Abstract:
The present invention is directed to a method of shimming a magnet assembly of an MR imaging system such that a desired B 0  field strength may be created with minimal inhomogeneities therethrough. With this method, sufficient shimming of the magnet assembly may be achieved without requiring mechanical variations to the magnet assembly after the magnet assembly has been assembled. The invention analyzes variations from the desired B 0  field and inhomogeneities at a number of target points along the magnet assembly or B 0  field. A comparison is then made at each point to determine a shimming or weighting factor such that the desired overall B 0  field strength and targeted field homogeneity is achieved. Active and/or passive shim elements may then be incorporated into the magnet assembly at each target point to achieve the desired overall field strength and minimum overall field homogeneity.

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
     The present application claims the benefit of U.S. Ser. No. 60/320,037 filed Mar. 21, 2003. 
    
    
     BACKGROUND OF THE INVENTION 
     The present invention relates generally to a method of B 0  controlled shimming of a magnet assembly of an MR system and, more particularly, to a method of shimming the magnet assembly of an MR system to achieve a near-homogeneous magnetic field having requisite signal strength without requiring mechanical adjustments to the magnet assembly once assembled. 
     It is generally known that when a substance such as human tissue is subjected to a uniform magnetic field (polarizing field B 0 ), the individual magnetic moments of the spins in the tissue attempt to align with this polarizing field, but precess about it in random order at their characteristic Larmor frequency. If the substance, or tissue, is subjected to a magnetic field (excitation field B 1 ) which is in the x-y plane and which is near the Larmor frequency, the net aligned moment, or “longitudinal magnetization”, Mz, may be rotated, or “tipped”, into the x-y plane to produce a net transverse magnetic moment M t . A signal is emitted by the excited spins after the excitation signal B 1  is terminated and this signal may be received and processed to form an image. 
     When utilizing these signals to produce images, magnetic field gradients (G x  G y  and G z ) are employed. Typically, the region to be imaged is scanned by a sequence of measurement cycles in which these gradients vary according to the particular localization method being used. The resulting set of received NMR signals are digitized and processed to reconstruct the image using one of many well known reconstruction techniques. 
     During fabrication and construction of the magnet assembly for an MR assembly, manufacturing tolerances and deviations in material make-up of the magnet assembly result in an inhomogeneous B 0  field being created by the magnet assembly absent shimming. As a result of the magnet manufacturing process, it is not uncommon for the magnet to produce a very inhomogeneous field ranging from several hundred parts per million (ppm) to several thousand ppm, and a non-accurate center magnetic field that is significantly out of range. The importance of these variations is glaringly apparent given that MR systems require an intense uniform magnetic field, typically less than 10 ppm of variations within a 40-50 cm spherical volume, but also an accurate center magnetic field value, typically less than 0.5% variation. 
     Shimming is a common process that is used to remove inhomogeneities from the B 0  field. Shimming is important for MR systems because the average B 0  field strength must be within a certain window for the RF hardware of the system. A simplistic example of the effects of shimming is graphically shown in FIG.  1 . As shown, a magnet assembly without shimming produces a magnet field represented by curve  2 . The variations of the magnetic field are quite clear. As is widely known, these variations negatively affect data acquisition and reconstruction of an MR image. As such, it is desirable to generate a shim field, represented by curve  4 , that counters or offsets the variations in the magnetic field. The combination of the shim field  4  with the magnetic field  2  yields, ideally, a homogeneous and uniform B 0  field represented by curve  6 . 
     The shimming process includes the precise placement of shim elements within the magnetic assembly such that numerous small magnetic fields are generated to offset variations in the B 0  field. The shim elements include active shims such as shim coils or permanent magnets as well as passive shims such as iron cores. Shim coils are common in superconducting magnet assemblies and their shimming may be controlled by regulating current thereto. The shimming characteristics of permanent magnets may be controlled by regulating the mass and polarity of the magnet and the shimming effect of iron cores may be controlled by regulating the mass of the iron incorporated into the magnet assembly. 
     Regardless of the type of shim element employed, the customary manufacturing and shimming process measures the B 0  field of the magnet assembly and then shims the magnet assembly with precise placement of shim elements. The placement of shim elements, however, is done without regard to the affects the shims have on the average field strength of the center B 0  field. That is, shimming is concerned with homogeneities in the field and mechanical adjustments to the magnet assembly are later done independently of to address issues regarding average field strength. For example, in a permanent magnet MRI system, mechanical adjustments may include changing the air gap between yokes of the magnet assembly. However, these mechanical adjustments may deviate sufficiently from the magnet design such that performance characteristics such as fringe field are adversely affected. Moreover, mechanical variations or adjustments to the magnet assembly are a time-consuming and costly process that often requires several iterations before sufficient shimming has occurred. In fact, it is not uncommon for the shimming process to take several days to complete. Other approaches include implementation of a mechanical device within the magnet assembly to increase or decrease the B 0  field. This device is generally referred to as a “B 0  plug” and it increases the overall weight, size, and cost of the magnet assembly. 
