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Ga-67 imaging with vector Shirmohammad, Maryam 2016

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GA-67 IMAGING WITH VECTOR by MARYAM SHIRMOHAMMAD A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE in THE FACULTY OF GRADUATE AND POSTDOCTORAL STUDIES  (Physics) THE UNIVERSITY OF BRITISH COLUMBIA  (Vancouver)  OCTOBER 2016 ยฉ MARYAM SHIRMOHAMMAD, 2016   	 ii	Abstract	Ga-67	decays	with	emission	of	gammas	of	93	(42%),	184	(21%),	300	(17%)	and	393	(5%)	keV.	 	The	energy	range	of	the	gammas	of	Ga-67	may	impact	the	quality	of	the	SPECT	imaging	data	 in	 a	 collimator	 type-dependent	way.	 The	MILABs	 VECTor	 is	 a	 preclinical	 SPECT	 scanner	utilizing	 multi-pinhole	 collimators	 (MPC).	 Several	 MPCs	 can	 be	 mounted	 on	 the	 camera.	 A	General	Purpose	Multi-Pinhole	(GPMP),	a	High	Energy	Clustered	Multi-Pinhole	(HECMP),	and	a	High	Sensitivity	Multi-Pinhole	(HSMP)	collimator	were	used	for	this	work.	The	main	objective	of	this	thesis	is	the	performance	characterization	of	the	VECTor	and	MPCs	 in	 imaging	 Ga-67.	 The	 sensitivity	 profiles	 of	 the	 MPCs,	 and	 uniformity	 and	 contrast	metrics	 in	 the	 acquired	 images	 were	 evaluated	 for	 this	 purpose.	 Other	 objectives	 include	evaluation	of	the	attenuation	and	scatter	correction,	and	finally	optimization	for	Ga-67	imaging	which	includes	proper	selection	of	a	MPC	and	the	photopeaks	for	data	reconstruction.	Our	 results	 showed	 that	 the	 peak	 sensitivity	 of	 the	 GPMP,	 HECMP,	 and	 HSMP	collimators	 at	 (93,	 184,	 300,	 393	 keV)	 is	 respectively	 (0.2%,	 0.3%,	 0.3%,	 0.4%),	 (0.4%,	 0.3%,	0.2%,	 0.2%),	 and	 (1.8%,	 1.6%,	 1.0%,	 0.8%).	Ga-67	 images	have	 the	best	 uniformity	when	 the	HECMP	collimator	 is	used	for	data	acquisition.	The	 integral	uniformity	of	 the	 images	with	the	GPMP,	HECMP,	and	HSMP	collimators	at	(93,	184,	300,	393	keV)	is	respectively	(24%,	26%,	62%,	83%),	(17%,	18%,	22%,	38%),	and	(49%,	45%,	42%,	56%).	The	best	contrast	at	93	and	184	keV	is	obtained	 using	 the	 GPMP	 collimator,	 and	 at	 300	 and	 393	 keV	 is	 obtained	 using	 the	 HECMP	collimator.	The	attenuation	and	scatter	correction	methods	are	performing	well	for	Ga-67	data.	Finally,	only	the	first	two	photopeaks	should	be	used	with	the	GPMP	and	the	HSMP	collimators,	and	 all	 the	 four	 photopeaks	 should	 be	 used	 with	 the	 HECMP	 collimator	 for	 the	 image	reconstruction.	 In	 addition,	 GPMP	 collimator	 should	 be	 the	 collimator	 to	 be	 used	 for	 Ga-67	studies	since	the	images	with	this	collimator	have	the	best	contrast	at	93	and	184	keV	and	for	object	sizes	<	0.85	mm.			 iii	Preface	All	the	experiments	for	this	thesis	were	supervised	by	my	supervisor	Dr.	Vesna	Sossi.	Dr.	Stephan	Blinder	and	Dr.	Cristina	Rodriguez	helped	me	set	up	the	experiments	and	collecting	the	data.	 I	was	 responsible	 for	all	data	acquisition,	 image	 reconstructions,	data	analysis	 including	the	 sensitivity,	 uniformity,	 resolution	 measurements,	 and	 evaluation	 of	 the	 quantification	corrections,	and	interpretation	of	the	results.															 iv	Table	of	contents		Abstract	..............................................................................................................................	ii	Preface	..............................................................................................................................	iii	Table	of	contents	...............................................................................................................	iv	List	of	tables	.....................................................................................................................	vii	List	of	figures	...................................................................................................................	viii	1	 Introduction	................................................................................................................	1	1.1	 Statement	of	the	problem	and	the	objectives	of	the	thesis	...............................	1	1.2	 Thesis	outline	......................................................................................................	4	1.3	 Nuclear	medicine	imaging	..................................................................................	4	1.4	 Photon	interactions	with	matter	........................................................................	5	1.5	 SPECT	principles	.................................................................................................	9	1.5.1	 Attenuation	correction	.................................................................................	11	1.5.2	 Scatter	correction	.........................................................................................	13	1.6	 Small	animal	SPECT/CT	scanners	......................................................................	16	1.7	 Pinhole	collimation	...........................................................................................	19		 v	1.8	 Mediso	NanoSPECT	small	animal	SPECT	scanner	.............................................	21	1.9	 Siemens	Inveon	small	animal	SPECT	scanner	...................................................	22	1.10	 MILABs	VECTor/CT	............................................................................................	23	1.11	 Multi-pinhole	collimators	used	for	the	experiments	........................................	25	1.12	 Image	formation	...............................................................................................	27	1.12.1	 Iterative	image	reconstruction	...................................................................	28	1.12.2	 Maximum	likelihood	expectation	maximization	reconstruction	................	29	2	 Experiments	and	methods	.......................................................................................	32	2.1	 Ga-67	imaging	with	VECTor	..............................................................................	32	2.2	 Ga-67	energy	spectrum	and	count	collecting	properties	.................................	32	2.3	 Quantification	accuracy	in	Ga-67	imaging	with	VECTor	...................................	34	2.3.1	 Evaluation	of	scatter	correction	in	Ga-67	studies	........................................	34	2.3.2	 Evaluation	of	attenuation	problem	in	Ga-67	studies	...................................	36	2.3.3	 The	count-rate	characterization	...................................................................	40	2.4	 Performance	characterization	of	VECTor/CT	in	Ga-67	imaging	........................	41	2.4.1	 Ga-67point	source	sensitivity	measurements	..............................................	41	2.4.2	 Uniformity	measurements	for	Ga-67	imaging	with	VECTor	.........................	42	2.4.3	 Contrast	measurements	for	Ga-67	imaging	with	VECTor	.............................	44		 vi	2.5	 Optimization	of	Ga-67	imaging	studies	with	VECTor	........................................	45	3	 Results	......................................................................................................................	46	3.1	 Ga-67	energy	spectrum	and	count	collecting	properties	.................................	46	3.2	 Evaluation	of	quantification	accuracy	in	Ga-67	imaging	..................................	49	3.2.1	 Assessment	of	the	scatter	correction	in	Ga-67	imaging	...............................	49	3.2.2	 Evaluation	of	attenuation	problem	in	Ga-67	studies	...................................	51	3.2.3	 Characterization	of	count-rate	performance	of	VECTor	..............................	53	3.3	 Assessment	of	image	quality	factors	in	Ga-67	imaging	....................................	54	3.3.1	 Point	source	sensitivity	measurements	........................................................	54	3.3.2	 Image	uniformity	measurement	for	Ga-67	imaging	with	VECTor	................	59	3.3.3	 Resolution	and	contrast	measurements	for	Ga-67	imaging	with	VECTor	....	60	3.4	 Optimization	of	Ga-67	studies	with	VECTor	.....................................................	64	3.4.1	 Uniformity	analysis	.......................................................................................	64	3.4.2	 Contrast	analysis	..........................................................................................	65	4	 Discussion	and	conclusion	........................................................................................	67	References	........................................................................................................................	70			 		 vii	List	of	tables	TABLE	1-1.	MULTI-PINHOLE	COLLIMATORS	PROPERTIES	ACCORDING	TO	MILABS	....................................................	27	TABLE	2-1.	SCAN	PARAMETERS	FOR	THE	UNIFORMITY	PHANTOM	............................................................................	33	TABLE	2-2.	SCAN	PARAMETERS	FOR	THE	THREE	INSERT	PHANTOM	..........................................................................	35	TABLE	2-3.	SCAN	PARAMETERS	FOR	THE	ATTENUATION	EVALUATION	EXPERIMENT	................................................	39	TABLE	2-4.	THE	SCAN	PARAMETERS	FOR	THE	COUNT-RATE	STUDY	...........................................................................	41	TABLE	2-5.	SCAN	PARAMETERS	FOR	THE	POINT	SOURCE	SENSITIVITY	MEASUREMENTS	..........................................	42	TABLE	2-6.	SCAN	PARAMETERS	FOR	THE	HOT	ROD	RESOLUTION	PHANTOM	SCANS	.................................................	45	TABLE	3-1.	QUANTIFIED	CONTRAST	FOR	HOT	AND	COLD	INSERT.	THE	VALUES	ARE	DIMENSIONLESS	BECAUSE	THEY	REPRESENT	A	RATIO	..........................................................................................................................................	50	TABLE	3-2.	THE	NUMBER	OF	DETECTED	COUNTS	BY	EACH	HEAD	FROM	GA-67	PHANTOMS.	....................................	53	TABLE	3-3.	PERCENTAGE	COLLIMATOR	WALL	PENETRATION	MEASURED	FOR	THE	MPCS	AT	DIFFERENT	ENERGIES.	THE	VALUES	WERE	OBTAINED	BY	COMPARING	THE	MEASURED	SENSITIVITY	OF	THE	COLLIMATOR	WHEN	THE	SOURCE	IS	IN	THE	CFOV	AND	15	MM	AWAY	IN	THE	AXIAL	DIRECTION.	............................................................	58			 		 viii		List	of	figures	FIGURE	1-1.	ATTENUATION	OF	A	BEAM	OF	PHOTON	AFTER	PASSING	THROUGH	MATTER	WITH	THICKNESS	OF	โˆ†๐‘‹.	REPRODUCED	WITH	PERMISSION	FROM	[19].	....................................................................................................	5	FIGURE	1-2.	SCHEMATIC	REPRESENTATION	OF	THE	PHOTOELECTRIC	EFFECT.	REPRODUCED	WITH	PERMISSION	FROM	[19].	...........................................................................................................................................................	6	FIGURE	1-3.	SCHEMATIC	REPRESENTATION	OF	COMPTON	SCATTERING	MECHANISM.	REPRODUCED	WITH	PERMISSION	FROM	[19].	.....................................................................................................................................	7	FIGURE	1-4.	SCHEMATIC	REPRESENTATION	OF	PAIR	PRODUCTION	EVENT.	REPRODUCED	WITH	PERMISSION	FROM	[19].	......................................................................................................................................................................	7	FIGURE	1-5.	PHOTOELECTRIC	(ฮค),	COMPTON	(ฮฃ),	PAIR-PRODUCTION	(ฮš),	AND	TOTAL	MASS	ATTENUATION	COEFFICIENT	๐œ‡๐‘š	FOR	WATER	AT	DIFFERENT	PHOTON	ENERGIES.	REPRODUCED	WITH	PERMISSION	FROM	[19].	......................................................................................................................................................................	8	FIGURE	1-6.	BASIC	IMAGE	OPERATION	OF	A	GAMMA	CAMERA.	REPRODUCED	WITH	PERMISSION	FROM	[19].	........	9	FIGURE	1-7	THE	MOST	COMMON	COLLIMATOR	TYPES	THAT	ARE	USED	IN	SPECT	IMAGING.	REPRODUCED	WITH	PERMISSION	FROM	[19].	...................................................................................................................................	10	FIGURE	1-8.	TRIPLE	ENERGY	WINDOW	AND	DUAL	ENERGY	WINDOW	SCATTER	CORRECTION.	THE	SCATTERED	COUNTS	ARE	ESTIMATED	AS	THE	AREA	OF	THE	TRAPEZOID	OR	THE	TRIANGLE	FORMED	BY	THE	SIDE	SCATTER	WINDOW(S).	REPRODUCED	FROM	[51].	............................................................................................................	16	FIGURE	1-9		MULTI-PINHOLE	SPECT	SYSTEMS	USED	FOR	SMALL-ANIMAL	SPECT.	A,	TWO	PINHOLES	SPACED	FAR	APART	TO	AVOID	OVERLAPPING	OF	PROJECTIONS.	B,	PARTIAL	OVERLAP	IN	THE	PROJECTION	DATA	VIEWED	THROUGH	ADJACENT	PINHOLES.	REPRODUCED	WITH	PERMISSION	FROM	[19].	.............................................	18	FIGURE	1-10.	PINHOLE	COLLIMATOR	AND	IMAGE	PROJECTION	ON	TO	THE	DETECTOR	PLANE.	REPRODUCED	WITH	PERMISSION	FROM	[19].	...................................................................................................................................	19		 ix	FIGURE	1-11.	KNIFE-EDGE	OF	A	PINHOLE	COLLIMATOR	WHERE	THE	THICKNESS	IS	SMALLER.	REPRODUCED	WITH	PERMISSION	FROM	[19].	...................................................................................................................................	20	FIGURE	1-12.	NANOSPECT	SCANNER	AND	THE	FOUR	DETECTOR	HEADS.	REPRODUCED	WITH	PERMISSION	FROM	MEDICO	WEBSITE	(HTTP://WWW.MEDISO.COM/PRODUCTS.PHP?FID=2,12).	.................................................	21	FIGURE	1-13	LEFT:	INVEON	SPECT	SCANNER.	RIGHT:	T-HE	INTERNAL	COMPONENT	SHOWN	SCHEMATICALLY.	REPRODUCED	FROM	[66].	.................................................................................................................................	22	FIGURE	1-14.	VECTOR	SCANNER	AND	THE	THREE	DETECTORS	IN	A	GEOMETRY.	THE	COLLIMATOR	CYLINDER	AND	THE	BED	INSIDE	THE	COLLIMATOR	IS	SHOWN	AS	WELL.	CT	COMPONENT	IS	LOCATED	IN	THE	REAR	OF	THE	SPECT	COMPONENT.	REPRODUCED	WITH	PERMISSION	FROM	[14].	................................................................	23	FIGURE	1-15	TOP)	TRANS-AXIAL	AND	LONGITUDINAL	VIEW	OF	A	MOUSE	SIZE	CYLINDRICAL	MULTI-PINHOLE	COLLIMATOR	USED	IN	VECTOR.	THE	FOV	AND	THE	CENTRAL	FOV	ARE	CLEARLY	SHOWN	IN	BOTH	THE	TRANS-AXIAL	AND	THE	LONGITUDINAL	VIEWS.	BOTTOM)	THE	SPIRAL	BED	TRAJECTORY	INSIDE	THE	COLLIMATOR	BORE.	REPRODUCED	WITH	PERMISSION	FROM	[71].	........................................................................................	25	FIGURE	1-16.	(A).	GENERAL	PURPOSE	MULTI-PINHOLE	COLLIMATOR	[73],	(B)	HIGH	ENERGY	CLUSTERED	MULTI-PINHOLE	COLLIMATOR	[11]	,	AND	(C)	HIGH	SENSITIVITY	MULTI-PINHOLE	COLLIMATOR	[10]	USED	FOR	THE	EXPERIMENTS	OF	THIS	THESIS.	ALL	FIGURES	REPRODUCED	WITH	PERMISSION	FROM	[73],			[11],	AND	[10].	.	26	FIGURE	1-17.	GENERAL	CONCEPTS	OF	ITERATIVE	IMAGE	RECONSTRUCTION	ALGORITHM.	ECT	SYSTEM	MEANS	AN	EMISSION	COMPUTED	TOMOGRAPHY	SYSTEM	SUCH	AS	PET	OR	SPECT.	THE	IMAGE	REPRODUCED	WITH	PERMISSION	FROM	[19].	...................................................................................................................................	28	FIGURE	1-18.	SINOGRAM	REPRESENTATION	OF	A	SET	OF	PROJECTION	PROFILES	FROM	A	POINT	SOURCE.	EACH	ROW	CORRESPONDS	TO	AN	INDIVIDUAL	PROJECTION	PROFILE.	IMAGE	REPRODUCED	FROM	[76].	................	29	FIGURE	2-1.	IMAGE	OF	THE	THREE	INSERT	PHANTOM	...............................................................................................	