Development of High-Field Permanent Magnetic Circuits for ... · and so the magnetic field homogeneity of𝐵0 magnet will increase. The magnetic field after passive shimming needs

Research ArticleDevelopment of High-Field Permanent Magnetic Circuits forNMRIMRI and Imaging on Mice

Guangxin Wang1 Huantong Xie2 Shulian Hou3 Wei Chen1 and Xiuhong Yang3

1College of Science North China University of Science and Technology Tangshan 063000 China2Shanghai Shining Global Science and Education Equipment Corporation Ltd Shanghai 201806 China3Fundamental Medical College North China University of Science and Technology Tangshan 063000 China

Correspondence should be addressed to Shulian Hou houshulian163com

Received 15 October 2015 Revised 24 January 2016 Accepted 27 January 2016

Academic Editor Guang Jia

Copyright copy 2016 Guangxin Wang et alThis is an open access article distributed under theCreativeCommonsAttribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

The high-field permanent magnetic circuits of 12 T and 15 T with novel magnetic focusing and curved-surface correction aredevelopedThepermanentmagnetic circuit comprises amagnetic yokemainmagnetic steel nonspherical curved-surfacemagneticpoles plugging magnetic steel and side magnetic steel In this work a novel shimming method is proposed for the effectivecorrection of base magnetic field (119861

0) inhomogeneities which is based on passive shimming on the telescope aspheric cutting

grinding and fine processing technology of the nonspherical curved-surface magnetic poles and active shimming adding higher-order gradient coils Meanwhile the magnetic resonance imaging dedicated alloy with high-saturation magnetic field inductionintensity and high electrical resistivity is developed and nonspherical curved-surface magnetic poles which are made of thededicated alloy have very good anti-eddy-current effect In addition the large temperature coefficient problemof permanentmagnetcan be effectively controlled by using a high quality temperature controller and deuterium external locking technique Combiningour patents such as gradient coil RF coil and integration computer software two kinds of small animal Micro-MRI instrumentsare developed by which the high quality MRI images of mice were obtained

1 Introduction

Magnetic resonance imaging (MRI) has become more andmore important for clinical and basicmedicineMRI technol-ogy has many important characteristics such as noninvasivehigh soft tissue contrast and can provide distinct anatom-ical information of lesions It has significant advantage infunctional imaging especially In addition a lot of medicalresearches have to be done on animals such as rats and miceTherefore the research and development of small animalMRI instrument are becoming more and more urgent Itis well known that the stronger magnetic field can providea higher signal-to-noise ratio (SNR) and images with goodquality [1] However the optimum field strength remainsunknown and depends upon many factors such as leakagemagnet image inhomogeneities and eddy currents inducedby fast switching gradients of the magnetic field gradients

At present the mainstream of small animal MRI pieces ofequipment with the magnetic field strength ge7 T [2 3] isgenerally produced on the basis of superconductor technol-ogy Moreover the price of these pieces of equipment is veryhigh and the laboratories in some universities cannot affordthem Actually it is not necessary to perform small animalsimaging by using ultra-high-field MRI instrument For per-manent magnet type MRI instrument when the magneticfield strength is about 15 T it can meet the requirements ofsmall animal structure imaging and preliminary functionalimaging

1198610magnet is the most important part of permanent

magnet type MRI instrument Currently the magnetic fieldstrength of 119861

0magnet is generally less than 1 T In order to

increase magnetic field intensity reduce leakage magnet andachieve shimming some researchers have adopted differentmethods such as adding yokes [4] pole shoes [5] and

Hindawi Publishing CorporationBioMed Research InternationalVolume 2016 Article ID 8659298 11 pageshttpdxdoiorg10115520168659298

2 BioMed Research International

shim rings [6] in 1198610magnet It is reported that 119861

0magnet

can generally be improved by the optimization of magneticpole shapes [7] adding adjustable shim pieces to the C-shaped magnetic poles [8] and changing magnet yokes [9]At present a 06 T MRI instrument with bore 450mm wasdeveloped successfully [10]The research and development of10 TMRI system is also reported [11 12] When the magneticfield strength of cylindrical permanentmagnet is up to 15 T itis very difficult to install the compensation coils and solve theproblem of base magnetic field uniformity Yamada et al [13]investigated the potential of such systems in functional MRimaging (fMRI) of somatosensory cortex activity elicited byforepaw stimulation in medetomidine-sedated rats by usinga 15 T compact imager Haishi et al [14] developed a 20 Tpermanent magnetic circuit for NMRMRI and obtainedMRI image of a human finger in vivo Moreover the imagesof a live animal are not obtained in this reference Tamadaet al [15] also developed a 20 T permanent magnet using abiplanar single-channel shim coil but the mass of this kindof permanent magnet is bigger and the space utilization of1198610magnet is lower Therefore the increase of 119861

0magnetic

field in keeping large utilization efficiency of magnetic spaceis very important for upgrading permanent magnetic circuitfor NMRIMRI The Magnetic Materials Research Centerof Shin-Etsu Chemical Co Ltd has successfully developedthe worldrsquos largest large-scale magnetic circuit for a Halbachtype permanent magnet with a total weight of approximately95 tons [16] Although it is the largest permanent magneticcircuit generating a strong magnetic field it will be usedmainly on the production processes for MR sensor for use inMRAMs (magnetoresistance random access memories) andencoders for position detection Moreover our developed12 T and 15 T permanent magnetic circuits for a half-Halbach type permanent magnet are used mainly for smallanimal Micro-MRI instruments

Shimming is also a key problem in the developmentof permanent magnetic circuit [17ndash20] which consists ofthe passive shimming and the active shimming The passiveshimming technology is invented in the early 1990s [17] Todate the passive shimming of permanent magnet mainlydraws from one of the superconducting magnets [21] Thereis no special shimming method tailored to the charac-teristics of permanent magnet and the shimming mainlydepends on experiences So the shimming of permanentmagnet has not made a substantial progress At presentmany optimization methods [22ndash29] on permanent magnetshimming are proposed such as linear programmingmethod[22] dynamic programming method [23] linear integerprogramming method [24] mixed integer programmingmethod [25] successive approximation method [26] andother passive shimming technologies [27ndash29] In order torealize the shimming of permanent magnet the workingspace should be away from shim pieces which produced anuneven local small magnetic field Therefore the effectiveworking space will become small This is also a primaryfactor restricting the development of permanent magnet Atpresent it is reported that shimming method adding thiniron pieces is often used Owing to the edge effect on thiniron piece shimming the effective shimming space becomes

small and the efficiency reduces In the study we adoptedthe passive shimming method of cutting grinding and fineprocessing technology in realizing the homogeneity fieldTheactive shimming of permanent magnet is generally obtainedby adding several high-order current coils These coils maycorrect the complex inhomogeneity of 119861

0magnet Tamada et

al [30] proposed a new planar single-channel shim coil in themagnet gap The coil design is based on the superposition ofmultiple circular currents and the stream functionmethod Inthis study the active shimming is obtained by adding higher-order current coils in the remaining spaces of RF coil andgradient coil which not only achieves the shimming but alsosaves the magnetic field space

The eddy current problem in permanent magnet is alsovery prominent due to the existence of more ferromagneticmaterials The eddy current will increase when ferromag-netic pieces and magnetic yokes are directly connected topermanent magnetic circuit [31ndash34] At present the activeself-shielding [31ndash33] is a most competent method on solvingthe eddy current The active self-shielding gradient coil maybe obtained by installing a shielding coil outside gradient coilWhen the current phases of self-shielding coil and gradientcoil remain strictly the same the eddy current of supercon-ducting magnet may effectively be eliminated However it isnot suitable for permanent magnet to install large active self-shielding coil because the active self-shielding coil takes up alot of spaceMaking an anti-eddy-current board is currently apopular method of reducing the eddy current for permanentmagnet instrument [34] Moreover the anti-eddy-currentboard will occupy valuable working spaceTherefore it is alsonot an ideal method of reducing eddy current

