideal Halbach cylinder  200 , as described in connection with  FIG. 2 . 
     In some embodiments, the non-ferromagnetic regions  420  may be gaps (e.g., air gaps) between the ferromagnetic rings  410 . Alternatively, the non-ferromagnetic regions  420  may include spacer rings formed of one or more non-magnetic materials (e.g., plastic, fiberglass). The spacer rings may be formed of transparent material to reduce claustrophobia of a patient within the MRI system during an MRI procedure. 
     In some embodiments, the magnet assembly  400  may be assembled by interspersing individual ferromagnetic rings  410  with individual non-ferromagnetic regions  420 . In other embodiments, the magnet assembly  400  may formed integrally as a single unit using a swaging manufacturing process. The magnet assembly  400  may be formed integrally as a single unit by interspersing regions of ferromagnetic powder alloy with regions of non-ferromagnetic powder alloy during the swaging manufacturing process. 
     In some embodiments, the magnet assembly  400  may be asymmetrical along the common longitudinal direction of the bore. For example, the inner diameter of the magnet assembly  400  may be larger at one end of the magnet assembly  400  than at the other end of the magnet assembly  400 . Such asymmetrical embodiments may enable a shorter distance from an entrance of the cylinder to the imaging region of the MRI system. This shorter distance may increase accessibility of the MRI system for patients and/or users. 
     The magnet assembly  400  may have a minimum length to obtain substantial field homogeneity within a suitably-sized imaging region (e.g., approximately within a volume having a diameter ranging from 15 cm to 30 cm). The dimensions of magnet assembly  400  may be scaled by the same ratio in all dimensions and preserve its magnetic properties (e.g., field strength, homogeneity, etc.). Herein, the dimensions of magnet assembly  400  will be expressed in terms of one reference dimension taken as unity. A convenient reference dimension is the inner radius of magnet assembly  400 . If the inner radius is set to 1, and the desired imaging region has a radius of 0.7 (e.g., 70% of the inner diameter of the magnet assembly  400  may be usable for imaging), then the minimum length of magnet assembly  400  may be approximately 3.5 with an outer radius of 1.1, which minimizes volume. With these dimensions, the magnet assembly  400  of  FIG. 4  may offer a B 0  magnetic field of 60 mT with approximately 10 ppm homogeneity over the imaging region volume. 
     However, such a structure may be limiting in terms of access. The diameter-to-length ratio (0.57) may be quite small, and a patient&#39;s head may not be able to be positioned in the imaging region if the patient&#39;s shoulders cannot fit within the bore. Such a structure may need to be increased to a typical MRI bore diameter to allow access for most patients. Accordingly, in some embodiments, for a magnet assembly  400  with an inner radius of 350 mm, the magnet assembly  400  may include approximately 380 kg of permanent magnet material. 
       FIG. 5A  illustrates an example of a cylindrical magnet assembly  500 , including regions of differing magnetization, for providing a B 0  magnetic field for an MRI system, in accordance with some embodiments of the technology described herein. Cylindrical magnet assembly  500  includes first ferromagnetic rings  510  and second ferromagnetic rings  520 . First ferromagnetic rings  510  and second ferromagnetic rings  520  may be formed of any suitable permanent magnet material, as described herein. First ferromagnetic rings  510  and second ferromagnetic rings  520  may be formed of a same permanent magnet material, in some embodiments, while in other embodiments first ferromagnetic rings  510  and second ferromagnetic rings  520  may be formed of different permanent magnet materials (e.g., to provide differently-sized contributions to the B 0  magnetic field). 
     In some embodiments, the first ferromagnetic rings  510  and second ferromagnetic rings  520  may have angularly-varying magnetizations. For example, the first ferromagnetic rings  510  and the second ferromagnetic rings  520  may have a continuously-rotating magnetization as in the example of Halbach cylinder  200 . In some embodiments, the first ferromagnetic rings  510  and second ferromagnetic rings  520  may have magnetizations with opposing polarities. Such embodiments may enable a shorter magnet assembly (e.g., having a shorter length along the common longitudinal direction) than a cylindrical magnet assembly including ferromagnetic rings and non-ferromagnetic regions (e.g., as described in relation to magnet assembly  400 ). 
     In some embodiments, first ferromagnetic rings  510  and second ferromagnetic rings  520  may be formed using a swaging manufacturing process. The first ferromagnetic rings  510  and second ferromagnetic rings  520  may be formed individually prior to assembling magnet assembly  500 . In such embodiments, stock ferromagnetic cylindrical shells with a desired inner and outer radii and a desired magnetization pattern may be formed using a swaging manufacturing process. The stock ferromagnetic cylindrical shells may be sliced into ferromagnetic rings of desired lengths, and the ferromagnetic rings may be assembled to form magnet assembly  500 . The ferromagnetic rings may be rotated relative to each other to appropriately orient the magnetization patterns (e.g., to orient the polarity of first ferromagnetic rings  510  in a first manner and to orient the polarity of second ferromagnetic rings  520  in a second, opposing manner). 
     In other embodiments, magnet assembly  500  may be integrally formed as a single piece using a swaging manufacturing process. For example, in such embodiments, a single ferromagnetic cylindrical shell may be manufactured. During a process of magnetizing the ferromagnetic cylindrical shell, the magnetic alignment fixture (e.g., electromagnetic coils, permanent magnet fixtures) may be rotated in order to change the polarity of the ferromagnetic cylindrical shell as a function of position along the common longitudinal direction (e.g., along the z-axis) of the ferromagnetic cylindrical shell. Alternatively, the polarity of the magnetic alignment fixture may be reversed by changing the direction of current flow (e.g., for electromagnetic alignment fixtures). 
     In some embodiments, a magnet assembly may also be discretized along the radial direction in addition to along the common longitudinal direction in order to increase the available degrees of freedom. An example of such a magnet assembly is magnet assembly  550  shown in  FIG. 5B , in accordance with some embodiments of the technology described herein. Such discretization along the radial direction may enable a shorter length along the common longitudinal direction. 
     Magnet assembly  550  includes first ferromagnetic rings  510  and second ferromagnetic rings  520 , the first ferromagnetic rings  510  having opposing polarities as the second ferromagnetic rings  520 . In such embodiments, the reduction of length along the common longitudinal direction may come at the cost of increased permanent magnet material weight. For example, for an inner radius of 350 mm and length of 700 mm (e.g., a 1:1 aspect ratio), the magnet assembly  550  may include approximately 4000 kg of permanent magnet material. For an inner radius of 150 mm, the magnet assembly  550  may include approximately 300 kg of permanent magnet material. 
     In some embodiments, computational optimization methods may be used to determine the layouts of the magnet assemblies (e.g., magnet assemblies  400 ,  500 , and/or  550 ). Such computational optimization methods may be performed using any suitable computing environment executing suitable optimization software. 
     In some embodiments, linear programming may be used to generate the magnet assembly layouts including ferromagnetic rings and non-ferromagnetic regions (e.g., magnet assembly  400 ). In such embodiments, a cylindrical shell may be defined in which magnetic material can be present. The geometric structure of the magnetic assembly may be constrained to have axial symmetry. The magnetization within the cylindrical shell may be constrained to be continuous and/or Halbach around the axis of symmetry, called O z  herein, so that the magnetic field in the bore of the cylindrical shell is along O x . The region of space where magnetized material can be positioned is located between points −b 0  and +b 0  along the common longitudinal axis and between p 1  and p 2  radially. This space may be discretized along the axis O z  into tubular slices. In some embodiments, the structure may be constrained to be symmetric with respect to the plane xOy. It can be shown that the scalar potential Φ* from which the field component B x  in the cavity derives is of the form: 
     