35	FIGURE	2-2.	THE	HOUSE	MADE	LINE	SOURCE	PHANTOM	...........................................................................................	38	FIGURE	2-3.	THE	POINT	SOURCES	AND	THE	FIELD	OF	VIEW	OF	THE	SCAN	.................................................................	40	FIGURE	2-4.	PLACEMENT	OF	THE	ROIS	AND	VOIS	FOR	MEASURING	THE	UNIFORMITY	ACCORDING	TO	DIFFERENT	DEFINITIONS	OF	UNIFORMITY.	THE	SPHERICAL	YELLOW	VOI	IS	USED	FOR	THE	IU	AND	THE	RMS	NOISE	MEASUREMENT,	AND	THE	CIRCULAR	ROIS	WERE	PLACED	FOR	THE	COV	MEASUREMENTS.	...........................	43		 x	FIGURE	3-1.	THE	NORMALIZED	COUNT	HISTOGRAMS	OBTAINED	BY	SCANNING	A	UNIFORMITY	PHANTOM	USING	THE	MPCS.	.........................................................................................................................................................	46	FIGURE	3-2:	(A)	TRUE	DETECTED	COUNTS	NORMALIZED	TO	THE	ACTIVITY	IN	THE	FOV	FOR	THE	MPCS,	(B)	THE	PERCENTAGE	RELATIVE	COLLECTED	COUNTS	ALONG	WITH	THE	NORMALIZED	BRANCHING	RATIONS	FOR	THE	DATA	ACQUIRED	WITH	THE	MPCS.	....................................................................................................................	47	FIGURE	3-3.	SCATTER	FRACTION	ESTIMATED	BY	THE	TEW	METHOD	IN	THE	MAIN	ENERGY	WINDOWS	OF	GA-67	USING	DIFFERENT	MPCS.	...................................................................................................................................	48	FIGURE	3-4.	RECONSTRUCTED	IMAGES	OF	THE	THREE	INSERT	PHANTOM	................................................................	49	FIGURE	3-5.	QUANTIFIED	RATIO	OF	HOT	:	WARM,	AND	COLD	:	WARM	ACTIVITY	CONCENTRATIONS	OBTAINED	FROM	THE	RECONSTRUCTED	IMAGES.	..............................................................................................................	50	FIGURE	3-6.	RECONSTRUCTED	IMAGES	OF	THE	LINE	SOURCE	PHANTOM	(A)	IN	AIR	AND	(B)	IN	WATER	..................	51	FIGURE	3-7.	THE	DIFFERENCE	BETWEEN	THE	SCANS	OF	THE	PHANTOM	IN	AIR	AND	IN	SCATTERING	MEDIUM	QUANTIFIED	EXPERIMENTALLY	AND	THEORETICALLY.	......................................................................................	52	FIGURE	3-8.	THE	RECONSTRUCTED	ACTIVITY	CONCENTRATION	VALUES	OF	THE	LINE	SOURCE	OBTAINED	FROM	THE	IMAGES	OF	THE	LINE	SOURCE	IN	AIR	AND	WATER	FOLLOWED	BY	SCATTER	AND	ATTENUATION	CORRECTION.	...........................................................................................................................................................................	52	FIGURE	3-9.	OBSERVED	COUNT-RATE	VS	THE	ACTIVITY	IN	THE	FIELD	OF	VIEW	THE	VECTOR	DETECTOR	HEADS	WITH	GA-67	SOURCE	MEASUREMENTS.	.....................................................................................................................	54	FIGURE	3-10.	SENSITIVITY	PROFILES	OF	THE	GPMP	COLLIMATOR	MEASURED	ALONG	THE	(A)	X	AXIS,	(B)	Y	AXIS,	AND	(C)	Z	AXIS	OF	THE	COLLIMATOR	.........................................................................................................................	55	FIGURE	3-11.	SENSITIVITY	PROFILES	OF	THE	HECMP	COLLIMATOR	MEASURED	ALONG	THE	(A)	X	AXIS,	(B)	Y	AXIS,	AND	(C)	Z	AXIS	OF	THE	COLLIMATOR	.................................................................................................................	56	FIGURE	3-12.	SENSITIVITY	PROFILES	OF	THE	HSMP	COLLIMATOR	MEASURED	ALONG	THE	(A)	X	AXIS,	(B)	Y	AXIS,	AND	(C)	Z	AXIS	OF	THE	COLLIMATOR	.........................................................................................................................	57	FIGURE	3-13.	THE	PEAK	SENSITIVITY	OF	THE	COLLIMATORS	MEASURED	AT	93	KEV,	184	KEV,	300	KEV,	AND	393	KEV.	...........................................................................................................................................................................	58		 xi	FIGURE	3-14.	IMAGES	OF	THE	UNIFORMITY	PHANTOM	RECONSTRUCTED	FROM	SEPARATE	PHOTO	PEAK	COUNTS	ARE	DISPLAYED	FOR	THE	GPMP	(TOP),	THE	HECMP	(MIDDLE),	AND	THE	HSMP	(BOTTOM)	COLLIMATORS.	THE	IMAGES	ARE	SMOOTHED	WITH	A	GAUSSIAN	FILTER	WITH	FWHM	OF	1.0	MM.	...............................................	59	FIGURE	3-15.	UNIFORMITY	MEASUREMENTS	FOR	GA-67	IMAGES	USING	ALL	THE	DEFINITIONS	OF	UNIFORMITY.	..	60	FIGURE	3-16.		(A)	IMAGES	OF	THE	RESOLUTION	PHANTOM	1,	AND	(B)	RESOLUTION	PHANTOM	2	RECONSTRUCTED	FROM	SEPARATE	ENERGY	WINDOWS	USING	ALL	THE	MPCS.	...........................................................................	61	FIGURE	3-17.	THE	QUALITATIVE	SMALLEST	ROD	SIZE	RESOLVABILITY	FOR	GA-67	IMAGING	USING	THE	DIFFERENT	MPCS.	.................................................................................................................................................................	62	FIGURE	3-18.	CONTRAST	AS	A	FUNCTION	OF	ROD	DIAMETER	MEASURED	FROM	RESOLUTION	PHANTOM	IMAGES	RECONSTRUCTED	P1,	P2,	P3,	AND	P4	PHOTO	PEAKS	OF	GA-67	........................................................................	63	FIGURE	3-19.	UNIFORMITY	MEASUREMENTS	FOR	GA-67	IMAGES	WHEN	MULTIPLE	PHOTO	PEAKS	ARE	COMBINED	DURING	THE	RECONSTRUCTION.	.......................................................................................................................	64	FIGURE	3-20.	(A)	IMAGES	OF	THE	RESOLUTION	PHANTOM	1,	AND	(B)	RESOLUTION	PHANTOM	2	RECONSTRUCTED	WITH	INCLUDING	MULTIPLE	PHOTO	PEAKS	USING	ALL	THE	MPCS.	..................................................................	65	FIGURE	3-21.	CONTRAST	AS	A	FUNCTION	OF	ROD	SIZE	MEASURED	FOR	IMAGES	FORMED	BY	COMBINING	PHOTO	PEAKS.	................................................................................................................................................................	66				 1		1 Introduction	1.1 Statement	of	the	problem	and	the	objectives	of	the	thesis	Ga-67	 SPECT	 imaging	 used	 to	 be	 the	 gold	 standard	 for	 inflammation	 and	 cancer	diagnosis	before	PET	became	clinically	available	 [1]โ€“[3].	With	 the	 successful	establishment	of	FDG	 (Fluorodeoxyglucose)	 PET,	 the	 use	 of	 Ga-67	 imaging	 has	 decreased,	 however	 it	 is	 still	widely	used	in	clinics	in	acute	and	chronic	infection,	inflammation,	and	lymphoma	scintigraphy	scans	[4]โ€“[7].	There	is	an	increasing	interest	in	the	preclinical	use	of	Ga-67,	since	it	binds	to	a	variety	 of	 proteins	 and	 anti-bodies;	 its	 labeling	 is	 relatively	 easy	 and	 it	 has	 suitable	 physical	properties	[8],	which	makes	it	a	favorable	isotope	for	bio-distribution	studies	and	testing	of	new	compounds	or	potential	novel	therapeutic	agents	[8],	[9].		Ga-67	decays	with	half-life	of	78.24	hours	by	emitting	gamma	rays	of	P1:	93	keV	(42%),	P2:	184	keV	(21%),	P3:	300	keV	(17%)	and	P4:	393	keV	(5%).	It	is	necessary	to	characterize	the	detection	systems	used	for	collecting	Ga-67	data,	due	to	the	presence	of	high	and	low	energy	gammas	in	the	decay	scheme	of	Ga-67.	The	branching	ratios	of	emitted	gammas	with	energies	greater	 than	393	keV	 is	 less	 than	1%	and	therefore	those	gammas	are	not	suitable	 for	 image	formation.	In	SPECT	imaging	with	general	purpose	collimators,	P1	and	P2	data	are	usually	used	for	image	formation.	P3	and	P4	gammas,	have	higher	probability	of	Compton	interactions	in	the	object	and	the	collimator	and	therefore	consequent	loss	of	spatial	information	in	the	images.	The	presence	of	high	energy	gammas	in	Ga-67	imaging	may	lead	to	two	problems,	even	if	the	appropriate	acquisition	energy	windows	are	used:	1-	down	scattering,	and	2-	collimator	wall	penetration.	Down	scattering	happens	when	a	Compton	scattered	gamma	 is	detected	 in	the	 lower	 energy	 window	 and	 with	 wrong	 gamma	 positioning.	 Photons	 that	 penetrate	 the	collimator	 introduce	 an	 overall	 background	 in	 the	 images	 with	 loss	 of	 correct	 spatial	information	about	the	source	distribution.	Given	that	Ga-67	emits	gammas	in	a	relatively	wide	energy	 range,	 images	obtained	with	different	 types	of	multi-pinhole	 collimators	 (MPCs)	 have		 2	different	characteristics	and	qualities.	For	this	thesis,	the	performance	of	three	types	of	multi	pinhole	collimator	was	evaluated	in	imaging	Ga-67	with	a	small	animal	SPECT	scanner	that	will	be	described	 in	 section	1.10.	 The	 collimators	 are	 a	 general,	 purpose	multi	 pinhole	 collimator	(GPMP),	a	high	energy	clustered	multi	pinhole	collimator	(HECMP),	and	a	high	sensitivity	multi	pinhole	collimator	(HSMP).	Although	comparing	the	performance	of	the	HSMP	collimator	with	the	 other	 two	 MPCs	 might	 not	 be	 a	 sound	 comparison	 due	 to	 their	 different	 application,	performance	evaluation	of	this	collimator	is	essential	to	discover	the	range	of	the	applicability	of	this	MPC	in	imaging	Ga-67.	All	the	mentioned	three	collimators	have	been	evaluated	by	the	manufacturer	or	other	groups	 in	 acquiring	 SPECT	 images	 of	 Tc-99m	 and	 F-18	 [10]โ€“[15].	 But	 to	 the	 best	 of	 our	knowledge,	 no	 study	 has	 been	performed	 to	 compare	 the	 performance	of	 the	 collimators	 in	imaging	Ga-67	considering	the	unique	decay	scheme	characteristics	of	Ga-67.		Evaluating	the	performance	of	the	MPCs	in	imaging	Ga-67	is	the	main	motivation	for	this	thesis.	This	study	will	yield	guidelines	for	 imaging	Ga-67	using	the	aforementioned	MPCs,	e.g.	an	optimum	selection	of	photopeaks	specific	to	each	collimator	and	the	object	dimension	range	over	which	each	MPC	performs	well.	One	 of	 the	 assumptions	 for	 this	 study	 is	 that,	 images	 obtained	 with	 the	 HECMP	collimator	may	be	of	higher	quality	compared	to	those	obtained	with	low	energy	multi	pinhole	collimators;	 indeed,	counts	from	all	 four	main	photo	peaks	could	 in	principle	be	included	into	the	 reconstruction,	 thus	 increasing	 the	 statistical	 quality	 of	 the	 data.	 This	 hypothesis	will	 be	evaluated	by	performing	this	study.	The	following	metrics	were	investigated	in	characterization	tests	for	comparing	data	obtained	with	the	MPCs:	energy	spectra,	count	acquisition	properties	from	an	extended	source	 (similar	 to	the	detection	sensitivity	 from	an	extended	source	rather	than	 a	 point	 source),	 detection	 sensitivity,	 image	 uniformity,	 resolution,	 and	 contrast	 over	 a	wide	object	dimensions.		 3	In	 addition	 to	 the	 performance	 characterization	 and	Ga-67	 optimization	 problem,	 the	factors	that	affect	the	quantification	accuracy	of	the	acquired	Ga-67	data	should	be	studied	and	the	extent	of	each	limiting	factor	should	be	identified.		Quantitative	accuracy	of	the	measurement	of	the	radioactivity	distribution	in	biological	tissues	is	compromised	by	several	physical	factors	including,	(i)	photon	attenuation,	(ii)	photon	Compton	 scattering	 in	 the	 tissue	 and	 detection	 system,	 (iii)	 partial	 volume	 effect	 (PVE),	 (iv)	physiological	 motion	 of	 the	 subject	 being	 images	 during	 the	 scans,	 etc.	 These	 factors	 if	 not	corrected	 for,	 result	 in	 inaccurate	 quantification	 of	 radioactivity	 concentration	 in	 vivo.	 There	are	also	other	effects	due	to	tracer	decay,	detection	system	dead	time	and	individual	detector	efficiency,	which	require	other	data	normalization	processes.		The	 main	 limiting	 factors	 in	 SPECT	 image	 quantification	 are	 attenuation	 and	 then	Compton	scattering.	In	the	domain	of	small	animal	imaging,	the	magnitudes	of	the	attenuation	and	scatter	are	smaller	compared	to	the	clinical	scanners	due	to	the	small	 size	of	 the	targets	and	 traditionally	 these	quantitative	corrections	were	not	performed	 for	 the	data	acquired	by	these	scanners.	Nowadays,	since	there	 is	an	 increasing	 interest	 in	pre-clinical	research,	to	get	precisely	and	accurately	quantified	images,	these	corrections	are	inevitable.		Evaluation	of	quantitative	corrections	in	Ga-67	imaging	is	another	goal	of	this	thesis.	For	the	 purpose	 of	 this	 study,	 Compton	 scattering,	 attenuation,	 and	 count	 rate	 effects	 in	 Ga-67	imaging	were	evaluated	by	performing	several	phantom	experiments.	The	objectives	of	this	thesis	can	be	listed	as	follows:	1. Performance	characterization	of	MILABs	VECTor/CT	and	the	MPCs	in	imaging	Ga-67	2. Quantification	accuracy	in	imaging	Ga-67	3. Optimization	of	data	acquisition	protocols	for	Ga-67	scans		 4	1.2 Thesis	outline	Chapter	 one	 discusses	 the	 statement	 of	 the	 problem,	 describes	 the	 general	 	 thesis	layout,	 an	 introduction	 to	 nuclear	 medicine	 imaging,	 the	 scanner	 that	 was	 used	 for	 the	experiments,	 the	MPCs	 that	 were	 characterized,	 and	 Ga-67	 imaging.	 In	 chapter	 two,	 all	 the	experiments	 and	 methods	 pertaining	 to	 aforementioned	 goals	 will	 be	 explained.	 In	 chapter	three	the	results	will	be	presented	and	discussed	and	chapter	four	will	proceed	with	conclusion	of	the	study.			1.3 Nuclear	medicine	imaging	Nuclear	medicine	imaging	emerged	by	the	innovations	of	Hal	O.	Anger	in	1950s.	He	first	invented	 a	well	 counter	 by	 drilling	 a	 hole	 into	 a	 scintillation	 crystal	 and	 placed	 a	 radioactive	sample	in	it	to	increase	the	count	measuring	efficiency	up	to	98%	in	1950.	This	made	it	possible	to	measure	small	amounts	of	radioactivity,	and	 is	still	 the	most	widely	used	nuclear	medicine	instrument	in	every	nuclear	medicine	lab.	Hal	Anger	created	the	foundations	for	sophisticated	nuclear	 imaging	systems	in	use	today	by	designing	and	developing	the	first	gamma	camera	 in	1957.	He	also	designed	the	first	positron	emission	detector	in	1959,	which	used	the	coincidence	detection	 technique	 [16].	 Current	 gamma	 cameras	 and	 SPECT	 scanners	 function	 based	 on	Anger	camera	[17],	[18].	Nuclear	 imaging	scans	start	with	the	administration	of	a	biological	compound	which	 is	tagged	by	a	radioisotope.	Photons	that	are	emitted	from	these	radioisotopes	are	detected	by	scintillation	detectors.	Data	are	collected	 in	either	2D	or	3D	mode	and	the	 information	about	radioactivity	 distribution	 in-vivo	 is	 displayed	 after	 sophisticated	 image	 reconstruction	techniques	[19].	Gamma	cameras	provide	a	2D	distribution	of	the	intensity	of	the	radioactivity	sources	in	physiological	organs.	This	is	referred	to	as	scintigraphy	scans	[20].	3D	distribution	of	radioactivity	is	done	through	single	photon	emission	computed	tomography	(SPECT)	[21],	[22]	and	Positron	Emission	Computed	Tomography	(PET)	[23],	[24].	Since	the	scope	of	this	thesis	is	performance	evaluation	of	VECTor,	 i.e.	a	small	animal	SPECT	scanner,	and	all	the	experiments		 5	were	 performed	 using	 that	 scanner,	 a	 description	 of	 SPECT	 will	 be	 given	 in	 the	 following	sections	with	a	very	brief	description	of	PET	scanners.		The	emitted	photons	from	the	radioisotopes	undergo	different	types	of	 interactions	 in	tissues	 and	 the	 detection	 system	before	 they	 are	 collected	 for	 image	 reconstruction.	 A	 brief	description	of	each	interaction	type	will	be	given	in	section	1.4.		1.4 Photon	interactions	with	matter	When	 a	 beam	 of	 photons	 passes	 through	 a	material	 with	 thickness	โˆ†๐‘‹,	 the	 photons	might	undergo	different	interactions.	The	most	important	interactions	of	photons	with	matter	that	are	of	interest	of	nuclear	medicine	are	photoelectric	effect,	Compton	scattering,	and	pair	production.		Figure	1-1.	Attenuation	of	a	beam	of	photon	after	passing	through	matter	with	thickness	of	โˆ†๐‘‹.	