To solve these problems we made the improvement fromthree aspects according to the characteristic of permanentmagnet (1) The improvement on 119861

0magnet of permanent

magnetic circuit in order to increase the magnetic fieldstrength of 119861

0magnet the space efficiency and unifor-

mity high-field permanent magnet system with magneticfocusing and curved-surface correction is developed (2)Theimprovement on the shimming of 119861

0magnet self-developed

novel shimming scheme is based on passive shimming andactive shimming In the passive shimming the traditionalpassive shimming method adding shim pieces is subvertedand the cutting grinding and fine processing technologyof magnetic poles is adopted for realizing the homogeneityfieldThe active shimming method adding higher-order coilsis proposed which helps reduce the shimming difficult andsaves the working space (3) The improvement of the anti-eddy-current technology on 119861

0magnet a new magnetic

pole is formed by connecting alloy magnetic pole with mainmagnetic steel together The nonspherical curved-surfacemagnetic poles made of the self-developed MRI dedicatedalloy replaced pole pieces and anti-eddy-current board TheMRI dedicated alloy is a kind of high electrical impedancepermanentmagnetmaterial whichmay effectively reduce theeddy current By using the above technologies along withgradient coil [35] RF coil [36] and integration computersoftware [37] 12 T and 15 T small animalMicro-MRI instru-ments (Figure 1) are developed by which the high qualityMRI images of mice were obtained

BioMed Research International 3

(a) (b)

Figure 1 MRI systems with 12 T (a) and 15 T (b) permanent magnetic circuits

1

4

5

3

2

Figure 2 Cross-section schematic of permanent magnetic circuit1 magnetic yoke 2 main magnetic steel 3 nonspherical curved-surface magnetic poles 4 plugging magnetic steel and 5 sidemagnetic steel The arrows represent the direction of magneticsusceptibility of magnetic steel

2 Development ofPermanent MRI Instrument

21 The Design of Permanent Magnetic Circuit The cross-section schematic and stereogram of permanent magnetcircuit are shown in Figures 2 and 3 respectively Hereinthe nonspherical curved-surface magnetic poles made of themagnetic resonance imaging dedicated alloy are two saddle-type rotary curved surfaces have the same shapes and aresymmetrically distributed at the center of the magnetic yokeTwo pieces of main magnetic steel (MMS) are respectivelypositioned behind the two magnetic poles the pluggingmagnetic steel is deviated from the center position and isrespectively positioned behind the two magnetic poles andpositioned on the two side surfaces of the main magneticsteel the sidemagnetic steel is respectively positioned on theside surfaces of the two magnetic poles and arranged on theouter side of the plugging magnetic steel The main magnetic

1234

5

Figure 3 Cross-sectional stereogram of permanent magnetic cir-cuit

steel and the plugging magnetic steel are made of permanentmagnet materials with high coercive force the side magneticsteel is made of permanent magnet materials with highercoercive force the coercive force of the side magnetic steel isover 20 percent higher than that of the main magnetic steel

The specific sizes of permanent magnetic circuit aredetermined by the inverse design of magnetic field distribu-tion and the design generally consists of three stages Firstthe magnetic field distribution of permanent 119861

0magnet is

determined within the magnetic field theory Second themagnetic circuit and the sizes of permanent magnet andferromagnetic parts are determined according to magneticproperties of special alloy and NdFeB material magnetworking gap and magnetic flux density (see Figure 4) Inorder to correct the error causingmore simplified processingthe structure parameters of permanent 119861

0magnet are further

optimized by means of MATLAB simulation At last the


L

L

L1

L1

L1

L1

L1

L1

L3

L3

L3

L3

L3

L3

L2

L2

Figure 4 The boundary schematic of selected 14 permanentmagnet in computation 119871

1is the boundary parallel to magnetic

induction lines 1198712denotes the symmetrical boundary perpendicu-

lar to magnetic induction lines 1198713denotes the border between two

materials such as iron and NdFeB air and NdFeB magnetic polesalloy andNdFeB andmagnetic poles alloy and air 119871 is the boundaryof magnetizing current

exact sizes of permanent magnetic circuit are determined onthe basis of the experiments of magnetic field design andpermanent magnetic circuit manufacture Considering highsymmetry of closed permanent magnet circuit the sizes oftwo-dimensional permanent magnet circuit are determinedfirstly by which the ones of three-dimensional permanentmagnet circuit are deduced The electromagnetic field equa-tion of the simplified main magnet model is given as in [38]We only drew boundary schematic of symmetric permanentmagnetic circuits in Figures 9 and 10Ω(119871

1cup 1198712cup 1198713cup 119871) in

(1) denotes the entire solution domain

120597

120597119909(V

120597119860

120597119909) +

120597

120597119910(V

120597119860

120597119910) = 0

Ω (1198711cup 1198712cup 1198713cup 119871)

(1)

119860 = 0 1198711 (2)

120597119860

120597119903= 0 119871

2 (3)

(V120597119860

120597119899)

119871+

3

= (V120597119860

120597119899)

119871minus

3

1198713 (4)

(V120597119860

120597119899)

119871+

minus (V120597119860

120597119899)

119871minus

= 119895 119871 (5)

where 119860 is the undetermined magnetic vector potential Thereluctivity V is equal to the reciprocal of the permeability120583 120583 denotes the relative permeability of permanent mag-netic material along the easy magnetization direction Thepermeability 120583 is regarded as the permeability of vacuum

1205830in computation 119895 is the density of bound current It

is very difficult to obtain analytical solutions of the aboveequations The sizes of magnetic poles and side magnets areobtained using the finite elementmethod and theCUDAGPUsoftware The objective function of utilization coefficient onpermanent magnet is given as

119872 =

int120592119888

10038161003816100381610038161198611198881003816100381610038161003816

2119889119881

int 120592119898

1003816100381610038161003816119869021003816100381610038161003816 119889119881

(6)

where 120592119888denotes the space area between two poles of 119861

0

magnet 119861119888is the magnetic density 120592

119898denotes the volume of

space occupied permanent magnet and 1198690is the modulus of

residual magnetization vector in permanent magnetic mate-rial In practical design we selected the utilization coefficientas large as possible (119872 = 07) The permanent magnet ismade of N50-type high-grade steel (residual magnetic flux119861119903= 14T) [39] Based on numerical calculation and man-

ufacturing experience the angles between main magneticsteel nonspherical curved-surface magnetic poles pluggingmagnetic steel and side magnetic steel are determined Thesizes of each part of 12 T and 15 T permanent circuits are alsodetermined Their specific sizes may be seen in Figures 5 9and 10 and Tables 1ndash3

The shape and structure schematic of nonsphericalcurved-surface magnetic poles is demonstrated in Figure 5The magnetic poles (3 in Figure 2) with saddle-type rotarycurved surfaces are symmetrically distributed at the centerof the magnetic yoke The closest distance 119889 between twomagnetic poles is the magnetic poles gap 119909 is the distancefrom a location point on the curved surface to the center ofthe magnet and 119910 is the distance between the correspondinglocation points of two rotating curved surfaces In designingthe curved-surface magnetic poles the magnetic poles gap(119889)must have higher precision at any angleThe relative errorof 119889 is less than 00003mm (03 120583m)The two curved surfacesmust have higher symmetry and the relative error is less than00003mm (03 120583m) And the two curved surfaces must behigh symmetrical on the center dotted line whose relativeerror is less than 00005mm (05 120583m) In Table 1 the sizeof magnetic poles with saddle-type rotary curved surfaces isdemonstrated by using the quadratic interpolation The dataerror in Table 1 is generally less than 01 By the adoption ofa magnetic focusing technology high-field 12ndash21 T intensitycan be achieved The uniform field of a magnet is correctedby the curved surfaces so that extremely high space efficiencyand more than ten times the uniformity are achieved

