Performance study of a fan beam collimator for a multi- modality small animal imaging device

Transcription

1 Performance study of a fan beam collimator for a multi- modality small animal imain device ASM SABBIR AHMED 1 Wolfrad Semmler 2 Jor Peter 2 1 University of Saskatchewan Saskatoon Canada & 2 German Cancer Research Centre University of Heidelber Germany Trabzon Turkey May

2 Study Objectives Desin of a fan beam collimator for a small animal imain device to perform rapid dynamic study with improved efficiency and spatial resolution. A Monte Carlo model to optimize the collimator s parameters to conduct a performance study by analyzin the scatterin and noise indexes for a 3D eometry. A S Ahmed Trabzon Turkey May Slide:*

3 Study Importance Pharmacokinetic data distribution revels important functional information of the livin bodies. Hih sensitive collimator is essentially required for rapid dynamic acquisition where hiher count rates are to be recorded in short time frame. A S Ahmed Trabzon Turkey May Slide: 3

4 Introduction Collimator s role in scintillation imain * The desired collimator material has hih linear attenuation coefficient; e.. tunsten lead tantalum etc. LLNL * Most desirable eometrically collimated rays pass the collimator without interactin the septal wall JAERI * Undesirable penetratin amma rays pass throuh one or more septal walls and scattered photons deflected by scatterin. Scintillation imain without proper collimation spoils the ultimate objective * Penetratin and scattered photons produce noises and substantially derade imae quality A S Ahmed Trabzon Turkey May Slide: 4

5 Introduction The small animal imain device Patent: EP26/ ; J. Peter et.al. IEEE 25 A S Ahmed Trabzon Turkey May Slide: 5

6 Introduction Theoretical formulation for modelin efficiency and resolution [Scatterin/attenuation/penetration=] A photon from source s z will pass throuh the collimator if the photon passes within front and back projections of the hole on imae plane. s As a collimator is composed of repeated lattice structure with respect to a source so the collimator response function is periodic with respect to source position and it depends on front and back aperture function: i.e. c r s z j k zbl hs r r z ' jk zb hs r r z ' jk A S Ahmed Trabzon Turkey May Slide: 6

7 Introduction Theory: efficiency and resolution If the collimator response function is decomposed in a Fourier series the above equation becomes N M MN m MN s i z r c z s r c ]. exp[ 2 where M and N are referred to as the hole-pattern harmonics. For a parallel hole collimator the point source response function is independent of the source position s; In that case all the harmonics except c vanish. Collimator eometric transfer function can be written in terms of the photon fluence at the collimator face and the two collimator-aperture functions where is the effective lenth of the collimator =d+t 2 is the area of a lattice. Hence hole pattern harmonics except M=N= can be nelected. N M MN m MN s i z c z z s r c z r z s 2 ]. exp[2 4 1 Takin the Fourier transform N M MN MN MN e m s i m l B z H m l l B z H l 2 ]. exp[ l e A S Ahmed Trabzon Turkey May Slide: 7

8 Introduction Theory: efficiency and resolution The Averae efficiency for the parallel-hole collimator p can be written as p H H 2 4l e Hole _ area 2 4l Lattice _ area e Total lattice area >FWHM The resolution of a parallel-hole collimator measures the width of the point source response function PSRF as a function of r. The width of the PSRF is stronly dependent on the source position in front of the collimator. The eometric resolution of the parallel-hole collimator R is p defined as the FWHM of the PSRF by the relation R p zd l e d l e B l b Henkin RE et.al. Nucl Med Mosby Ins 1996 A S Ahmed Trabzon Turkey May Slide: 8

9 Introduction Theory: : Fan beam efficiency and resolution For fan beam eometry individual hole-axis alins differently at every position on the collimator face and hence the efficiency of the fan beam collimator depends stronly on source position. The eometric efficiency for the fan beam collimator is iven as f b p [cos 2 ] f f b 2 wherez B l b is object distance p is efficiency of the parallel collimator q is the anle between collimator axis and the object position. The distance b varies from to f; i.e. <b<f. The resolution of the fan beam collimator R f R p 1 cos le / 2 b f b [Tsui BMW IEEE 1996] A S Ahmed Trabzon Turkey May Slide: 9

10 Introduction Theory: : Equation derivation for line and point source If a line source of lenth L is placed in air the eometric efficiencies for a parallel hole and a fan beam collimator are : p l p L b b f l f dz L b L 1 cos 2 2 L b f b f f f L l p No scatterin or attenuation included For attenuatin medium: exp h h p a p exp h b h b f a f L p L b b p al p e L dz b z L L 1 ] exp[ 1 [Point source] [Line source] B e B BE A e A AE e f L h L B i A i A p al f cos 2 2 No scatterin included A S Ahmed Trabzon Turkey May Slide: 1