Reproduced	with	permission	from	[19].	In	the	photoelectric	effect,	an	atom	absorbs	the	total	energy	of	an	incident	photon	and	the	 photon	 energy	 is	 used	 to	 eject	 an	 orbital	 electron	 from	 the	 atom,	 which	 is	 called	 a	photoelectron	(Figure	1-2).	The	kinetic	energy	of	 the	photoelectron	 is	equal	 to	the	difference	between	the	incident	photon	energy	and	the	binding	energy	of	the	electron	shell	from	which	it		 6	was	ejected.	 In	 the	photoelectric	 effect,	 the	photon	 is	 totally	 removed	 from	 the	 initial	 beam	[19].		Figure	1-2.	Schematic	representation	of	the	photoelectric	effect.	Reproduced	with	permission	from	[19].	Compton	 scattering	 is	 an	 interaction	 between	 a	 photon	 and	 an	 outer-shell	 orbital	electron	of	an	atom	(Figure	1-3).	The	photon	does	not	disappear	in	Compton	scattering,	but	it	is	deflected	with	scattering	angle	ฮธ.	Part	of	the	photon	energy	is	transferred	to	the	recoil	electron	and	 the	 photon	 continues	 in	 the	 deflected	 direction	with	 a	 lower	 energy.	 The	 energy	 of	 the	scattered	photon	and	the	recoil	electron	are	obtained	according	to:	๐ธ'( = ๐ธ* [1 + (๐ธ* 0.511)(1 โˆ’ cos ๐œƒ)]	๐ธ9: = ๐ธ* โˆ’ ๐ธ'( 	where	๐ธ'( 	 ,	๐ธ*,	 and	 	๐ธ9:are	 the	 scattered	 photon,	 incident	 photon,	 and	 the	 recoil	 electron	energies	in	MeV,	respectively.				 7		Figure	1-3.	Schematic	representation	of	Compton	scattering	mechanism.	Reproduced	with	permission	from	[19].	Pair	production	 is	 the	 result	of	 the	 interaction	of	a	photon	with	 the	electric	 field	of	a	charged	particle.	 In	pair	production,	 the	photon	disappears	and	 its	energy	 is	used	to	create	a	positron-electron	pair	(Figure	1-4).	The	minimum	photon	energy	required	for	pair	production	to	occur	is	1.022	MeV.				Figure	1-4.	Schematic	representation	of	pair	production	event.	Reproduced	with	permission	from	[19].		 8	The	mass	attenuation	coefficient	๐œ‡;	of	the	medium	at	the	energy	of	the	beam	can	be	broken	down	into	different	components	according	to	๐œ‡; = ๐œ + ๐œŽ + ๐œ…	where	 ๐œ	 is	 the	 contribution	 by	 the	 photo-electric	 effect,	 ๐œŽ	is	 the	 contribution	 by	 Compton	scattering,	and	๐œ…	 is	 the	contribution	by	pair	production.	Figure	1-5	shows	 the	contribution	of	different	interactions	in	the	mass	attenuation	coefficient	of	water	for	different	energies	of	the	incident	 beam.	 For	 the	 energy	 of	 the	 isotopes	 used	 in	 nuclear	 medicine	 imaging,	 the	 main	attenuating	factor	is	the	Compton	scattering	effect	(99%)	in	water.		Figure	1-5.	Photoelectric	(ฯ„),	Compton	(ฯƒ),	pair-production	(ฮบ),	and	total	mass	attenuation	coefficient	๐œ‡;	for	water	at	different	photon	energies.	Reproduced	with	permission	from	[19].		Attenuation	correction	is	one	of	the	main	quantitative	corrections	in	SPECT	imaging.			 9	1.5 SPECT	principles	Single	photon	emission	computed	tomography	(SPECT)	visualizes	in-vivo	distribution	of	single	gamma	emitters	or	multiple	gamma	emitters.	The	most	common	radioisotope	used	for	SPECT	imaging	is	TC-99m	with	half	life	of	6	hours.	TC-99m	is	the	daughter	product	of	Mo-99.	TC-99m	decays	 to	 TC-99	by	 emission	of	 140	 keV	 gammas.	Most	 clinical	 SPECT	 scanners	 operate	based	 on	 a	 rotating	 gamma	 camera	 or	 anger	 camera,	 where	 2D	 projections	 from	 different	angles	 are	 collected	 to	 reconstruct	 a	 3D	 image	 volume	 [19],	 [25].	 There	 are	 also	 some	specialized	SPECT	 scanners	with	 fixed	detectors	 that	 are	used	 for	 cardiac	 imaging	or	 in	 small	animal	imaging.	The	 main	 components	 of	 gamma	 cameras	 are	 a	 collimator,	 a	 large	 area	 NaI(TI)	scintillation	crystal,	a	light	guide	and	an	array	of	photo	multiplier	tubes	(PMT)	shown	in	Figure	1-6.		Figure	1-6.	Basic	image	operation	of	a	gamma	camera.	Reproduced	with	permission	from	[19].		 10	A	 collimator	 is	 usually	 made	 of	 lead,	 tungsten,	 or	 materials	 with	 high	 attenuation	coefficient	 that	 stops	 the	 rays	 from	 penetrating	 through	 the	 septa.	 The	 collimator	 is	 closest	component	 to	 the	 object	 and	 defines	 the	 acceptance	 angle	 for	 detection	 of	 the	 emitted	gammas.	 A	 collimator	 projects	 an	 image	 (I)	 of	 the	 source	 (O)	 distribution	 onto	 the	 detector	plane	by	accepting	only	certain	rays	parallel	to	the	holes	(this	type	of	collimator	forms	the	most	common	 type	 known	 as	 parallel	 hole	 collimator)	 to	 reach	 the	 detector.	 The	 most	 common	collimator	 types	 are	 shown	 in	 Figure	 1-7.	 The	 parallel-hole	 collimator	 is	 the	 most	 popular	collimator	used	in	clinics	which	consists	of	a	 lead	plate	with	closely	packed	parallel	hexagonal	holes.	The	image	size	is	the	same	as	the	object	size.	The	pinhole	collimator	is	the	most	popular	collimator	used	in	pre-clinical	research	which	will	be	described	later.	The	gamma	energy	range	and	 the	 desired	 resolution/sensitivity	 determines	 the	 selection	 of	 the	 collimator	 parameters	such	as	hole	diameter,	septal	length	and	the	septal	thickness	of	the	collimator.																		 																																					 	Figure	1-7	The	most	common	collimator	types	that	are	used	in	SPECT	imaging.	Reproduced	with	permission	from	[19].			 11	The	thickness	of	the	scintillation	crystal	is	about	1	cm,	which	provides	a	high	detection	probability	 for	 the	 gamma	 energy	 range	 of	 isotopes	 used	 in	 SPECT	 imaging.	 The	 scintillation	crystals	 should	 have	 a	 high	 density,	 high	 effective	 atomic	 number,	 and	 high	 photon	 yield.	NaI(Tl)	 is	 the	most	 common	 scintillation	 crystal	 used	 in	 nuclear	medicine.	 It	 has	 a	 density	 of	3.67	gr/cm3,	an	effective	atomic	number	of	50,	and	a	photon	yield	of	38	per	keV.	The	index	of	refraction	of	NaI(Tl)	crystal	is	1.85,	and	its	peak	emission	is	at	415	nm.	When	a	gamma	interacts	in	the	crystal,	 light	photons	are	created.	The	number	of	 light	photons	 is	 proportional	 to	 the	 energy	 deposited	 in	 the	 crystal.	 The	 generated	 light	 photons	reach	the	PMTs	through	light	guides.		The	PMTs	convert	the	light	photon	signal	to	an	electronic	signal.	PMTs	consist	of	a	photocathode,	an	anode	and	dynode	chain	which	amplify	the	number	of	electrons	created	at	 the	photocathode.	This	 results	 in	a	measurable	electrical	pulse	at	 the	anode	of	the	PMTs	that	are	hit	by	the	 light	photons.	The	amplitude	of	the	electronic	signal	 is	proportional	to	the	location	of	the	gamma	photon	interaction,	and	the	energy	deposited	in	the	crystal.	 The	 output	 electronic	 signals	 are	 processed	 through	 logical	 and	 discrimination	processes	to	sort	out	the	interactions	that	should	contribute	to	the	image	[19],	[26].	The	 main	 quantitative	 corrections	 for	 SPECT	 imaging	 are	 attenuation	 and	 scatter	correction	which	are	necessary	steps	to	acquire	an	accurate	quantitative	image	[27]โ€“[29].	1.5.1 Attenuation	correction		Attenuation	refers	to	the	loss	of	gammas	that	are	incident	on	the	detectors.	The	loss	of	gammas	can	happen	through	photoelectric	absorption	and	Compton	scattering	for	the	energy	range	of	 isotopes	that	are	used	for	SPECT	imaging	(Energy	<	400	keV).	As	an	example	for	140	keV	 gammas	 passing	 through	 water,	 more	 than	 99%	 of	 attenuation	 is	 due	 to	 Compton	scattering	 and	 less	 than	 1%	 is	 due	 to	 photoelectric	 effect.	 Photoelectric	 effect	 completely	removes	 the	gamma	 from	the	beam	but	 the	 in	Compton	scattering,	 the	gamma	 is	dislocated	with	 a	 lower	 energy.	 Attenuation	 correction	 in	 SPECT	 imaging	 is	 depth	 dependent	 [19].	 The	simplest	 attenuation	 correction	method	 is	 assigning	 a	 constant	 attenuation	 factor	 to	 all	 the		 12	tissues	in	the	image.	This	method	is	based	on	Chang	attenuation	correction	method	[30].	In	this	method	it	is	assumed	that	the	linear	attenuation	coefficient	at	a	given	energy	is	constant	for	all	body	 tissues.	 	 The	 attenuation	 correction	 factor	 for	 each	 pixel	 of	 the	 image	 is	 calculated	according	to	๐ด๐ถ๐น = 	 11๐‘ ๐‘’DEFGHIJK 	where	 N	 is	 the	 number	 of	 projection	 views,	 ยต	 is	 the	 constant	 linear	 attenuation	coefficient,	 and	 ๐‘‘I 	 is	 the	 attenuation	 path	 length	 of	 the	 pixel.	 The	 reconstructed	 image	 is	corrected	pixel	based	by	multiplication	by	the	corresponding	ACF.		Chang	 based	methods	 yield	 reasonable	 results	 in	 the	 brain	 and	 abdomen,	where	 the	attenuation	coefficient	values	are	more	uniform,	since	the	amount	of	bone	and	air	spaces	are	small.	However,	these	methods	do	not	work	well	in	the	thorax	or	in	the	pelvic	region	[19].		A	 more	 accurate	 attenuation	 correction	 approach	 for	 SPECT	 imaging	 that	accommodates	 regions	 with	 non	 uniform	 attenuation	 is	 to	 derive	 the	 tissue	 attenuation	properties	using	a	transmission	scan.	This	can	be	done	using	an	external	radiation	source	such	as	a	radionuclide	(similar	to	the	PET	transmission	scan)	[31]	or	computed	tomography	(CT)	scan	[32].	 The	 transmission	 scan	 is	 used	 to	 acquire	 transmission	 profiles	 that	 reflect	 the	 linear	attenuation	coefficient	of	the	tissue	or	the	attenuation	map.		CT	 based	 attenuation	 correction	 is	 the	 common	method	 in	 recent	 commercial	 hybrid	SPECT/CT	 scanners.	 CT	 images	 show	 the	 linear	 attenuation	 coefficient	 (ยต)	 of	 tissues	 at	 the	effective	energy	of	the	x-ray	beam.	These	ยต	values	are	converted	to	ยต	values	at	the	energy	of	the	 SPECT	 isotope	 using	 different	 energy	 mapping	 methods	 [33]โ€“[35].	 The	 most	 common	method	is	using	a	bilinear	curve	that	converts	the	Hounsfield	Units	of	the	CT	image	to	ยต	values	at	 the	 energy	 of	 the	 radioisotope.	 The	 derived	 attenuation	 map	 can	 be	 used	 in	 the	 Chang	method	 by	 taking	 into	 account	 the	 non-uniform	 attenuation	 at	 each	 pixel	 location	 to	 more		 13	accurately	 compute	 the	 attenuation	 correction	 factors.	 The	 attenuation	 map	 can	 also	 be	incorporated	directly	into	iterative	reconstruction	algorithms	[34].		1.5.2 Scatter	correction	Detection	 of	 scattered	 counts	 degrades	 the	 contrast	 in	 the	 images	 and	 should	 be	accounted	 for	 in	 order	 to	 have	 an	 accurate	 attenuation	 correction.	 Detection	 of	 scattered	counts	is	the	result	of	Compton	interaction	in	the	body,	collimator,	and	the	scintillation	crystal	[36].		There	 are	 several	 approaches	 for	 scatter	 correction	 that	 range	 from	 very	 simple	 and	approximate	methods	to	theoretically	ideal	but	complex	correction	methods.	In	general	scatter	correction	 techniques	 are	 performed	 by	 direct	 measurement	 or	 scatter	 spatial	 response	modelling	(or	a	combination	of	both)	to	estimate	the	scatter	present	in	the	acquired	photopeak	data.	Examples	of	direct	measurement	methods	include	dual	and	triple	energy	window	scatter	correction	 that	are	described	 in	1.5.2.1.	Examples	of	modelling	approaches	 include	Analytical	models	 based	 on	 Kleinโ€“Nishina	 scatter	 equations	 [37],	 transmission-dependent	 convolution	subtraction	 [38],	 and	Object	 shape	 or	 slab-derived	 scatter	 estimation	 [39].	 It	 is	 important	 to	know	that	correction	methods	can	fall	into	two	other	categories:	scatter	correction	based	on	a	measured	 or	 modelled	 scatter	 estimate	 that	 is	 constant	 and	 correction	 based	 on	 a	 scatter	estimate	that	is	iteratively	updated	during	the	reconstruction.	In	the	first	category	correction	is	done	 by	 direct	 subtraction	 of	 the	 scatter	 estimate	 from	 the	 acquired	 projections	 or	incorporation	 into	 the	 iterative	 reconstruction,	 irrespective	 of	 whether	 measurement	 or	modelling	 is	 used	 to	 estimate	 the	 scatter.	 	 In	 the	 second	 category,	 the	 scatter	 estimate	 is	included	in	the	forward	projection	step	of	the	iterative	reconstruction	[40].		In	 reconstruction	 based	 scatter	 correction	methods,	 an	 estimated	 attenuation	map	 is	used	to	calculate	the	contribution	of	scatter	 in	the	projection	data	[41],	 [42].	The	accuracy	of	reconstruction	based	scatter	correction	methods	depends	on	the	accuracy	of	modeling	scatter,	which	 is	 computationally	 intensive	 [43].	 As	 an	 example	 for	 reconstruction	 of	 a	 64	 x	 64	 x	 64		 14	image	volume	acquired	from	64	projection	views,	a	reconstruction	system	matrix	consisting	of	644	point	spread	functions	each	consisting	of	64	x	64	terms	is	required.	In	addition,	the	system	matrix	used	in	reconstruction	ideally	should	be	patient	specific.	Such	a	matrix	could	be	obtained	by	 obtaining	 the	 patient	 attenuation	 map	 in	 which	 a	 point	 source	 can	 be	 positioned	independently	in	each	voxel	to	allow	measurement	of	the	point	spread	functions.	However,	the	point	source	imaging	time	is	prohibitive	in	terms	of	clinical	use	and	memory	and	disk	storage.	Therefore,	the	terms	in	the	matrix	are	normally	calculated	as	needed	without	saving	them,	and	with	various	levels	of	approximation.			An	 alternative	 to	 point	 spread	 function	 measurement	 is	 scatter	 function	 modelling	based	 on	 Monte	 Carlo	 simulations	 [44].	 One	 method	 is	 modeling	 the	 system	 response	 to	primary	 and	 scattered	 counts	 using	 two	 separate	 Gaussian	 functions.	 A	 distance	 dependent	Gaussian	 for	 the	primary	photons,	and	a	depth-dependent	Gaussian	 for	 the	scatter	response.	The	scatter	response	is	then	convolved	with	the	appropriate	system	response	for	the	distance	from	the	collimator	[45].		Another	modelling	approach	 is	 to	 calculate	 the	 scatter	 response	analytically	using	 the	the	 Klein-Nishina	 formula	 for	 Compton	 scattering	 using	 the	 patientโ€™s	 attenuation	maps	 [46].	Analytical	calculation	of	scatter	function	yields	a	noise	free	estimates	in	a	short	amount	of	time	compared	to	Monte	Carlo	simulation	methods	where	noise	in	the	estimate	and	calculation	time	are	directly	 linked.	 To	 reduce	 the	 calculation	 time,	only	 first	 and	 second	order	 scattering	are	included	in	the	calculation	[47].		The	scatter	correction	method	performed	on	the	images	obtained	by	the	VECTor	for	the	purpose	 of	 this	 thesis	 is	 done	 using	 the	 triple	 energy	 window	 (TEW)	 and	 therefore	 it	 is	described	in	1.5.2.1.	1.5.2.1 Dual	energy	window	(DEW)	and	triple	energy	window	(TEW)	scatter	correction	Dual	energy	window	(DEW)	and	triple	energy	window	(TEW)	scatter	correction	are	the	most	 popular	 methods	 in	 SPECT	 data	 acquisition	 (Figure	 1-8)[48].	 Energy	 window	 based		 15	methods	 estimate	 the	 scatter	 contribution	 within	 the	 photopeak	 window	 using	 simple	geometric	shapes	(area	of	a	trapezoid	or	a	triangle),	but	they	are	frequently	applied	for	clinical	use	because	of		their	speed	and	simplicity	[32].	The	acquired	projection	data	are	composed	of	primary	photons	and	scattered	photons.	Direct	measurement	 scatter	 correction	methods	 such	 as	DEW	or	 TEW	 correct	 the	 projection	data	for	scatter	but	enhance	the	statistical	noise	in	the	data,	because	these	methods	subtract	the	 scatter	 estimate	 from	 the	projection	data	 and	 the	noise	 is	 enhanced	 the	projection	data	[32],	 [40].	 Energy	window	methods	 	 estimate	 the	 amount	 of	 scatter	 in	 a	 photo-peak	 energy	window	 pixel	 by	 placing	 additional	 energy	 windows	 beside	 the	 photo-peak	 window,	 and	therefore	a	scatter	estimate	is	obtained	for	each	pixel	in	the	photo-peak	window	data	[49].	