22 1198610 Magnet Shimming The highly homogeneous mag-netic field is required in permanentmagnet typeMRI systemThe basic magnetic field cannot meet the high uniformityrequirement of MRI systems so it is rather important toachieve the shimming of 119861

0magnet At present the shim-

ming methods mainly include the active shimming and thepassive shimming The passive shimming adding ferromag-netic pieces is a popular method of achieving permanentmagnet shimming Moreover the uneven local small mag-netic field generating shim pieces seriously interferes with thebasic magnetic field In order to weaken the interference of


Table 1 The size of magnetic poles with saddle-type rotary curved surfaces 119889 is the magnetic poles gap 119909 is the distance from a locationpoint on the curved surface to the center of the magnet and 119910 is the distance between the corresponding location points of two rotatingcurved surfaces

119909119889 000 04 08 12 16 20 24 28 32 324 328 332 336 34 352119910119889 108 1076 1063 1042 1014 10 10 1023 118 121 124 127 130 134 146

Table 2 The size of permanent magnetic circuit with the magnetic field strength 15 T 119909 is the distance from a location point on the curvedsurface to the center of the magnet 119910 is the distance between the corresponding location points of two rotating curved surfaces The units of119909 and 119910 are mm

119909 0 12 24 36 48 60 72 84 96 972 984 996 1008 102119910 432 4304 4254 4169 4056 400 400 4093 4738 4841 4953 5074 5205 5346


119909 0 28 56 84 112 140 168 196 224 2268 2296 2324 2352 238119910 756 7532 7444 7295 7098 700 700 7163 8291 8472 8667 8880 9108 9355

x

yd

3

3

Figure 5 The shape and structure schematic of nonsphericalcurved-surface magnetic poles is demonstratedThemagnetic poles(see label 3 in Figure 2) with saddle-type rotary curved surfaces aresymmetrically distributed at the center of the magnetic yoke

the local small magnetic field the working space should beaway from these shim piecesTherefore the effective workingspace and the space utilization efficiencywill greatly decreaseIn keeping the invariable working space the magnetic gapshould become large which will lead to the decrease of themagnetic field strength It is well known that the utilizationspace of permanent magnet is proportional to the cube of 119861

0

magnet sizesThemagnetic steelmass will greatly increase forkeeping the same base magnetic field which also increasesthe difficulty of manufacturing permanent magnet systemIn addition the mutual interference between ferromagneticpieces and magnetic poles will further increase the difficultyof achieving the shimming of permanent magnet The abovefactors are also the main reasons hindering the breakthroughof high-field permanent Micro-MRI instrument so far Inthis study the cutting grinding and polishing techniquesof aspheric optical components were transplanted to theprocessing of magnetic poles surface and the shimmingpractice by which the shimming difficulty of permanentmagnet is reduced

The good shimming is dependent on a high-precisionmeasurement technology In order to achieve high-accuracyshimming of permanent magnet it is necessary to have ahigh-precision measurement technology In designing per-manent magnet system the magnetic field data of 2048collected points are measured point by point by usingfrequency-spectrum method and then the processing planis determined according to measuring magnetic field dataof these points In the practical work measurement andhigh-precision processing may be carried out synchronouslywithout the interferences of shim pieces and the cuttinggrinding and polishing technology does not need to occupymuch space Therefore the computation difficulty will dra-matically decrease Based on accumulated fine processingexperience the magnet poles with high-fineness surface areobtained by using the processing technology The surfaceevenness of magnetic poles can be controlled in 03sim01 120583mand so the magnetic field homogeneity of 119861

0magnet will

increase The magnetic field after passive shimming needsfurther optimization by adding several groups of currentcoils on two-opposite-poles surface of magnet The basicmagnetic field is a constant field and the scalar magneticpotential 119881 satisfies Laplace equation that is Δ119881 = 0The expansion equation of magnetic field 119861

119911in rectangular

coordinate system is given as [38]

119861119911(119909 119910 119911) = 119860

0

1+ 21198600

2+ 31198601

2119909 + 3119861

1

2119910

+3

21198600

3(21199112minus 1199092minus 1199102) + 12119860

1

3119911119909

+ 121198611

3119911119910 + 15119860

2

3(1199092minus 1199102) + 30119861

2

3119909119910

+ 41198600

4119911 [1199112minus2

31199092+ 1199102]

+15

21198601

4119909 [41199112minus 1199092minus 1199102]

+15

21198611

4119910 [41199112minus 1199092minus 1199102] + sdot sdot sdot

(7)


Generally only 119861119911is computed in the shimming The first

term in (7) is a uniformity field value preserved in shimmingThe nonuniformity parts of the base magnetic field afterpassive shimminghave usually a certain gradientThe secondthird and fourth terms denote linear gradients along 119909 119910and 119911 coordinate axes respectively The fifth sixth seventhand eighth terms are second-order nonuniformity parts Theninth tenth eleventh and twelfth terms are third-ordernonuniformity parts The developed high-order gradientcoils still retain the early MRI technique characteristic ofcompensating the gradient of base magnetic field When themagnetic field induced by these high-order gradient coilsexactly offsets the gradient of main magnet itself in a specificdirection these high-order gradient coils are regarded as theshimming coils In addition when the resonance frequenciesof these points in the high uniform magnetic field tend tobe the same the vibration amplitude of every point is thebiggest by which 27 groups of higher-order shimming coilsincluding 119909 119910 119911 119909119910 119910119911 119909119911 1199092 minus 119910

2 1198772 1198773 1198771199112 (1199092 minus1199102)119911 1199103 119909119910119911 and other third-order parts are preliminary

designed The shimming method adding high-order currentcoils is named as the active shimming In the study a novelshimming scheme is based on passive shimming and activeshimming In addition we took a year to track the imagingof small animal permanent magnet type MRI instrumentand fulfill correction of magnetic poles continuously A goodshimming of permanent magnet is obtained when the high-order shimming coils reduce to 9 groups

23 Eddy Current of Permanent Magnet In the conven-tional permanent magnetic circuit two possible magneticflux routes generating gradient magnetic field are shownin Figure 6 Although the pole shoes are made from highpermeability and impedance material it is also very difficultfor permanent magnetic poles to prevent the closed gradientmagnetic flux passing through magnetic yokes At presentadding an anti-eddy-current board between gradient coilsand magnetic poles is the most mainstream and effectivemethod of eliminating the eddy current in permanentmagnetic circuit However the anti-eddy-current board willoccupy large working space It is also not an ideal method ofreducing eddy current In order to eliminate the eddy currentwe replaced pole pieces and anti-eddy-current board withan alloy magnetic pole These magnetic induction lines ofmagnetic circuits 1 and 2 in Figure 7 interrupt in nonsphericalcurved-surface alloy magnetic poles which may effectivelyprevent generation of eddy current Considering the symme-try of the magnetic circuit the upper part of the magneticcircuit schematic diagram was given in Figures 6 and 7

The medical magnetic resonance imaging system can beregarded as the magnetic field stacking a rapidly changedgradient magnetic field based on the uniform magnetic fieldThe system consists of119883 119884 119885 three groups of gradients Thespatial information is determined by changing the sizes of119883 119884 119885 gradients So the accuracy and switching speed ofthe gradient magnetic field determine the imaging qualityThe main factor affecting the accuracy and switching speedof the gradient magnetic field is the eddy current inducing