11 Methodoloy The small animal imain device: Collimator s Specifications The scintillation crystal consists of 66x66 array.2 cm separation of square shaped individual NaITl crystal elements.13 x.13 x.6 cm 3. The proposed collimator is desined to match with the crystal dimension. Tunsten material attenuation coefficient m=36.34 cm -1 is proposed for this collimator. Thickness t=.2 cm Hole size d=.13 cm focal lenth f=18 cm. A S Ahmed Trabzon Turkey May Slide: 11

12 Methodoloy Collimator Desin consideration The proposed fan beam collimator was desined to study the whole body dynamic study. The focal lenth f was calculated as 18 cm. A hole lenth l =1.8 cm was calculated for the new converin collimator. A fan beam is a combination of parallel and converin collimator. Collimator s hole axis s are convered toward the object short axis and parallel to object lon axis. A S Ahmed Trabzon Turkey May Slide: 12

13 Methodoloy Collimator Desin A S Ahmed Trabzon Turkey May Slide: 13

14 Methodoloy Calculation of Scatterin index SI Monte Carlo method MCNP was used to calculate the fluence for individual detector-element for point and line sources. This fluence included scattered and unscattered photons emitted from the source. F4 tally calculated the number of photons over a cell that was normalized per incident particle. F4 tally r E t vn r E t Same number of particles were tallied for all cases. r E t dedt V E T dv V wvt V w V T L Scatterin index SI= Total fluence unscattered fluence Particle density N = Particle weiht/volume w/v T L = vt = Track lenth in the medium 17x17 detector blocks were included in the model study. The sources were biased within the solid anle. A S Ahmed Trabzon Turkey May Slide: 14

15 Methodoloy Anular dependency of 3D object A water filled cylindrical object r=3 cm that compares to standard mouse was placed at a distance b from collimator face. Because of symmetry the upper half A B C was only considered where A and B exist in the most and the least depth points inside attenuatin medium C in the middle. For every q anle at the object center a correspondin q anle was calculated at the focal point. q varied from f to +f -f<q<f. A S Ahmed Trabzon Turkey May Slide: 15

16 Methodoloy Calculation of Sinal noise index SNI A rin source radius 1.5 cm consists of four point sources were placed inside water filled cylinder at different depths. All sources make same manitude of anle with the collimator axis. The shortest distance between two consecutive peaks was lon enouh not to interrupt each other. The sinal at the rin-center can be taken as the averae of the sinals at j k m n with four sources at these locations. The noise at the center is calculated as the noise calculated at j k m n with a point source at the center c. s c SNI = N c s s s s S j k m n c ; sources j k. m. n 4 N N N N N j k m n c ; source c 4 A S Ahmed Trabzon Turkey May Slide: 16

17 Results & Discussion Point source profile for the collimator A point source in air at 1 cm away from the collimator face. Focal lenth f=18 cm b=1 cm A S Ahmed Trabzon Turkey May Slide: 17

18 Results & Discussion Point and line source in air For point source the detector efficiency increases 1.2E+3 times near the focal point. For line source it s increases 3.3E+1 times A S Ahmed Trabzon Turkey May Slide: 18

19 Results & Discussion Point and line source in water At.5 cm depth scatterin 14 % for parallel 19 % for fan beam At.5 cm depth scatterin 19 % for parallel 3 % for fan beam A S Ahmed Trabzon Turkey May Slide: 19

20 Results & Discussion Relative efficiency and Scatterin index for point source in water The attenuatin medium was fixed at 3 cm away from the collimator face. For point source relative efficiency increases about 6 times than that of Parallel The fan beam scatterin index increases about 11 times than that of parallel collimator A S Ahmed Trabzon Turkey May Slide: 2

21 Results & Discussion Relative efficiency and Scatterin index for line source in water The relative efficiency is linear for line source The scatterin index is linear for line source A S Ahmed Trabzon Turkey May Slide: 21

22 Results & Discussion Anular dependency of a 3D object A S Ahmed Trabzon Turkey May Slide: 22

23 Results & Discussion Anular dependency of a 3D object A S Ahmed Trabzon Turkey May Slide: 23

24 Results & Discussion Sinal noise index SNI With fan beam the SNI increases about 2.3 times than the that of the parallel collimator A S Ahmed Trabzon Turkey May Slide: 26

25 Conclusion * The performance characteristic of the proposed fan beam collimator has been studied for different source confiurations based on analytic formulation and Monte Carlo simulation studies. * The results shown in this study revealed that a fan beam collimator is useful for scintillation imain. But the advantae of fan beam is not predictable from mathematical derivation with a point source in air alone. Details particle transport calculation is essential. * Its performance stronly dependent on the source distribution and differs sinificantly for different source confiuration. * Inside attenuatin medium the increased attenuatin effect outweihs the fan beam increased eometric efficiency when a line source moves toward the focal point Supported by: Tsui BMW IEEE 1996; brain imain. * The performance of a fan beam collimator should be evaluated for specific application and purpose. A S Ahmed Trabzon Turkey May Slide: 25

26 A S Ahmed Trabzon Turkey May QUESTIONS?