introduction to k-space trajectories

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