Prospects for achieving < 100 ps FWHM coincidence resolving time - - PowerPoint PPT Presentation

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Dennis R. Schaart Delft University of Technology

Prospects for achieving < 100 ps FWHM coincidence resolving time in time-of-flight PET

Dennis R. Schaart, 28-Feb-2012, ICTR-PHE, Geneva, Switzerland

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114 kg; BMI = 32.2 13.4 mCi; 2 hr post-inj

State-of-the-art clinical PET: coincidence resolving time (CRT) ≈ 500 ps

TOF (CRT ~650 ps) Non-TOF

Images: J. Karp, University of Pennsylvania

Time-of-flight PET

Colon cancer, left upper quadrant peritoneal node

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Dennis R. Schaart Delft University of Technology

Silicon Photomultiplier (SiPM)

• Array of many self-quenched

Geiger-mode APDs (microcells) connected in parallel

• Increasingly interesting as

replacement for PMTs:

• high gain (~106)
• high PDE
• compact and rugged
• transparent to γ-photons
• fast response (ns)
• insensitive to magnetic fields

1 mm - 3 mm 20 µm – 100 µm

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In lab, 100 ps barrier has been broken

D.R. Schaart et al, Phys Med Biol 55, N179-N189, 2010

100 ps FWHM = > 15 mm FWHM

Made possible by the combination of:

• Small LaBr3:Ce(5%) crystals (3 mm x 3 mm x 5 mm)
• Silicon Photomultipliers (Hamamatsu MPPC-S10362-33-050C)
• Digital Signal Processing (DSP)

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Recent measurements with LSO:Ce,Ca

• 3 mm x 3 mm x 5 mm LSO:Ce,Ca (U Tennessee)
• 3 mm x 3 mm SiPM (MPPC-S10362-33-050C)

FWHM = 125 ps

• S. Seifert et al, NDIP 2011

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Digital SiPMs

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).

SPADs, TDC and digital readout circuitry integrated on a single chip

120 ps FWHM D.R. Schaart et al, IEEE NSS-MIC 2011

What is the best possible timing resolution achievable with a given scintillation detector?

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Dennis R. Schaart Delft University of Technology

Te = {te,1, te,2, …, te,Nsc} Td = {td,1, td,2, …, td,N} at t = Θ

γ emission γ absorption Emission of Nsc optical photons Detection of N optical photons

Scintillation photon counting statistics

N = η Nsc, where η is the photodetection efficiency (PDE)

Ξ (= estimate of Θ)

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Dennis R. Schaart Delft University of Technology

• The Cramér–Rao inequality defines the lower bound
• n the CRT of a pair of scintillation detectors
• To calculate this lower bound (CRTLB) we need the

Fisher information I Td in the set Td

Fisher information and the Cramér–Rao lower bound ( )

d

LB

CRT 2.35 2 var( ) 2.35 2 /

T

I = ⋅ Ξ ≥ Θ

( )

d

1 var( )

T

I Ξ ≥ Θ

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Dennis R. Schaart Delft University of Technology

Calculation of CRTLB

Parameters included in the calculation:

• Scintillation light yield Y
• Photodetection efficiency η
• Scintillation pulse shape,

→ For example, bi-exponential pulse with rise time constant τr and decay time constant τd

• 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
• f scintillation detectors,” Phys Med Biol 57, 1797-1814, 2012

r

τ

d

τ

What are the physical limits on the timing resolution

• f PET scintillation detectors?

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Dennis R. Schaart Delft University of Technology

Transit Time Spread, σ (ps)

Lower bound on the CRT of LSO:Ce,Ca

Lower bound on the CRT of LSO:Ce,Ca + MPPC as a function of PDE and TTS Photodetection efficiency (PDE)

N = 7500, σ = 50 ps

Measured: ~125 ps CRTLB: ~110 ps

( ) ( )

d

1 var

T

I Ξ ≥ Θ

CRT < 100 ps seems feasible with further SiPM improvements (PDE and TTS)

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Dennis R. Schaart Delft University of Technology

Density (g/cm3) Effective Z

• Atten. l. 511 keV (mm)

Decay time (ns) # photons /MeV Emission max. (nm) Hygroscopic 7.13 75 10.4 300 8,500 480 no 7.4 66 11.4 40-45 30,000 420 no NaI:Tl BGO LSO:Ce LSO:Ce,Ca LaBr3:Ce 3.67 51 29.1 230 40,000 410 yes 7.4 66 11.4 30-35 30,000 420 no 5.1 47 21.3 16 70,000 380 yes

PET scintillators

d LB sc

CRT N τ ∝

From our CR model:

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Dennis R. Schaart Delft University of Technology

< 50 ps feasible ?

