Transcript Lesson 10

M.Tech. (CS), Semester III, Course B50
Functional Brain Signal
Processing: EEG & fMRI
Lesson 10
Kaushik Majumdar
Indian Statistical Institute
Bangalore Center
[email protected]
Mezrich, 1995
K Space
Localization in
terms of spatial
frequency   1 .

Wave number
2
k  2 

K space is
named after
the wave
number k.
K space in MR imaging
http://www.psy.vanderbilt.edu/courses/hon185/SpatialFrequency/Spat
ialFrequency.html
3D Magnetic Gradient
B(z) = B0 + G.z
Z
B(x) = B0 + G.x
B(y) = B0 - G.y
B(y) = B0 + G.y
X
B(x) = B0 - G.x
B(z) = B0 - G.z
Y
Slice Location: Location Along Z
axis
For Hydrogen gyromagnetic ratio is 42.6
MHz/T. For a 2.5 T gradient magnetic field
strength (say in a 3 T scanner) the RF pulse
should be in a band 106.5 ± δ MHz.
Kandel et al., 2000
Pooley, 2005
Buxton, 2009
Frequency Encoding: Location
Along X Axis
Buxton, 2009
Phase Encoding: Location Along Y
Axis
Buxton, 2009
Magnetic Pulses Along X, Y and Z
Axes
Mezrich, 1995
MR Signal Representation in K
Space
S (t )   e

t
T2
e
 j 2 (  B0t )
f (x)e  j 2 ( Gt .x ) dx

S (t )  A f (x)e
 j 2 ( k . x )

k   Gt
Ae

t
T2
e
 j 2 (  B 0 t )
ƒ(x) is the variable magnetic field
dx
Trade Off Challenge in MR Imaging
Simultaneous achieving of
(1)
(2)
(3)
high spatial resolution,
high temporal resolution, and
high SNR.
http://www.talairach.org
Talairach Coordinate System
www.brainvoyager.com
Talairach Coordinate (cont.)
Talairach origin is at the
intersection of posterior
and superior margins of
the anterior
commissure (AC) on
the midhemispheric
plane.
Lancaster et al., 2007
Cerebral Dimension of Brain
Templates
References


R. Mezrich, A perspective on K space,
RSNA, 195: 297 – 315, 1995, available
online at
http://pages.stat.wisc.edu/~mchung/teaching/
MIA/reading/fourier.kspace.mezrich.1995.pdf
R. B. Buxton, Introduction to Functional
Magnetic Resonance Imaging, 2e,
Cambridge University Press, Cambridge, UK,
2009.
References (cont.)


http://www.talairach.org
J. L. Lancaster et al., Bias between MNI and
Talairach coordinates analyzed using ICBM152 brain template, Hum. Brain Mapp., 28:
1194 – 1205, 2007.
THANK YOU
This lecture is available at http://www.isibang.ac.in/~kaushik