     It would therefore be desirable to have a system and method capable of prescribing shimming of an MR magnet assembly such that time consuming and costly mechanical variations to the magnet assembly are avoided. It would also be desirable to design a model wherein peak-to-peak homogeneity and central field issues are addressed simultaneously. 
     BRIEF DESCRIPTION OF THE INVENTION 
     The present invention overcomes the aforementioned drawbacks by providing a method of shimming a magnet assembly of an MR imaging system such that a desired B 0  field strength may be created with minimal inhomogeneities therethrough. With this method, sufficient shimming of the magnet assembly may be achieved without requiring mechanical variations to the magnet assembly after the magnet assembly has been assembled. The method, which may be carried out as a set of instructions of a computer program by one or more computers, analyzes variations from the desired B 0  field and inhomogeneities at a number of target points along the magnet assembly or B 0  field. A comparison is then made at each point to determine a shimming or weighting factor such that the desired B 0  field strength and targeted field homogeneity are achieved during data acquisition. Active and/or passive shim elements may then be incorporated into the magnet assembly at each target point to achieve the desired overall field strength and minimum overall field homogeneity. The shimming or weighting factors are used to determine the amount of “shimming material” that is used at each target point. 
     “Shimming material” varies according to the type of shim element. For example, for active shim elements, i.e. shim coils, the shimming material corresponds to the amount of current applied to the coils. By varying the amount of current applied to the coils, the amount contributed to the magnetic field can be varied. As a result, the shim coils can be independently controlled such that field contribution is precisely controlled. For passive shim elements, i.e. iron shims or permanent magnets, the shimming material corresponds to the amount of magnetic element that is added to the magnet assembly. 
     Therefore, in accordance with one aspect of the present invention, a method of shimming a magnet for an MR imaging system includes the steps of determining a desired B 0  field strength for a B 0  field having a number of target points and determining a minimum acceptable field inhomogeneity for the B 0  field. The method also includes the step of determining at least one of a field strength variation from the desired B 0  field strength and an inhomogeneity variation from the minimum acceptable field inhomogeneity at each target point. Each target point of the B 0  field is then shimmed such that at least one of an actual B 0  field strength at least approximates the desired B 0  field strength and an actual field inhomogeneity does not exceed the minimum acceptable field inhomogeneity. 
     In accordance with another aspect of the present invention, a computer readable storage medium having a computer program stored thereon to develop a shimming model for a magnet assembly of an MR imaging system, the computer program representing a set of instructions that when executed by a computer causes the computer to map a B 0  field generated by an assembled magnet assembly. From the map, a number of target points within the B 0  field or, alternately, a set of harmonics are identified. The set of instructions then causes the computer to determine an amount of shimming required at each of the target points such that a desired field strength of the B 0  field is maintained simultaneously with substantial cancellation of inhomogeneities within the B 0  field. 
     According to another aspect of the invention, a method of manufacturing a magnet assembly for an MR imaging system is provided. The method includes the step of constructing a permanent magnet assembly designed to generate a B 0  field at a desired field strength about a volume-of-interest (VOI). Variations in field strength along the B 0  field are then determined. Variations in the field strength are then minimized without requiring mechanical adjustments to the permanent magnet assembly. 
     Various other features, objects and advantages of the present invention will be made apparent from the following detailed description and the drawings. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     The drawings illustrate one preferred embodiment presently contemplated for carrying out the invention. 
     In the drawings: 
     FIG. 1 is a series of curves illustrating a magnetic field generated by a magnet assembly, a shim field generated by shim elements incorporated into a magnet assembly, and a uniform B 0  field that is desired when the magnetic field is combined with the shim field. 
     FIG. 2 is a schematic block diagram of an MR imaging system for use with the present invention. 
     FIG. 3 is a flow chart setting forth the steps of a process of shimming a magnet assembly of an MR imaging system such that mechanical adjustments to an assembled magnet assembly are minimized. 