       
         
           
             
               
                 Φ 
                 * 
               
                
               
                 ( 
                 
                   r 
                   , 
                   θφ 
                 
                 ) 
               
             
             = 
             
               
                 ∑ 
                 
                   n 
                   = 
                   1 
                 
                 ∞ 
               
                
               
                 
                   r 
                   n 
                 
                  
                 X 
                  
                 
                   Φ 
                   n 
                   1 
                 
                  
                 cos 
                  
                 φ 
                  
                 
                   
                     P 
                     n 
                     1 
                   
                    
                   
                     ( 
                     
                       cos 
                        
                       θ 
                     
                     ) 
                   
                 
               
             
           
         
       
     
     The main component of the field B x  may then be given by: 
     
       
         
           
             
               B 
               x 
             
             = 
             
               
                 Z 
                 0 
               
               + 
               
                 
                   ∑ 
                   
                     n 
                     = 
                     1 
                   
                   ∞ 
                 
                  
                 
                   
                     r 
                     n 
                   
                   ( 
                   
                     
                       
                         
                           Z 
                           n 
                         
                          
                         
                           
                             P 
                             n 
                           
                            
                           
                             ( 
                             
                               cos 
                                
                               θ 
                             
                             ) 
                           
                         
                       
                       + 
                       
                         
                           X 
                           n 
                           2 
                         
                          
                         
                           
                             P 
                             n 
                             2 
                           
                            
                           
                             ( 
                             
                               cos 
                                
                               θ 
                             
                             ) 
                           
                         
                          
                         
                           cos 
                            
                           
                             ( 
                             
                               2 
                                
                               φ 
                             
                             ) 
                           
                         
                          
                         
                           
 
                         
                          
                         
                           where 
                           : 
                           
                             
 
                           
                            
                           
                             Z 
                             n 
                           
                         
                       
                     
                     = 
                     
                       
                         
                           - 
                           
                             μ 
                             0 
                           
                         
                          
                         
                           
                             
                               ( 
                               
                                 n 
                                 + 
                                 1 
                               
                               ) 
                             
                              
                             
                               ( 
                               
                                 n 
                                 + 
                                 2 
                               
                               ) 
                             
                           
                           2 
                         
                          
                         X 
                          
                         
                           Φ 
                           
                             n 
                             + 
                             1 
                           
                           1 
                         
                          
                         
                           
 
                         
                          
                         
                           X 
                           n 
                           2 
                         
                       
                       = 
                       
                         
                           
                             μ 
                             0 
                           
                           2 
                         
                          
                         X 
                          
                         
                           Φ 
                           
                             n 
                             + 
                             1 
                           
                           1 
                         
                       
                     
                   
                 
               
             
           
         
       
     
     Obtaining a homogeneous field in the imaging region may require canceling as many XΦ n   1  terms as necessary, with n&gt;1. The symmetry in xOy eliminates every even term of the potential (e.g., every odd term of the field). The optimization may be performed by building a matrix of effect of each tube slice on each term to be considered which we call W, with elements w n   i  where n is the order of the term and i is the index of the slice. The goal is to minimize the amount of material used within the allowed space to achieve a given field strength and homogeneity. This can be treated with a linear programming approach, where the linear program problem may be described by the objective function: 
     
       
         
           
             
               
                 min 
                  
                 imize 
               
               X 
             
              
             
               
                 ∑ 
                 i 
               
                
               
                 
                   x 
                   i 
                 
                  
                 
                   v 
                   i 
                 
               
             
           
         
       
     
     subject to the following linear constraints: 
     
       
         
           
             
               
                 
                   b 
                   0 
                 
                 - 
                 
                   Δ 
                    
                   b 
                 
               
               ≤ 
               
                 
                   ∑ 
                   i 
                 
                  
                 
                   
                     w 
                     1 
                     i 
                   
                    
                   
                     x 
                     i 
                   
                 
               
               ≤ 
               
                 
                   b 
                   0 
                 
                 + 
                 
                   Δ 
                    
                   b 
                 
               
             
              
             
               
 
             
              
             
               
                 
                   - 
                   δ 
                 
                  
                 b 
               
               ≤ 
               
                 
                   ∑ 
                   i 
                 
                  
                 
                   
                     w 
                     n 
                     i 
                   
                    
                   
                     x 
                     i 
                   
                 
               
               ≤ 
               
                 
                   + 
                   δ 
                 
                  
                 b 
                  
                 
                     
                 
                  
                 for 
                  
                 
                   
                       
                   
                    
                   
                       
                   
                 
                  
                 all 
                  
                 
                     
                 
                  
                 2 
               
               ≤ 
               n 
               ≤ 
               N 
             
           
         
       
       
         
           
