Laue lens for Nuclear Medicine

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1 Laue lens for Nuclear Medicine PhD in Physics Gianfranco Paternò Ferrara, Supervisor: prof. Vincenzo Guidi Sensors and Semiconductors Lab, Department of Physics and Earth Science, University of Ferrara - Italy

2 Outline Functional Imaging (PET/SPECT) X-ray diffraction in crystals Laue lens design

3 SPECT vs PET SPECT (Single Photon Emission Computed Tomography) γemitter (e.g. Tc99m kev T 1/ 6h) collimator in front of the gamma camera PET (Positron Emission Tomography) β + emitter (e.g. 18FDG T 1/ 110m) > e + annihilates with an e - > γ 511 kev (180 ) coincidence control

4 Parallel holes collimator the most used in commercial SPECT ε 16 l 1 d d ( d + s) a R ( b + l + d ) l mm efficiency resolution

5 SPECT image Thyroid scan using Tc99m improving resolution > Laue Lens

6 X-ray Diffraction in Crystals There are possible diffraction geometry: Bragg (reflection ) geometry Diffraction planes parallel to crystal surface Incident photons Crystal surface Diffracted photons d spacing sin θ hc d hkl 1 E Laue (transmission ) geometry Diffraction planes normal to crystal surface Incident photons Crystal surface Diffracted photons d spacing

7 Flat Crystals Limitation on perfect crystals Incident photons ½ of the photons ½ of the photons

8 RC of flat Crystals (flat Ge crystal, (111) planes, To5 mm, E140.6 kev) dhkl FWHM δ 1 Λ 0 arcsec, πv cosθ Λ c B 0 ; λre C Fhkl R peak 1 low acceptance and reflectivity

9 Curved Crystals Curved crystals prevent factor ½ effect, due to continuous change of the incidence angle so that only a single diffraction occurs onto curved crystalline planes. Methods for curving a crystal: using an external device (holder) applying a force on the crystal applying a thermal gradient perpendicular to the considered planes growing a two-component crystal (e.g. Si 1-x Ge x ) whose composition varies along the crystal growth axis depositing a coating or by grinding or grooving a face of the crystal

10 RC of Curved Crystals (curved Ge crystal, (111) planes, To1 mm, Ω10, E140.6 kev) R peak (1 e π d Λ hkl 0 R C ) e µ T0 cosθ B T, R 0 C Malgrange Ω high acceptance and high reflectivity

11 Laue lens in Nuclear Medicine Curved crystal Opticsin LAUE geometry Detector Gamma-ray source A Laue Lens is composed by a set of (curved) crystal disposed in concentric rings, each with a different crystallographic orientation (different d means different θ B ). In fact, photons have the same energy E, but impinges in to the crystal surface with different angle so, in order to focus most of them into a common point, the lens must offer a wide acceptance.

12 lens design detector lens equation: 1 f L S L D, where L S R tan( θ α) B L D R tan( θ + α) B f R tan( θ ) B L S +L D is minimum when α 0, thus LS LD f θ B 1 > sin θ B θ B, thus, for each ring R θ B L S θ B hc 1 E h + k a + l setting E, L S and material > R not all orientation (h,k,l) can be used because of the superpositions isotropic monochromatic source setting Lt, Lr > n n π/atan(lt /(R -Lr ))

13 Lens efficiency calculation peak N c N eff eff R A A A 1 1 g r t S t c A L L L L A < Ω 4 S s L L N π Φ each crystal can diffract only photons with θ θ-θ B <Ω, thus, only a portion of the crystal is useful > Lr small The collecting area of each crystal is Effective area of the lens eff L D A N Φ Ω N peak N B S eff S D R L A N N ε θ π ε photons diffracted/s incident flux Efficiency of the lens

14 Lens efficiency calculation ε do not depends on n R peak is low for the outermost rings > N < 15 ε do not depends on Lt and Lr T 0 is set for maximising R peak (ε ) Ω as high as possible 1 ε θ B Ω (1 e T k Ω 0 ) e µ T cosθ 0 B

15 Lens PSF calculation The beam diffracted by a crystal produces, on the focal plane, a rectangular response with width equal to T 0 θ B -ΩL S. By considering the contribution of each crystal in every ring, the PSF can be calculated: RES x f f ( T 0, Ω, L S ) ph RES has a minimum for T 0 T 0opt RES decreases if Ω and L S increase CSNR S N N S >> N N A d CG CSNR CSNR lens spect ε ε lens spect RES RES spect lens Φ Φ d G L f ph A A eff d

16 Lens features input E Ls lens crystals To Lt Lr Ω Rc Na Nc 640 Φ e 1,6 cm FF performance ε ε RES f ph RES CG G 140,6 kev 15 cm Ge 3,56-6,4 mm 0,50-0,5 mm 0,30-0,40 mm 90'' 11,46 m 10 48,61% 1,08E-05 8,61E-06 0, µm,15 19

17 Lens features 708 8,11 0,40 0,50 6, (444) Ge ,40 0,36 0,50 6, (60) Ge ,6 0,3 0,50 5, (440) Ge ,08 0,31 0,50 6, (333) Ge ,73 0,30 0,50 5, (4) Ge ,10 0,30 0,50 5, (331) Ge ,68 0,30 0,51 4, (400) Ge ,88 0,30 0,51 5, (311) Ge ,31 0,30 0,51 3, (0) Ge 0,0 0,30 0,5 3, (111) Ge 1 R [µm] R [mm] Lr [mm] Lt [mm] To [mm] Ω [''] n diffracting planes crystals ring

18 Lens simulation Monte Carlo Simulation: isotrope radioactive source generate a random photons (θ,φ) check if θ-θ B <Ω / check if φ-φ Mi < φ ok check if rand(1,1)<r peak calculate the diffraction point calculate the spot on the focal plane

19 Lens simulation

20 Lens simulation

21 Lens simulation

22 Conclusions By using a Laue Lens, could be obtained diagnostic images having both a better resolution (more than 0 times) and a better CSNR (,15 times at least) with respect of a standard gamma-camera system (considering the same dose given to the patient). The lens maps each point of the source in a narrow spot on the focal plane (ideally a point). Therefore, by moving the lens, or an array of lenses, along three axis, a whole scan of the source could be performed without need of tomography.

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