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¡  Magne&c	Resonance	Imaging	
§  Past	
§  Present	
§  Glimpse	of	the	future
¡  John	Bap&ste	Fourier	
§  Officer	in	Napoleon's	
army	
§  Mathema&cs	for	
thermodynamics	
§  Invented	the	Fourier	
Transform	which	lies	at	
the	core	of	MRI	today	
[1]		Tal	Geva	JCMR	2006
¡  Nikola	Tesla	
§  Serbian	
§  Inventor	of	AC	
§  Tesla	coil	
§  Sta&onary	terrestrial	
waves	
§  Unit	of	magne&c	field	
strength	named	aQer	
him	
[1]		Tal	Geva	JCMR	2006
¡  Independently	discovered	the	nuclear	magne&c	
resonance	effect	
¡  Awarded	Nobel	Prize	in	1952	for	their	discoveries	
[1]		Tal	Geva	JCMR	2006
Vivekananda	
Memorial	
Kargil	1999
§  1971:	Raymond	Damadian	–	relaxa&on	&mes	
for	tumors	in	rat	models	of	cancer		
§  1973:	Abe	Zenuemon	and	others,		
file	patent	for	the	first	targeted		
NMR	for	evalua&on	of	informa&on	
	inside	from	outside		
§  1974:	Magne&c	Resonance	Imaging	is	born	by	
the	use	of	gradients,	thanks	to	Paul	Lauterbur	
and	Peter	Mansfield	
§  1975:	Richard	Ernst	(Anil	Kumar	et.	al)	
described	the	use	of	FT	for	MRI	
[1]		Tal	Geva	JCMR	2006
[2]	hfp://www.cis.rit.edu/htbooks/mri/
§  1980:	Average	&me	to	make	an	MR	
image	is	5	minutes	
§  1985:	Average	&me	to	make	an	MR	
image	is	5	seconds	
§  1983:	T2	weighted	imaging	befer	for	
highligh&ng	pathology	
§  1984	-	85:	Cardiac	MRI,	blood	flow,	
CE-MRI,		Steady	state	free	precession	
Research	labs	to	clinical	
prac&ce	
[1]		Tal	Geva	JCMR	2006	
[3]	hfp://www.fonar.com/&melineofmri.htm
¡  1988:	Echo	Planar	
Imager	for	pediatrics,	
Larry	Crooks	at	UCSF	
¡  1987:	Mul&ple	RF	coils	
used	for	MRI	
¡  1987	–	90:	Parallel	
imaging	is	born	thanks	
to	Carlson
• 	Good	data	quality	but	takes	a	long	&me!		
• 	Hence,	may	not	be	suitable	for	certain	imaging	protocols.	
• 	Limits	spa&al	and	temporal	resolu&ons	
• 	Higher	spa&al	resolu&on	aids	in	morphological	analysis	of	tumors	
–	breast	DCE-MRI	
• 	Temporal	resolu&on	is	important	for	accurate	pharmacokine&c		
analysis.	
• 	Several	approaches	like	keyhole,	parallel	imaging	and	other	fast	
sequences	have	been	used.	2D FFT
2D
IFFT
50
100
150
200
X	
1 0 Data	provided	by	Baek
[4]	Larkman	et.	al	PMBS	2007
¡  2008:	Compressed	sensing	is	applied	to	MRI	
¡  2012:	Keynote	speeches	at	ISMRM	on	compressed	
sensing	
¡  CS	applied	to	MRSI,	DCE-MRI,	cardiac	imaging,	brain	
imaging,	almost	every	known	MR	method
X	
2D
IFFT
10
20
30
40
50
60
70
10
20
30
40
50
60
70
Uniform	
Sampling	
X	
2D
IFFT
20
40
60
80
100
120
20
40
60
80
100
120
Incoherent	
Sampling
Complete	data	reconstruc0on	
Wavelet		
Transform	
Data	provided	by	Baek	
[1]	David	L.	Donoho,	IEEE	Transac0ons	on	Informa0on	theory,	Vol.52,	no.	4,	April	2006	
[2]	Candes,	E.J.	et	al.,	IEEE	Transac0ons	on	Informa0on	theory,	Vol.52,	no.2,	Feb.	2006	
• 	Most	objects	in	nature	are	approximately	sparse	in	a	transformed	domain.	