             0 
             ≤ 
             
               x 
               i 
             
             ≤ 
             1 
           
         
       
     
     where X is the vector of material density in a slice, V is the vector of volume for each slice, b 0  is the desired field, Δb is a tolerance on the desired field strength, and δb is a tolerance of deviation for each term, which translates to a maximum field variation at a given radius. N is the maximum order to be considered for the terms. 
     In other embodiments including two ferromagnetic rings of opposing polarities, the linear program may be augmented by variables and constraints to describe the “negative” polarization. A vector D of positive variables may be introduced. The vector D may have components d i , and the vector D may be used for the objective function in the same manner as previously and may be used to constrain the free variable X, such that the linear optimization problem may be described by the objective function: 
     
       
         
           
             
               
                 min 
                  
                 imize 
               
               
                 D 
                 , 
                 X 
               
             
              
             
               
                 ∑ 
                 i 
               
                
               
                 
                   d 
                   i 
                 
                  
                 
                   v 
                   i 
                 
               
             
           
         
       
     
     subject to the following linear constraints: 
     
       
         
           
             
               
                 
                   b 
                   0 
                 
                 - 
                 
                   Δ 
                    
                   b 
                 
               
               ≤ 
               
                 
                   ∑ 
                   i 
                 
                  
                 
                   
                     w 
                     1 
                     i 
                   
                    
                   
                     x 
                     i 
                   
                 
               
               ≤ 
               
                 
                   b 
                   0 
                 
                 + 
                 
                   Δ 
                    
                   b 
                 
               
             
              
             
               
 
             
              
             
               
                 
                   - 
                   δ 
                 
                  
                 b 
               
               ≤ 
               
                 
                   ∑ 
                   i 
                 
                  
                 
                   
                     w 
                     n 
                     i 
                   
                    
                   
                     x 
                     i 
                   
                 
               
               ≤ 
               
                 
                   + 
                   δ 
                 
                  
                 b 
                  
                 
                     
                 
                  
                 for 
                  
                 
                     
                 
                  
                 all 
                  
                 
                     
                 
                  
                 2 
               
               ≤ 
               n 
               ≤ 
               
                 N 
                  
                 
                   
 
                 
                 - 
                 
                   d 
                   i 
                 
               
               ≤ 
               
                 x 
                 i 
               
               ≤ 
               
                 
                   + 
                   
                     d 
                     i 
                   
                 
                  
                 
                   ∀ 
                   i 
                 
               
             
           
         
       
       
         
           
             0 
             ≤ 
             
               d 
               i 
             
             ≤ 
             1 
           
         
       
