ASIMA PET Analytical Simulator
Claude Comtat
SimSET/Asim user group meeting26 October, 2011Valencia, Spain
ASIM, an Analytical Simulator Valencia, 26 October, 2011
a Non Monte Carlo Simulator
• GoalSimulator for whole-body and dynamic PETimaging
• ApplicationsTest statistical methods, based on multiplerealizations of a same scan
• Requirements•Rapid•Realistic Noise and Resolution Properties
ASIM, an Analytical Simulator Valencia, 26 October, 2011
Three-step simulation
I) Analytical calculation: simul• true un-scattered coincidences• scattered coincidences• random coincidences
II) Add noise to simulate the raw data: noise• prompt coincidences• delayed coincidences
III) Same correction procedures as used in practice:normalize
Accurate simulation of the detection in the crystals the random and scattered coincidences the noise properties for the corrected data
ASIM, an Analytical Simulator Valencia, 26 October, 2011
Emission and attenuation description
• Geometric
Analytical 3D projection
prevent non-physical interactions with projections /back-projections used in reconstructions
• Voxel-based approach
Numerical 3D projection
realistic morphological geometries (Zubal, MNI,NCAT, …)
ASIM, an Analytical Simulator Valencia, 26 October, 2011
Geometric description
Collection of truncated ellipsoids:
• emission density e(x) [Bq/cc]
• linear attenuation coefficient µ(x) [1/cm]
e(x), µ(x) e(x) e(x)
ASIM, an Analytical Simulator Valencia, 26 October, 2011
Voxel-based description
3D numerical images:
• emission density ei
• linear attenuation coefficient µi
ASIM, an Analytical Simulator Valencia, 26 October, 2011
Analytic: Input parameters
• Phantom description, its offset and orientation
• Scanner model (cylindrical scanners)
• Multi-bed acquisition
• Initial bed position
• Number of bed positions
• Amount of bed overlap
• Optional
• normalization factors
ASIM, an Analytical Simulator Valencia, 26 October, 2011
Analytic: True coincidences
ei(x), µi(x)
normalization factors ε
Ray driven 3D forward-projection
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ASIM, an Analytical Simulator Valencia, 26 October, 2011
Intrinsic Scanner Resolution
Two 2-D convolutions by thecrystal detector intrinsic P.S.F.
ASIM, an Analytical Simulator Valencia, 26 October, 2011
Analytic: Random & scatters• Not accurate• Effect on the noise of emission data• Same analytical distribution to simulate the contamination and
the correction term
Promptcoincidences
Delayedcoincidences
Truecoincidences
tE tE + 2·rE + sE
tE tE
Mean Variance
[ ] [ ] EEEEE srsrt !!++ PoissonPoisson
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ASIM, an Analytical Simulator Valencia, 26 October, 2011
Activity outside FOV
Brain Heart LiverScatters/Trues 0.3 1.0 0.8Randoms/Trues 0.2 1.3 1.2
ASIM, an Analytical Simulator Valencia, 26 October, 2011
1D model
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ASIM, an Analytical Simulator Valencia, 26 October, 2011
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Analytic Axial Random profile
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ASIM, an Analytical Simulator Valencia, 26 October, 2011
θCompton
Analytic Axial Scatter profile
z1
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⎝ Annihilation location
⎝ Compton scatter location
⎝ Compton scatter angle
⇒ Monte Carlo integrationtechnique
( )=!+ 2121// , zzzzsE
ASIM, an Analytical Simulator Valencia, 26 October, 2011
Analytic scatter & random radial profiles
• Not calculated• Input to the simulation
• 20-cm diameter cylinder scan• random: uniform profile• scatter: bell-shaped profile
( ) ( )sssr !!EE ,
ASIM, an Analytical Simulator Valencia, 26 October, 2011
Noise modelAnalytical sinograms (true, random, and scattered coincidences)
• Arbitrary unit, does NOT predict the number of coincidences
Noise level• Total numbers of true unscattered (NtE), random (NrE), and
scattered (NsE) coincidences for some range of bed positions[b1,b2] or frames [f1,f2]
• Half-life of isotope T½ (λ = ln2/ T½)
• Scan duration Δt and start time tb
⇒ calibration factors αtE, αrE, and αsE
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ASIM, an Analytical Simulator Valencia, 26 October, 2011
Noise model
Alternatively
Noise level
• Calibration factors αtE, αrE, and SF• Half-life of isotope T½ (λ = ln2/ T½)
• Scan duration Δt and start time tb
( ) EE t
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ASIM, an Analytical Simulator Valencia, 26 October, 2011
Full noise simulation
1) Acquired data
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ASIM, an Analytical Simulator Valencia, 26 October, 2011
UseUses
• Multiple realizations of a same acquisition• noise and SNR• human observer studies
Don’t use:• To evaluate Scatter correction techniques• To predict Detector response
measured simulated
ASIM, an Analytical Simulator Valencia, 26 October, 2011
ASIM, an Analytical Simulator Valencia, 26 October, 2011
Scatter & random: comparison with cylinders
hotwarm
Detector rings
Shielding
FOV
ASIM, an Analytical Simulator Valencia, 26 October, 2011
Scatter & random: comparison with patients
ASIM, an Analytical Simulator Valencia, 26 October, 2011
Validation
• Statistical distribution of the simulated events (cE)
Measured Simulated
Std. Dev.
Bed position 1 2 3
44 MBq 7 MBq 2 MBq
Gated acquisitions
ASIM, an Analytical Simulator Valencia, 26 October, 2011
Programs
1) simul• analytic emission scan (tE, sE, rE)• voxelized image (to check geometric phantom)• attenuation correction factors (ACF)• run also under MPI
2) noise• prompt and delayed emission data
3) normalize• normalization factors• scatter and random correction• attenuation correction