The	scatter	 projection	 is	multiplied	by	 a	 scaling	 factor	 followed	by	 subtraction	 from	 the	 acquired	projection	to	yield	a	scatter	corrected	projection.	In	this	method	it	is	assumed	that,	the	spatial	distribution	 of	 Compton	 scattering	 in	 the	 photo-peak	window	and	 the	 scatter	window	 is	 the	same	[50].		In	DEW	scatter	correction	methods,	the	scatter	is	estimated	as	the	area	under	a	triangle		with	height	equal	to	the	average	count	per	keV	in	the	lower	scatter	window,	and	with	the	base	as	the	width	of	the	photo-peak	window	in	keV	(Figure	1-8).	 In	TEW	method,	an	upper	scatter	window	 is	 added	 to	 correct	 for	 the	 down-scattered	 counts	 โ€“	 and	 also	 for	 a	 finite	 energy	resolution.	With	the	addition	of	the	upper	window,	scatter	is	estimated	as	the	area	under	the	trapezoid	formed	by	the	heights	of	the	counts	per	keV	in	each	of	the	two	scatter	windows,	and	a	base	with	the	width	of	the	photo-peak	window	[48].		๐‘†๐‘๐‘Ž๐‘ก๐‘ก๐‘’๐‘Ÿ	๐ธ๐‘ ๐‘ก๐‘–๐‘š๐‘Ž๐‘ก๐‘’ = ๐ถ๐‘œ๐‘ข๐‘›๐‘ก๐‘ WXY:9๐‘Š๐‘–๐‘‘๐‘กโ„ŽWXY:9 + ๐ถ๐‘œ๐‘ข๐‘›๐‘ก๐‘ \]]:9๐‘Š๐‘–๐‘‘๐‘กโ„Ž\]]:9 ร—๐‘Š๐‘–๐‘‘๐‘กโ„Ž]_X`XD]:ab2 		 16		Figure	1-8.	Triple	energy	window	and	dual	energy	window	scatter	correction.	The	scattered	counts	are	estimated	as	the	area	of	the	trapezoid	or	the	triangle	formed	by	the	side	scatter	window(s).	Reproduced	from	[51].	1.6 Small	animal	SPECT/CT	scanners	Pre-clinical	SPECT	scanners	are	developed	for	the	purpose	of	small	animal	imaging	and	they	play	an	 increasingly	 important	role	 in	biomedical	 research.	They	are	used	to	study	small	animal	models	of	human	disease	 in	neuroscience,	 cardiovascular	 research,	 cancer	 treatment,	and	development	of	new	drugs	[52]โ€“[55].	The	 small	 animal	 SPECT	 scanners	 are	 combined	with	 a	 CT	 scanner	 for	 the	purpose	of	attenuation	correction.	The	CT	components	of	 these	systems	usually	use	a	 lower	voltage	and	lower	current	x-ray	tubes	compared	to	the	clinical	CT	scanners,	because	of	the	smaller	size	of	the	 objects	 being	 scanned	 [19].	 The	 x-ray	 tube	 being	 used	 has	 a	 smaller	 focal	 spot	 size	 and	higher	resolution	detectors	are	used.	The	detectors	used	 in	a	CT	scanner	are	usually	made	of	scintillator	materials	such	as	CsI(Tl)	or	ceramic	scintillators	coupled	to	silicon	photodiodes.	Two-dimensional	detector	arrays	or	flat	panels	are	used	in	modern	scanners	to	image	multiple	slices	through	the	body	simultaneously	[19].	The	SPECT	part	of	pre-clinical	SPECT/CT	scanners	is	composed	of	similar	components	as	clinical	scanners,	i.e.	collimator,	scintillation	crystal,	light	guide,	and	PMT	tubes.	However,	there		 17	are	some	differences	in	design	and	performance	of	small	animal	SPECT	scanners	compared	with	the	clinical	SPECT	scanners.	These	differences	include	stationery	detector	heads	rather	than	the	rotating	detector	heads	in	clinical	scanners,	the	capability	of	 imaging	with	substantially	higher	resolution,	and	differences	in	size	of	the	field	of	view,	and	frequent	use	of	pinhole	collimators	rather	than	parallel	hole	collimators.	In	 small	 animal	 SPECT,	 higher	 spatial	 resolution	 is	 obtained	 through	 utilizing	 two	 key	factors.	The	first	 factor	 is	the	small	size	of	the	target	which	permits	high	magnification	of	the	object	onto	the	detector	plane	specifically	with	using	pinhole	collimation.	The	second	factor	is	minimizing	the	distance	between	the	small	 target	and	the	collimator.	Therefore,	 the	organ	of	interest	can	be	positioned	within	a	few	millimeters	(versus	many	centimeters	in	humans)	of	the	collimator.	 Since	 the	 spatial	 resolution	 is	 dependent	 on	 source	 to	 collimator	 distance,	much	higher	resolution	can	therefore	be	obtained.		Furthermore,	small	animal	imaging	typically	relies	on	 the	 pinhole	 collimation	 (described	 in	 1.7)	 and	 therefore,	 the	 sensitivity	 also	 increases	 as	targets	are	moved	closer	to	the	pinhole	aperture	[19].	Dedicated	 small	 animal	 SPECT	 scanners	 have	 been	 developed	 to	 achieve	 optimal	resolution	 and	 sensitivity	 performance	 for	 imaging	 laboratory	 animals.	 Examples	 include,	NanoSPECT	 (1.8)	 by	Mediso	Medical	 Imaging	 Systems,	 Inveon	 by	 Siemens	Medical	 Solutions,	and	 VECTor	 by	 MILABs.	 Although	 there	 are	 several	 different	 designs,	 these	 systems	 have	 a	series	of	compact	detector	heads,	with	interchangeable	pinhole	collimators	that	allow	the	user	to	 select	 the	 desired	 collimator	 in	 terms	 of	 trade	 off	 between	 improved	 spatial	 resolution	(smaller	pinholes)	or	improved	sensitivity	(larger	pinholes).		The	 recent	 advanced	 preclinical	 SPECT	 systems	 employ	 multi-pinhole	 collimators	 to	improve	sensitivity.	In	addition,	they	can	increase	the	field	of	view	in	the	axial	direction	without	translating	 the	 animal.	 The	 pinholes	 form	 the	 projections	 on	 the	 detector	 plane	 during	 data	acquisition.	 In	 some	 systems	 (Figure	 1-9)	 pinholes	 are	 arranged	 with	 sufficient	 distance	between	 them	 to	 avoid	 overlapping	 of	 the	 projections	 from	 adjacent	 pinholes	 (VECTor).	 In	some	other	systems,	the	projections	are	allowed	to	overlap	to	a	certain	degree,	which	enables		 18	more	pinholes	to	be	used	for	a	given	detector	area	and	magnification	(NanoSPECT).	Advanced	image	 reconstruction	 algorithms	 have	 been	 developed	 to	 model	 the	 ambiguity	 in	 the	overlapping	projections	[19].			A	 	 	 	 	 	 					B	Figure	1-9		Multi-pinhole	SPECT	systems	used	for	small-animal	SPECT.	A,	two	pinholes	spaced	far	apart	to	avoid	overlapping	of	projections.	B,	partial	overlap	in	the	projection	data	viewed	through	adjacent	pinholes.	Reproduced	with	permission	from	[19].		Some	 preclinical	 SPECT	 systems	 are	 completely	 stationary	 (VECTor)	 and	 can	 acquire	sufficient	angular	projections	for	tomographic	reconstruction	by	using	pinholes	built	around	a	cylindrical	volume	[56].	This	type	of	system	is	well	suited	for	dynamic	studies	and	evaluating	the	bio-distribution	of	a	novel	drug.	However,	 in	some	other	systems	the	detector	heads	need	to	rotate	to	acquire	projections	from	different	angles	(NanoSPECT	and	Inveon	with	two	detector	heads).		Small	 animal	 SPECT	 scanners	 are	 required	 to	 obtain	 sufficient	 details	 from	 the	 small	target	organs.	In	most	small	animal	SPECT	scanners	the	ultra	high	spatial	resolution	is	achieved	by	using	pinhole	collimation	[57]โ€“[60].	The	fundamental	basics	of	pinhole	camera	and	pinhole	magnification	have	been	known	for	many	years,	however	important	design	parameters	such	as		 19	optimum	collimator	wall	thickness,	size	of	the	pinhole,	material	of	the	pinhole,	and	etc.,	need	to	be	developed	to	use	pinholes	 for	small	animal	SPECT	 imaging	to	obtain	high	resolution	3D	images	that	show	the	accurate	distribution	of	radioactivity	in-vivo.	1.7 Pinhole	collimation	A	pinhole	collimator	consists	of	a	small	aperture	in	a	piece	of	lead,	tungsten,	platinum,	or	other	metals	with	a	high	linear	attenuation	coefficient	to	stop	gamma	rays	in	the	collimator	walls.	The	pinhole	collimator	makes	the	shape	of	a	cone.	The	pinhole	diameter	is	typically	a	few	millimeters.	The	size	of	the	pinhole	aperture,	is	inversely	proportional	to	the	spatial	resolution	and	is	directly	proportional	to	the	detection	sensitivity	[19].	In	pinhole	imaging,	the	gamma	rays	passing	 through	 the	 pinhole	 project	 an	 inverted	 magnified	 image	 of	 the	 source	 distribution	onto	the	detector	plane.			Figure	1-10.	Pinhole	collimator	and	image	projection	on	to	the	detector	plane.	Reproduced	with	permission	from	[19].	From	 Figure	 1-10,	 the	 image	 size	 I	 and	 object	 size	 O	 are	 related	 according	 to	 the	magnification	equation:	๐ผ๐‘‚ = ๐‘“๐‘		 20	Therefore,	a	large	magnification	factor	is	obtained	by	reducing	the	source	to	collimator	distances.	Pinhole	collimators	are	mainly	used	for	obtaining	magnified	 images	of	small	organs	such	as	thyroid,	heart,	and	in	pre-clinical	small-animal	imaging	[19].	In	sub-millimeter	scale	of	small	animal	SPECT,	pinhole	collimation	is	frequently	used	to	obtain	high	resolution	images	of	fine	details	of	interest	at	the	cost	of	lower	detection	sensitivity	and	 higher	 collimator	 penetration	 due	 to	 pinhole	 knife	 edge	 penetration.	 Analytical	relationships	 between	 pinhole	 edge	 penetration,	 sensitivity	 and	 resolution	 of	 the	 pinhole	collimation	have	already	been	derived	by	other	research	groups	[61],	[62]	according	to	which,	collimator	wall	penetration	 increases	 in	 the	knife	edge	of	 the	pinholes	due	 to	having	 smaller	thickness	 (Figure	 1-11),	 in	 imaging	 high	 energy	 gammas,	 and	 with	 decreasing	 the	 pinhole	diameter.	To	increase	the	detection	sensitivity	of	pinhole	collimation,	several	pinholes	might	be	used	to	collect	the	gammas	simultaneously.			Figure	1-11.	Knife-edge	of	a	pinhole	collimator	where	the	thickness	is	smaller.	Reproduced	with	permission	from	[19].			Knife-Edge			 21	1.8 Mediso	NanoSPECT	small	animal	SPECT	scanner		Figure	1-12.	NanoSPECT	scanner	and	the	four	detector	heads.	Reproduced	with	permission	from	Medico	website	(http://www.mediso.com/products.php?fid=2,12).	The	 NanoSPECT	 camera	 by	 Mediso	 Medical	 Imaging	 Systems	 Inc.,	 is	 a	 multiplexed	(overlapping	projections)	multi-pinhole	SPECT	scanner	capable	of	high	sensitivity	SPECT	imaging	with	 sub-mm	 spatial	 resolution.	 NanoSPECT	 consists	 of	 four	 NaI(Tl)	 detector	 heads	 with	dimension	of	 215mm	x	 230mm	connected	 to	 33	PMTs.	 The	detectors	 can	 rotate	 around	 the	animal	 for	 scanning	 a	 large	 object	 through	 helical	 scanning	 or	 stay	 stationery	 for	 scanning	 a	single	position.	Each	detector	is	outfitted	with	an	interchangeable	nine	pinholes	for	a	total	of	36	pinholes	covering	the	FOV.	Pinhole	diameter	and	FOV	are	chosen	according	to	the	type	of	scan	and	 the	 size	 of	 the	 object	 (i.e.	mouse,	 rat,	 or	 rabbit).	 The	 diameters	 of	 the	 pinholes	 for	 the	general	purpose	collimator	 is	1	mm	and	that	of	other	collimators	are	1.4	mm	and	2	mm.	The	size	of	the	FOV	in	axial	direction	ranges	from	2.6	cm	(single	position)	to	27	cm	(helical	scan)	and	in	 trans-axial	 direction	 is	 up	 to	 20	 cm.	 The	 sensitivities	 of	 the	 pinhole	 collimators	 are	approximately	>1200	cps/MBq,	>2200	cps/MBq,	and	>3500	cps/MBq	with	a	resolution	of	โ‰ค0.8	mm,	โ‰ค1mm,	and	โ‰ค1.45mm	for	the	1	mm,	1.4	mm	and	2	mm	apertures	respectively	[63]โ€“[65].		 22	1.9 Siemens	Inveon	small	animal	SPECT	scanner		Figure	1-13	Left:	Inveon	SPECT	scanner.	Right:	t-he	internal	component	shown	schematically.	Reproduced	from	[66].	Inveon	 is	 a	preclinical	 tri-modality	 imaging	 scanner	manufactured	by	Siemens	Medical	Solutions	Inc. Inveon	platform	is	composed	of	SPECT,	PET	and	CT	detectors	to	feed	the	research	study	needs.	The	SPECT,	PET	and	CT	components	can	be	combined	in	a	common	gantry,	with	SPECT	 and	CT	placed	 at	 the	 front	 and	PET	 at	 the	 rear.	 The	 imaging	bed	 can	be	 translated	 in	between	 the	 three	 modalities	 to	 be	 used	 individually	 or	 in	 combination	 with	 all	 the	 three	modalities	[67].		The	 SPECT	 component	 of	 Inveon	 can	 have	 two	 or	 four	 150	 mm	 ร—	 150	 mm	 NaI(Tl)	pixilated	detectors.	Each	detector	head	has	68	ร—	68	pixelated	scintillator	array	of	2.0	mm	ร—	2.0	mm.	 The	 thickness	 of	 scintillation	 crystals	 is	 10	 mm	 and	 the	 crystal	 is	 coupled	 to	 position	sensitive	 photomultiplier	 tube	 readout	 system.	 For	 the	 dual	 head	 Inveon	 system,	 the	 gantry	rotates	to	acquire	angular	projections	from	the	object	[66].		Various	 interchangeable	tungsten	pinhole	collimators	can	be	attached	to	the	detector.	The	 dimension	 of	 the	 pinhole	 aperture	 can	 be	 0.5	 mm,	 1.0	 mm,	 2.0	 mm	 or	 3.0	 mm.	 The	acceptance	angle	of	the	aperture	is	90ยฐ,	with	a	focal	length	of	90	or	95	mm.	The	trans-axial	and		 23	axial	FOV	size	vary	from	28	to	45	mm	depending	on	the	size	of	the	object	being	scanned.	In	the	continuous	bed	motion	in	axial	direction,	the	axial	FOV	size	can	be	as	large	as	250	mm	[67].		The	measured	 resolution	of	 the	0.5	mm	and	1.0	mm	aperture	pinholes	at	140	keV,	 is	respectively	0.84	mm	and	1.2	mm	at	source	to	collimator	distance	of	25	mm.	The	point	source	sensitivity	of	the	0.5	mm	and	1.0	mm	pinholes	is	respectively	35.3	cps/MBq	and	76.7	cps/MBq	at	source	to	collimator	distance	of	25	mm	[67].	1.10 MILABs	VECTor/CT			Figure	1-14.	VECTor	scanner	and	the	three	detectors	in	a	geometry.	The	collimator	cylinder	and	the	bed	inside	the	collimator	is	shown	as	well.	CT	component	is	located	in	the	rear	of	the	SPECT	component.	Reproduced	with	permission	from	[14].	VECTor	 (Figure	 1-14)	 is	 a	 preclinical	 SPECT	 scanner	manufactured	 by	MILABs	 (MILABs	B.V.,	Utrecht,	The	Netherlands)	that	utilizes	multi	pinhole	collimation	to	acquire	high	resolution	and	high	 sensitivity	SPECT	 images	of	 laboratory	 rodents.	As	 stated	 in	1.7,	pinhole	 collimation	produces	magnified	images	of	fine	structures	on	the	detector	plane.	In	addition,	the	sensitivity	increases	by	decreasing	the	distance	between	the	source	and	pinhole	which	is	achievable	in	a	dedicated	 small	 animal	 collimator.	 VECTor	 is	 an	 upgrade	 to	 the	 U-SPECT-II	 scanner	 [15]	 by	CT		 24	MILABs	that	can	perform	SPECT	imaging	from	high	energy	gammas	and	even	positron	emitters	using	 a	 high	 energy	 clustered	multi-pinhole	 collimator	 [13].	 VECTor	 is	 equipped	with	 a	 small	animal	 CT	 scanner	which	 is	 located	 at	 the	 rear	 of	 the	 SPECT	part	 to	be	used	 for	 attenuation	correction	and	animal	positioning	in	the	collimator.	There	 are	 three	 detector	 heads	 configured	 in	 a	 triangular	 geometry	 with	 full	 360ยฐ	coverage	which	makes	 stationary	 data	 acquisition	 possible.	 Each	 detection	 head	 has	 a	 large	NaI(Tl)	scintillation	crystal	with	dimension	of	508	(mm)	ร—	381	(mm)	ร—	9.5	(mm)	and	there	are	55	PMTs	per	detector	head	[15].	Different	 cylindrical	 multi-pinhole	 collimators	 (general	 purpose	 collimator,	 high	sensitivity	collimator,	high	energy	collimator,	etc)	can	be	mounted	on	the	system	to	 facilitate	optimal	 imaging	 for	 animals	 with	 different	 sizes,	 scanning	 times,	 and	 tracer	 doses.	 The	collimator	tubes	have	diameters	of	44	mm	or	98	mm	respectively	for	mouse	or	rat	imaging.	The	scanner	 is	 stationary	 and	 counts	 are	 collected	 without	 moving	 the	 collimator,	 detectors,	 or	animal	for	imaging	of	organs	that	fit	inside	the	collimator	FOV.	All	the	pinholes	focus	on	a	small	volume	 called	 Central	 FOV	 (CFOV)	 to	 collect	 the	 counts	 from	 that	 part	 of	 the	 object.	 For	scanning	a	large	object	the	bed	moves	inside	the	collimator	bore	and	counts	are	collected	from	a	sequence	of	several	FOVs	in	a	spiral	trajectory	(Figure	1-15)	[14],	[15].	Before	starting	the	scan,	the	animal	is	placed	between	3	optical	cameras	and	the	user	selects	the	FOV	of	the	scan,	and	the	acquisition	software	calculates	the	sequence	of	positions	 and	 the	number	 of	 bed	positions	 required	 to	 sample	 the	whole	 FOV	 volume	[68],	[69].	The	data	acquisition	is	done	in	list	mode.	The	projections	by	the	pinholes	are	non-overlapping	and	the	projections	will	be	used	in	an	iterative	reconstruction	algorithm	for	image	reconstruction	[70].		