Pole Magnetic pole

Yoke1 1

2 2

shoe

Figure 6 Magnetic circuits with traditional gradient coils

MMS

Alloy pole

Yoke

1 1

22

Figure 7 High-impedance special alloy magnetic poles withoutpole shoes The magnetic circuit may block the gradient pulse andprevent the eddy currents

the nearest magnetic poles extreme The eddy current is aresult of the interaction between the magnetic field and thecurrent inducing the conductor in the variablemagnetic fieldAdding the active self-shielding coils is an effective methodof reducing the eddy currents in superconducting magneticcircuit to date Moreover it is not very ideal for permanentmagnetic circuit to add the active self-shielding coils Theactive self-shield coils will take up too much space and needto pay a high price [31] At present making magnetic poleswith the amorphousmagnetic material sheet lamination andsilicon steel splicing are the popular solution methods ofeliminating the eddy current The above schemes can onlybe used below the 10 T magnetic resonance system owing tothe low saturation magnetic intensity In order to eliminatethe eddy currents themagnetic resonance imaging dedicatedalloy with high-saturation magnetic field induction intensityand high electrical resistivity is developed and nonsphericalcurved-surface magnetic poles made of the dedicated alloyreplaced traditionalmagnetic poles and pole pieces which areeasy to induce the eddy currents A preparation method ofthe magnetic resonance imaging dedicated alloy is given asfollowsThe dedicated alloy is Fe-Co-Al fe-co-based alloy themass percent of the Co content is 5ndash35 the mass percentof Al content is 2ndash6 the mass percent of Si content is05ndash1 the mass percent of Mo content is 2-3 requiredimpurities include C P S and Ni which are smaller than001 and the rest is FeThe electrical resistivity of the alloy islarger than 50 lowast 10minus8Ωm the saturation flux density is largerthan 14ndash23 T the initial permeability is larger than 2000 themagnetic permeability at 10ndash15 T is larger than 10000 andpreparation is performed by a vacuum metallurgy method


(a)

Decoupling capacitor

Coupling capacitorCoaxial cable

Four segments of the coil

Resonant capacitorCoupling capacitor

(b)

1

23

4

(c)

Figure 8 (a) Gradient coil (b) RF coil (c) The optimal allocation of all kinds of coil 1 shimming coil 2 gradient coil 3 RF coil 4 DSV

According to the magnetic resonance imaging dedicatedalloy and the preparation method high-saturation magneticfield induction intensity and high electrical resistivity can beachieved the alloy is a magnetic pole material that is used for10 Tndash21 T permanent magnet magnetic resonance imagerand the anti-eddy effect is good

24 Gradient Coil RF Coil and Temperature Control Wedeveloped a self-shielding gradient coil with straw-hatcurved-surface shape The self-shielding gradient coil withhigh linearity high efficiency and small size is not onlydifferent from cylindrical superconducting gradient coil

but also different from the planar gradient coils The eddycurrents are effectively minimized by installing three groupsof high-order gradient coils in small animal permanent MRIsystem at 05 T [40] When the main magnetic field strengthis up to 15 T [41] the stronger eddy current which worsensthe linearity of the gradient magnetic field cannot effectivelybe eliminated by only adding self-shielding gradient coilsIn addition the magnetic resonance imaging dedicated alloyreplaced traditionalmagnetic poles and pole pieces which areeasy to induce the eddy currents The self-shielding gradientcoil picture is shown in Figure 8(a) Self-developed RF coilnot only absorbs the advantage in which the saddle-shaped


coil can provide the uniform RF field in the vertical directionof 1198610magnetic field but also absorbs the advantage of the

solenoid-shaped coil with high sensitivity and uniformityfield The single-channel integral coil formed orthogonaltransmitter coil and receiver coil avoids the complex array coilcircuit The single-channel integral coil has a faster imagingspeed owing to selecting higher magnetic field strength andsuperior gradient coils The RF coil picture is also shown inFigure 8(b) For improving the space utilization of magneticpoles gap and reducing the volume of 119861

0magnet all kinds

of coils were arranged scientifically in Figure 8(c) Takingthe curved type gradient coils for example three groups ofcoils were placed in the remaining gaps between the uniformfield coils This design not only obtained the self-shieldinggradient coil but also did not take up too much space

The spatial distribution of the magnetic field may alsovary with temperature The stability of 119861

0magnetic field

determines the image quality Therefore the frequency orcurrent compensation is an effective method of obtainingthe stable magnetic field Haishi et al [42] developed a10 T MR microscope using a NdFeB permanent magnetand they developed an internal NMR locking techniqueor the imaging sequences because the magnetic field ofthe permanent magnet had a large temperature coefficient(minus1200 ppmdeg) In the study the temperature drift can beeffectively controlled by using a high quality temperaturecontroller and ldquodeuterium external lockingrdquo technique Theldquodeuterium external lockingrdquo technique is a method of com-pensating the magnetic field drift by the additional magneticfield inducing the current of the lock field coil and the currentof the lock field coil is adjusted by detecting the deuteriumsignalThe temperature drift is controlled around 1 ppm in 10minutes (2sim3 ppmh) in imaging experiments

3 Discussion

As the experiment two kinds of permanent magnetic circuitsare developed One magnetic circuit is with a main mag-netic field strength 15 T a magnetic gap 43mm a cylindershimming space with 35mm (diameter) times 60mm (height)and a space utilization efficiency of 81 (the space utilizationefficiency is the ratio of the volume of the working space tothe volume between magnetic poles) the static homogeneityis 1 ppmhomogeneity over 20mmDSVAccording to the datain Table 2 the specific dimensions of the 15 T permanentmagnetic circuit are given in Figure 9 The other one iswith a main magnetic field strength 12 T a magnetic gap70mm a cylinder shimming space with 60mm (diameter) times100mm (height) and a space utilization efficiency of 85 thestatic homogeneity is 1 ppm homogeneity over 20mm DSVAccording to the data in Table 3 the specific dimensions ofthe 12 T permanent magnetic circuit are given in Figure 1012 T and 15 T permanent magnetic circuits gradient coilsRF coils and integrated software systems with independentintellectual property rights are assembled into 12 T and15 T MRI instruments The high quality images of mice areobtained by using self-developed two kinds of Micro-MRIinstruments The 12 T and 15 T Micro-MRI instruments aredemonstrated in Figure 1

100

250

43150

800

100

600

30∘

30∘

45∘

75∘

Unit (mm)

Figure 9 The size of each part of 15 T permanent magnetic circuit

150

70200

400

1000

100

800

30∘

30∘

45∘

75∘

Unit (mm)

Figure 10The size of each part of 12 T permanent magnetic circuit

In order to implement mice imaging 12 healthy malemice with the age of 4 weeks were obtained from ShanghaiExperimental Animal Center Their masses are between 17and 20 grams With the approval of the Ethical Committeeof North China University of Science and Technology theexperiment of live mice and the injection of carcinogenicurethane to livemicewere performedThedosage of urethaneanesthesia injecting into the abdomen of the healthy malemice is 1 gkg It took 4 minutes to 10 minutes for one 3D-T1 data set of one mouse under the anesthesia The imagingscans of mice were performed after 5 minutes The coronalimages of a live mouse are obtained by using the 12 T smallanimalMRI instrumentThe cross-sectional images of a deadmouse are obtained by using the 15 T small animal MRIinstrument


51 53 55 57 59

Figure 11 Coronal images of the 51st 53rd 55th 57th and 59th layer slices on live mice are demonstrated from left to right Parameters ofMRI at 12 T TRTE = 100ms15ms cylindrical shimming volume 60mm times 100mm FOV = 60mm times 100mm slice thickness 03mm datamatrix 512 times 36 times 256 and imaging matrix 1024 times 1024