     
     The inventors have recognized that a swaging manufacturing process may also be used to make magnetic assemblies for MRI systems that may be supported by a ferromagnetic frame, sometimes termed a “yoke.”  FIG. 6  illustrates an example of a magnet assembly  600  for providing a B 0  magnetic field for an MRI system, in accordance with some embodiments of the technology described herein. The magnet assembly  600  may include one or more sets of concentric ferromagnetic rings  610   a - d . The magnet assembly  600  may be bi-planar in configuration, with two sets of opposing ferromagnetic rings  610   a - d , as shown in  FIG. 6 . Alternatively, the magnet assembly  600  may only have one set of ferromagnetic rings  610   a - d . In some embodiments, one or more of ferromagnetic rings  610   a - d  may have different heights. In other embodiments, one or more of ferromagnetic rings  610   a - d  may have substantially the same heights. 
     In some embodiments, the magnet assembly  600  may be configured to provide a B 0  magnetic field in a range from 0.05 T to 0.2 T. Additionally or alternatively, magnet assembly  600  may be configured to provide a B 0  magnetic field in a range from 0.05 T to 0.1 T. In other embodiments, magnet assembly  600  may be configured to provide a B 0  magnetic field of 64 mT. 
     In some embodiments, one or more of the ferromagnetic rings  610   a - d  may be formed of ferromagnetic sub-rings  612 . In some embodiments, ferromagnetic sub-rings  612  may be formed of any suitable permanent magnetic materials, as described herein. The ferromagnetic sub-rings  612  may be manufactured using a swaging manufacturing process, such as a process as described in the &#39;818 and &#39;190 patent applications described previously herein. For example, stock ferromagnetic cylindrical shells having desired inner and outer diameters may be formed using a swaging manufacturing process, and the ferromagnetic cylindrical shells may be partitioned into individual ferromagnetic sub-rings  612 . The ferromagnetic sub-rings  612  may be assembled to form one or more of ferromagnetic rings  610   a - d . Alternatively, in some embodiments, one or more of the ferromagnetic rings  610   a - d  may be monolithically formed as a solid ring having a uniform magnetization rather than comprising an assembly of ferromagnetic sub-rings  612 . 
     In some embodiments, each ferromagnetic sub-ring  612  may have a uniform magnetization through its volume. The magnetization of each ferromagnetic sub-ring  612  may have radial and/or axial components, may have only a radial component, or may have only an axial component. In some embodiments, ferromagnetic sub-rings  612  may have different magnetizations with different radial and axial components from each other. In such embodiments the ferromagnetic rings  610   a - d  may have varying magnetization orientations within their assemblies, as shown in the example of  FIG. 7 . 
       FIG. 7  depicts an example of magnetic orientations of ferromagnetic sub-rings  612  within each ferromagnetic ring  610   a - d , in accordance with some embodiments of the technology described herein. The cross-section of  FIG. 7  is shown along the radial and axial directions, as the magnetization is substantially the same at each angular position within magnet assembly  600 . The magnetic orientation of each ferromagnetic sub-ring  612  is represented in  FIG. 7  by an arrow and may have axial and/or radial components. The magnetic orientations may be determined based on a desired B 0  magnetic field strength and/or field homogeneity. 
     In some embodiments, ferromagnetic rings  610   a - d  may have triangle-like radial cross-sections, as may be seen in  FIG. 7 . Such triangle-like cross-sections are difficult to produce using traditional sintered magnet blocks, but may reduce the amount of permanent magnetic material needed to produce a same B 0  magnetic field (e.g., such a triangle-like cross-section may increase B 0  magnetic field efficiency). For example, magnet assembly  600  may include less than 40 kg of permanent magnetic material to produce a same B 0  magnetic field as a conventional magnet assembly with a rectangular cross-section which includes 60 kg of permanent magnetic material. Alternatively, in some embodiments, one or more of ferromagnetic rings  610   a - d  may have a rectangular cross-section (not shown) in a plane parallel to the axial and radial directions. 
     When integrated into an MRI system, the magnet assembly  600  may be supported by a ferromagnetic frame.  FIG. 8  illustrates an example of an apparatus  800  including a C-shaped yoke  820  configured to support the bi-planar magnet assembly  600  of  FIG. 6 , in accordance with some embodiments of the technology described herein. Such C-shaped yokes  820  may be formed of ferromagnetic material (e.g., steel, silicon steel, CoFe, etc.) to direct magnetic flux produced by the magnet assembly  600  and increase B 0  magnetic field efficiency. Aspects of C-shaped ferromagnetic yokes  820  are described in U.S. Pat. No. 10,353,030, granted on Jul. 16, 2019, filed on Sep. 13, 2019, and titled “Low-Field Magnetic Resonance Imaging Methods and Apparatus,” which is incorporated by reference in its entirety herein. 
     In some embodiments, the magnet assembly  600  may be coupled to the ferromagnetic frame through a non-magnetic support (not shown). For example, non-ferromagnetic components (e.g., plastic components, fiberglass components) with a profile mirroring the profile of the magnet assembly  600  may house and support the magnet assembly  600 . The non-ferromagnetic components may be coupled to the ferromagnetic frame. 
