introduction to k-space trajectories
TRANSCRIPT
Introduc)ontok-spacetrajectories
Agenda• OverviewofMRIsystem• Magne)cfields:thethreefields
• TheFouriertransformandk-space:Whyisitcalled‘k’space?
• Understanding‘k-spacetrajectory’
• Somebasick-spacetrajectories
• Problem1:Cartesiantrajectory
• Problem2:Echo-planarimaging
• Problem3:Radialtrajectory
• Problem4:Spiraltrajectory
• Conclusions
Gradientcoils
Subject
Radiofrequency
coil
Magnet
OverviewofaMRIsystem
Imagecourtesy:MRIscannercutaway:Colinmcnulty.com
y
x
z
Larmor Equation
Magne)sm:EffectoftheB0,G.randB1fields
f
t
A
A
DiscreteFourierTransform
Avisualrepresenta)onofk-space
Topviewofk-space
• Idealk-spaceisHermi)aninnature,discoun)ngerrorsfrommeasurement
• Usedinacquisi)onslikeHASTE
Theory
ThesignalacquiredistheFreeInduc)onDecay(FID)fromallthespinsofthepar)cularslice
TheLarmorfrequencyisgivenby
JargonforengineersJ
Frontview Topview
Ananalogyfork-spacetrajectory
Considerahill
20 40 60 80 100 120
50
100
150
200
250
Fewk-spacetrajectoriestrajectories
y
x
Exampleproblem1:DesignCartesiank-spacetrajectory
Givenparameters: ∆x = 1 mm ∆y = 1 mm Lx = 25.6 cm L y = 25.6 cm
Evaluatetheunknowns:
Variable Value
Nx
Ny
256
256 3.9 m-1
3.9 m-1
[-500, 500] m-1
[-500, 500] m-1
kx
ky
RF Pulse
Gz
Gy
Gx
TimingDiagramDepic)ngCartesianSampling
Gx
Gy
Gz
RF Pulse
Reconstruc)on&ar)facts
Exampleproblem2:DesignEPIk-spacetrajectory
Givenparameters: ∆x = 1 mm ∆y = 1 mm L = 25.6 cm tesp = 1 ms N = 15 SR = 50 Tm-1/s Evaluatetheunknowns:
Variable Value
Nx
Ny
Gy
Aphase
256
256 3.9 m-1
3.9 m-1
[-500, 500] m-1
[-500, 500] m-1
0.117 mT/m 1.81 mT . ms/m
kx
ky
RF Pulse
Gz
Gy
Gx
TimingDiagramDepic)ngEPISampling
*EPIreconstruc)onandar)factswillbeaddressedbyDr.ManojSaranathan,StanfordUniversity
Gx
Gy
Gz
RF Pulse
Exampleproblem3:DesignRadialk-spacetrajectory
Givenparameters: ∆x = 1 mm ∆y = 1 mm L = 25.6 cm
Evaluatetheunknowns:
Variable Value
Nx
Ny
Nphase
Leff
256
256 3.9 m-1
3.9 m-1
[-500, 500] m-1
402 256
0.256 m-1
ky
kx
RF Pulse
Gz
Gy
Gx
TimingDiagramDepic)ngRadialSampling
Gx
Gy
Gz
RF Pulse
Reconstruc)on&ar)facts
Exampleproblem4:Designspiralk-spacetrajectory
Evaluatetheunknowns:
Variable Value
Nx
Ny
256
256 3.9 m-1
3.9 m-1
[-500, 500] m-1
ky
kx
RF Pulse
Gz
Gy
Gx
TimingDiagramDepic)ngSpiralSampling
Gx
Gy
Gz
RF Pulse
Reconstruc)on&ar)facts
ComparisonofBasick-spaceTrajectories
Cartesian• UniformFFT• Localizedar9facts• Longacquisi9on9me• Clinicians’choice
Spiral• Efficientcoverage• SNRcontrolled• Gradientdemands• NUFFT/gridding
Radial• Variabledensity
coverage• Mo9onapplica9ons• NUFFT/gridding• Outeredgeshave
gaps
EPI• Rapidacquisi9on• UniformFFT• B0dependence• GradientSR
Otherk-spacetrajectories
• Rose_e• Lissajou• Stackofspirals• Stackofradials• Stars• SPINS• Kooshball• Bayesiancartesiantrajectories(MathiasSeegeretal.2010,MRM)
Acknowledgements
• Mr.NutanDevBJ,B.E.,GraduateResearchAssistantMIRC
• Mr.PavanPoojar,M.Tech.,ResearchAssociate,MIRC
• Prof.JefferyFesslerandgroup,UniversityofMichiganAnnHarbor,fortheNUFFTcodeintheImagereconstruc)ontoolbox
• MedicalImagingResearchCentre:studentsandfaculty
• DayanandaSagarIns)tu)ons