60 90 93 96 104

Figure 12 Cross-sectional images of the 60th 90th 93rd 96th and 104th layer slices on a dead mouse are demonstrated from left to rightParameters of MRI at 15 T TRTE = 200ms15ms cylindrical shimming volume 35mm times 60mm FOV = 35mm times 60mm slice thickness04mm data matrix 32 times 512 times 256 and imaging matrix 512 times 512

The SE sequence and T1-weighted images of mice areobtained by using self-developed 12 T and 15 T small animalMRI instruments 119909 and 119910 direction phase codes 119911 directionfrequency code and sinc form RF pulse are selected incoronal and cross-sectional scans of several mice The 128layers images of a live mouse are obtained in every imagingexperiment The imaging parameters of 12 T and 15 T MRIinstruments are set as follows respectively (1) Coronalimaging parameters on the 12 T MRI instrument TRTE= 100ms15ms cylindrical shimming volume is 60mm times

100mm the field of view (FOV) = 60mm times 100mm slicethickness is 03mm data matrix is 512 times 36 times 256 andimaging matrix is 1024 times 1024 The 51st 53rd 55th 57th and59th layer coronal images of a live mouse were demonstratedin Figure 11 These randomly selected coronal images of micefrom head to tail can be clearly observed (2) Cross-sectionalimaging parameters on the 15 T MRI instrument TRTE= 200ms15ms cylindrical shimming volume is 35mm times

60mm FOV = 35mm times 60mm slice thickness is 04mmdata matrix is 32 times 512 times 256 and imaging matrix is 512 times 512The randomly selected 60th 90th 93rd 96th and 104th layercross-sectional images of a dead mouse were demonstratedin Figure 12 The internal organs of the dead mouse can beclearly observed in Figure 12 The results show that higherfield intensity of permanent magnet may improve greatly theimaging quality of small animals

4 Conclusions

In the study we developed a magnetic resonance imagingdedicated alloywith high-saturationmagnetic field inductionintensity and high electrical resistivity and high-field perma-nent magnetic circuits of 12 T and 15 T with novel magneticfocusing and curved-surface correction The nonsphericalcurved-surface magnetic poles made of the dedicated alloys

are two saddle-type rotary curved surfaces have the sameshapes and are symmetrically distributed at the center ofthe magnetic yoke A new magnetic pole is formed byconnecting the nonspherical curved-surface alloy magneticpole with main magnetic steel together which replacedtraditional magnetic pole and poles pieces easily inducedthe eddy currents The plugging magnetic steel is deviatedfrom the center position and is respectively positionedbehind the two magnetic poles and positioned on the twoside surfaces of the main magnetic steel the side magneticsteel is respectively positioned on the side surfaces of thetwo magnetic poles and arranged on the outer side of theplugging magnetic steel the main magnetic steel and theplugging magnetic steel are made of permanent magnetmaterials with high coercive force the side magnetic steel ismade of permanent magnet materials with higher coerciveforce the coercive force of the side magnetic steel is over20 percent higher than that of the main magnetic steelBy the adoption of a magnetic focusing technology high-field 12ndash21 T intensity can be achieved and the uniformfield of a magnet is corrected by the curved surfaces Interms of shimming the conventional passive shimming fieldmethod adding shim pieces is abandoned and a telescopeaspheric cutting grinding and fine processing technologyof the nonspherical curved-surface magnetic poles is usedMeanwhile the active shimming technology adding higher-order gradient coils is adopted which effectively correctsthe uniform field of 119861

0magnet Based on accumulated fine

processing experience the magnet poles with high-finenesssurface are obtained by using the telescope aspheric cuttinggrinding and fine processing technology The surface even-ness of magnetic poles can be controlled in 03sim01 120583m Afteradding third-order shimming coils the static homogeneityis 1 ppm homogeneity over 20mm DSV In addition thelarge temperature coefficient problem of permanent magnet


can be effectively controlled by using a good temperaturecontroller and ldquodeuterium external lockingrdquo technique thenewmagnetic poles and gradient coils are optimally designedin terms of shape and structure The shimming coils occupythe space between gradient coil and concave magnetic polesTherefore all the parts are optimally arranged and occupy thesmallest magnetic field space Combining our patents suchas gradient coil RF coil and integration computer software12 T and 15 T small animal Micro-MRI instruments aredeveloped by which the high quality coronal and cross-sectional images of mice are obtained Therefore it is verynecessary to strengthen the study of permanent magnetsystem for updating small animal MRI instruments

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

This work was supported byThe Scientific and TechnologicalDepartment Foundation of Hebei Province (08202133D and13202001D)

References

[1] C-N Chen V J Sank S M Cohen and D I Hoult ldquoThefield dependence of NMR imaging I Laboratory assessmentof signal-to-noise ratio and power depositionrdquo Magnetic Res-onance in Medicine vol 3 no 5 pp 722ndash729 1986

[2] Y Lvovsky E W Stautner and T Zhang ldquoNovel technologiesand configurations of superconducting magnets for MRIrdquoSuperconductor Science and Technology vol 26 no 9 ArticleID 093001 2013

[3] C K Kang M K Woo S M Hong Y B Kim and Z HCho ldquoIntracranial microvascular imaging at 7 T MRI withtransceiver RF coilsrdquo Magnetic Resonance Imaging vol 32 no1 pp 1133ndash1138 2014

[4] T Tominaka M Okamura and T Katayama ldquoAnalytical fieldcalculation of helical magnets with an axially symmetric ironyokerdquo Nuclear Instruments and Methods in Physics ResearchSection A vol 484 no 1ndash3 pp 36ndash44 2002

[5] Z Jin X Tang B Meng D L Zu and W M Wang ldquoA SQPoptimizationmethod for shimming a permanentMRImagnetrdquoProgress in Natural Science vol 19 no 10 pp 1439ndash1443 2009

[6] Y Cheng W He L Xia and F Liu ldquoDesign of shimmingrings for small permanent MRI magnet using sensitivity-analysis-based particle swarm optimization algorithmrdquo Journalof Medical and Biological Engineering vol 35 no 4 pp 448ndash454 2015

[7] D-H Kim B-S Kim J-H Lee W-S Nah and I-H Park ldquo3-D optimal shape design of ferromagnetic pole in MRI magnetof open permanent-magnet typerdquo IEEE Transactions on AppliedSuperconductivity vol 12 no 1 pp 1467ndash1470 2002

[8] U Rapport ldquoField adjusting mechanisms and methods forpermanent magnet arrangement with backplaterdquo US PatentUS20020097122 A1 2002-07-25

[9] T Shirai T Haishi S Utsuzawa Y Matsuda and K KoseldquoDevelopment of a compact mouse MRI using a yokeless

permanent magnetrdquo Magnetic Resonance in Medical Sciencesvol 4 no 3 pp 137ndash143 2005

[10] Q L Wang W H Yang Z P Ni et al ldquoAdvances in NMRItechnologyrdquo High-Technology amp Industrialization vol 211 no12 pp 46ndash53 2013

[11] D L Longo F Arena L Consolino et al ldquoGd-AAZTA-MADEC an improved blood pool agent for DCE-MRI studieson mice on 1 T scannersrdquo Biomaterials vol 75 pp 47ndash57 2016

[12] S Kannala T Toivo T Alanko and K Jokela ldquoOccupationalexposure measurements of static and pulsed gradient magneticfields in the vicinity of MRI scannersrdquo Physics in Medicine andBiology vol 54 no 7 pp 2243ndash2257 2009

[13] M Yamada K Takano Y Kawai and R Kato ldquoHemodynamic-based mapping of neural activity in medetomidine-sedated ratsusing a 15T compact magnetic resonance imaging system apreliminary studyrdquoMagnetic Resonance inMedical Sciences vol14 no 3 pp 243ndash250 2015