     FIG. 4 is a flow chart setting for the high level acts carried out by one or more computers to determine minimal shimming of an MR magnet assembly in accordance with the present invention. 
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT 
     Referring to FIG. 2, the major components of a preferred magnetic resonance imaging (MRI) system  10  incorporating the present invention are shown. The operation of the system is controlled from an operator console  12  which includes a keyboard or other input device  13 , a control panel  14 , and a display screen  16 . The console  12  communicates through a link  18  with a separate computer system  20  that enables an operator to control the production and display of images on the display screen  16 . The computer system  20  includes a number of modules which communicate with each other through a backplane  20   a . These include an image processor module  22 , a CPU module  24  and a memory module  26 , known in the art as a frame buffer for storing image data arrays. The computer system  20  is linked to disk storage  28  and tape drive  30  for storage of image data and programs, and communicates with a separate system control  32  through a high speed serial link  34 . The input device  13  can include a mouse, joystick, keyboard, track ball, touch activated screen, light wand, voice control, or any similar or equivalent input device, and may be used for interactive geometry prescription. 
     The system control  32  includes a set of modules connected together by a backplane  32   a . These include a CPU module  36  and a pulse generator module  38  which connects to the operator console  12  through a serial link  40 . It is through link  40  that the system control  32  receives commands from the operator to indicate the scan sequence that is to be performed. The pulse generator module  38  operates the system components to carry out the desired scan sequence and produces data which indicates the timing, strength and shape of the RF pulses produced, and the timing and length of the data acquisition window. The pulse generator module  38  connects to a set of gradient amplifiers  42 , to indicate the timing and shape of the gradient pulses that are produced during the scan. The pulse generator module  38  can also receive patient data from a physiological acquisition controller  44  that receives signals from a number of different sensors connected to the patient, such as ECG signals from electrodes attached to the patient. And finally, the pulse generator module  38  connects to a scan room interface circuit  46  which receives signals from various sensors associated with the condition of the patient and the magnet system. It is also through the scan room interface circuit  46  that a patient positioning system  48  receives commands to move the patient to the desired position for the scan. 
     The gradient waveforms produced by the pulse generator module  38  are applied to the gradient amplifier system  42  having G x , G y , and G z  amplifiers. Each gradient amplifier excites a corresponding physical gradient coil in a gradient coil assembly generally designated  50  to produce the magnetic field gradients used for spatially encoding acquired signals. The gradient coil assembly  50  forms part of a magnet assembly  52  which includes a polarizing magnet  54  and a whole-body RF coil  56 . A transceiver module  58  in the system control  32  produces pulses which are amplified by an RF amplifier  60  and coupled to the RF coil  56  by a transmit/receive switch  62 . The resulting signals emitted by the excited nuclei in the patient may be sensed by the same RF coil  56  and coupled through the transmit/receive switch  62  to a preamplifier  64 . The amplified MR signals are demodulated, filtered, and digitized in the receiver section of the transceiver  58 . The transmit/receive switch  62  is controlled by a signal from the pulse generator module  38  to electrically connect the RF amplifier  60  to the coil  56  during the transmit mode and to connect the preamplifier  64  to the coil  56  during the receive mode. The transmit/receive switch  62  pan also enable a separate RF coil (for example, a surface coil) to be used in either the transmit or receive mode. 
     The MR signals picked up by the RF coil  56  are digitized by the transceiver module  58  and transferred to a memory module  66  in the system control  32 . A scan is complete when an array of raw k-space data has been acquired in the memory module  66 . This raw k-space data is rearranged into separate k-space data arrays for each image to be reconstructed, and each of these is input to an array processor  68  which operates to Fourier transform the data into an array of image data. This image data is conveyed through the serial link  34  to the computer system  20  where it is stored in memory, such as disk storage  28 . In response to commands received from the operator console  12 , this image data may be archived in long term storage, such as on the tape drive  30 , or it may be further processed by the image processor  22  and conveyed to the operator console  12  and presented on the display  16 . 
     The present invention will be described with respect to a method of controlling shimming of the B 0  field generated by the magnet assembly of an MR imaging system. While the invention will be described as a series of steps carried out by a process or technique, the invention may be equivalently carried out by one or more computers or processors in accordance with executable instructions of a computer program. Additionally, the present invention will be described relative to shimming a permanent magnet, but the invention is equivalently applicable with other magnet types including, but not limited to superconducting magnets. Moreover, the hereinafter shimming processes may be carried out in a factory setting, at the installation site, or a combination of both. 