     Alternatively, magnet assembly  600  may be incorporated into an apparatus including a symmetric frame structure, examples of which are shown in  FIGS. 9-11 , in accordance with some embodiments of the technology described herein. In the example of  FIG. 9 , symmetric frame structure  920  may include two or more posts to direct and concentrate the magnetic flux produced by the magnet assembly  600 . By capturing magnetic flux and directing it to the region between B0 magnets  210 , less permanent magnet material can be used in B0 magnets  210  to achieve a desired field strength, thus reducing the size, weight, and cost of the B0 magnet. Alternatively, for given permanent magnets, the field strength can be increased, thus improving the signal-to-noise ratio (SNR) of the system without having to use increased amounts of permanent magnet material. 
     In some embodiments, apparatus  900  includes blades  940  configured to enhance gradient magnetic fields generated by an MRI system that includes apparatus  900 , in accordance with some embodiments of the technology described herein. Blades  940  may be arranged to cover the surface behind the gradient coils (not pictured) in a sparse manner, providing improved gradient field efficiency while minimizing eddy current conduction. In some embodiments, the blades  940  may be arranged in a radial manner, extending towards a common center in the collection area between the multi-pronged members of frame structure  920 . Blades  940  may not meet or touch the common center in order to prevent the formation of a conduction path for eddy currents between opposing blades  940 . As a result, the eddy current time constants for exemplary apparatus  900  may be less than half the eddy current time constants for comparable C-shaped designs. 
     In some embodiments, to provide improved gradient field efficiency, blades  940  may be formed of a ferromagnetic material. The blades may be formed of, for example, low carbon steel, CoFe, and/or silicon steel to provide the desired magnetic properties. The blades  940  may be formed of a same ferromagnetic material as frame structure  920 , or may be formed of a different ferromagnetic material as frame structure  920 . 
     As shown in the example of  FIG. 10 , magnet assembly  600  may be incorporated into an apparatus  1000  comprising a frame  1020  having an alternative arrangement of blades  1026 , in accordance with some embodiments of the technology described herein. In some embodiments, frame  1020  includes posts coupled to multi-pronged members. Frame  1020  also may include one or more connectors  1025  extending between opposite ends of posts  1022 . The connectors  1025  may secure the posts to one another, increasing structural rigidity. In some embodiments, the connectors  1025  may be substantially parallel to one of the x- or y-gradient fields, providing additional improvement to the gradient field efficiency in that direction. 
     In some embodiments, apparatus  1000  may include blades  1026 . Blades  1026  may be similar to blades  940  of apparatus  900 . Blades  1026 , however, may be arranged substantially parallel to a direction of one of the other gradient fields (e.g., one of the x- or y-gradient fields) rather than in a radial arrangement as in apparatus  900 . Blades  1026  may be arranged substantially parallel to a direction of one of the gradient fields to provide improved gradient field efficiency during operation of the MRI system. 
     In some embodiments, the apparatus  1000  may include one or more non-conductive supports  1030  configured to cover the components of the frame  1020  and provide support to B 0  magnets  610   a - d  and blades  1026 . In some embodiments, structural foam may be inserted into the spaces between the non-conductive supports  1030 , the frame  1020 , connectors  1025 , and/or blades  1026 . The non-conductive supports  1030  may be formed of a non-conductive laminate material such as G-10. 
     As shown in the example of  FIG. 11 , magnet assembly  600  may be incorporated into an apparatus  1100  including posts  112  secured to plates  1130  by connection assemblies  1124 , in accordance with some embodiments of the technology described herein. In some embodiments, the connection assemblies  1124  may include a first connector  1124   a  and a second connector  1124   b . The first connector  1124   a  may connect one of the posts  1122  to one of the plates  1130 . For example, and as shown in  FIG. 11 , the first connector  1124   a  may be a substantially planar plate extending over the plate  1130  so that fasteners may extend through the first connector  1124   a  and secure the first connector  1124   a  to the plate  1130 . First connector  1124   a  may be secured to the post  1122  by additional fasteners extending through the second connector  1124   b , the first connector  1124   a , and the post  1122 . Forming the connection assembly  1124  out of multiple “layered” components may reduce manufacturing costs (e.g., by simplifying machining processes) and/or reduce magnetic saturation effects within the apparatus  1100 . 
     In some embodiments, the second connector  1124   b  may be configured to increase the magnetic flux capacity of the apparatus  1100 . For example, the second connector  1124   b  may have a wedge-like shape as shown in the examples of  FIG. 11  to direct and concentrate magnetic flux from the posts  1122  back into the imaging region between the B 0  magnets  610   a - d.    