τr = 150 ps, σ = 50 ps, PDE = 0.5

• Faster scintillator: LaBr3:Ce(>10%)

In principle, a CRT of ~50 ps might be feasible using LaBr3:Ce with high Ce concentration and by increasing SIPM PDE to ~50% and TTS to ~50 ps Transit Time Spread, σ (ps) Rise Time Constant (ps)

( ) ( )

d

1 var

T

I Ξ ≥ Θ

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Dennis R. Schaart Delft University of Technology

The holy grail: “10-picosecond PET”

detector 1 detector 2

Tube or Line of Response (LOR)

t1-t2 t1 t2

position x along LOR

d

/ 2 Aim: 2 / Clinical PET: 2 mm 4 mm 20 ps x c CRT x d CRT d c d CRT ∆ = ⋅ ∆ ≤ ⇒ ≤ ≤ ≤ ⇒ ≤

With a CRT less than ~20 ps events an be localized directly:

• image reconstruction no longer necessary!
• nly attenuation correction
• real-time image formation

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Dennis R. Schaart Delft University of Technology

Ultrafast scintillators: example

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

CRT < 20 ps in principle feasible

Example: τd and τr equal to ZnO:Ga

Transit Time Spread, σ (ps) Light Yield (photons/MeV)

( ) ( )

d

1 var

T

I Ξ ≥ Θ

We have reported experimental CRTs close to CRTLB in small

• crystals. But how about larger ones?

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Dennis R. Schaart Delft University of Technology

scintillation photon speed:

γ1

gamma photon speed:

WW Moses and SE Derenzo IEEE Trans. Nucl. Sci. 46, 474-478 (1999)

Depth-of-interaction (DOI) variations deteriorate timing resolution

DOI-dependent signal delay in crystal

γ2

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Depth-of-interaction determination

Methods to determine DOI: (a) layered design, (b) single crystals with dual- sided 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

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Detector Module System

Images courtesy of Philips

Real-time signal processing Immediate digitization

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

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Dennis R. Schaart Delft University of Technology

Key enablers required:

• Bright (>> 103 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

Conclusion

CRT < 20 ps in principle feasible

Transit Time Spread (ps) Light Yield (photons/MeV)

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!

( ) ( )

d

1 var

T

I Ξ ≥ Θ

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Dennis R. Schaart Delft University of Technology

Thank You

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Dennis R. Schaart Delft University of Technology

Backup slides

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Dennis R. Schaart Delft University of Technology

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Dennis R. Schaart Delft University of Technology

∆x = uncertainty in position along LOR = c . CRT/2, where c is the speed of light. The accuracy of source position localization along line of response depends on the coincidence resolving time (CRT)

Time-of-flight PET

D ∆x The TOF benefit is proportional to ∆x/D, where D is the effective patient diameter. => The smaller the CRT, the better. State-of-the-art: CRT ≈ 500 ps ⇒ ∆x ≈ 7.5 cm.

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Some essential findings

Lower bound on the FWHM coincidence resolving time (CRTLB) for 2 detectors, assuming Gaussian time difference spectra:

LB

1 CRT N ∝

( )

d

LB LB

CRT 2.35 2 var ( ) 2.35 2 /

T

I = ⋅ Ξ = Θ

r d d LB d

1 CRT τ τ σ τ τ << ∧ << ⇒ ∝

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.

r LB

C RT τ ↓ ⇒ ↓

• S. Seifert et al, “The lower bound on the timing resolution of scintillation detectors,”

Phys Med Biol 57, 1797-1814, 2012

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Dennis R. Schaart Delft University of Technology

n = 1 n = 5 n = 10 n = 15 n = 20

Order Statistics

Timestamp for the nth detected scintillation photon Exemplary probability density functions for the nth order statistic for LYSO:Ce on MPPC-S10362-33-050C

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Lower bound for LYSO:Ce

Lower bound on the CRT for LYSO:Ce on MPPC-S10362-33-050C, using the nth, the first n, or all detected photons (“order statistics”) for timing

Parameters: τr = 90 ps τd = 44 ns σ = 120 ps Ndet = 4700

• S. Seifert et al, “The lower bound on the timing resolution of scintillation detectors,”

Phys Med Biol 57, 1797-1814, 2012

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Lower bound for LYSO:Ce

• S. Seifert et al, IEEE Transactions on Nuclear Science 59, 190-204, 2012

Calculated lower bound Measured CRT It appears possible to closely approach the CR lower bound using a leading edge trigger set at the optimum threshold level

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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