Rapid Slice-bby-Slice Calculation of Susceptibility ... · slice. -é k G The si practic which...
1
Introd from a used t requir suscep natura Theor where and ݕ′ domai multip ܤ෨ ௗ ൫ Here ~ letter k respec slice. ܭ෩ ൫ The si practic which thickn For a ܤ෨ ௗ ൫ ܭ෩ ൫ with th Figure field m the bre axial d In viv anatom B 0 m air/lun induce maps can b error, 50 cm (Math Discu upper includ precis contra time o lies in of sum genera these c Ackno 19B:2 Jordan duction: Suscep all the magnetize to calculate subje res a large compu ptibility-induced ally allows comp ry: The z-compo ܤe ܤ is the main m ′ gives the dipola in, in which conv plication of susc ௫ , ௬ ݖ;ݖ,ᇱ ൯ൌ ܤ~ indicates Four k, ܭ෩ is the Fouri ct to ݔെ ݔ′ and ݕThe function ܭ෩ ௫ , ௬ , ൯ ൌ െ 2 3 ingularity at ൌ ce by defining ܭ෩ h is the average o ness of the suscep sagittal pair of s ,ݔ ௬ , ௭ ݔ;′൯ ൌ , ௬ , ௭ ൯ൌ 1 3 ߜሺ he provision ܭ෩ ൫ e 1 shows the res map of a uniform east B 0 map in a dipolar field con vo validation: A mical image in t apping (IDEAL ng/tissue-segmen ed B 0 map in a are compared in e due to motio background fiel m imaged ana hworks, MA) run ussion: In the 3 torso at 1.5 mm ding buffer vol sion data type, ast, the 2D metho of N x N y N z log(N x n the fact that in mmations in the ate measureable cases to allow ra owledgement: T 26-34 (2003) [2] n CD et al. Proc. Rapid Slice-b ptibility-induced ed voxels in the ect-induced B 0 in uter memory (> d B 0 field which parison of contrib onent of the dipo ܤௗ ሺ ݔ;,ݖ,ݕ,ݔᇱ ݕ,ᇱ magnetic field a ar field map on t volution implied eptibility and dip ܤ ݖ߂ᇱ ܭ෩ ൫ ௫ , ௬ , ier transform wi ier transform of t ݕെ ݕ′, and Δݖ′ i turns out to have 2 3 ߜሺሻ 1 2 exp ൌ 0 in the Dirac d ܭ෩ ൫ ௫ , ௬ , 0൯ ≡ െ of Eq. (3) over െ ptibility slice at slices, Eqs (2,3) a ܤ Δ ݔᇱ ܭ෩ ൫, ௬ , ሻ െ ௭ ଶ 2 expሺെ 0, ௬ , ௭ ൯ ≡ 1/ሺ sult of applying m sphere. Figure a susceptibility-s ntributions from A healthy volun the upper torso a L[5]) in the bre nted anatomica a single breast s n Fig. 3. Good on in the non-b ld, and any dipo atomy. All ca nning on a 32 bit 3D Fourier meth m isotropic resolu umes to avoid such matrix oc od would do wit x N y N z ). If B 0 ma 2D calculation, slice direction. B 0 effects. Exa apid patient-spec This work was Marques JP, Bo . ISMRM 17:212 by-Slice Calcu 1 G off-resonance fi subject in the m nhomogeneity in gigabyte) to han is highly memor butions from dif olar magnetic fie ᇱ ݖ,ᇱ ሻൌ ܤ Δ ݒ nd is the susce the slice at z con d in Eq. (1) is co polar field funct ൯൫ ௫ , ௬ ݖ,ᇱ ൯, ith respect to the the quantity in { is the thickness o e a simple form, pሺെ||ሻ , ≡ delta function ߜሺ െ2/ሺ3Δሻ ሺ1/Δ െΔ/2 ൏ ൏ Δ/ h = 0. are replaced by t ௭ ൯൫ ݔᇱ , ௬ , ௭ ൯, ||ሻ , ≡ ට ௬ ଶ ሺ3Δሻ െ ௭ ଶ /ሺ ଶ Δ Eqs. (2-5) to cal e 2 shows applic egmented femal 578 slices are ea teer was scanne and Dixon’s fat- east. Our metho al image to p slice. The calcu agreement is ob reath-held IDEA olar B 0 contribut alculations wer t laptop PC with hod, susceptibili ution can be as l Fourier replic ccupies 2 GB c th only a few, 2 M ap of a single sli one can use thic Due to the long amples are lung- cific shim calcul supported by th owtell R. Conep 25 (2009) [5] Re lation of Susc Seung-Kyun GE Global Researc ield in high field main magnetic fie n brain [3] and a ndle large matric ry-efficient and fferent body part eld at (ݖ ,ݕ ,ݔ) con ሺ ݔᇱ ݕ,ᇱ ݖ,ᇱ ሻ⋅ቊ 1 4 ߨeptibility. Consid ntributed by the s onveniently repla tions: ≡ ݖെ ݖᇱ e variables denot { } in Eq. (1) wit of the susceptibi ට ௫ ଶ ௬ ଶ ሺሻ is avoided in Δሻሼ1 െ exp ሺെΔ 2 where Δ is the the following, , ≡ ݔെ ݔ௬ ଶ ௭ ଶ Δሻሼ1 െ exp ሺെΔ lculation of the d cation of the meth le human body m asily compared. ed for a breath-h -water separatio od was applied produce suscep ulated and measu bserved. The dif AL scan, segme ed by tissue out e done with h 2 GB of RAM. ity matrix repre large as 512×512 a effect. With contiguous mem MB matrices in ice is desired, th cker slices to rep g range nature o volume-induced lations with grea he NIH grant 1R pts Magn Reson eeder SB et al. M ceptibility-Ind n Lee 1 , and Ileana H ch, Niskayuna, NY, d MRI can be acc eld. For 3D calcu a single breast [4 ces. In this work attains comparab ts to the B 0 map ntributed by a si ߨ⋅ 2ሺ ݖെ ݖᇱ ሻ ଶ െ ሾሺ ݔെ ݔᇱ ሻ ଶ der two axial sli susceptibility of aced by . ሺ2ሻ ted with th ility ሺ3ሻ n Δ/2ሻሽ e ᇱ ሺ4ሻ ሺ5ሻ Δ/2ሻሽ. dipolar hod to model; held 3D on-based d to the ptibility- ured B 0 fference entation tside the Matlab esenting 2×1024, double mory. In this example. In he 2D method ta present susceptib f the dipolar ma d B 0 offset in ne ater computation R01CA154433-0 25B:65-78 (200 MRM 51:35-45 ( Fig sph repr calc Fig the cali susc In-p uced B 0 Map Hancu 1 , United States curately calculat ulation, a much f 4]. Extension of t we introduce a ble speed of calc of a given slice. ingle susceptibil െ ሺ ݔെ ݔᇱ ሻ ଶ െ ሺ ሺ ݕെ ݕᇱ ሻ ଶ ሺ ݖces at z and ݖ′. I the slice at ݖ′. T n terms of speed, akes N x N y N z log( bility in distant s agnetic field, sus euroimaging and nal efficiency and 01A1. Referenc 05) [3] Koch KM (2004) gure 1. Calculated here with χ = –9 pp resent field profile culation, respectiv gure 3. Compariso proposed method ibrated out off-lin ceptibility-segmen plane matrix was 5 in the Fourier ted in the spatial faster, Fourier-d the method to hi 2D Fourier-base culation in a sma . lity voxel of volu ሺ ݕെ ݕᇱ ሻ ଶ െ ݖᇱ ሻ ଶ ሿ ହ/ଶ ቋ In this case, doub This integral can , 3D FFT on a N (N x N y ), a clear g slices, which can sceptibility in re d metallic implan d flexibility. ces: [1] Salomir M et al. Phys Me d off-resonance fi pm at 3 T. Dotted es obtained by the vely. (a) Axial mid on of breast B 0 map d (middle). For ID e. Anatomy-based nted 3D image cov 512×512 including r Domain l domain by add domain method [ igh resolution bo ed, slice-by-slice all number of sli ume Δ ݒat ( ݔᇱ ݕ,ሺ1ሻ ble integral of E n be performed in N x ×N y ×N z matrix ain over 3D. Th n substantially re elatively distant nts. Our method r R et al. Conce ed Biol 51:6381 ield in and aroun and solid lines in e proposed method d-plane. (b) Sagitta Figure 2 induced an axial breast (in from all Woman. segment air/lung/ –9 ppm. ps produced by ID DEAL, the scanne d dipolar B 0 map w vering 50cm S/I f g buffer; slice thick B 0 [Hz] ing dipolar field [1,2] has been ody imaging e calculation of ices. The method ᇱ ݖ,′ሻ is Eq. (1) over ݔ′ n the Fourier takes calculatio he advantage als educe the numbe voxels can ofte d can be useful i epts Magn Reso -6402 (2006) [4 nd a homogeneou the plot on the lef d and by analytica al mid-plane. 2. Susceptibility- B 0 map at 3 T in slice through nset) contributed slices in Visible . Susceptibility tation was: /tissue = 0/–2.25/ DEAL (left), and by er’s shim field wa was obtained from from belly to neck kness was 6 mm. ds d n o er n n n 4] s ft al y s m k. 612 Proc. Intl. Soc. Mag. Reson. Med. 20 (2012)
Transcript of Rapid Slice-bby-Slice Calculation of Susceptibility ... · slice. -é k G The si practic which...
