Prospects for achieving < 100 ps FWHM coincidence resolving time in time-of-flight PET, 28-Feb-2012, ICTR-PHE, Geneva, Switzerland 1
Time-of-flight PET Colon cancer, left upper quadrant peritoneal node 114 kg; BMI = 32.2 13.4 mci; 2 hr post-inj Non-TOF TOF (CRT ~650 ps) State-of-the-art clinical PET: coincidence resolving time (CRT) 500 ps Images: J. Karp, University of Pennsylvania 2
Silicon Photomultiplier (SiPM) 1 mm - 3 mm Array of many self-quenched Geiger-mode APDs (microcells) connected in parallel 20 µm 100 µm Increasingly interesting as replacement for PMTs: high gain (~10 6 ) high PDE compact and rugged transparent to γ-photons fast response (ns) insensitive to magnetic fields 3
In lab, 100 ps barrier has been broken Made possible by the combination of: Small LaBr 3 :Ce(5%) crystals (3 mm x 3 mm x 5 mm) Silicon Photomultipliers (Hamamatsu MPPC-S10362-33-050C) Digital Signal Processing (DSP) 100 ps FWHM => 15 mm FWHM D.R. Schaart et al, Phys Med Biol 55, N179-N189, 2010 4
Recent measurements with LSO:Ce,Ca FWHM = 125 ps 3 mm x 3 mm x 5 mm LSO:Ce,Ca (U Tennessee) 3 mm x 3 mm SiPM (MPPC-S10362-33-050C) S. Seifert et al, NDIP 2011 5
Digital SiPMs SPADs, TDC and digital readout circuitry integrated on a single chip 120 ps FWHM Photograph of Ca-codoped LSO:Ce crystal mounted on a dsipm Time difference spectrum measured with a Na-22 point source. Measured CRT = 120 ps FWHM (for two detectors in coincidence). D.R. Schaart et al, IEEE NSS-MIC 2011 6
What is the best possible timing resolution achievable with a given scintillation detector?
Scintillation photon counting statistics γ emission γ absorption at t = Θ Emission of N sc optical photons Detection of N optical photons N = η N sc, where η is the photodetection efficiency (PDE) T e = {t e,1, t e,2,, t e,nsc } T d = {t d,1, t d,2,, t d,n } Ξ (= estimate of Θ) 8
Fisher information and the Cramér Rao lower bound var( Ξ) I T d 1 Θ ( ) CRTLB 2.35 2 var( ) 2.35 2 / IT = Ξ Θ The Cramér Rao inequality defines the lower bound on the CRT of a pair of scintillation detectors To calculate this lower bound (CRT LB ) we need the Fisher information I Td in the set T d d ( ) 9
Calculation of CRT LB Parameters included in the calculation: Scintillation light yield Y Photodetection efficiency η Scintillation pulse shape, For example, bi-exponential pulse τ r τ d with rise time constant τ r and decay time constant τ d Probability density function describing the single-photon timing uncertainty comprises optical path length variations in crystal, transit time spread (TTS) of sensor, trigger jitter, etc. for a very small crystal and near-perfect detector readout, this contribution is dominated by the photosensor TTS here represented by a Gaussian with standard deviation σ The math involves order statistics, it can be found in: S. Seifert, H.T. van Dam, and D.R. Schaart, The lower bound on the timing resolution of scintillation detectors, Phys Med Biol 57, 1797-1814, 2012 10
What are the physical limits on the timing resolution of PET scintillation detectors?
Lower bound on the CRT of LSO:Ce,Ca Measured: ~125 ps CRT LB : ~110 ps var ( ) Ξ I T d 1 ( Θ) CRT < 100 ps seems feasible with further SiPM improvements (PDE and TTS) Transit Time Spread, σ (ps) N = 7500, σ = 50 ps Photodetection efficiency (PDE) Lower bound on the CRT of LSO:Ce,Ca + MPPC as a function of PDE and TTS 12
PET scintillators From our CR model: CRT LB τ d N sc NaI:Tl BGO LSO:Ce LSO:Ce,Ca LaBr 3 :Ce Density (g/cm 3 ) 3.67 7.13 7.4 7.4 5.1 Effective Z 51 75 66 66 47 Atten. l. 511 kev (mm) 29.1 10.4 11.4 11.4 21.3 Decay time (ns) 230 300 40-45 30-35 16 # photons /MeV 40,000 8,500 30,000 30,000 70,000 Emission max. (nm) 410 480 420 420 380 Hygroscopic yes no no no yes 13
Faster scintillator: LaBr 3 :Ce(>10%) Transit Time Spread, σ (ps) τ r = 150 ps, σ = 50 ps, PDE = 0.5 o var ( ) Ξ I T ( Θ) < 50 ps feasible? d 1 Rise Time Constant (ps) In principle, a CRT of ~50 ps might be feasible using LaBr 3 :Ce with high Ce concentration and by increasing SIPM PDE to ~50% and TTS to ~50 ps 14
The holy grail: 10-picosecond PET With a CRT less than ~20 ps events an be localized directly: image reconstruction no longer necessary! only attenuation correction real-time image formation detector 1 t 1 t 1 -t 2 position x along LOR x = c CRT /2 Aim: x d Tube or Line of Response (LOR) detector 2 t 2 CRT 2 d / c Clinical PET: 2 mm d 4 mm d CRT 20 ps 15
Ultrafast scintillators: example Transit Time Spread, σ (ps) Example: τ d and τ r equal to ZnO:Ga CRT < 20 ps in principle feasible var ( ) Ξ I T d 1 ( Θ) Light Yield (photons/mev) If a sub-ns scintillator emitting at least several thousand photons per MeV around ~400 nm can be made, sub-20 ps PET may come within reach 16
We have reported experimental CRTs close to CRT LB in small crystals. But how about larger ones?