The	measured	sensitivity	of	three	of	the	pinhole	collimators	with	aperture	size	of	0.35	mm	(44	mm	bore	diameter),	0.6	mm	(44	mm	bore	diameter),	and	1.0	mm	(98	mm	bore	diameter)	is	respectively,	525	cps/MBq,	1500	cps/MBq,	and	700	cps/MBq	using	TC-99	 m	 point	 source	 measurements	 [70].	 The	 reconstructed	 resolution	 of	 the	 images		 25	obtained	with	these	collimators	are	0.35	mm,	0.4	mm,	and	0.8	mm	[70].					Figure	1-15	Top)	Trans-axial	and	longitudinal	view	of	a	mouse	size	cylindrical	multi-pinhole	collimator	used	in	VECTor.	The	FOV	and	the	central	FOV	are	clearly	shown	in	both	the	trans-axial	and	the	longitudinal	views.	Bottom)	The	spiral	bed	trajectory	inside	the	collimator	bore.	Reproduced	with	permission	from	[71].	1.11 Multi-pinhole	collimators	used	for	the	experiments	All	 the	 experiments	 of	 this	 thesis	were	 performed	using	 three	of	 the	 interchangeable	multi-pinhole	collimators	shown	 in	Figure	1-16.	The	collimators	were	a	general	purpose	multi	pinhole	(GPMP)	collimator	[15],	a	high	energy	clustered	multi	pinhole	(HECMP)	collimator	[72],	and	a	high	sensitivity	multi	pinhole	(HSMP)	collimator	[10].	All	the	three	collimators	have	bore	diameter	of	44	mm	which	is	suitable	for	mouse	imaging.	The	size	of	the	CFOV	of	the	collimators	is	given	in	Table	1-1.			 26			 	 				 																																																a																																	b																																										c	Figure	1-16.	(a).	General	purpose	multi-pinhole	collimator	[73],	(b)	High	energy	clustered	multi-pinhole	collimator	[11]	,	and	(c)	High	sensitivity	multi-pinhole	collimator	[10]	used	for	the	experiments	of	this	thesis.	All	figures	reproduced	with	permission	from	[73],			[11],	and	[10].	The	size	of	the	FOV	 is	 larger	than	the	CFOV	and	covers	a	cylinder	with	diameter	of	44	mm	 and	 a	 length	 equal	 to	 the	 axial	 length	 of	 the	 collimators.	 The	 properties	 of	 these	collimators	 are	 listed	 in	 Table	 1-1.	 The	 HECMP	 collimator	 is	 especially	 designed	 for	 the	detection	of	gammas	with	energies	up	to	511	KeV,	therefore	rendering	VECTor	very	well	suited	for	imaging	of	positron	emitting	radiotracers	or	radionuclides	emitting	gamma	rays	with	higher	energies	 compared	 to	 those	 of	 typical	 SPECT	 energy	 range	 (E	 <	 350	 keV).	 What	 makes	 the	HECMP	 collimator	 suitable	 for	 SPECT	 imaging	 of	 high	 energy	 gammas,	 is	 having	 a	 thicker	collimator	wall	thickness	to	stop	high	energy	gammas	and	having	clusters	of	pinholes	instead	of	individual	pinholes.	Each	cluster	consists	of	four	pinholes	sampling	from	the	same	FOV.	As	 the	naming	of	 the	collimators	 represents,	each	collimator	 is	designed	 for	a	 specific	imaging	task.	The	GPMP	collimator	is	suitable	for	imaging	of	gammas	with	energies	<	350	keV.	The	HECMP	collimator	is	suitable	for	imaging	of	high	energy	gammas	and	positron	emitters	(E	>	350	keV	and	up	to	511	keV).	Finally,	the	high	sensitivity	collimator	is	used	for	imaging	studies	(E	<	350	keV)	where	the	injected	dose	is	so	small	or	the	imaging	time	is	limited	due	to	isotope	half	life	or	the	type	of	the	study	(e.g.	a	dynamic	scan).			 27	Table	1-1.	Multi-pinhole	collimators	properties	according	to	MILABs		 GPMP	 HECMP	 HSMP	Resolution	(mm)	with	TC-99m	 0.45	 0.75	 1.0	Sensitivity	(%)	with	TC-99m	 0.15	 0.3	 1.3	Resolution	(mm)	with	F-18	 N/A	 0.5	 N/A	Sensitivity	(%)	with	F-18	 N/A	 0.25	 N/A	Number	of	pinholes	 75	 192	 54	Central	FOV	dimension	(mm3)	 12	ร—	12	ร—	7	 12	ร—	12	ร—	9	 12	ร—	12	ร—	7	Pinhole	Diameter	(mm)	 0.6	 0.7	 2.0	Material	 Tungsten	 Tungsten	 lead	1.12 Image	formation	The	data	acquisition	is	done	in	list	mode	and	the	recorded	counts	are	binned	according	to	 their	 energies	 and	 then	 reconstructed	 with	 an	 iterative	 pixel	 based	 ordered	 subsets	expectation	 maximization	 (POSEM)	 algorithm	 [74].	 Data	 acquisition	 and	 reconstruction	 are	done	 using	 dedicated	 software	 developed	 by	 the	 manufacturer.	 Images	 are	 corrected	 for	Compton	scattering	using	the	triple	energy	window	method	during	the	iterative	reconstruction	[48].	 All	 data	 acquisitions	 are	 followed	 by	 a	 CT	 scan	 to	 be	 used	 for	 the	 post	 reconstruction	attenuation	correction	by	the	non-uniform	Chang	method	[12],	[75].								 28	1.12.1 Iterative	image	reconstruction		The	iterative	image	reconstruction	procedures	a	shown	in	Figure	1-17.			Figure	1-17.	General	concepts	of	iterative	image	reconstruction	algorithm.	ECT	system	means	an	emission	computed	tomography	system	such	as	PET	or	SPECT.	The	image	reproduced	with	permission	from	[19].	The	 true	 image	 is	 ๐‘“(๐‘ฅ, ๐‘ฆ)	 and	 the	 estimated	 image	 is	 ๐‘“โˆ—(๐‘ฅ, ๐‘ฆ)	 and	 the	 algorithm	calculates	the	true	image,	by	means	of	successive	approximations.	Often	the	initial	estimate	is	a	uniform	 activity	 distribution.	 	 The	 projections	 from	 the	 initial	 image	 are	 computed	 (forward	projection	 step)	 and	 then	 compared	with	 the	measured	projections.	 The	difference	between	the	 estimated	 and	 actual	 projections	 is	 then	 used	 to	 update	 the	 estimated	 image	 and	 to	achieve	 a	 better	 agreement.	 The	 update-compare	 process	 is	 repeated	 until	 the	 difference	between	 the	 estimated	 sinograms	 and	 the	 measured	 sinograms	 meets	 a	 certain	 threshold,	where	the	estimated	image	eventually	converges	toward	the	true	image	[19].		A	sinogram	is	a	two	dimensional	representation	of	a	full	set	of	projection	data.	Figure	1-18	 displays	 sinogram	 representation	 of	 a	 set	 of	 projections	 from	 a	 simple	 point	 source		 29	obtained	 over	๐œƒ	view	 angles.	 Each	 row	of	 the	 sinogram,	 depicts	 the	 intensity	 across	 a	 single	projection	acquired	at	angle	๐œƒ.	 The	name	sinogram	 is	 taken	 from	 the	 fact	 that	 the	path	of	 a	point	source	in	the	two	dimensional	representation	of	projections	(sinogram	space)	traces	out	a	sinusoidal	path.																	 	Figure	1-18.	Sinogram	representation	of	a	set	of	projection	profiles	from	a	point	source.	Each	row	corresponds	to	an	individual	projection	profile.	Image	reproduced	from	[76].	Iterative	 algorithms	 often	 incorporate	 scanner	 characteristics,	 such	 as	 collimator	 and	object	scatter,	system	geometry,	and	finite	detector	resolution	into	the	system	matrix.	Iterative	algorithms	 are	 computationally	 intensive	 due	 to	 update-compare	 process.	 A	 number	 of	methods	have	been	developed	to	speed	up	the	process.	One	of	the	most	popular	approaches	is	called	ordered	subsets	expectation	maximization	(OSEM).	In	this	method	only	a	small	subset	of	projection	 angles	 is	 used	 in	 each	 iteration.	 This	 speeds	 up	 the	 algorithm,	 since	 the	 time	 per	iteration	is	directly	proportional	to	the	number	of	projection	profiles	that	must	be	computed.		1.12.2 Maximum	likelihood	expectation	maximization	reconstruction	The	 expectation	 maximization	 (EM)	 algorithm	 incorporates	 the	 effects	 of	 counting	statistics	 to	 obtain	 the	 maximum	 likelihood	 (ML)	 source	 distribution	 that	 has	 created	 the		 30	measured	projection	data.	 The	 algorithm	assigns	 greater	weight	 to	high	 count	 elements	of	 a	profile	and	less	weight	to	low	count	regions.	The	reconstruction	algorithm	is	represented	as	follows	๐‘m = ๐‘€I,m๐‘“I 	where	fi	is	the	intensity	in	the	ith	pixel	in	the	image,	pj	is	the	measured	intensity	in	the	jth	projection	element,	and	Mi,j	 is	 the	probability	 that	 radiation	emitted	 from	the	 ith	pixel	will	be	detected	 in	 the	 jth	projection.	The	matrix	M	 is	 called	 the	 reconstruction	 system	matrix	and	 is	very	large	and	contains	information	about	the	characteristics	of	the	imaging	system.	The	MLEM	algorithm,	 provides	 a	 more	 accurate	 approach	 for	 relating	 projection	 profiles	 to	 the	 source	distribution	than	simple	forward	projection	[19].		The	matrix	 is	determined	by	calculations	or	 simulations	or	a	combination	of	both.	For	example,	 a	 point	 source	 can	 be	 positioned	 at	 all	 locations	 within	 the	 imaged	 slice	 and	 the	counts	in	all	elements	of	all	the	projections	be	recorded.	This	process	is	very	time	consuming.	In	practice,	many	 of	 the	 geometric	 effects	 such	 as	 collimator	 response	 can	 be	 calculated	 from	simple	models	 and	more	 complicated	 effects	 such	 as	 collimator	 scatter	 can	 be	 simulated	 or	derived	from	theoretical	models.	Once	 the	 system	matrix	 is	 obtained	 and	 the	 projections	 are	measured,	 the	 following	equation	 is	 used	 to	 estimated	 intensity	 value	 f	 of	 pixel	 i	 in	 the	 (k	 +	 1)st	 iteration	 of	 the	 EM	algorithm:	๐‘“IboK = ๐‘“Ib๐‘€I,mm ร— ๐‘€I,mm ๐‘m๐‘€W,m๐‘“WbW 	where	 k	 is	 the	 iteration	 index.	 The	 iteration	 is	 terminated	when	 some	 conditions	 are	met.	 For	 instance,	 the	 sum	 of	 the	 squares	 of	 differences	 for	 all	 pixels	 in	 the	 reconstructed	image	falls	below	some	predetermined	value.	In	theory	where	measured	projections	are	noise	free,	 the	matrix	 elements	 are	 exactly	 determined,	 the	 algorithm	eventually	 converges	 to	 the		 31	point	where	the	estimated	projection	data	are	exactly	equal	to	the	measured	projection	data,	i.e.	๐‘“IboK = ๐‘“Ib	However,	 in	 practice,	 this	 never	 happens,	 due	 to	 statistical	 noise	 and	 approximated	system	matrix	elements.	Therefore,	some	error	criteria	must	be	set	for	an	acceptable	difference	that	will	be	used	to	terminate	the	iteration	process	[19].		The	 MLEL	 algorithm	 can	 produce	 accurate	 quantitative	 SPECT	 images	 and	 is	 the	common	reconstruction	algorithm	for	most	SPECT	scanners.	 		 32	2 Experiments	and	methods	2.1 Ga-67	imaging	with	VECTor	As	described	in	chapter	1,	the	main	objective	of	this	thesis	was	the	evaluation	of	Ga-67	imaging	with	VECTor.	This	evaluation	consisted	of	the	following:	performance	characterization	of	VECTor	in	imaging	Ga-67	in	terms	of	sensitivity,	uniformity,	and	contrast	metrics,	assessment	of	the	factors	that	affect	the	quantification	accuracy	of	Ga-67	imaging	including	the	attenuation	and	scatter	correction	procedure,	and	 finally	optimization	of	Ga-67	 imaging	with	VECTor.	The	latter	 includes	 the	 proper	 selection	 of	 the	 collimators	 and	 the	 inclusion	 of	 the	 proper	 photo	peaks	 in	 the	 image	 reconstruction	step	which	 lead	 to	Ga-67	SPECT	 images	with	 the	optimum	quality.	The	very	first	evaluation	consisted	of	the	analysis	of	energy	spectra	and	count	collecting	properties	using	the	three	multi	pinhole	collimators	(MPCs)	that	are	used	in	this	thesis	for	Ga-67	 imaging.	 These	 experiments	 specify	 what	 the	 camera	 detects	 when	 a	 Ga-67	 sample	 is	scanned	 and	 what	 are	 the	 substantial	 differences	 in	 detection	 of	 Ga-67	 gammas	 using	 the	different	 MPCs.	 This	 experiment	 gives	 useful	 information	 about	 the	 characteristics	 of	 the	collimators	in	Ga-67	imaging	and	lead	to	optimization	of	Ga-67	studies	with	VECTor.		2.2 Ga-67	energy	spectrum	and	count	collecting	properties	Energy	 spectra	 and	 count	 collection	 properties	 for	 Ga-67	 imaging	 with	 VECTor	 were	investigated	 by	 scanning	 a	 phantom	 filled	 with	 a	 uniform	 radioactivity	 concentration	(โ€˜uniformity	phantomโ€™)	inside	the	field	of	view	(FOV)	of	the	MPCs.	The	uniformity	phantom	was	made	of	a	12	ml	 syringe	with	an	 inner	diameter	of	16	mm	filled	with	~	3	mL	with	a	uniform	solution	 of	 Ga-67	 (with	 length	 of	 15	mm).	 The	 scan	 parameters	 are	 listed	 in	 Table	 2-1.	 The	volume	of	the	CFOV	of	the	GPMP	and	HSMP	collimators	are	~1	mL	(12ร—12ร—7mm3)	and	that	of	the	HECMP	collimator	 is	 ~	1.3	mL	 (12ร—12ร—9	mm3).	 The	phantom	dimension	was	 larger	 than	the	size	of	the	CFOV	and	therefore,	a	number	of	bed	positions	were	required	to	scan	the	whole	volume	 of	 the	 syringe.	 The	 number	 of	 bed	 positions	 is	 automatically	 calculated	 by	 the	acquisition	software.			 33	This	 phantom	 was	 later	 used	 for	 image	 uniformity	 measurements.	 The	 amount	 of	activity	 (concentration)	 in	 the	phantom	was	smaller	when	the	phantom	was	 imaged	with	 the	HSMP	 collimator	 to	 avoid	 the	 pulse	 pile-up	 and	 dead	 time	 effects	 when	 detecting	 gammas	using	this	high	sensitivity	collimator.	Table	2-1.	Scan	parameters	for	the	uniformity	phantom	MPC	 Activity	(MBq)	Activity	Concentration	(MBq/mL)	Volume	(mL)	Acquisition	Time	(min)	#	Bed	Positions	HECMP	 116.4	 37.5	 3.1	 60	 26	GPMP	 122.0	 39.3	 3.1	 60	 13	HSMP	 30.2	 9.3	 3.2	 60	 13	The	 energy	 spectrum	obtained	with	using	different	MPCs	were	 compared	 in	 terms	of	the	relative	number	of	recorded	counts	and	the	estimated	scatter	fraction	in	the	main	energy	windows	of	Ga-67.	The	main	photo	peak	energies	of	Ga-67	gammas	are	93	keV,	184	keV,	300	keV,	and	393	keV	that	are	 respectively	denoted	by	P1,	P2,	P3,	and	P4.	The	scatter	 fraction	 is	defined	 as	 the	 ratio	 of	 the	 scattered	 counts	 estimated	 by	 the	 triple	 energy	 window	 (TEW)	method	 to	 the	 total	 photo	 peak	 counts.	 The	 scattered	 counts	 in	 the	 photopeak	window	 are	estimated	as	the	area	of	the	trapezoid	that	is	formed	by	the	two	side	scatter	windows	as	shown	in	Figure	1-8.	%๐‘†๐น = ๐‘†๐‘๐‘Ž๐‘ก๐‘ก๐‘’๐‘Ÿ๐‘’๐‘‘	๐ถ๐‘œ๐‘ข๐‘›๐‘ก๐‘ 	๐ธ๐‘ ๐‘ก๐‘–๐‘š๐‘Ž๐‘ก๐‘’	๐‘๐‘ฆ	๐‘‡๐ธ๐‘Š	๐‘š๐‘’๐‘กโ„Ž๐‘œ๐‘‘๐‘‡๐‘œ๐‘ก๐‘Ž๐‘™	๐‘…๐‘’๐‘๐‘œ๐‘Ÿ๐‘‘๐‘’๐‘‘	๐‘ƒโ„Ž๐‘œ๐‘ก๐‘œ๐‘๐‘’๐‘Ž๐‘˜	๐ถ๐‘œ๐‘ข๐‘›๐‘ก๐‘  	The	scattered	counts	include	the	detection	of	Compton	scattered	gammas,	the	natural	background	gammas,	and	detected	gammas	arising	from	collimator	wall	penetration,	which	all	fall	in	the	energy	windows	of	Ga-67.	The	term	โ€˜scatter	fractionโ€™	is	thus	used	loosely	to	indicate	the	contribution	from	all	these	events.			 34	2.3 Quantification	accuracy	in	Ga-67	imaging	with	VECTor	The	 two	 main	 limiting	 factors	 in	 quantitative	 SPECT,	 i.e.	 attenuation	 and	 Compton	scattering	were	 evaluated	 in	 Ga-67	 imaging	with	 VECTor	 for	 the	 purpose	 of	 this	 thesis.	 Two	experiments	 were	 performed	 to	 evaluate	 the	 attenuation	 and	 scatter	 effects.	 The	 first	experiment	consisted	of	scanning	an	in-house	made	phantom	(three-insert	phantom)	to	assess	the	accuracy	of	 the	 correction	of	Compton	 scattered	counts	using	 the	TEW	method	 in	Ga-67	studies.	 The	 second	 experiment	 was	 performed	 using	 a	 line	 source	 phantom,	 designed	 and	made	 in	 our	 center	 to	 evaluate	 the	 accuracy	 of	 attenuation	 and	 scatter	 correction	 using	 the	manufacturer	software.		2.3.1 Evaluation	of	scatter	correction	in	Ga-67	studies	A	three	inserts	phantom	was	made	by	using	three	3	ml	syringes	taped	together	side	by	side.	The	diameters	of	the	syringes	were	~	9	mm	and	the	volume	of	the	whole	phantom	was	comparable	to	the	volume	of	a	mouse.	A	CT	scan	of	this	phantom	is	shown	in	Figure	2-1.	Two	of	the	inserts	were	filled	with	Ga-67	solutions	with	different	concentrations,	and	the	third	 insert	was	filled	with	cold	water.	The	cold	syringe	activity	level	in	the	reconstructed	image	will	reflect	that	the	scattered	counts	are	not	accurately	corrected	by	the	TEW	scatter	correction.	The	ratio	of	activity	concentration	between	the	hot	and	warm	syringes	was	8.5:1	to	simulate	a	realistic	tumor	to	background	concentration	ratio.	The	volume	of	the	solution	in	each	syringes	was	1.9	ml	and	the	axial	length	of	the	solution	was	~	30	mm.	