Introdfrom aused trequirsuscepnaturaTheor
whereand ′domaimultip
Here ~letter krespecslice.
The sipracticwhichthicknFor a
with thFigurefield mthe breaxial dIn vivanatomB0 mair/luninducemaps can berror, 50 cm(MathDiscuupper includpreciscontratime olies inof sumgenerathese cAckno19B:2Jordan
duction: Suscepall the magnetizeto calculate subjeres a large compuptibility-inducedally allows compry: The z-compo
e is the main m′ gives the dipolain, in which convplication of susc, , ;~ indicates Fourk, is the Fourict to ′ and The function , , 23ingularity at ce by defining
h is the average oness of the suscepsagittal pair of s, , ; ′, , 13he provision e 1 shows the resmap of a uniformeast B0 map in adipolar field convo validation: Amical image in tapping (IDEALng/tissue-segmened B0 map in aare compared ine due to motiobackground fielm imaged ana
hworks, MA) runussion: In the 3
torso at 1.5 mmding buffer volsion data type, ast, the 2D methoof NxNyNz log(Nxn the fact that in mmations in the ate measureable cases to allow raowledgement: T
26-34 (2003) [2] n CD et al. Proc.
Rapid Slice-b
ptibility-induced ed voxels in the ect-induced B0 inuter memory (>
d B0 field which parison of contribonent of the dipo, , , ; ,magnetic field aar field map on tvolution impliedeptibility and dip, ,ier transform wiier transform of t′, and Δ ′ iturns out to have23 12 exp0 in the Dirac d, , 0 ≡of Eq. (3) over ptibility slice at
slices, Eqs (2,3) aΔ , ,2 exp0, , ≡ 1/sult of applying
m sphere. Figurea susceptibility-sntributions from A healthy volunthe upper torso a
L[5]) in the brented anatomicaa single breast sn Fig. 3. Good
on in the non-bld, and any dipoatomy. All canning on a 32 bit3D Fourier methm isotropic resolu
umes to avoid such matrix ocod would do witxNyNz). If B0 ma2D calculation, slice direction. B0 effects. Exa
apid patient-specThis work was Marques JP, Bo
. ISMRM 17:212
by-Slice Calcu1G
off-resonance fisubject in the mnhomogeneity ingigabyte) to hanis highly memorbutions from difolar magnetic fie, Δ nd is the suscethe slice at z cond in Eq. (1) is copolar field funct, , ,ith respect to thethe quantity in {is the thickness oe a simple form,p | | , ≡delta function 2/ 3Δ 1/ΔΔ/2 Δ/h = 0. are replaced by t, , ,| | , ≡3Δ / ΔEqs. (2-5) to cal
e 2 shows applicegmented femal578 slices are eateer was scanneand Dixon’s fat-east. Our methoal image to pslice. The calcuagreement is obreath-held IDEA
olar B0 contributalculations wert laptop PC withhod, susceptibiliution can be as l
Fourier replicccupies 2 GB cth only a few, 2 Map of a single slione can use thicDue to the long
amples are lung-cific shim calculsupported by thowtell R. Conep25 (2009) [5] Re
lation of SuscSeung-Kyun
GE Global Researc
ield in high fieldmain magnetic fie
n brain [3] and andle large matricry-efficient and fferent body parteld at ( , , ) con, , ⋅ 14eptibility. Considntributed by the sonveniently replations: ≡e variables denot{ } in Eq. (1) witof the susceptibi
is avoided inΔ 1 exp Δ2 where Δ is the
the following, , ≡Δ 1 exp Δlculation of the d