     Referring now to FIG. 3, the steps of a manufacturing process  70  for shimming an MR magnet assembly begins at  72  with the construction and assembly of a magnet assembly. Upon construction of the magnet assembly, a test B 0  field is generated  74  and analyzed such that variations or inhomogeneities in the B 0  field as well as field strength may be addressed and, if possible, corrected. As previously discussed, the magnetic field of an assembled magnet assembly is often inhomogeneous as a result of deviation in material properties and tolerances in the manufacturing process. Further, ferromagnetic objects placed in relative proximity to the magnet assembly may negatively affect field homogeneity and therefore must be taken in consideration. 
     From the field map generated at  74 , the B 0  field can be analyzed to determine if the field strength and homogeneity are within specified limits  76 . If both are within limits  76 ,  78 , the shimming process  70  is complete add ends at  80  with incorporation of the magnet assembly into an MR assembly and subsequent downstream processing. However, if either the field strength or field homogeneity is outside acceptable limits  76 ,  82 , shimming process  70  continues with the input of system and shim constraints into one or more computers programmed to determine shimming parameters at  84 . 
     The constraints input include the desired B 0  field strength and the minimum acceptable field inhomogeneity. Other inputs include magnet system geometry constraints as well as shimming constraints. The shimming constraints include the physical limitations on each type of potential shim and placement of the shims within the magnet. For example, for active shims, constraints may include the maximum or minimum acceptable current that may be applied to the shim to control field contributions. In another example, mass constraints may be input for passive shims such as iron cores. As will be described in greater detail below, these constraints are utilized by a shimming algorithm to determine shim placement, type of shim, and amount of shim at  86 . 
     Because both field strength and desired field homogeneity are input as shimming constraints, the determination of shim placement, type, and amount at  86  are such that implementation of shims according to the output of the algorithm does not result in substantial changes to the B 0  field strength or achieves the desired B 0  field strength while taking field homogeneity into account. As such, mechanical variations or changes to the magnet to increase or decrease field strength are unnecessary. Accordingly, shims are installed at  88  at each of the locations or target points identified at step  86  and the amount of “shimming material” applied at each shim location is likewise known from output of the algorithm or model at  86 . As indicated above, the amount of “shimming material” is such that, as a whole, the desired field strength is attained and homogeneity is substantially achieved. 
     A verification of the B 0  field is then undertaken with re-generation of the B 0  field map at  74 . An analysis is then made again at step  76  to determine if the field strength and inhomogeneity are within acceptable limits. If so, the shimming process is complete and ends at  80 . If not, the shimming process continues with re-running of the shimming algorithm and adjustments to the shims applied. However, mechanical adjustments to the magnet assembly are avoided, as discussed above. 
     Referring now to FIG. 4, a high level illustration of acts of the shimming algorithm discussed above with respect to FIG. 3 is shown. The algorithm or technique  90 , which is carried out by one or more computers, begins at  92  with the reception of system and shim constraints input at  94 . From the system and shim constraints, an objective function is formulated at  96 . The objective function, which may take one of many forms, is defined to determine a minimum amount of shimming required throughout the magnet assembly such that field inhomogeneities are removed and the desired field strength is achieved or, if applicable, maintained. Two examples of an objective function are described in greater detail below. 
     After formulating the appropriate objective function, the constraints input at  94  are applied at  98 . From the constraints relative to the objective function, an ideal solution is determined at  100 . The ideal solution sets forth the amount of shimming required at a number of locations or target points within the magnet assembly. However, it is necessary to take into consideration that the amount of shimming identified at each location may not be precisely possible. For example, iron shims are fabricated with varying degrees of mass. As such, there may not be an iron shim having the exact particular shim value identified as “ideal”. Therefore, it is necessary to discretize the ideal solution at  102  to address variations between the “ideal” shim values and the shim values that are available. From the discretizing process, shim locations and shim amounts are output such that the shimming process described with respect to FIG. 3 may be carried out. 
     As noted above, the shimming algorithm may utilize one of a number of objective functions designed to address field inhomogeneities and field strength simultaneously. For example, a Linear Programming (LP) approach or implementation may be used or a least squares method. In one LP approach, the objective function may be defined as: 
     
