The talk gives an overview on pulse sequence design components in general and k-space trajectories in particular. Design problems are solved step by step for multiple trajectories with examples of applications. A few simulations of artifacts from these trajectories are also illustrated

1. Introduc)on to k-space trajectories

2. Agenda
• Overview of MRI system
• Magne)c fields: the three fields
• The Fourier transform and k-space: Why is it called ‘k’ space?
• Understanding ‘k-space trajectory’
• Some basic k-space trajectories
• Problem 1: Cartesian trajectory
• Problem 2: Echo-planar imaging
• Problem 3: Radial trajectory
• Problem 4: Spiral trajectory
• Conclusions

3. Gradient
coils
Subject
Radio
frequency
coil
Magnet
Overview of a MRI system
Image courtesy: MRI scanner cutaway: Colinmcnulty.com

4. y
x
z
Larmor Equation
Magne)sm: Effect of the B0 , G.r and B1 fields

5. f
t
A
A
Discrete Fourier Transform

6. A visual representa)on of k-space

7. Top view of k-space
• Ideal k-space is
Hermi)an in nature,
discoun)ng errors from
measurement
• Used in acquisi)ons like
HASTE

8. Theory
The signal acquired is the Free Induc)on Decay (FID) from all the spins of the par)cular slice
The Larmor frequency is given by

9. Jargon for engineers J

10. Front view Top view
An analogy for k-space trajectory
Consider a hill

11. 20 40 60 80 100 120
50
100
150
200
250
Few k-space trajectories trajectories
y
x

12. Example problem 1:
Design Cartesian k-space trajectory
Given parameters:
∆x = 1 mm
∆y = 1 mm
Lx = 25.6 cm
L y = 25.6 cm
Evaluate the unknowns :
Variable Value
Nx
Ny
256
256
3.9 m-1
3.9 m-1
[-500, 500] m-1
[-500, 500] m-1

13. kx
ky
RF
Pulse
Gz
Gy
Gx
Timing Diagram Depic)ng Cartesian Sampling
Gx
Gy
Gz
RF
Pulse

14. Reconstruc)on & ar)facts

15. Example problem 2:
Design EPI k-space trajectory
Given parameters:
∆x = 1 mm
∆y = 1 mm
L = 25.6 cm
tesp = 1 ms
N = 15
SR = 50 Tm-1/s
Evaluate the unknowns :
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

16. kx
ky
RF
Pulse
Gz
Gy
Gx
Timing Diagram Depic)ng EPI Sampling
* EPI reconstruc)on and ar)facts will be addressed by Dr. Manoj Saranathan, Stanford
University
Gx
Gy
Gz
RF
Pulse

17. Example problem 3:
Design Radial k-space trajectory
Given parameters:
∆x = 1 mm
∆y = 1 mm
L = 25.6 cm
Evaluate the unknowns :
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

18. ky
kx
RF
Pulse
Gz
Gy
Gx
Timing Diagram Depic)ng Radial Sampling
Gx
Gy
Gz
RF
Pulse

19. Reconstruc)on & ar)facts

20. Example problem 4:
Design spiral k-space trajectory
Evaluate the unknowns :
Variable Value
Nx
Ny
256
256
3.9 m-1
3.9 m-1
[-500, 500] m-1

21. ky
kx
RF
Pulse
Gz
Gy
Gx
Timing Diagram Depic)ng Spiral Sampling
Gx
Gy
Gz
RF Pulse

22. Reconstruc)on & ar)facts

23. Comparison of Basic k-space Trajectories
Cartesian
• Uniform FFT
• Localized ar9facts
• Long acquisi9on
9me
• Clinicians’ choice
Spiral
• Efficient coverage
• SNR controlled
• Gradient demands
• NUFFT/gridding
Radial
• Variable density
coverage
• Mo9on applica9ons
• NUFFT/gridding
• Outer edges have
gaps
EPI
• Rapid acquisi9on
• Uniform FFT
• B0 dependence
• Gradient SR

24. Other k-space trajectories
• Rose_e
• Lissajou
• Stack of spirals
• Stack of radials
• Stars
• SPINS
• Kooshball
• Bayesian cartesian trajectories (Mathias Seeger et al. 2010, MRM)

25. Acknowledgements
• Mr. Nutan Dev B J, B.E.,
Graduate Research Assistant
MIRC
• Mr. Pavan Poojar, M.Tech.,
Research Associate, MIRC
• Prof. Jeffery Fessler and group, University of Michigan Ann Harbor, for the
NUFFT code in the Image reconstruc)on toolbox
• Medical Imaging Research Centre: students and faculty
• Dayananda Sagar Ins)tu)ons