[14] T Haishi M Aoki and E Sugiyama ldquoDevelopment of a 20Tesla permanent magnetic circuit for NMRMRIrdquo in Proceed-ings of the International Society for Magnetic Resonance inMedicine (ISMRM rsquo13) vol 13 p 869 May 2005

[15] D Tamada K Kose and T Haishi ldquoMagnetic field shimmingof a 20 T permanent magnet using a bi-planar single-channelshim coilrdquo in Proceedings of the International Society for Mag-netic Resonance in Medicine (ISMRM rsquo12) vol 20 p 2579 2012

[16] The Magnetic Materials Research Center of Shin-Etsu Chem-ical ldquoDevelopment of worldrsquos largest Halbach-type magneticcircuitrdquo httpwwwshinetsucojpseremerdmchtml

[17] C Juchem B Muller-Bierl F Schick N K Logothetis and JPfeuffer ldquoCombined passive and active shimming for in vivoMR spectroscopy at high magnetic fieldsrdquo Journal of MagneticResonance vol 183 no 2 pp 278ndash289 2006

[18] H Sanchez F Liu A Trakic and S Crozier ldquoA magnetizationmapping approach for passive shim design in MRIrdquo in Proceed-ings of the 28th Annual International Conference Engineering inMedicine and Biology Society (EMBS rsquo06) vol 1 pp 1893ndash1896New York NY USA September 2006

[19] B Dorri ldquoMethod for passively shimming amagnetrdquo US PatentUS5677854A 1995

[20] K M Koch P B Brown D L Rothman and R A deGraaf ldquoSample-specific diamagnetic and paramagnetic passiveshimmingrdquo Journal of Magnetic Resonance vol 182 no 1 pp66ndash74 2006

[21] A Belov V Bushuev M Emelianov et al ldquoPassive shimmingof the superconducting magnet for MRIrdquo IEEE Transactions onApplied Superconductivity vol 5 no 2 pp 679ndash681 1995

[22] B Dorri M E Vermilyea andW E Toffolo ldquoPassive shimmingof MR magnets algorithm hardware and resultsrdquo IEEE Trans-actions on Applied Superconductivity vol 3 no 1 pp 254ndash2571993

[23] D X Xie E L Wang and Y L Zhang ldquoPassive shimming ofpermanent magnet for MRI based on dynamic programmingrdquoJournal of Shenyang University of Technology vol 29 no 4 pp396ndash399 2007

[24] Z Ren D Xie and H Li ldquoShimming method for open MRIpermanent main magnetrdquo Transactions of China Electrotechni-cal Society vol 25 no 3 pp 1ndash5 2010

[25] X F You Z Wang X B Zhang W Yang and T SongldquoPassive shimming based on mixed integer programming forMRI magnetrdquo Science China Technological Sciences vol 56 no5 pp 1208ndash1212 2013


[26] G Aubert ldquoPermanent magnet device for generating an offsetuniform magnetic fieldrdquo US Patent US20130193973 2013

[27] Z Jin X Tang B Meng D Zu and W Wang ldquoA SQPoptimizationmethod for shimming a permanentMRImagnetrdquoProgress in Natural Science vol 19 no 10 pp 1439ndash1443 2009

[28] J Lee and J Yoo ldquoTopology optimization of the permanentmagnet typeMRI considering the magnetic field homogeneityrdquoJournal ofMagnetism andMagneticMaterials vol 322 no 9ndash12pp 1651ndash1654 2010

[29] H S Lopez F Liu E Weber and S Crazier ldquoPassive shimdesign and a shimming approach for bi-planar permanentmagnetic resonance imaging magnetsrdquo IEEE Transactions onMagnetics vol 44 no 3 pp 394ndash402 2008

[30] D Tamada K Kose and T Haishi ldquoA new planar single-channel shim coil using multiple circular currents for magneticresonance imagingrdquo Applied Physics Express vol 5 no 5 pp6701ndash6706 2012

[31] D L Zu L M Hong X M Cao et al ldquoPermanent magnetMRI pulsed eddy current magnetic field gradient backgroundanalysisrdquo Scientia Sinica Technologica vol 40 no 10 pp 1221ndash1226 2010

[32] J O Nieminen P T Vesanen K C J Zevenhoven et alldquoAvoiding eddy-current problems in ultra-low-field MRI withself-shielded polarizing coilsrdquo Journal of Magnetic Resonancevol 212 no 1 pp 154ndash160 2011

[33] C P Bidinosti I S Kravchuk and M E Hayden ldquoActiveshielding of cylindrical saddle-shaped coils application to wire-wound RF coils for very low field NMR and MRIrdquo Journal ofMagnetic Resonance vol 177 no 1 pp 31ndash43 2005

[34] G Sinha and S S Prabhu ldquoAnalytical model for estimationof eddy current and power loss in conducting plate and itsapplicationrdquo Physical Review Special TopicsmdashAccelerators andBeams vol 14 no 6 pp 62401ndash62416 2011

[35] H T Xie ldquoSelf-shielding gradient coils used in magneticresonance imagingrdquo CN Patent CN 202189140 U 2012

[36] H T Xie ldquoRF coil apparatus for magnetic resonance imagingrdquoCN Patent CN 202189138 U 2012

[37] H T Xie Huantong 3 Dimensional NMR Integration PeoplersquosRepublic of China National Copyright Administration of Inte-grated Software Computer 2012

[38] P H XiaThe Permanent Magnet Mechanism Beijing IndustrialUniversity Press 2000

[39] Ningbo Jinyu Magnet ldquoN33ndashN52 Strong Rare Earth SinteredNeodymium Magnets Ring With Epoxy Coatedrdquo httpwwwsinteredneodymiummagnetscomsale-5908666-n33-n52-strong-rare-earth-sintered-neodymium-magnets-ring-with-epoxy-coatedhtml

[40] S L Hou H T Xie W Hou S Y Li and W Chen ldquoGradientcoil of permanentmagnetmini-magnetic resonance imager andimage qualityrdquo Chinese Journal of Magnetic Resonance vol 29no 4 pp 508ndash520 2012

[41] G X Wang H T Xie S L Hou W Chen Q Zhao and S YLi ldquoDevelopment of the 12T sim 15T permanent magnetic res-onance imaging device and its application for mouse imagingrdquoBioMed Research International vol 2015 Article ID 858694 8pages 2015

[42] T Haishi T Uematsu Y Matsuda and K Kose ldquoDevelopmentof a 10 TMRmicroscope using a Nd-Fe-B permanent magnetrdquoMagnetic Resonance Imaging vol 19 no 6 pp 875ndash880 2001


shim rings [6] in 1198610magnet It is reported that 119861

0magnet

can generally be improved by the optimization of magneticpole shapes [7] adding adjustable shim pieces to the C-shaped magnetic poles [8] and changing magnet yokes [9]At present a 06 T MRI instrument with bore 450mm wasdeveloped successfully [10]The research and development of10 TMRI system is also reported [11 12] When the magneticfield strength of cylindrical permanentmagnet is up to 15 T itis very difficult to install the compensation coils and solve theproblem of base magnetic field uniformity Yamada et al [13]investigated the potential of such systems in functional MRimaging (fMRI) of somatosensory cortex activity elicited byforepaw stimulation in medetomidine-sedated rats by usinga 15 T compact imager Haishi et al [14] developed a 20 Tpermanent magnetic circuit for NMRMRI and obtainedMRI image of a human finger in vivo Moreover the imagesof a live animal are not obtained in this reference Tamadaet al [15] also developed a 20 T permanent magnet using abiplanar single-channel shim coil but the mass of this kindof permanent magnet is bigger and the space utilization of1198610magnet is lower Therefore the increase of 119861