     In some embodiments, plates  1130  may be configured to support B 0  magnets  610   a - d . Plates  1130  may be formed from solid ferromagnetic sheet material. In some embodiments, plates  1130  may include one or more holes to reduce the weight of the plates  1130  and/or to allow for cooling or venting of the apparatus  1100  during MR imaging. 
     In some embodiments, apparatus  1100  may include additional permanent magnets  1126  positioned on inward-facing surfaces of posts  1122 . The permanent magnets  1126  may be positioned and/or shaped to reduce inhomogeneity of the B 0  magnetic field and may be used in addition to or as a replacement for shim coils and/or passive shims positioned adjacent the B 0  magnets  610   a - d . In some embodiments, permanent magnets  1126  may be polarized along a direction perpendicular to a plane of the inward-facing surfaces of the posts  1122  (e.g., toward or away from a common center of the concentric B 0  permanent magnet rings  610   a - d ). In some embodiments having two permanent magnets  1126 , each of the two permanent magnets  1126  may have opposing polarizations. For example, a first of the permanent magnets  1126  may have a polarization directed toward the inward-facing surfaces of the posts  1122  and a second of the permanent magnets  1126  may have a polarization direction away from the inward-facing surfaces of the posts  1122 . It should also be appreciated that permanent magnets  1126  may be included in any of the embodiments described herein, including apparatuses  800 ,  900 , and/or  1000  described herein. 
     Using the techniques described herein, the inventors have developed portable, low power MRI systems capable of being brought to the patient, providing affordable and widely deployable MRI where it is needed.  FIG. 12  shows an example of a portable, low-field MRI system  1000  including the magnet assembly  800  of  FIG. 8 , in accordance with some embodiments of the technology described herein. The magnet assembly  800  may be surrounded by a non-ferromagnetic housing  1205  and supported by a base  1210 , as shown in the example of  FIG. 12 . Base  1210  may house the power components and/or electronics discussed in connection with  FIG. 1 , including power components configured to operate the MRI system  1200 . 
     Base  1210  may also include one or more transport mechanisms  1220  which enable point-of-care use of MRI system  1200 , in accordance with some embodiments of the technology described herein. In the example of  FIG. 12 , the transport mechanisms  1220  are depicted as wheels, but other transport mechanisms may be used. In some embodiments, transport mechanisms  1220  may include a motorized component  1225  may be provided to allow the MRI system  1200  to be driven from location to location, for example, using a control such as a joystick or other control mechanism provided on or remote from the MRI system  1000 . In this manner, MRI system  1200  can be transported to the patient and maneuvered to the bedside to perform imaging, as illustrated in  FIG. 13 . 
       FIG. 13  depicts the use of the portable MRI system of  FIG. 12  to perform a brain scan of a patient, in accordance with some embodiments of the technology described herein. During the brain scan, the MRI system  1200  may be used to capture at least one magnetic resonance image of the patient for clinical use. 
       FIG. 14  shows, schematically, an illustrative computer  1400  on which any aspect of the present disclosure may be implemented. 
     In the embodiment shown in  FIG. 14 , the computer  1400  includes a processing unit  1401  having one or more processors and a non-transitory computer-readable storage medium  1402  that may include, for example, volatile and/or non-volatile memory. The memory  1402  may store one or more instructions to program the processing unit  1401  to perform any of the functions described herein. The computer  1400  may also include other types of non-transitory computer-readable medium, such as storage  1405  (e.g., one or more disk drives) in addition to the system memory  1402 . The storage  1405  may also store one or more application programs and/or resources used by application programs (e.g., software libraries), which may be loaded into the memory  1402 . 
     The computer  1400  may have one or more input devices and/or output devices, such as devices  1406  and  1407  illustrated in  FIG. 14 . These devices can be used, among other things, to present a user interface. Examples of output devices that can be used to provide a user interface include printers or display screens for visual presentation of output and speakers or other sound generating devices for audible presentation of output. Examples of input devices that can be used for a user interface include keyboards and pointing devices, such as mice, touch pads, and digitizing tablets. As another example, the input devices  1407  may include a microphone for capturing audio signals, and the output devices  1406  may include a display screen for visually rendering, and/or a speaker for audibly rendering, recognized text. As another example, the input devices  1407  may include sensors (e.g., electrodes in a pacemaker), and the output devices  1406  may include a device configured to interpret and/or render signals collected by the sensors (e.g., a device configured to generate an electrocardiogram based on signals collected by the electrodes in the pacemaker). 