The	phantom	was	scanned	using	the	three	MPCs.	Scan	parameters	are	listed	in	Table	2-2.			 35		Figure	2-1.	Image	of	the	three	insert	phantom	Table	2-2.	Scan	parameters	for	the	three	insert	phantom	Collimator	Activity	(MBq)	 Activity	Concentration	(MBq/ml)	 #	bed	positions	Scan	Duration	(min)	Hot	 Warm	 Hot	 Warm	CMP	 58.8	 7.0	 30.94	 3.62	 94	 30	GPMP	 57.8	 6.9	 30.45	 3.56	 47	 30	HSMP	 56.9	 6.7	 29.98	 3.51	 47	 30	The	acquired	data	were	reconstructed	from	93	keV	photo	peak	since	this	peak	was	the	best	peak	in	the	energy	spectrum	in	terms	of	the	branching	ratio,	energy	resolution	(width	of	the	peak),	and	the	height	of	the	peak.	Data	were	reconstructed	using	an	energy	window	width	of	20%	centered	on	the	center	of	the	93	keV	photo	peak.	Two	side	windows	with	width	of	5%	were	selected	on	the	histograms	for	scatter	correction	using	the	TEW	method.		All	the	images	were	 scatter	 and	 attenuation	 corrected	 using	 the	 manufacturer	 software.	 Images	 were	smoothed	with	a	Gaussian	filter	with	FWHM	of	1.0	mm	to	minimize	the	noise	in	the	images.	Since	Ga-67	has	several	photo	peaks,	the	93	keV	peak	is	most	likely	to	be	affected	by	the	down-scatter	counts	 from	other	photo	peaks.	The	TEW	method	 is	supposed	to	correct	object	scatter	and	down	scatter	counts	and	therefore	activity	in	the	cold	region	is	related	to	the	TEW	scatter	correction	deficit.	Therefore,	evaluation	of	cold	 insert	activity	reveals	 the	efficiency	of	scatter	correction	using	the	TEW	method.		 36	In	order	to	quantify	the	reconstructed	activity	concentration	in	the	hot,	warm,	and	cold	inserts,	the	definitions	of	contrast	recovery	for	the	hot	and	cold	inserts	were	adapted	from	the	NEMA	contrast	definitions	[77].	Three	volumes	of	interest	(VOI)	with	equal	volume	of	0.53	mL	were	drawn	on	the	reconstructed	hot,	warm,	and	cold	 insert	 images	 in	order	to	measure	the	reconstructed	activity	concentration	in	the	three	inserts,	and	the	average	value	within	each	VOI	was	used	for	the	analysis.		๐ถ๐‘œ๐‘›๐‘ก๐‘Ÿ๐‘Ž๐‘ ๐‘กx = ๐ถx๐ถy โˆ’ 1๐‘Žx๐‘Žy โˆ’ 1ร—100	๐ถ๐‘œ๐‘›๐‘ก๐‘Ÿ๐‘Ž๐‘ ๐‘กz = 1 โˆ’ ๐ถz๐ถy ร—100	In	 the	 above	 definitions,	 CH,	 CW,	 CC	 are	 the	 reconstructed	 concentrations	 in	 the	 hot,	warm,	and	cold	inserts,	and	aH	and	aW	are	the	actual	activity	concentration	in	the	hot	and	warm	inserts	as	measured	 in	 the	dose	calibrator.	The	 ideal	values	 for	 the	hot	and	cold	contrast	are	100.		According	 to	 the	 above	 definitions,	 any	 reconstructed	 activity	 observed	 in	 the	 cold	insert	is	due	to	the	detection	of	scattered	counts	and	hence	implies	the	inaccuracy	of	the	TEW	method	 scatter	 correction	 for	Ga-67	 studies.	 Therefore,	 the	extent	of	 the	detected	 scattered	counts	in	scanning	a	mouse	size	object	is	estimated	by	evaluating	the	contrast	of	the	cold	insert	metric.		2.3.2 Evaluation	of	attenuation	problem	in	Ga-67	studies	Attenuation	 is	 the	 result	 of	 the	 photoelectric	 effect	 and	 the	 Compton	 scattering	 of	gammas	in	the	tissues.	For	the	energy	range	of	Ga-67	gammas,	the	main	contributing	factor	is	the	Compton	scattering	effect.	Scattering	results	in	losing	the	information	on	the	position	of	the	radiotracer	 and	 a	 loss	 of	 contrast	 and	 an	 apparent	 higher	 detection	 of	 gammas	 from	 the	positions	where	 the	 gammas	do	 not	 originate	 from.	 These	 issues	will	 result	 in	 quantification		 37	errors	 in	 the	 acquired	 images	 if	 not	 corrected.	 Scatter	 correction	 methods,	 estimate	 or	calculate	the	amount	of	the	scattered	counts	and	remove	them	from	the	detected	counts.	It	is	in	this	step	that	the	attenuation	correction	becomes	necessary.	Scatter	correction	results	 in	a	lower	amount	of	 reconstructed	activity	 concentration	by	 removing	 some	of	 the	counts.	After	scatter	 correction,	 the	 attenuation	 correction	 compensates	 for	 the	 gammas	 that	 have	 been	removed	from	the	beam	as	well	as	 the	gammas	that	have	not	been	detected.	Some	gammas	will	 never	 be	 detected	 by	 the	 detector	 even	 without	 being	 scattered	 because	 of	 geometric	sensitivity.	Therefore,	both	scatter	and	attenuation	correction	should	be	performed	to	improve	quantification	accuracy	in	SPECT	imaging.	Attenuation	correction	itself	does	not	correct	for	the	acquisition	 limited	 solid	 angle	 โ€“	 and	 indeed	 that	 is	 what	 the	 absolute	 calibration	 step	 does.	Absolute	calibration	of	the	images	is	not	within	the	scope	of	this	thesis.		If	 either	 the	 scatter	 correction	 or	 attenuation	 correction	 steps	 is	 not	 performed	properly,	 the	 immediate	 results	would	be	quantification	 inaccuracy	 in	 SPECT	 images.	 For	 the	purpose	 of	 this	 thesis,	 we	 evaluated	 the	 quantification	 accuracy	 by	 an	 experimental	 set-up	comparing	 two	 similar	 scans,	 one	 with	 negligible	 amount	 of	 attenuation/scattering	 and	 the	other	with	considerable	amount	of	attenuation/scattering.		A	phantom	was	designed	 in	house	with	using	a	 tube	 representing	a	 line	 source	and	a	cylindrical	volume	shown	in	Figure	2-2.	The	diameter	of	the	cylindrical	volume	was	22	mm	and	its	length	was	~7	cm.	The	size	of	this	phantom	matches	the	size	of	a	mouse	therefore	the	extent	of	 the	 attenuation	 of	 gammas	 in	 the	 phantom	 is	 similar	 to	 the	 extent	 of	 the	 attenuation	 of	gammas	 in	 an	 actual	mouse.	 The	 line	 source	 in	 the	 phantom	was	 filled	with	 Ga-67	 and	 the	phantom	was	scanned	once	with	the	cylindrical	volume	filled	with	water	and	once	without	any	attenuating	medium	present.	The	scan	parameters	are	listed	in	Table	2-3.		This	 experiment	 was	 performed	 only	 using	 the	 HSMP	 collimator	 because	 the	attenuation	 that	 happens	 in	 the	 phantom	 is	 independent	 of	 the	 collimator	 type.	 The	attenuation	 in	 the	 collimator	 is	 indeed	 collimator	 dependent	 but	 we	were	 interested	 in	 the	object	attenuation	which	 is	 indeed	 independent	of	 the	collimator	 type.	 In	addition,	 there	are		 38	several	 studies	 that	 have	 characterized	 the	 amount	 of	 scattering	 in	 the	 collimator	 in	 small	animal	SPECT	using	Monte	Carlo	simulations.	According	to	these	studies,	the	collimator	scatter	fraction	(ratio	of	scatter	counts	in	the	collimator	to	the	total	photopeak	counts)	for	energies	up	to	250	keV,	is	less	than	5%	[78],	[79].	There	is	also	another	study	that	has	simulated	the	object	and	 collimator	 scatter	 for	 different	 isotopes	 and	 for	 different	 pinhole	 collimators	 made	 of	tungsten	 [80].	 According	 to	 this	 study,	 the	 collimator	 scatter	 can	 be	 neglected	 for	 different	collimators	and	different	 isotopes	and	what	matters	 is	mainly	the	object	scattering.	Therefor,	we	 assumed	 collimator	 scatter	 fraction	 is	 negligible	 and	 we	 focused	 our	 evaluation	 on	 the	object	 scatter	 (attenuation)	 and	 therefore	 we	 only	 performed	 the	 evaluation	 in	 the	 HSMP	collimator.		Figure	2-2.	The	house	made	line	source	phantom	By	comparing	the	scans	of	the	line	source	with	and	without	the	attenuating	medium,	it	is	possible	to	estimate	the	extent	of	the	attenuation	problem	in	small	animal	scans.	In	addition,	the	 attenuation	 correction	 procedure	 performed	 using	 the	 manufacturer	 algorithm	 can	 be	assessed	 in	 terms	 of	 its	 accuracy	 in	 correcting	 the	 attenuated	 gammas.	 The	 attenuation	correction	 method	 is	 performed	 based	 on	 the	 non-uniform	 Chang	 attenuation	 correction	method	 [30].	The	performance	of	 the	non-uniform	Chang	attenuation	correction	method	has	already	 been	 evaluated	 by	 several	 groups	 according	 to	 which,	 Chang	method	 works	 well	 in	quantitative	 SPECT	 imaging	 using	 different	 tracers	 especially	 in	 regions	 of	 the	 body	 with	uniform	distribution	of	attenuating	media	such	as	soft	tissues	[81]โ€“[83].		 39	The	differences	between	the	scans	of	the	line	source	in	air	and	attenuating	medium	is	due	to	the	scattering	in	the	volume	of	water	and	the	consequent	attenuation	of	the	gammas.	This	 difference	 reflects	 an	 experimental	 measurement	 of	 the	 amount	 of	 attenuation	 in	 the	body	of	water,	which	should	match	the	amount	calculated	analytically.	It	should	be	noted	that	due	to	geometrical	sensitivity	of	the	detection	system	and	the	collimator,	not	all	the	counts	are	detected.	 This	 is	 corrected	 by	 performing	 absolute	 calibration	 step	 and	 the	 attenuation	correction	does	not	correct	it	all	by	itself.	The	evaluation	of	the	overall	absolute	calibration	of	the	Ga-67	images	is	outside	the	scope	of	this	thesis.	Analytical	calculation	of	attenuation	of	93	keV	gammas	in	water,	and	the	difference	in	reconstructed	 activity	 concentration	 between	 the	 two	 scans,	 reveal	 the	 extent	 of	 the	attenuation	problem	and	the	accuracy	of	attenuation	correction	in	Ga-67	imaging	with	VECTor.	The	analytical	calculation	of	attenuation	of	93	keV	gammas	of	Ga-67	was	performed	according	to	the	exponential	attenuation	of	photons	in	a	medium.	๐‘ = ๐‘*๐‘’DE({)|	In	 the	 above	 equation	 ยต	 is	 the	 linear	 attenuation	 coefficient	 of	 the	 medium	 at	 the	specified	energy	of	the	gamma,	and	x	is	the	thickness	of	the	medium.	The	XCOM	photon	cross	section	 database	 [84]	was	 used	 for	 finding	 the	 linear	 attenuation	 coefficients	 of	water	 at	 93	keV.	The	thickness	of	water	and	the	ยต	of	water	used	in	the	above	calculation	were	1.1	cm	and		0.1747	cm-1	respectively.		Table	2-3.	Scan	parameters	for	the	attenuation	evaluation	experiment	MPC	 Activity	(MBq)	 Acquisition	Time	(min)	 #	Bed	Positions	Without	Attenuating	Medium	1.0	 45	 15	With	Attenuating	Medium	 1.0	 45	 15		 40	2.3.3 The	count-rate	characterization		When	 the	 number	 of	 detected	 counts	 in	 a	 unit	 of	 time	 (count-rate)	 observed	 by	 the	detectors	 exceeds	 a	 threshold	 value,	 pulse	 pile-up	 and	 dead-time	 issues	 may	 rise	 up	 as	 a	degrading	factor	in	quantitative	SPECT	imaging.	The	purpose	of	this	study	was	to	measure	the	count	rate	performance	of	VECTor	detectors	and	to	find	the	maximum	observed	count	rate	that	can	 be	 quantified	 before	 the	 dead-time	 issues	 and	 the	 consequent	 loss	 of	 counts	 become	 a	major	source	of	degradation	of	quantitative	imaging.	This	study	was	performed	using	the	HSMP	collimator.	For	this	study,	9	phantoms	with	different	amounts	of	Ga-67	activity	were	prepared	by	placing	a	small	amount	of	activity	in	Eppendorf	pellets.	The	volume	of	activity	was	such	that	it	could	be	scanned	in	the	CFOV	of	the	collimator	(Figure	2-3).	The	scan	parameters	are	listed	in	Table	2-4.	The	number	of	collected	counts	by	each	detector	was	obtained	and	the	count-rate	response	curves	for	the	detector	heads	were	measured	and	the	maximum	accurate	quantifiable	observed	count-rate	for	the	camera	was	estimated.			Figure	2-3.	The	point	sources	and	the	field	of	view	of	the	scan		 41	Table	2-4.	The	scan	parameters	for	the	count-rate	study		 Activity	(MBq)	 Acquisition	Time	(min)	 #	Bed	Positions	Source	1	 66.4	 10	 1	Source		2	 37.4	 10	 1	Source	3	 29.2	 10	 1	Source	4	 25.3	 10	 1	Source	5	 19.3	 10	 1	Source	6	 14.8	 10	 1	Source	7	 11.6	 10	 1	Source	8	 6.2	 10	 1	Source	9	 1.5	 10	 1	2.4 Performance	 characterization	 of	 VECTor/CT	 in	 Ga-67	imaging		2.4.1 Ga-67point	source	sensitivity	measurements	The	sensitivity	curves	were	measured	by	scanning	a	point	source	containing	Ga-67	using	all	three	MPCs	(HSMP,	HECMP,	and	GPMP).	The	sensitivity	curves	show	the	number	of	detected	counts	by	the	detectors	normalized	to	the	activity	in	the	FOV	for	different	axial	positions	inside	the	collimator.	The	point	source	was	made	by	placing	a	drop	of	activity	 inside	a	small	3/10	cc	insulin	syringe	(a	common	insulin	injection	syringe)	with	an	inner	diameter	of	~4	mm.	The	scan	parameters	 are	 listed	 in	 Table	 2-5.	 Sensitivity	 profiles	 were	 obtained	 by	 moving	 the	 point	source	 in	 1	mm	 intervals	 along	 the	 X,	 Y,	 and	 Z	 axis	 inside	 the	 collimators.	 The	 point	 source	progression	 into	 the	 collimator	was	 controlled	 automatically	 by	 the	 acquisition	 software	 and	the	 user	 didnโ€™t	 need	 to	move	 the	 source	manually	 in	 1	mm	 intervals.	 At	 each	 scan	 interval	counts	were	collected	for	30	seconds.	In	order	to	remove	the	natural	background	counts	from	the	acquired	counts,	natural	background	count	rate	for	the	MPCs	were	also	measured	without	any	source	present	in	the	collimators.			 42	Table	2-5.	Scan	parameters	for	the	point	source	sensitivity	measurements	MPC	Activity	(MBq)	Acquisition	Time	(S)	X	Axis	Interval	 Y	Axis	Interval	Z	Axis	Interval	HECMP	 3.0	 30	 [-10:10]	 [-10:10]	 [-22:22]	GPMP	 3.0	 30	 [-9:11]	 [-10:10]	 [-22:22]	HSMP	 3.0	 30	 [-10:12]	 [-11:11]	 [-22:22]	The	sensitivity	was	calculated	according	to:	%๐‘†๐‘’๐‘›๐‘ ๐‘–๐‘ก๐‘–๐‘ฃ๐‘–๐‘ก๐‘ฆ = ๐ธ๐‘›๐‘’๐‘Ÿ๐‘”๐‘ฆ	๐‘Š๐‘–๐‘›๐‘‘๐‘œ๐‘ค	๐ถ๐‘œ๐‘ข๐‘›๐‘ก๐‘ /๐ด๐‘๐‘ก๐‘–๐‘ฃ๐‘–๐‘ก๐‘ฆ ๐ต๐‘ž ร—๐ต๐‘…ร—๐‘‡(sec)ร—100		In	 the	 above	 relation	BR	 is	 the	branching	 ratio	of	 the	 gamma	 for	 the	energy	 that	 the	sensitivity	is	measured,	and	T	is	the	scan	duration.	The	energy	window	counts	were	obtained	by	placing	energy	windows	with	width	of	 18%,	12%,	12%,	 and	10%	 respectively	on	 the	93,	 184,	300,	 and	 393	 keV	 photo	 peaks	 of	 Ga-67	 spectra.	 Scattered	 counts	 were	 removed	 by	 TEW	method	 scatter	 estimation.	 The	energy	window	 counts	 in	 the	 above	 relation	 are	 true	 counts	recorded	under	the	photo	peak	window	following	the	scatter	correction	and	subtracting	natural	background	counts	from	the	acquired	counts.		This	estimate	of	sensitivity	does	not	separate	the	counts	 coming	 directly	 from	 the	 source	 through	 the	 pinholes	 and	 those	 coming	 through	 the	collimator	wall.	2.4.2 Uniformity	measurements	for	Ga-67	imaging	with	VECTor	The	 images	 of	 the	 uniformity	 phantom	 described	 in	 section	 2.2	 were	 used	 for	 the	uniformity	measurements	and	comparison	of	uniformity/noise	in	the	Ga-67	images	obtained	by	three	MPCs.	The	acquired	data	were	 reconstructed	 from	 the	P1,	P2,	P3,	and	P4	photo	peaks	with	8	subsets	and	12	iterations	followed	by	smoothing	with	a	Gaussian	filter	with	FWHM	of	1.0	mm.	 The	 images	 obtained	with	 the	 GPMP	 and	 the	 HECMP	 collimator	 (except	 the	 P4	 image)	were	 reconstructed	with	 0.2	mm	voxel	 size	 and	 the	 images	 obtained	with	 the	HSMP	and	P4	image	 with	 the	 HECMP	 collimator	 were	 reconstructed	 with	 0.4	 mm	 voxel	 size.	 All	 the		 43	reconstructions	 were	 corrected	 for	 attenuation	 using	 the	 CT	 data	 acquired	 by	 the	 CT	component	of	the	VECTor.	Three	 uniformity-related	 figures	 of	merit	were	 used	 for	 the	 analysis	 of	 uniformity:	 1-	Coefficient	of	variation	(CoV),	2-	Integral	uniformity	(IU),	and	3-	Root	mean	square	(RMS)	Noise.	The	 last	two	were	adapted	from	the	AAPM	report	No.52,	Quantitation	of	SPECT	performance	[85].		Figure	2-4.	Placement	of	the	ROIs	and	VOIs	for	measuring	the	uniformity	according	to	different	definitions	of	uniformity.	The	spherical	yellow	VOI	is	used	for	the	IU	and	the	RMS	noise	measurement,	and	the	circular	ROIs	were	placed	for	the	COV	measurements.		COV:	30	circular	ROIs	with	diameter	of	4	mm	were	placed	on	the	 images	 (Figure	2-4).	ROIs	were	defined	by	drawing	five	ROIs	on	a	plane	and	repeating	them	on	six	axial	planes.	