• 	U&lize	above	concept	to	obtain	very	few	measurements	and	yet	reconstruct	with	
high	fidelity	 [5,6]		
Only	33%	of	complete	data	X
¡  Coils	in	India	
¡  Combina&on	of	parallel	
imaging	and	
compressed	sensing	
¡  Parallel	transmit	MRI	
[7] Andrew Thomas et. al.,2007 International Journal of Biomedical
Imaging
MR		VOLUME	
COILS		
for	
	0.5	Tesla	
BIRDCAGE	
1:2	ra&o,	8	rung		
VOLUME	coil	
1:2	ra&o	
BIRDCAGE	
1:1	ra&o,	4	rung		
BIRDCAGE	-1:2	ra&o,	4	rung
§  To	have	minimum	aliasing	due	to	sampling	below	the	Nyquist	rate,	the	
following	proper&es	of	idea	sampling	have	to	be	met.	
§  The	near	zero	region	around	the	main	lobe	of	the	PSF	should	be	as	large	as	
possible	and	outside	that	region,	PSF	should	resemble	white	noise.		
§  The	 samples	 should	 be	 placed	 randomly	 but	 with	 a	 restricted	 maximum	
distance	between	samples.		
§  These	 two	 condi&ons	 are	 met	 by	 Poisson	 disc	 sampling	 but	 it	 has	
imprac&cal	gradient	requirements.	
§  Constrained	 random	 pafern	 is	 a	 normal	 lasce	 pafern	 with	 samples	
shiQed	 along	 one	 dimension	 randomly	 by	 -1,	 0	 and	 +1	 i.e.	 constrained	
randomiza&on	added	along	one	direc&on.		
§  It	has	moderate	gradient	requirements.
§  Performance	 of	 compressed	 sensing	 (CS)	 algorithms	 depends	 on	
the	sparsity	level	of	the	signal,	the	type	of	sampling	pafern	used	
and	the		reconstruc&on	method	applied.		
§  The	 higher	 the	 incoherence	 of	 the	 sampling	 pafern	 used	 for	
undersampling,	 less	 aliasing	 is	 no&ced	 resul&ng	 in	 befer	 CS	
reconstruc&on.	
§  The	theory	of	CS	requires	acquisi&on	of	randomized	set	of	
measurements	(random	sampling),	leading	to	incoherant	aliasing	
ar&facts.	
§  But	random	sampling	requires	bigger	changes	in	amplitudes	and	
polarity	of	MR	system	gradients,	which	is	not	feasible	in	MR	
system.
Three candidate sampling patterns and their corresponding PSFs: top to bottom:
random, Poisson disc and constrained random
Usman et. al., Sampta 2009
21	
¡  Joint k-space trajectory allows for the specification of a region
of interest(ROI), which improves excitation accuracy at high
speedup factors
¡  It allows for magnetic field inhomogenetiy compensation
during excitation k-space
¡  Optimized accelerated selective excitation is useful for
reducing specific absorption rate(SAR) and shortening
multidimensional RF pluses
¡  Normal transmission
§  In a normal transmission, the data/signals are sent one at a time
over the transmission channel
¡  Parallel transmission
§  Parallel transmission means simultaneous transmission
of N signals. These signals are sent simultaneously over
N different channels
Radartutorial.eu
23	
Reconstruc&on	
of	image	
Pulse
sequence to
generate k-
space
1.  Target organ
2.  K-space trajectory focus on
heart and use spiral
2D-IFT	
Pa&ent		
Spiral k-space
trajectory
24	
SAR
§  Specific absorption rate (SAR) is a measure of the rate at
which energy is absorbed by the body when exposed to a radio
frequency (RF) electromagnetic field
§  It is defined as the power absorbed per mass of tissue and has units
of watts per kilogram(W/kg)
¡  SAR can be calculated from the electric field within the tissue as:
where
¡  σ is the sample electrical conductivity
¡  E is the RMS electric field
¡  ρ is the sample density
( ) ( )
( )
dr
r
rEr
SAR
sample
∫=
2
2ρ
σ
25	
¡  Errors and SAR will be increasing, we need to decrease them
¡  So we have a formula as
C= є + λ (SAR) …2
Here C= cost, є= excitation error, λ = Lagrange multiplier
¡  As λ increases SAR reduces to some extent then remains constant and
error also remain constant
L-curve
L-curve Subset virtual observation points for RF
¡  Faculty	and	management	
§  Prof.	A.N.N.	Murthy,	Principal,	DSCE	
§  Dr.	Premchandra	Sagar,	CEO,	DSCE	
¡  Students	
§  Padma	C.R.	(coils)	
§  Sneha	Potdar	(Parallel	transmit	background)	
¡  MIRC	faculty	and	students,	collaborators	and	
industrial	partners
28	
¡  The image of the target organ in which we are interested is
taken using 2D-FT
¡  The scanned image obtained by parallel transmit from MRI is
called as k-space, obtained k-space undergoes sampling at ROI
¡  Then 2D-IFT is done to achieve a desired excitation pattern
Echo-Planar Imaging (EPI) k-space raster. Brazilian journal of physics

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