0magnetic

field in keeping large utilization efficiency of magnetic spaceis very important for upgrading permanent magnetic circuitfor NMRIMRI The Magnetic Materials Research Centerof Shin-Etsu Chemical Co Ltd has successfully developedthe worldrsquos largest large-scale magnetic circuit for a Halbachtype permanent magnet with a total weight of approximately95 tons [16] Although it is the largest permanent magneticcircuit generating a strong magnetic field it will be usedmainly on the production processes for MR sensor for use inMRAMs (magnetoresistance random access memories) andencoders for position detection Moreover our developed12 T and 15 T permanent magnetic circuits for a half-Halbach type permanent magnet are used mainly for smallanimal Micro-MRI instruments

Shimming is also a key problem in the developmentof permanent magnetic circuit [17ndash20] which consists ofthe passive shimming and the active shimming The passiveshimming technology is invented in the early 1990s [17] Todate the passive shimming of permanent magnet mainlydraws from one of the superconducting magnets [21] Thereis no special shimming method tailored to the charac-teristics of permanent magnet and the shimming mainlydepends on experiences So the shimming of permanentmagnet has not made a substantial progress At presentmany optimization methods [22ndash29] on permanent magnetshimming are proposed such as linear programmingmethod[22] dynamic programming method [23] linear integerprogramming method [24] mixed integer programmingmethod [25] successive approximation method [26] andother passive shimming technologies [27ndash29] In order torealize the shimming of permanent magnet the workingspace should be away from shim pieces which produced anuneven local small magnetic field Therefore the effectiveworking space will become small This is also a primaryfactor restricting the development of permanent magnet Atpresent it is reported that shimming method adding thiniron pieces is often used Owing to the edge effect on thiniron piece shimming the effective shimming space becomes

small and the efficiency reduces In the study we adoptedthe passive shimming method of cutting grinding and fineprocessing technology in realizing the homogeneity fieldTheactive shimming of permanent magnet is generally obtainedby adding several high-order current coils These coils maycorrect the complex inhomogeneity of 119861

0magnet Tamada et

al [30] proposed a new planar single-channel shim coil in themagnet gap The coil design is based on the superposition ofmultiple circular currents and the stream functionmethod Inthis study the active shimming is obtained by adding higher-order current coils in the remaining spaces of RF coil andgradient coil which not only achieves the shimming but alsosaves the magnetic field space

The eddy current problem in permanent magnet is alsovery prominent due to the existence of more ferromagneticmaterials The eddy current will increase when ferromag-netic pieces and magnetic yokes are directly connected topermanent magnetic circuit [31ndash34] At present the activeself-shielding [31ndash33] is a most competent method on solvingthe eddy current The active self-shielding gradient coil maybe obtained by installing a shielding coil outside gradient coilWhen the current phases of self-shielding coil and gradientcoil remain strictly the same the eddy current of supercon-ducting magnet may effectively be eliminated However it isnot suitable for permanent magnet to install large active self-shielding coil because the active self-shielding coil takes up alot of spaceMaking an anti-eddy-current board is currently apopular method of reducing the eddy current for permanentmagnet instrument [34] Moreover the anti-eddy-currentboard will occupy valuable working spaceTherefore it is alsonot an ideal method of reducing eddy current

To solve these problems we made the improvement fromthree aspects according to the characteristic of permanentmagnet (1) The improvement on 119861

0magnet of permanent

magnetic circuit in order to increase the magnetic fieldstrength of 119861

0magnet the space efficiency and unifor-

mity high-field permanent magnet system with magneticfocusing and curved-surface correction is developed (2)Theimprovement on the shimming of 119861

0magnet self-developed

novel shimming scheme is based on passive shimming andactive shimming In the passive shimming the traditionalpassive shimming method adding shim pieces is subvertedand the cutting grinding and fine processing technologyof magnetic poles is adopted for realizing the homogeneityfieldThe active shimming method adding higher-order coilsis proposed which helps reduce the shimming difficult andsaves the working space (3) The improvement of the anti-eddy-current technology on 119861

0magnet a new magnetic

pole is formed by connecting alloy magnetic pole with mainmagnetic steel together The nonspherical curved-surfacemagnetic poles made of the self-developed MRI dedicatedalloy replaced pole pieces and anti-eddy-current board TheMRI dedicated alloy is a kind of high electrical impedancepermanentmagnetmaterial whichmay effectively reduce theeddy current By using the above technologies along withgradient coil [35] RF coil [36] and integration computersoftware [37] 12 T and 15 T small animalMicro-MRI instru-ments (Figure 1) are developed by which the high qualityMRI images of mice were obtained


(a) (b)


1

4

5

3

2




1234

5




0magnet is


0magnet are further



L

L

L1

L1

L1

L1

L1

L1

L3

L3

L3

L3

L3

L3

L2

L2







1cup 1198712cup 1198713cup 119871) in


120597

120597119909(V

120597119860

120597119909) +

120597

120597119910(V

120597119860

120597119910) = 0

Ω (1198711cup 1198712cup 1198713cup 119871)

(1)

119860 = 0 1198711 (2)

120597119860

120597119903= 0 119871

2 (3)

(V120597119860

120597119899)

119871+

3

= (V120597119860

120597119899)

119871minus

3

1198713 (4)

(V120597119860

120597119899)

119871+

minus (V120597119860

120597119899)

119871minus

= 119895 119871 (5)




119872 =

int120592119888

10038161003816100381610038161198611198881003816100381610038161003816

2119889119881

int 120592119898

1003816100381610038161003816119869021003816100381610038161003816 119889119881

(6)


0












119909119889 000 04 08 12 16 20 24 28 32 324 328 332 336 34 352119910119889 108 1076 1063 1042 1014 10 10 1023 118 121 124 127 130 134 146


119909 0 12 24 36 48 60 72 84 96 972 984 996 1008 102119910 432 4304 4254 4169 4056 400 400 4093 4738 4841 4953 5074 5205 5346


119909 0 28 56 84 112 140 168 196 224 2268 2296 2324 2352 238119910 756 7532 7444 7295 7098 700 700 7163 8291 8472 8667 8880 9108 9355

x

yd

3

3



0



0magnet will




119861119911(119909 119910 119911) = 119860

0

1+ 21198600

2+ 31198601

2119909 + 3119861

1

2119910

+3

21198600

3(21199112minus 1199092minus 1199102) + 12119860

1

3119911119909

+ 121198611

3119911119910 + 15119860

2

3(1199092minus 1199102) + 30119861

2

3119909119910

+ 41198600

4119911 [1199112minus2

31199092+ 1199102]

+15

21198601

4119909 [41199112minus 1199092minus 1199102]

+15

21198611


(7)








Pole Magnetic pole

Yoke1 1

2 2

shoe


MMS

Alloy pole

Yoke

1 1

22




(a)





(b)

1

23

4

(c)








0magnet all kinds



0magnetic field


3 Discussion


100

250

43150

800

100

600

30∘

30∘

45∘

75∘

Unit (mm)


150

70200

400

1000

100

800

30∘

30∘

45∘

75∘

Unit (mm)




51 53 55 57 59


60 90 93 96 104





4 Conclusions









Acknowledgment


References














































(a) (b)


1

4

5

3

2




1234

5




0magnet is


0magnet are further



L

L

L1

L1

L1

L1

L1

L1

L3

L3

L3

L3

L3

L3

L2

L2







1cup 1198712cup 1198713cup 119871) in


120597

120597119909(V

120597119860

120597119909) +

120597

120597119910(V

120597119860

120597119910) = 0

Ω (1198711cup 1198712cup 1198713cup 119871)

(1)

119860 = 0 1198711 (2)

120597119860

120597119903= 0 119871

2 (3)

(V120597119860

120597119899)