       
         Minimize Obj=Σ V   i ( I   i   +   −I   i   − )+Σ Wj*Yj   (Eqn. 1). 
       
     
     The function is limited or subjected to the following constraints: 
     
       
         − I   max   ≦I   i   − ≦0  (Eqn. 2); 
       
     
     
       
         0≦ I   i   30   ≦I   max   (Eqn. 3); 
       
     
     
       
           Y   L   ≦Yj≦Y   U   (Eqn. 4); 
       
     
     and 
     
       
           B   L   ≦AX≦B   U   (Eqn. 5); 
       
     
     where: 
     I i   − , I i   +  are state variables for active shims, such as resistive, superconducting or permanent magnet shims. For shimming coils, these are the amount of currents of appropriate sign required in the coil. For permanent magnet shims, these are the amounts of permanent magnet material of the appropriate polarity. 
     Yj is the state variables for passive shims. These are the amount of passive shims placed at each location. 
     V i  is the weighting factors for the active shims; 
     W j  is the weighting factors for the passive shims; 
     A is a shim strength matrix of the active and passive at each shim location, either in terms of field contributions to each shimming points or in terms of spherical harmonics including the B 0  contribution; 
     X is a vector of all the state variables; and 
     B L  and B U  are the constraint lower and upper bound vectors, in terms of field (Gauss, Tesla) or harmonics (ppm). These are the actual constraints that define the field homogeneity and the desired center field (B 0 ). 
     It should be noted that Eqn. 5 may be characterized as |AX−B target |≦ε where B target  is the target field or harmonics, and ε is the allowable tolerance vector. 
     In another LP approach, the following objective function may be defined and used to determine or compute a useful solution. 
     
       
         Minimize Obj =Σa   i   X   i   +T+βQ   (Eqn. 6). 
       
     
     The function is subjected to the following constraints:                    ∑     Δ                   B   ij          X   i         +     B   j   input     -     B   mean       ≤       T   2     +       E   j     2         ;           (     Eqn   .              7     )                     ∑     Δ                   B   ij          X   i         +     B   j   input     -     B   mean       ≥       -     T   2       -       E   j     2         ;           (     Eqn                 8     )                     B   upper     -     B   mean       ≤     Q   2       ;   and           (     Eqn                 9     )                     B   mean     -     B   lower       ≤     Q   2       ;           (     Eqn                 10     )                               0 ≦X   i   ≦t   i   (Eqn. 11); 
     
       
           Q,T,B   mean ≦0  (Eqn. 12); 
       