The	distance	 between	 the	 central	 ROI	 and	 the	 peripheral	 ROIs	was	 5	mm	 in	 each	 plane	 and	 the	planes	separation	was	2	mm.	๐ถ๐‘œ๐‘‰	(%) = 100ร—๐œŽย…*	ย†ย‡ยˆ/๐œ‡ย…*	ย†ย‡ยˆ		 44	In	the	above	definition,	ฯƒ	 is	the	standard	deviation	between	the	mean	value	of	the	30	ROIs	and	ฮผ	is	their	mean	value.	A	lower	value	of	this	metric	indicates	a	better	uniformity.	IU:	 A	 spherical	 VOI	 with	 radius	 of	 6.4	 mm	 was	 drawn	 in	 the	 reconstructed	 volume	(Figure	2-4).	๐ผ๐‘›๐‘ก๐‘’๐‘”๐‘Ÿ๐‘Ž๐‘™	๐‘ˆ๐‘›๐‘–๐‘“๐‘œ๐‘Ÿ๐‘š๐‘–๐‘ก๐‘ฆ % = ๐‘š๐‘Ž๐‘ฅยŠX|:W	ยŠaW\: โˆ’ ๐‘š๐‘–๐‘›ยŠX|:W	ยŠaW\:๐‘š๐‘Ž๐‘ฅยŠX|:W	ยŠaW\: + ๐‘š๐‘–๐‘›ยŠX|:W	ยŠaW\: ร—100	where	๐‘š๐‘Ž๐‘ฅยŠX|:W	ยŠaW\:		and	๐‘š๐‘–๐‘›ยŠX|:W	ยŠaW\: 	are	the	maximum	value	and	minimum	values	in	the	ROI	respectively.	(a) RMS	 Noise:	 RMS	 Noise	 is	 measured	 from	 the	 same	 VOI	 drawn	 for	 the	 IU	measurements.		๐‘…๐‘€๐‘†	๐‘๐‘œ๐‘–๐‘ ๐‘’	(%) = 100ร—๐œŽยŠย‡ยˆ/๐œ‡ยŠย‡ยˆ	where,	ฯƒ	is	the	standard	deviation	of	the	VOI	voxel	values	and	ฮผ	is	the	mean	value	inside	the	VOI.	A	lower	value	of	this	metric	indicates	a	better	uniformity.	2.4.3 Contrast	measurements	for	Ga-67	imaging	with	VECTor	Two	mini	 Jaszczak	 hot	 rod	 phantoms	 with	 different	 sizes	 were	 used	 to	 compare	 the	resolution	and	contrast	of	Ga-67	images	obtained	by	the	MPCs.	Phantom1	consisted	of	six	sets	of	rods	with	diameters	of	0.4,	0.5,	0.6,	0.7,	0.8,	and	1.0	mm.	Phantom2	also	consisted	of	six	sets	of	rods	but	with	diameters	of	0.85,	0.95,	1.1,	1.3,	1.5,	and	1.7	mm.	The	scan	parameters	for	the	phantoms	are	listed	in	Table	2-6.	The	phantoms	were	filled	from	two	vials	with	different	activity	concentrations,	therefore	phantom	2	was	scanned	longer	to	compensate	for	its	lower	activity	in	a	reasonable	total	scan	time.	Images	were	reconstructed	individually	from	the	P1,	P2,	P3,	and	P4	photo	peaks	using	20	iterations	and	8	subsets	followed	by	smoothing	with	a	Gaussian	filter	with	FWHM	of	1.0	mm.				 45	Table	2-6.	Scan	parameters	for	the	hot	rod	resolution	phantom	scans	Phantoms	Phantom1	Activity	(MBq)	Phantom2	Activity	(MBq)	Phantom1	Acquisition	Time	(min)	Phantom2	Acquisition	Time	(min)	Phantom1						#	bed	positions	Phantom2						#	bed	positions	HECMP	 95	 16	 60	 120	 14	 12	GPMP	 95	 16	 60	 120	 8	 6	HSMP	 95	 16	 60	 120	 8	 6	Contrast	was	estimated	by	manually	placing	circular	ROIs	on	the	images	of	the	rods	(hot	regions)	and	 in	between	 the	 rods	 (cold	 regions).	The	diameter	of	 the	ROIs	was	0.8	 times	 the	diameter	of	the	rods	and	the	ROIs	were	repeated	on	five	axial	planes.	Contrast	was	calculated	separately	for	each	rod	size	according	to:	๐‘๐‘œ๐‘›๐‘ก๐‘Ÿ๐‘Ž๐‘ ๐‘ก = โ„Ž๐‘œ๐‘ก โˆ’ ๐‘๐‘œ๐‘™๐‘‘โ„Ž๐‘œ๐‘ก 	where	โ„Ž๐‘œ๐‘ก	is	 the	 average	 radioactivity	 concentration	 value	 of	 the	 ROIs	 placed	 on	 the	same	size	hot	rods	and	๐‘๐‘œ๐‘™๐‘‘	is	 the	average	radioactivity	concentration	value	of	the	same	size	ROIs	placed	on	the	cold	regions.	The	ideal	value	for	this	metric	is	1.	2.5 Optimization	of	Ga-67	imaging	studies	with	VECTor	The	 acquired	 data	 from	 the	 uniformity	 and	 the	 hot	 rod	 resolution	 phantoms	 were	reconstructed	 by	 including	 multiple	 photo	 peaks	 in	 the	 reconstructions.	 Similar	 analyses	 of	uniformity	and	contrast	as	described	before	were	performed	on	the	images.	The	images	were	then	compared	 to	obtain	 the	optimum	 image	 in	 terms	of	 image	quality	metrics.	 It	 should	be	mentioned	 that	 the	 reconstruction	 parameters	 were	 the	 same	 as	 in	 the	 characterization	studies.			 		 46	3 Results	3.1 Ga-67	energy	spectrum	and	count	collecting	properties	All	 the	detected	counts	per	detector	were	used	 for	 this	analysis.	The	 recorded	counts	per	 detector	 were	 summed	 and	 then	 were	 normalized	 to	 the	 activity	 in	 the	 field	 of	 view	(devision	by	the	total	activity	in	MBq)	and	the	scan	duration	(division	by	the	scan	duration)	for	cross	 comparison	between	 the	 collimators.	 Therefore,	 the	Y	axis	of	 the	histogram	 represents	the	CPS/MBq,	and	the	X	axis	represents	the	energy	bins.	The	normalized	โ€˜counts	per	second	per	MBq	-	energy	histograms	are	shown	in	Figure	3-1.			Figure	3-1.	The	normalized	count	histograms	obtained	by	scanning	a	uniformity	phantom	using	the	MPCs.	The	 detected	 counts	 corrected	 for	 scatter	 (primary	 or	 true	 photons)	 and	 the	 relative	true	counts	detected	under	the	main	photo	peaks	of	Ga-67	are	shown	in	Figure	3-2.	In	Figure	0 100 200 300 400 500 600050100150200250300350Energy (KeV)CPS/MBq  GPMPHECMPHSMP	 47	3-2b,	the	branching	ratios	of	Ga-67	are	normalized	to	100%	in	order	to	be	comparable	with	the	relative	collected	counts	using	the	MPCs.		(a)		(b)	Figure	3-2:	(a)	True	detected	counts	normalized	to	the	activity	in	the	FOV	for	the	MPCs,	(b)	the	percentage	relative	collected	counts	along	with	the	normalized	branching	rations	for	the	data	acquired	with	the	MPCs.	P1 P2 P3 P400.511.522.533.54 x 106Counts/MBq  HSMPGPMPHECMPNormalized BR HSMP HECMP GPMP0102030405060708090100% Relative Collected Gammas  P1P2P3P4	 48	The	number	of	collected	gammas	using	the	HSMP	collimator	is	higher	compared	to	the	HECMP	and	 the	GPMP	collimators	 for	an	equal	amount	of	activity	 in	 the	FOV	 for	all	 the	 four	photo	peak	energies	of	Ga-67.	This	 is	expected	since	this	high	sensitivity	collimator	has	 larger	pinholes	and	 its	specific	application	 is	 low	count	scans.	Comparison	between	the	HECMP	and	the	 GPMP	 collimators	 is	 more	 meaningful	 since	 in	 imaging	 Ga-67	 both	 can	 be	 used	 in	 a	comparable	situation.	Figure	3-2	(a)	shows	that,	 the	GPMP	collimator	collects	more	counts	at	93	and	184	keV	and	the	latter	collects	more	counts	at	300	and	393	keV	from	an	equal	amount	of	activity	in	the	FOV	and	for	equal	scan	duration.	Figure	3-2	(b)	also	indicates	that	the	relative	collected	 counts	 using	 the	 GPMP	 collimator	 has	 the	 highest	 deviation	 from	 the	 normalized	branching	ratios	of	Ga-67	compared	to	the	HECMP	collimator.	The	higher	normalized	collected	counts	 using	 the	 GPMP	 collimator	 from	 the	 300	 and	 393	 keV	 photo	 peaks,	 arises	 from	 the	collimator	wall	penetration	rather	than	actual	higher	detection	sensitivity.		The	scatter	fraction	values	estimated	by	the	TEW	method	for	different	MPCs	in	imaging	the	uniformity	phantom	are	shown	in	Figure	3-3.		Figure	3-3.	Scatter	fraction	estimated	by	the	TEW	method	in	the	main	energy	windows	of	Ga-67	using	different	MPCs.	P1 P2 P3 P40102030405060708090100% Scatter Fraction  HSMPGPMPHECMP	 49	The	scatter	 fraction	values	estimated	 for	 the	data	acquired	with	 the	GPMP	and	HSMP	collimators	are	in	general	higher	compared	to	the	HECMP	collimator,	reflecting	the	inability	of	these	MCPs	to	stop	high	energy	gammas	from	penetrating	through	the	wall	and	further	down	scattering	into	the	low	energy	peaks.	These	preliminary	results	indicate	the	HECMP	collimator	leads	 to	 the	 lowest	 amount	 of	 accepted	 scattered	 events	 and	 therefore	 ranks	 the	 highest	 in	terms	of	the	estimated	scatter	fraction	especially	for	93,	184,	and	300	keV	imaging.	The	GPMP	collimator	 ranks	 the	 lowest	 at	 all	 the	 four	 photo	 peak	 energies	 which	 is	 an	 indicator	 of	 the	collimator	wall	penetration	through	this	collimator.	The	HSMP	collimator	ranks	in	between	the	other	two	collimators.	3.2 Evaluation	of	quantification	accuracy	in	Ga-67	imaging	3.2.1 Assessment	of	the	scatter	correction	in	Ga-67	imaging	The	reconstructed	images	of	the	three	insert	phantom	are	shown	in	Figure	3-4.	 		 	 	HECMP	 GPMP	 HSMP	Figure	3-4.	Reconstructed	images	of	the	three	insert	phantom	The	quantified	hot	and	cold	insert	contrast	values	are	listed	in	Table	3-1.	The	quantified	contrast	value	of	the	cold	insert	is	an	indicator	of	the	accuracy	of	the	scatter	correction	for	the	acquisition	 based	 on	 the	 93keV	 photopeak.	 The	 cold	 contrast	 values	 show	 that	 the	 TEW	method	 is	 accurately	 correcting	 the	 Compton	 scattered	 counts	 when	 using	 the	 HECMP	 and		 50	HSMP	collimators.	The	cold	contrast	value	is	the	lowest	when	using	the	GPMP	collimator,	which	might	be	due	to	the	fact	that	the	high	energy	gammas	of	Ga-67	down	scatter	in	the	collimator	and/or	in	the	phantom,	and	fall	in	the	93	keV	energy	window.	In	the	other	hand,	the	hot	insert	contrast	 values	 indicate	 that,	 the	 recovered	 ratio	 between	 the	 hot	 and	 warm	 inserts	 is	overestimated	 significantly	 by	 using	 all	 the	 three	 MPCs.	 The	 overall	 results	 show	 that	 the	quantification	 of	 Ga-67	 images	 is	 not	 accurate	 and	 further	 investigation	 into	 this	 problem	 is	required	which	might	be	beyond	the	scope	of	this	thesis.	The	ideal	values	for	contrast	should	be	100	in	Table	3-1.	Table	3-1.	Quantified	contrast	for	hot	and	cold	insert.	The	values	are	dimensionless	because	they	represent	a	ratio		HECMP	 GPMP	 HSMP	Contrast_H	 162.4	 198.0	 185.4	Contrast_C	 99.5	 93.6	 99.7	The	 ratio	 of	 Cold	 :	Warm,	 and	Hot	 :	Warm	 activity	 concentrations	 obtained	 from	 the	images	compared	to	the	actual	ratios	are	shown	in	Figure	3-5.	To	clarify,	the	data	in	Table	3-1	shows	the	contrast	for	hot	and	cold	inserts	and	the	data	in	Figure	3-5	shows	the	ratios	between	the	hot	and	warm	and	cold	and	warm	inserts.		 	Figure	3-5.	Quantified	ratio	of	hot	:	warm,	and	cold	:	warm	activity	concentrations	obtained	from	the	reconstructed	images.		024681012141618Actual HECMP GPMP HSMPHot	:	Warm	Ratio01234567Actual HECMP GPMP HSMPCold	 :	Warm	 51	3.2.2 Evaluation	of	attenuation	problem	in	Ga-67	studies	Reconstructed	 images	 of	 the	 line	 source	 scanned	 with	 and	 without	 the	 attenuating	medium	are	shown	in	Figure	3-6.																																							(a)																																																																																									(b)	Figure	3-6.	Reconstructed	images	of	the	line	source	phantom	(a)	in	air	and	(b)	in	water	The	 difference	 between	 the	 scans	 of	 the	 line	 source	 in	 air	 and	 in	 water	 quantified	experimentally	and	theoretically	are	shown	in	Figure	3-7.	The	scan	of	the	line	source	in	air	was	the	reference	image	and	scan	of	the	line	source	in	water	corrected	for	scattering	was	compared	with	 the	 reference	 image.	 The	 left	 bar	 plot	 in	 Figure	 3-7	 is	 obtained	 by	 calculating	 the	percentage	of	attenuation	of	93	keV	photons	by	passing	through	water	(using	the	exponential	attenuation	formula).	The	right	bar	plot	in	Figure	3-7	is	obtained	by	theoretically	calculating	the	difference	between	the	reconstructed	activity	concentration	of	 the	 line	source	 in	the	air	scan	and	 in	 the	 attenuating	 medium	 scan.	 This	 is	 actually	 representing	 the	 experimental	measurement	of	the	attenuation	of	gammas	in	water	which	should	match	the	theoretical	value.		 52		Figure	3-7.	The	difference	between	the	scans	of	the	phantom	in	air	and	in	scattering	medium	quantified	experimentally	and	theoretically.	The	 results	 show	 that	 the	 experimental	 measurement	 of	 the	 attenuation	 of	 93	 keV	gammas	in	the	mouse	size	phantom	composed	of	water	is	19%.	Theoretical	calculations	show	a	17%	 attenuation	 in	 the	 body	 of	 water.	 Therefore,	 the	 extent	 of	 the	 attenuation	 problem	 in	mouse	imaging	when	93	keV	gammas	are	used	is	less	than	20%.		In	order	to	evaluate	the	accuracy	of	the	attenuation	correction,	the	scan	of	the	phantom	in	water	was	reconstructed	with	attenuation	correction.		Performing	the	scatter	correction	and	attenuation	 correction	 steps	 should	 result	 in	 a	 final	 image	 with	 similar	 quantified	 activity	concentration	 as	 the	 scan	 of	 the	 phantom	 in	 air.	 Figure	 3-8	 confirms	 this	 statement	 (it	 only	differs	by	3%).			Figure	3-8.	The	reconstructed	activity	concentration	values	of	the	line	source	obtained	from	the	images	of	the	line	source	in	air	and	water	followed	by	scatter	and	attenuation	correction.	-30-25-20-15-10-5Analytical	Calculation	of	Attenuation Decrease	 in	Reconstructed	Activity	Concentration%Line	source	scan	in	air	and	water0.00E+002.00E-034.00E-036.00E-038.00E-031.00E-021.20E-02Air+Sc+Ac Water	SC	ACReconstructed	Activity	Concentration	[arb	unit]Line	source	in	air	and	water	 53	The	 results	 of	 this	 step	 show	 that	 the	 attenuation	 correction	 process	 brings	 up	 the	reconstructed	 activity	 concentration	 of	 the	 line	 source	 in	 water	 to	 match	 that	 of	 the	 non-attenuating	scan.	Therefore,	it	can	be	concluded	that	attenuation	correction	process	accurately	corrects	the	loss	 in	counts	due	to	scattering.	The	attenuation	and	scatter	correction	steps	are	done	properly	for	Ga-67	imaging	with	VECTor	using	the	manufacturer	software.	3.2.3 Characterization	of	count-rate	performance	of	VECTor	The	 total	 collected	 counts	 by	 each	 detector	 head	were	measured	 and	 the	 results	 are	reported	 in	 Table	 3-2.	 The	 detected	 counts	 were	 obtained	 by	 integrating	 the	 count-energy	histograms	over	the	entire	range	and	without	subtracting	for	scatter.	Table	3-2.	The	number	of	detected	counts	by	each	head	from	Ga-67	phantoms.		 Activity	(MBq)	 Head	1	 Head	2	 Head	3	Source	1	 66.4	 1.73E+08	 1.73E+08	 1.70E+08	Source		2	 37.4	 1.12E+08	 1.17E+08	 1.14E+08	Source	3	 29.2	 9.11E+07	 8.96E+07	 8.90E+07	Source	4	 25.3	 7.37E+07	 7.36E+07	 7.34E+07	Source	5	 19.3	 5.90E+07	 5.99E+07	 6.07E+07	Source	6	 14.8	 5.06E+07	 5.03E+07	 5.00E+07	Source	7	 11.6	 3.88E+07	 3.97E+07	 3.86E+07	Source	8	 6.2	 2.19E+07	 2.22E+07	 2.14E+07	Source	9	 1.5	 5.21E+06	 5.25E+06	 5.20E+06	The	observed	count-rate	for	each	detector	head	as	a	function	of	activity	in	the	field	of	view	was	obtained	for	each	head	and	the	results	are	plotted	for	each	detector	head	separately	in	Figure	3-9.	As	the	plots	show,	when	the	observed	count-rate	exceeds	105	CPS,	the	 linearity	between	the	observed	CPS	and	the	activity	is	lost	and	therefore	sensitivity	drops.	This	happens	as	a	result	of	dead	time	and	pulse	pile	up	issues.	For	the	experiments	that	we	performed	with	the	HSMP	collimator,	the	maximum	quantifiable	observed	count-rate	is	equivalent	to	<	20	MBq	of	Ga-67	activity	in	the	field	of	view.			 54			Figure	3-9.	Observed	count-rate	VS	the	activity	in	the	field	of	view	the	VECTor	detector	heads	with	Ga-67	source	measurements.	3.3 Assessment	of	image	quality	factors	in	Ga-67	imaging	3.3.1 Point	source	sensitivity	measurements		The	sensitivity	profiles	measured	along	the	X,	Y,	Z	axis	of	the	collimators	are	shown	in	Figure	3-10-Figure	3-12.		 55		(a) 																																																																																							(b)		(c)	Figure	3-10.	Sensitivity	profiles	of	the	GPMP	collimator	measured	along	the	(a)	X	axis,	(b)	Y	axis,	and	(c)	Z	axis	of	the	collimator			-8 -6 -4 -2 0 2 4 6 8 100.050.10.150.20.250.30.350.4X [mm]%SensitivityGPMP  P1P2P3P4-10 -8 -6 -4 -2 0 2 4 6 8 100.050.10.150.20.250.30.350.4Y [mm]%SensitivityGPMP  P1P2P3P4-20 -15 -10 -5 0 5 10 15 2000.050.10.150.20.250.30.350.4Z [mm]%SensitivityGPMP  P1P2P3P4	 56		(a) 																																																																																							(b)		(c)	Figure	3-11.	