DOI-dependent signal delay in crystal Depth-of-interaction (DOI) variations deteriorate timing resolution γ 1 γ 2 gamma photon speed: scintillation photon speed: WW Moses and SE Derenzo IEEE Trans. Nucl. Sci. 46, 474-478 (1999) 18
Depth-of-interaction determination Methods to determine DOI: (a) layered design, (b) single crystals with dualsided readout, (c) phoswich design, (d) monolithic scintillator, (e) dual layer with offset, (f) dual layer with mixed shapes From: Peng & Levin, Current Pharmaceutical Biotechnology 11, 555-571, 2010 19
Digital PET system Local position decoding and time-stamping no limit on no. of channels, no loss of (Fisher) information Real-time DOI correction of timing and spatial information Fast, accurate & repeatable system calibration and time alignment Real-time signal processing Immediate digitization Detector Module System Images courtesy of Philips 20
Conclusion var ( ) Ξ I T d 1 ( Θ) With existing scintillators and photosensors, CRT s of ~100 ps FWHM are close to the lower bound imposed by photon counting statistics further improvement only possible by decreasing the lower bound! Key enablers required: Bright (>> 10 3 ph/mev), ultrafast (~ 1 ns) scintillation materials Ultraprecise (<< 100 ps TTS), highly efficient (PDE 1) photon counters Detector design mitigating optical transit time spread (<< 100 ps) while maintaining high gamma detection efficiency ( 1) None of these are available yet, but none are physically impossible Transit Time Spread (ps) CRT < 20 ps in principle feasible Light Yield (photons/mev) 21
Thank You 22
Backup slides 23
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Time-of-flight PET The accuracy of source position localization along line of response depends on the coincidence resolving time (CRT) x = uncertainty in position along LOR = c. CRT/2, where c is the speed of light. x The TOF benefit is proportional to x/d, where D is the effective patient diameter. => The smaller the CRT, the better. D State-of-the-art: CRT 500 ps x 7.5 cm. 25
Some essential findings Lower bound on the FWHM coincidence resolving time (CRT LB ) for 2 detectors, assuming Gaussian time difference spectra: CRTLB 2.35 2 var LB( ) 2.35 2 / IT d ( ) = Ξ = Θ CRT LB 1 N τ << τ σ << τ CRT r d d LB τ r CRTLB 1 τ d The latter 2 properties are due to the fact that most of the timing information is carried by the first detected photons, i.e. in the rising part of the pulse. S. Seifert et al, The lower bound on the timing resolution of scintillation detectors, Phys Med Biol 57, 1797-1814, 2012 26
Order Statistics Timestamp for the n th detected scintillation photon n = 1 n = 5 n = 10 n = 15 n = 20 Exemplary probability density functions for the n th order statistic for LYSO:Ce on MPPC-S10362-33-050C 27
Lower bound for LYSO:Ce Parameters: τ r = 90 ps τ d = 44 ns σ = 120 ps N det = 4700 Lower bound on the CRT for LYSO:Ce on MPPC-S10362-33-050C, using the n th, the first n, or all detected photons ( order statistics ) for timing S. Seifert et al, The lower bound on the timing resolution of scintillation detectors, Phys Med Biol 57, 1797-1814, 2012 28
Lower bound for LYSO:Ce It appears possible to closely approach the CR lower bound using a leading edge trigger set at the optimum threshold level Calculated lower bound Measured CRT S. Seifert et al, IEEE Transactions on Nuclear Science 59, 190-204, 2012 29
Comparison to measured values S. Seifert et al, The lower bound on the timing resolution of scintillation detectors, Phys Med Biol 57, 1797-1814, 2012 30