     
     where: 
     X i , are state variables for active shims, such as resistive, superconducting or permanent magnet shims. For shimming coils, these are the amount of currents of appropriate sign required in the coil. For permanent magnet shims, these are the amounts of permanent magnet material of the appropriate polarity. 
     a i  is the weighting factors for the shims, and may be constant for all shims or may vary by type or even individual shims 
     ΔB ij  is a shim strength matrix of the active and passive elements at each shim location, either in terms of field contributions to each shimming points or in terms of spherical harmonics. 
     B Lower  and B Upper  are the constraint lower and upper bound vectors, in terms of field. These are the actual constraints that define the field homogeneity and the desired center field (B 0 ). 
     B mean , Q, and T are solver variables that represent the average field, the amount above or below the B 0  target window, and the amount above or below the PPM target, respectively. 
     t i  represents the maximum value constraint for each shim, which can be, for example, a maximum current, mass or volume. 
     β is the weighting factor between Uniformity and B 0  target; and 
     B input  is the measured field value at each point. 
     The LP approach is preferred as it yields a fast and optimum solution. Further the LP approach allows the flexibility to set a window on the desired B 0  level as well as a relative weighting for the importance of the B 0  field level versus the homogeneity. Constraints on harmonics may be added in a similar for to or used in lieu of equations (7) and (8). 
     Another approach is implementation of a Least Squares solution. With this approach the solution is not necessarily optimal. As such, the desired field profile and center field strength may not be achieved. The specifics of this approach are as follows: 
     
       
         Minimize Obj =ΣV   i *( B   i     —     B   i−target ) 2   +ΣWj*Yj   2   (Eqn. 13). 
       
     
     Subject to the following constraint: 
     
       
           Y   L   ≦Yj≦Y   U   (Eqn. 14); 
       
     
     where: 
     B i  is the predicted fields at the target points or the predicted harmonics and B 0  (0 th  order harmonic is the B 0 ); 
     B i     —     target  is the desired fields at the target points or the desired harmonics and B 0  (0 th  order harmonic is the B 0 ): 
     Yj is the state variables for the shims. These are the amount of passive or permanent magnet shim materials placed at each location, or the amount of current required for each shim coil. 
     V i  is the weighting factors for the field or harmonic requirements; and 
     W j  is the weighting factors for the shim material. 
     Either approach recognizes desired field strength and desired homogeneity as a constraint on a shimming solution. Moreover, each approach determines a solution from the constraints on field strength and field inhomogeneity together with constraints on the type of shim and amount of shimming material available. As such, a solution can be generated that achieves the appropriate homogeneity and desired center field thereby avoiding mechanical adjustments to the magnet assembly. Additionally, with the above approaches, a deviation from the desired field strength or homogeneity is determined at a number of target points or locations. From this deviation or error, the amount of shimming material needed at each shim location can be minimized. Further, the shimming solutions may be developed based on the amount of field contribution of each shim at each of the determined locations or based on spherical harmonics including B 0  contributions of each shim at each of the determined locations. These approaches are considered a “target field approach” and a “target harmonics approach”, respectively. 
     Therefore, in accordance with one embodiment of the present invention, a method of shimming a magnet for an MR imaging system includes the steps of determining a desired B 0  field strength for a B 0  field having a number of target points and determining a minimum acceptable field inhomogeneity for the B 0  field. The method also includes the step of determining at least one of a field strength variation from the desired B 0  field strength and an inhomogeneity variation from the minimum acceptable field inhomogeneity at each target point. Each target point of the B 0  field is then shimmed such that at least one of an actual B 0  field strength at least approximates the desired B 0  field strength and an actual field inhomogeneity does not exceed the minimum acceptable field inhomogeneity. 
     In accordance with another embodiment of the present invention, a computer readable storage medium having a computer program stored thereon to develop a shimming model for a magnet assembly of an MR imaging system, the computer program representing a set of instructions that when executed by a computer causes the computer to map a B 0  field generated by an assembled magnet assembly. From the map, a number of target points within the B 0  field are identified. The set of instructions then causes the computer to determine an amount of shimming required at each of the target points such that a desired field strength of the B 0  field is maintained simultaneously with substantial cancellation of inhomogeneities within the B 0  field. 
     According to another embodiment of the invention, a method of manufacturing a magnet assembly for an MR imaging system is provided. The method includes the step of constructing a permanent magnet assembly designed to generate a B 0  field at a desired field strength about a volume-of-interest (VOI). Variations in field strength along the B 0  field are then determined. Variations in the field strength are then minimized without requiring mechanical adjustments to the permanent magnet assembly. 
     The present invention has been described in terms of the preferred embodiment, and it is recognized that equivalents, alternatives, and modifications, aside from those expressly stated, are possible and within the scope of the appending claims.