     As shown in  FIG. 14 , the computer  1400  may also comprise one or more network interfaces (e.g., the network interface  1410 ) to enable communication via various networks (e.g., the network  1420 ). Examples of networks include a local area network or a wide area network, such as an enterprise network or the Internet. Such networks may be based on any suitable technology and may operate according to any suitable protocol and may include wireless networks, wired networks or fiber optic networks. Such networks may include analog and/or digital networks. 
     Having thus described several aspects of at least one embodiment of this technology, it is to be appreciated that various alterations, modifications, and improvements will readily occur to those skilled in the art. 
     The above-described embodiments of the technology described herein can be implemented in any of numerous ways. For example, the embodiments may be implemented using hardware, software or a combination thereof. When implemented in software, the software code can be executed on any suitable processor or collection of processors, whether provided in a single computer or distributed among multiple computers. Such processors may be implemented as integrated circuits, with one or more processors in an integrated circuit component, including commercially available integrated circuit components known in the art by names such as CPU chips, GPU chips, microprocessor, microcontroller, or co-processor. Alternatively, a processor may be implemented in custom circuitry, such as an ASIC, or semi-custom circuitry resulting from configuring a programmable logic device. As yet a further alternative, a processor may be a portion of a larger circuit or semiconductor device, whether commercially available, semi-custom or custom. As a specific example, some commercially available microprocessors have multiple cores such that one or a subset of those cores may constitute a processor. Though, a processor may be implemented using circuitry in any suitable format. 
     Also, the various methods or processes outlined herein may be coded as software that is executable on one or more processors running any one of a variety of operating systems or platforms. Such software may be written using any of a number of suitable programming languages and/or programming tools, including scripting languages and/or scripting tools. In some instances, such software may be compiled as executable machine language code or intermediate code that is executed on a framework or virtual machine. Additionally, or alternatively, such software may be interpreted. 
     The techniques disclosed herein may be embodied as a non-transitory computer-readable medium (or multiple computer-readable media) (e.g., a computer memory, one or more floppy discs, compact discs, optical discs, magnetic tapes, flash memories, circuit configurations in Field Programmable Gate Arrays or other semiconductor devices, or other non-transitory, tangible computer storage medium) encoded with one or more programs that, when executed on one or more processors, perform methods that implement the various embodiments of the present disclosure described above. The computer-readable medium or media may be transportable, such that the program or programs stored thereon may be loaded onto one or more different computers or other processors to implement various aspects of the present disclosure as described above. 
     The terms “program” or “software” are used herein to refer to any type of computer code or set of computer-executable instructions that may be employed to program one or more processors to implement various aspects of the present disclosure as described above. Moreover, it should be appreciated that according to one aspect of this embodiment, one or more computer programs that, when executed, perform methods of the present disclosure need not reside on a single computer or processor, but may be distributed in a modular fashion amongst a number of different computers or processors to implement various aspects of the present disclosure. 
     Various aspects of the technology described herein may be used alone, in combination, or in a variety of arrangements not specifically described in the embodiments described in the foregoing and is therefore not limited in its application to the details and arrangement of components set forth in the foregoing description or illustrated in the drawings. For example, aspects described in one embodiment may be combined in any manner with aspects described in other embodiments. 
     Use of ordinal terms such as “first,” “second,” “third,” etc., in the claims to modify a claim element does not by itself connote any priority, precedence, or order of one claim element over another or the temporal order in which acts of a method are performed, but are used merely as labels to distinguish one claim element having a certain name from another element having a same name (but for use of the ordinal term) to distinguish the claim elements. 
     Also, the phraseology and terminology used herein is for the purpose of description and should not be regarded as limiting. The use of “including,” “comprising,” or “having,” “containing,” “involving,” and variations thereof herein, is meant to encompass the items listed thereafter and equivalents thereof as well as additional items. 
     The terms “approximately” and “about” may be used to mean within ±20% of a target value in some embodiments, within ±10% of a target value in some embodiments, within ±5% of a target value in some embodiments, within ±2% of a target value in some embodiments. The terms “approximately” and “about” may include the target value.