cation of the methle human body masily compared.ed for a breath-h-water separatiood was appliedproduce suscep
ulated and measubserved. The difAL scan, segmeed by tissue oute done with
h 2 GB of RAM.ity matrix reprelarge as 512×512a effect. With
contiguous memMB matrices in ice is desired, thcker slices to repg range nature ovolume-inducedlations with greahe NIH grant 1Rpts Magn Reson eeder SB et al. M
ceptibility-Indn Lee1, and Ileana Hch, Niskayuna, NY,
d MRI can be acceld. For 3D calcua single breast [4ces. In this work attains comparabts to the B0 map ntributed by a si⋅ 2der two axial slisusceptibility of aced by . 2 ted with th ility
3
n Δ/2 e
4 5 Δ/2 . dipolar hod to
model;
held 3D on-based d to the ptibility-ured B0 fference entation tside the
Matlab
esenting 2×1024,
double mory. In
this example. Inhe 2D method tapresent susceptibf the dipolar ma
d B0 offset in neater computationR01CA154433-025B:65-78 (200
MRM 51:35-45 (
Figsphreprcalc
Figthe calisuscIn-p
uced B0 Map Hancu1
Y, United States
curately calculatulation, a much f4]. Extension of tk we introduce a ble speed of calcof a given slice.
ingle susceptibil
ces at z and ′. If the slice at ′. T
n terms of speed,akes NxNyNz log(Nbility in distant sagnetic field, suseuroimaging andnal efficiency and01A1. Referenc05) [3] Koch KM(2004)
gure 1. Calculatedhere with χ = –9 ppresent field profileculation, respectiv
gure 3. Comparisoproposed method
ibrated out off-linceptibility-segmenplane matrix was 5
in the Fourier
ted in the spatialfaster, Fourier-dthe method to hi2D Fourier-baseculation in a sma. lity voxel of volu
/ In this case, doubThis integral can
, 3D FFT on a N(NxNy), a clear gslices, which cansceptibility in re
d metallic impland flexibility. ces: [1] SalomirM et al. Phys Me
d off-resonance fipm at 3 T. Dotted es obtained by the
vely. (a) Axial mid
on of breast B0 mapd (middle). For IDe. Anatomy-basednted 3D image cov512×512 including
r Domain
l domain by adddomain method [igh resolution boed, slice-by-sliceall number of sli
ume Δ at ( , 1
ble integral of En be performed in
Nx×Ny×Nz matrix ain over 3D. Th
n substantially reelatively distant nts. Our method
r R et al. Conceed Biol 51:6381
field in and arounand solid lines in
e proposed methodd-plane. (b) Sagitta
Figure 2induced an axial breast (infrom allWoman.segmentair/lung/–9 ppm.
ps produced by IDDEAL, the scanned dipolar B0 map wvering 50cm S/I fg buffer; slice thick
B0[Hz]
ding dipolar field[1,2] has been ody imaging e calculation of ices. The method, ′ is
Eq. (1) over ′ n the Fourier
takes calculatiohe advantage alseduce the numbevoxels can ofte
d can be useful i
epts Magn Reso-6402 (2006) [4
nd a homogeneouthe plot on the lef
d and by analyticaal mid-plane.
2. Susceptibility-B0 map at 3 T in slice through nset) contributed slices in Visible
. Susceptibility tation was: /tissue = 0/–2.25/
DEAL (left), and byer’s shim field wawas obtained fromfrom belly to neckkness was 6 mm.
ds
d
n o
er n n
n 4]
s ft al
y s
m k.
612Proc. Intl. Soc. Mag. Reson. Med. 20 (2012)