119871+

3

= (V120597119860

120597119899)

119871minus

3

1198713 (4)

(V120597119860

120597119899)

119871+

minus (V120597119860

120597119899)

119871minus

= 119895 119871 (5)




119872 =

int120592119888

10038161003816100381610038161198611198881003816100381610038161003816

2119889119881

int 120592119898

1003816100381610038161003816119869021003816100381610038161003816 119889119881

(6)


0












119909119889 000 04 08 12 16 20 24 28 32 324 328 332 336 34 352119910119889 108 1076 1063 1042 1014 10 10 1023 118 121 124 127 130 134 146


119909 0 12 24 36 48 60 72 84 96 972 984 996 1008 102119910 432 4304 4254 4169 4056 400 400 4093 4738 4841 4953 5074 5205 5346


119909 0 28 56 84 112 140 168 196 224 2268 2296 2324 2352 238119910 756 7532 7444 7295 7098 700 700 7163 8291 8472 8667 8880 9108 9355

x

yd

3

3



0



0magnet will




119861119911(119909 119910 119911) = 119860

0

1+ 21198600

2+ 31198601

2119909 + 3119861

1

2119910

+3

21198600

3(21199112minus 1199092minus 1199102) + 12119860

1

3119911119909

+ 121198611

3119911119910 + 15119860

2

3(1199092minus 1199102) + 30119861

2

3119909119910

+ 41198600

4119911 [1199112minus2

31199092+ 1199102]

+15

21198601

4119909 [41199112minus 1199092minus 1199102]

+15

21198611


(7)








Pole Magnetic pole

Yoke1 1

2 2

shoe


MMS

Alloy pole

Yoke

1 1

22




(a)





(b)

1

23

4

(c)








0magnet all kinds



0magnetic field


3 Discussion


100

250

43150

800

100

600

30∘

30∘

45∘

75∘

Unit (mm)


150

70200

400

1000

100

800

30∘

30∘

45∘

75∘

Unit (mm)




51 53 55 57 59


60 90 93 96 104





4 Conclusions









Acknowledgment


References














































L

L

L1

L1

L1

L1

L1

L1

L3

L3

L3

L3

L3

L3

L2

L2







1cup 1198712cup 1198713cup 119871) in


120597

120597119909(V

120597119860

120597119909) +

120597

120597119910(V

120597119860

120597119910) = 0

Ω (1198711cup 1198712cup 1198713cup 119871)

(1)

119860 = 0 1198711 (2)

120597119860

120597119903= 0 119871

2 (3)

(V120597119860

120597119899)

119871+

3

= (V120597119860

120597119899)

119871minus

3

1198713 (4)

(V120597119860

120597119899)

119871+

minus (V120597119860

120597119899)

119871minus

= 119895 119871 (5)




119872 =

int120592119888

10038161003816100381610038161198611198881003816100381610038161003816

2119889119881

int 120592119898

1003816100381610038161003816119869021003816100381610038161003816 119889119881

(6)


0












119909119889 000 04 08 12 16 20 24 28 32 324 328 332 336 34 352119910119889 108 1076 1063 1042 1014 10 10 1023 118 121 124 127 130 134 146


119909 0 12 24 36 48 60 72 84 96 972 984 996 1008 102119910 432 4304 4254 4169 4056 400 400 4093 4738 4841 4953 5074 5205 5346


119909 0 28 56 84 112 140 168 196 224 2268 2296 2324 2352 238119910 756 7532 7444 7295 7098 700 700 7163 8291 8472 8667 8880 9108 9355

x

yd

3

3



0



0magnet will




119861119911(119909 119910 119911) = 119860

0

1+ 21198600

2+ 31198601

2119909 + 3119861

1

2119910

+3

21198600

3(21199112minus 1199092minus 1199102) + 12119860

1

3119911119909

+ 121198611

3119911119910 + 15119860

2

3(1199092minus 1199102) + 30119861

2

3119909119910

+ 41198600

4119911 [1199112minus2

31199092+ 1199102]

+15

21198601

4119909 [41199112minus 1199092minus 1199102]

+15

21198611


(7)








Pole Magnetic pole

Yoke1 1

2 2

shoe


MMS

Alloy pole

Yoke

1 1

22




(a)





(b)

1

23

4

(c)








0magnet all kinds



0magnetic field


3 Discussion


100

250

43150

800

100

600

30∘

30∘

45∘

75∘

Unit (mm)


150

70200

400

1000

100

800

30∘

30∘

45∘

75∘

Unit (mm)




51 53 55 57 59


60 90 93 96 104





4 Conclusions









Acknowledgment


References















































119909119889 000 04 08 12 16 20 24 28 32 324 328 332 336 34 352119910119889 108 1076 1063 1042 1014 10 10 1023 118 121 124 127 130 134 146


119909 0 12 24 36 48 60 72 84 96 972 984 996 1008 102119910 432 4304 4254 4169 4056 400 400 4093 4738 4841 4953 5074 5205 5346


119909 0 28 56 84 112 140 168 196 224 2268 2296 2324 2352 238119910 756 7532 7444 7295 7098 700 700 7163 8291 8472 8667 8880 9108 9355

x

yd

3

3



0



0magnet will




119861119911(119909 119910 119911) = 119860

0

1+ 21198600

2+ 31198601

2119909 + 3119861

1

2119910

+3

21198600

3(21199112minus 1199092minus 1199102) + 12119860

1

3119911119909

+ 121198611

3119911119910 + 15119860

2

3(1199092minus 1199102) + 30119861

2

3119909119910

+ 41198600

4119911 [1199112minus2

31199092+ 1199102]

+15

21198601

4119909 [41199112minus 1199092minus 1199102]

+15

21198611


(7)








Pole Magnetic pole

Yoke1 1

2 2

shoe


MMS

Alloy pole

Yoke

1 1

22




(a)





(b)

1

23

4

(c)








0magnet all kinds



0magnetic field


3 Discussion


100

250

43150

800

100

600

30∘

30∘

45∘

75∘

Unit (mm)


150

70200

400

1000

100

800

30∘

30∘

45∘

75∘

Unit (mm)




51 53 55 57 59


60 90 93 96 104





4 Conclusions









Acknowledgment


References




















































Pole Magnetic pole

Yoke1 1

2 2

shoe


MMS

Alloy pole

Yoke

1 1

22




(a)





(b)

1

23

4

(c)








0magnet all kinds



0magnetic field


3 Discussion


100

250

43150

800

100

600

30∘

30∘

45∘

75∘

Unit (mm)


150

70200

400

1000

100

800

30∘

30∘

45∘

75∘

Unit (mm)




51 53 55 57 59


60 90 93 96 104





4 Conclusions









Acknowledgment


References














































(a)





(b)

1

23

4

(c)








0magnet all kinds



0magnetic field


3 Discussion


100

250

43150

800

100

600

30∘

30∘

45∘

75∘

Unit (mm)


150

70200

400

1000

100

800

30∘

30∘

45∘

75∘

Unit (mm)




51 53 55 57 59


60 90 93 96 104





4 Conclusions









Acknowledgment


References
















































0magnet all kinds



0magnetic field


3 Discussion


100

250

43150

800

100

600

30∘

30∘

45∘

75∘

Unit (mm)


150

70200

400

1000

100

800

30∘

30∘

45∘

75∘

Unit (mm)




51 53 55 57 59


60 90 93 96 104





4 Conclusions









Acknowledgment


References














































51 53 55 57 59


60 90 93 96 104





4 Conclusions









Acknowledgment


References

















































Acknowledgment


References































































Documents

Development of High-Field Permanent Magnetic Circuits for ... · and so the magnetic field homogeneity of𝐵0 magnet will increase. The magnetic field after passive shimming needs