Laue lens for Nuclear Medicine PhD in Physics Gianfranco Paternò Ferrara, 6-11-013 Supervisor: prof. Vincenzo Guidi Sensors and Semiconductors Lab, Department of Physics and Earth Science, University of Ferrara - Italy
Outline Functional Imaging (PET/SPECT) X-ray diffraction in crystals Laue lens design
SPECT vs PET SPECT (Single Photon Emission Computed Tomography) γemitter (e.g. Tc99m 140.6 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
Parallel holes collimator the most used in commercial SPECT ε 16 l 1 d d 5 4 10 10 ( d + s) a R ( b + l + d ) 10 15 l mm efficiency resolution
SPECT image Thyroid scan using Tc99m improving resolution > Laue Lens
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
Flat Crystals Limitation on perfect crystals Incident photons ½ of the photons ½ of the photons
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
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
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
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.
lens design detector lens equation: 1 f 1 1 + 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 ))
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 1 1 1 4 ε θ π ε photons diffracted/s incident flux Efficiency of the lens
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
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
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 0,80 400 µm,15 19
Lens features 708 8,11 0,40 0,50 6,4 90 99 (444) Ge 10 783 7,40 0,36 0,50 6,06 90 90 (60) Ge 9 540 6,6 0,3 0,50 5,79 90 81 (440) Ge 8 348 6,08 0,31 0,50 6,08 90 74 (333) Ge 7 633 5,73 0,30 0,50 5,39 90 70 (4) Ge 6 40 5,10 0,30 0,50 5,73 90 6 (331) Ge 5 800 4,68 0,30 0,51 4,77 90 56 (400) Ge 4 571 3,88 0,30 0,51 5,10 90 46 (311) Ge 3 18 3,31 0,30 0,51 3,75 90 39 (0) Ge 0,0 0,30 0,5 3,56 90 3 (111) Ge 1 R [µm] R [mm] Lr [mm] Lt [mm] To [mm] Ω [''] n diffracting planes crystals ring
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
Lens simulation
Lens simulation
Lens simulation
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.