Sensitivity	profiles	of	the	HECMP	collimator	measured	along	the	(a)	X	axis,	(b)	Y	axis,	and	(c)	Z	axis	of	the	collimator			-10 -8 -6 -4 -2 0 2 4 6 8 100.050.10.150.20.250.30.350.4X [mm]%SensitivityHECMP  P1P2P3P4-10 -8 -6 -4 -2 0 2 4 6 8 100.050.10.150.20.250.30.350.4Y [mm]%SensitivityHECMP  P1P2P3P4-20 -15 -10 -5 0 5 10 15 20-0.0500.050.10.150.20.250.30.350.4Z [mm]%SensitivityHECMP  P1P2P3P4	 57		 	(a) 																																																																																							(b)			(c)	Figure	3-12.	Sensitivity	profiles	of	the	HSMP	collimator	measured	along	the	(a)	X	axis,	(b)	Y	axis,	and	(c)	Z	axis	of	the	collimator			The	sensitivity	decreases	by	deviating	the	point	source	from	the	CFOV	because	many	of	the	pinholes	are	not	zoomed	at	the	point	source	anymore.	The	tails	of	 the	sensitivity	profiles	can	be	an	indicator	of	the	amount	of	collimator	wall	penetration.	These	values	were	measured	for	all	the	MPCs	by	measuring	the	ratio	between	the	sensitivity	value	where	the	source	is	>15	mm	 away	 from	 the	 center	 in	 the	 axial	 direction	 (on	 the	 tail	 of	 the	 graph)	 and	 the	 peak	sensitivity	at	the	CFOV.		-10 -8 -6 -4 -2 0 2 4 6 8 10 120.40.60.811.21.41.61.82X [mm]%SensitivityHSMP  P1P2P3P4-10 -8 -6 -4 -2 0 2 4 6 8 100.40.60.811.21.41.61.82Y [mm]%SensitivityHSMP  P1P2P3P4-20 -15 -10 -5 0 5 10 15 2000.20.40.60.811.21.41.61.82Z [mm]%SensitivityHSMP  P1P2P3P4	 58	The	quantified	collimator	wall	penetration	values	are	 listed	 in	Table	3-3.	The	values	 in	Table	3-3	shows	when	the	source	is	15	mm	away	from	the	center	 in	Z	direction	on	the	tail	of	the	 curve,	what	 is	 the	 recorded	 counts	 relative	 to	 the	 CFOV	 counts	 (where	 the	 sensitivity	 is	maximum)	.	Therefore,	all	the	wall	penetration	values	are	represented	normalized	to	the	peak	sensitivity	(peak	counts).	There	is	significant	collimator	wall	penetration	for	the	GPMP	and	the	HSMP	collimators	at	393	and	300	keV	compared	to	the	HECMP	collimator.	Table	3-3.	Percentage	collimator	wall	penetration	measured	for	the	MPCs	at	different	energies.	The	values	were	obtained	by	comparing	the	measured	sensitivity	of	the	collimator	when	the	source	is	in	the	CFOV	and	15	mm	away	in	the	axial	direction.		%	GPMP	penetration	 %	HSMP	penetration	 %	HECMP	penetration	93	keV	 4	 2	 0.8	184	keV	 8	 2	 0.8	300	keV	 14	 5	 0.8	393	keV	 39	 16	 1.8	The	peak	sensitivity	of	the	collimators	measured	at	93	keV,	184	keV,	300	keV,	and	393	keV	are	shown	in	Figure	3-13.		Figure	3-13.	The	peak	sensitivity	of	the	collimators	measured	at	93	keV,	184	keV,	300	keV,	and	393	keV.	93 keV 184 keV 300 keV 393 keV00.511.52Peak Sensitivity  HECMPGPMPHSMP	 59	The	 higher	 apparent	 sensitivity	 of	 the	 GPMP	 collimator	 compared	 to	 the	 HECMP	collimator	at	300	keV	and	393	keV	is	due	to	collimator	wall	penetration	and	the	inability	of	this	collimator	to	stop	high	energy	gammas	of	Ga-67.	3.3.2 Image	uniformity	measurement	for	Ga-67	imaging	with	VECTor	The	reconstructed	images	of	the	uniformity	phantom	are	shown	in	Figure	3-14.			Figure	3-14.	Images	of	the	uniformity	phantom	reconstructed	from	separate	photo	peak	counts	are	displayed	for	the	GPMP	(top),	the	HECMP	(middle),	and	the	HSMP	(bottom)	collimators.	The	images	are	smoothed	with	a	Gaussian	filter	with	FWHM	of	1.0	mm.	The	uniformity	figures	of	merit	measured	from	the	images	using	all	the	MPCs	are	shown	in	Figure	3-15.			 60			Figure	3-15.	Uniformity	measurements	for	Ga-67	images	using	all	the	definitions	of	uniformity.	To	summarize,	the	images	obtained	with	the	HECMP	collimator	have	better	uniformity	using	all	definitions	of	uniformity	for	all	the	energies.		3.3.3 Resolution	and	contrast	measurements	for	Ga-67	imaging	with	VECTor	The	reconstructed	images	of	the	two	resolution	phantoms	obtained	using	the	MPCs	are	shown	in	Figure	3-16(a)	and	(b).		0.02.04.06.08.010.012.014.016.018.020.0P1 P2 P3 P4%	CoV%	Coefficient	of	VariationsHECMPHSMPGPMP	 61		(a).	The	rod	sizes	are	1.0,	0.8,	0.7,	0.6,	0.5,	and	0.4	mm.		(b).	The	rod	sizes	are	1.7,	1.5,	1.3,	1.1,	0.95,	and	0.85	mm	Figure	3-16.		(a)	Images	of	the	resolution	phantom	1,	and	(b)	resolution	phantom	2	reconstructed	from	separate	energy	windows	using	all	the	MPCs.		 62	3.3.3.1 Qualitative	resolution	measurements	for	Ga-67	imaging	The	resolution	of	the	MPCs	at	different	energies	is	qualitatively	plotted	in	Figure	3-17	as	well.	When	data	are	obtained	using	the	GPMP	and	the	HSMP	collimator,	none	of	the	rods	are	resolved	at	300	and	393	keV,	therefore,	the	curves	for	these	two	MPCs	are	plotted	only	at	the	lower	energies.			Figure	3-17.	The	qualitative	smallest	rod	size	resolvability	for	Ga-67	imaging	using	the	different	MPCs.	3.3.3.2 Quantitative	contrast	measurements	for	Ga-67	imaging	The	quantitative	analyses	of	the	contrast	of	the	resolution	phantom	images	acquired	by	the	MPCs	are	shown	in	Figure	3-18.	The	data	from	both	phantoms	are	grouped	together.	The	graphs	are	plotted	for	the	smallest	rod	size	that	could	be	resolved	in	the	images.	93 keV 184 keV 300 keV 393 keV0.40.50.60.70.80.911.1Enrgy (keV)Rod size resolvability [mm]  GPMPHSMPHECMP	 63			Figure	3-18.	Contrast	as	a	function	of	rod	diameter	measured	from	resolution	phantom	images	reconstructed	P1,	P2,	P3,	and	P4	photo	peaks	of	Ga-67	To	summarize	the	results,	the	contrast	of	the	images	acquired	by	the	HSMP	collimator	is	not	 comparable	 to	 that	 of	 the	 images	with	 the	HECMP	and	 the	GPMP	 collimators	 since	 that	collimator	 is	a	high	sensitivity	collimator	and	 is	not	meant	 to	provide	high	 resolution	 images.	The	performance	of	 the	GPMP	collimator	 is	not	 comparable	 to	 the	HECMP	collimator	at	300	and	393	keV,	which	is	expected	since	the	HECMP	collimator	is	specifically	designed	for	imaging	of	high	energy	isotopes.	The	GPMP	collimator	has	the	best	performance	in	terms	of	contrast	at	93	and	184	keV.		0 0.5 0.6 0.7 0.8 0.85 0.95 1.0 1.1 1.3 1.5 1.700.10.20.30.40.50.60.70.80.91Rod Size [mm]ContrastP1  GPMPHECMPHSMP0 0.5 0.6 0.7 0.8 0.85 0.95 1 1.1 1.3 1.5 1.700.10.20.30.40.50.60.70.80.91Rod Size [mm]ContrastP2  GPMPHECMPHSMP0 0.5 0.6 0.7 0.8 0.85 0.95 1.0 1.1 1.3 1.5 1.7-0.100.10.20.30.40.50.60.70.80.9Rod Size [mm]ContrastP3  GPMPHECMPHSMP0 0.5 0.6 0.7 0.8 0.85 0.95 1.0 1.1 1.3 1.5 1.7-0.4-0.200.20.40.60.81Rod Size [mm]ContrastP4  GPMPHECMPHSMP	 64	3.4 Optimization	of	Ga-67	studies	with	VECTor	As	 stated	 in	 2.5,	 similar	 analyses	of	 uniformity	 and	 contrast	were	performed.	But	 the	images	 of	 the	 phantoms	 were	 reconstructed	 by	 combining	multiple	 photopeaks	 together	 to	find	the	optimum	combination	of	photopeaks	in	terms	of	the	uniformity	and	resolution	figures	of	merits.	The	analyses	were	performed	for	each	MPC.	3.4.1 Uniformity	analysis	The	 uniformity	 results	 represented	 by	 the	 CoV,	 integral	 uniformity,	 and	 RMS	 noise	definitions	 are	 shown	 in	 Figure	 3-19.	All	measures	 indicate	 that	 image	uniformity	 is	 the	best	using	the	HECMP	collimator	for	all	peak	combinations.			Figure	3-19.	Uniformity	measurements	for	Ga-67	images	when	multiple	photo	peaks	are	combined	during	the	reconstruction.		 65	3.4.2 Contrast	analysis	Images	 of	 the	 resolution	 phantoms	 reconstructed	with	 including	multiple	 photo	 peak	counts	in	the	reconstruction	of	Ga-67	are	shown	in	Figure	3-20.	The	rod	sizes	are	1.7,	1.5,	1.3,	1.1,	0.95,	and	0.85	mm.			(a).	The	rod	sizes	are	1.0,	0.8,	0.7,	0.6,	0.5,	and	0.4	mm.		(b).	The	rod	sizes	are	1.7,	1.5,	1.3,	1.1,	0.95,	and	0.85	mm	Figure	3-20.	(a)	Images	of	the	resolution	phantom	1,	and	(b)	resolution	phantom	2	reconstructed	with	including	multiple	photo	peaks	using	all	the	MPCs.		 66	The	measured	 contrast	 as	 a	 function	 of	 rod	 size	 for	 all	 the	 three	MPCs	 are	 shown	 in	Figure	3-21.	The	contrast	was	measured	for	the	smallest	rod	size	resolved	by	each	collimator.			Figure	3-21.	Contrast	as	a	function	of	rod	size	measured	for	images	formed	by	combining	photo	peaks.	The	 results	 suggest	 that,	 when	 using	 the	 GPMP	 and	 the	 HSMP	 collimators,	 only	 the	counts	from	the	first	two	photo	peaks	should	be	used	in	the	reconstruction.	However,	when	the	HECMP	collimator	is	used,	all	the	counts	from	the	four	main	photo	peaks	should	be	used	for	the	image	 reconstruction.	 In	 addition,	 the	 GPMP	 should	 be	 the	 collimator	 to	 be	 used	 for	 Ga-67	studies.	0 0.5 0.6 0.7 0.8 0.85 0.95 1.0 1.1 1.3 1.5 1.700.10.20.30.40.50.60.70.80.91Rod Size [mm]contrastGPMP  P1P1+P2P1+P2+P3P1+P2+P3+P40 0.5 0.6 0.7 0.8 0.85 0.95 1.0 1.1 1.3 1.5 1.70.10.20.30.40.50.60.70.80.91Rod Size [mm]contrastHECMP  P1P1+P2P1+P2+P3P1+P2+P3+P40 0.5 0.6 0.7 0.8 0.85 0.95 1.0 1.1 1.3 1.5 1.70.10.20.30.40.50.60.70.80.91Rod Size [mm]contrastHSMP  P1P1+P2P1+P2+P3P1+P2+P3+P4	 67	4 Discussion	and	conclusion	The	main	objective	of	this	thesis	was	performance	evaluation	of	VECTor/CT,	in	imaging	Ga-67.	 The	 other	 objectives	were	 optimization	 for	 Ga-67	 scans	 as	well	 as	 the	 assessment	 of	quantitative	corrections	in	Ga-67	imaging.	The	 performances	 of	 three	 multi-pinhole	 SPECT	 collimators	 were	 evaluated.	 The	collimators	 were	 a	 general	 purpose	 multi-pinhole	 (GPMP),	 a	 high	 energy	 multi-pinhole	(HECMP),	and	a	high	sensitivity	multi-pinhole	(HSMP).	The	GPMP	and	the	HSMP	were	designed	for	 imaging	of	gammas	with	energies	<	350	keV	and	the	HECMP	collimator,	was	optimum	for	gammas	with	energies	up	to	511	keV	with	slightly	lower	resolution	than	the	GPMP	collimator.	The	 collimators	 were	 compared	 in	 terms	 of	 the	 count	 collecting	 efficiency,	 point	 source	detection	sensitivity,	uniformity,	and	contrast.	The	principle	metrics	to	determine	the	optimum	selection	of	the	photo	peaks	and	the	type	of	the	collimator	to	be	used	in	Ga-67	imaging	were	contrast	 of	 the	 images.	 The	 attenuation	 correction,	 scatter	 correction,	 and	 the	 count	 rate	effects	were	assessed	for	studying	the	quantitative	corrections	in	Ga-67	imaging.	The	analysis	of	 the	energy	spectra	and	sensitivity	experiments	 indicate	 that	 the	HSMP	collimator	has	the	highest	sensitivity	as	specified	by	the	manufacturer	as	well.	Therefore,	 it	 is	more	 relevant	 to	 compare	 the	 performance	 of	 the	 GPMP	 and	 the	 HECMP	 together	 because	they	have	similar	resolution	with	a	similar	pinhole	dimension.	The	HEMP	collimator	has	higher	detection	sensitivity	at	93	keV	and	184	keV,	whereas	the	GPMP	collimator	has	higher	detection	sensitivity	at	300	keV,	and	393	keV.	Although	the	number	of	collected	counts	from	the	300	and	393	keV	photo	peaks	is	higher	with	the	GPMP	collimator,	these	counts	carry	very	little	spatial	information	 since	 they	 are	 mostly	 related	 to	 collimator	 wall	 penetration.	 Accordingly,	 our	results	 show	 that	 the	 estimated	 scatter	 fraction,	 interpreted	 in	 its	 broader	 sense,	 associated	with	 each	 photo	 peak	 is	 higher	 with	 the	 GPMP	 and	 the	 HSMP	 collimators	 compared	 to	 the	HECMP	collimator.	This	again	 indicates	the	presence	of	collimator	wall	penetration	and	down	scattered	counts	that	fall	under	the	lower	energy	photopeak	windows.			 68	The	 images	with	 the	 HECMP	 collimator	 have	much	 better	 uniformity,	 compared	with	images	 obtained	with	 the	 GPMP	 and	 the	 HSMP	 collimators.	 Using	 the	 GPMP	 and	 the	 HSMP	collimators,	only	the	first	two	photo	peaks	should	be	used	in	the	reconstruction.			The	 contrast	measurement	 results	 showed	 that,	 the	GPMP	collimator	performance	 is	the	best	when	 images	are	reconstructed	from	the	93	keV	gammas.	At	this	energy	the	 images	with	the	GPMP	collimator	have	the	highest	contrast	for	all	object	rod	sizes.	The	images	formed	by	184	keV	gammas	showed	that	for	object	sizes	smaller	than	0.85	mm,	the	GPMP	collimator	still	has	the	best	performance,	however	for	object	sizes	larger	than	0.85	mm	the	performance	of	 the	HECMP	collimator	exceeds.	The	 images	with	the	HECMP	collimator	have	always	better	contrast	when	 images	are	 reconstructed	 from	300	and	393	keV	gammas	confirming	 that	 this	collimator	 is	 indeed	 capable	 of	 imaging	 gammas	 with	 a	 broad	 range	 of	 energies.	 While	obtaining	some	insight	into	the	scanner	performance	for	a	range	of	gamma	energy,	we	believe	that	these	conclusions	are	relevant	to	Ga-67	imaging	and	cannot	be	immediately	generalized	to	either	other	radioisotopes	or	multi-isotope	imaging.		Ga-67	decay	branching	ratio	is	such	that	it	greatly	 favors	 gammas	with	 lower	 energy,	 thus	making	 the	 overall	 effect	 of	 down-scattering	and	septal	penetration	still	limited.			The	assessment	of	the	quantitative	corrections	showed	that	the	attenuation	and	scatter	correction	procedures	are	in	general	performed	properly.	The	analytical	calculation	and	the	and	experimental	measurement	of	the	attenuation	of	93	keV	gammas	of	Ga-67	matched	closely	and	the	quantified	activity	concentration	in	the	scan	without	the	attenuating	medium	and	the	one	with	attenuating	medium	matched	properly	after	all	the	quantitate	corrections.	Therefore,	our	measurements	 confirm	 that	 attenuation	 correction	 is	 well	 done.	 Regarding	 the	 scatter	correction	experiment,	the	three	insert	phantom	results	indicated	that	the	activity	quantified	in	the	 cold	 syringe	 is	 negligible	which	means	 scatter	 correction	 using	 the	 TEW	method	 is	 done	properly	 in	Ga-67	studies.	However,	there	is	still	an	ambiguity	 in	the	relative	quantification	of	warm	 to	 hot	 insert	 values.	 This	 issue	 requires	 further	 evaluation	 which	 can	 be	 done	 as	 the	future	work.		 69	Image	quality	is	a	trade-off	between	noise	and	resolution.	Including	multiple	photo	peak	counts	in	the	reconstruction	means	lower	noise	but	at	the	same	time	the	resolution	is	adversely	affected	by	including	higher	energy	gammas	of	Ga-67.	Therefore,	it	 is	 important	to	obtain	the	optimum	selection	of	photo	peaks	in	Ga-67	imaging	studies.	In	addition,	each	MPC	is	designed	for	a	specific	imaging	application	in	terms	of	the	energy	of	the	isotope,	the	amount	of	activity	being	scanned,	the	desired	spatial	resolution,	and	etc.	Taking	into	account	the	decay	scheme	of	Ga-67,	it	is	required	to	perform	optimization	studies	to	obtain	the	highest	performance	possible	in	Ga-67	scans.	The	aim	of	the	optimization	studies	is	to	obtain	which	MPC	is	best	suited	for	Ga-67	studies	and	what	is	the	proper	selection	of	photo	peaks	for	the	image	reconstruction.		The	optimization	studies,	confirm	that,	the	best	collimator	for	Ga-67	scans,	is	the	GPMP	collimator	and	the	photopeaks	to	include	in	the	reconstruction	are	93	and	184	keV	peaks.	Given	that	 the	 amount	 of	 activity	 in	 the	 field	 of	 view	 is	 sufficient,	 the	 GPMP	 collimator	 provides	images	with	the	best	contrast	and	with	better	resolution.		We	also	found	that,	although	using	the	HECMP	collimator	it	is	possible	to	combine	all	the	four	photo-peaks	to	increase	the	counts	without	a	significant	decrease	in	contrast,	the	images	with	the	GPMP	collimator	and	only	from	93	and	184	keV	gammas,	still	have	higher	contrast	in	comparison.	If	due	to	having	not	enough	activity	in	the	FOV,	the	HSMP	collimator	should	be	used,	only	the	first	two	photo	peaks	should	be	combined	and	it	should	be	noted	that	object	sizes	larger	than	1.3	mm	can	be	resolved.	It	 should	 be	 mentioned	 that	 the	 absolute	 calibration	 of	 the	 images	 was	 outside	 the	scope	of	this	thesis.	However,	as	the	future	direction	of	this	study,	it	is	a	worthy	evaluation	to	perform.	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