Simulation of emission tomography Robert L. Harrison University of Washington Medical Center...
-
date post
20-Dec-2015 -
Category
Documents
-
view
213 -
download
0
Transcript of Simulation of emission tomography Robert L. Harrison University of Washington Medical Center...
![Page 1: Simulation of emission tomography Robert L. Harrison University of Washington Medical Center Seattle, Washington, USA Supported in part by PHS grants CA42593.](https://reader035.fdocuments.us/reader035/viewer/2022062714/56649d535503460f94a2fcc2/html5/thumbnails/1.jpg)
Simulation of emission tomography
Robert L. Harrison
University of Washington Medical Center
Seattle, Washington, USA
Supported in part by PHS grants CA42593 and CA126593
![Page 2: Simulation of emission tomography Robert L. Harrison University of Washington Medical Center Seattle, Washington, USA Supported in part by PHS grants CA42593.](https://reader035.fdocuments.us/reader035/viewer/2022062714/56649d535503460f94a2fcc2/html5/thumbnails/2.jpg)
What is emission tomography?
(www.imaginis.com)
(Wikipedia)
(Stieber et al)
Radiology
Nuclear MedicineRadiotherapy
![Page 3: Simulation of emission tomography Robert L. Harrison University of Washington Medical Center Seattle, Washington, USA Supported in part by PHS grants CA42593.](https://reader035.fdocuments.us/reader035/viewer/2022062714/56649d535503460f94a2fcc2/html5/thumbnails/3.jpg)
The difference between transmission and emission
Nuclear MedicineRadiology Unclear Medicine(Wikipedia)
X-ray CTX-ray computed
tomography
PETPositron emission
tomography
![Page 4: Simulation of emission tomography Robert L. Harrison University of Washington Medical Center Seattle, Washington, USA Supported in part by PHS grants CA42593.](https://reader035.fdocuments.us/reader035/viewer/2022062714/56649d535503460f94a2fcc2/html5/thumbnails/4.jpg)
Different informationX-ray CT
X-ray computedtomography
PETPositron emission
tomographyPET/CT
Anatomy/Form
Metabolism/Function
ComplementaryInformation
(Wikipedia)
![Page 5: Simulation of emission tomography Robert L. Harrison University of Washington Medical Center Seattle, Washington, USA Supported in part by PHS grants CA42593.](https://reader035.fdocuments.us/reader035/viewer/2022062714/56649d535503460f94a2fcc2/html5/thumbnails/5.jpg)
Different information
What’s the diagnosis?
Dead…
![Page 6: Simulation of emission tomography Robert L. Harrison University of Washington Medical Center Seattle, Washington, USA Supported in part by PHS grants CA42593.](https://reader035.fdocuments.us/reader035/viewer/2022062714/56649d535503460f94a2fcc2/html5/thumbnails/6.jpg)
Emission tomography:what should we simulate?
Patient
Digital phantom
(Segars)
![Page 7: Simulation of emission tomography Robert L. Harrison University of Washington Medical Center Seattle, Washington, USA Supported in part by PHS grants CA42593.](https://reader035.fdocuments.us/reader035/viewer/2022062714/56649d535503460f94a2fcc2/html5/thumbnails/7.jpg)
Emission tomography:what should we simulate?
SPECT scannerSingle photon emission computed tomography
(George et al)
PET scannerHalf scanners with and without collimation
(Suetens)
![Page 8: Simulation of emission tomography Robert L. Harrison University of Washington Medical Center Seattle, Washington, USA Supported in part by PHS grants CA42593.](https://reader035.fdocuments.us/reader035/viewer/2022062714/56649d535503460f94a2fcc2/html5/thumbnails/8.jpg)
Emission tomography:what should we simulate?
y
x
blue photon
position =
(x1,y1,z1)
a
pink photon
position =
(x2,y2,z2)
d
Signal processing / output event position
![Page 9: Simulation of emission tomography Robert L. Harrison University of Washington Medical Center Seattle, Washington, USA Supported in part by PHS grants CA42593.](https://reader035.fdocuments.us/reader035/viewer/2022062714/56649d535503460f94a2fcc2/html5/thumbnails/9.jpg)
An example: SimSET
A Simulation System for Emission Tomography
• Goals- Flexible- Extensible- Portable- Easy-to-use- FAST
![Page 10: Simulation of emission tomography Robert L. Harrison University of Washington Medical Center Seattle, Washington, USA Supported in part by PHS grants CA42593.](https://reader035.fdocuments.us/reader035/viewer/2022062714/56649d535503460f94a2fcc2/html5/thumbnails/10.jpg)
SimSET overview
![Page 11: Simulation of emission tomography Robert L. Harrison University of Washington Medical Center Seattle, Washington, USA Supported in part by PHS grants CA42593.](https://reader035.fdocuments.us/reader035/viewer/2022062714/56649d535503460f94a2fcc2/html5/thumbnails/11.jpg)
Object = patientGeometric description
Voxelized description
Attenuation
Activity
![Page 12: Simulation of emission tomography Robert L. Harrison University of Washington Medical Center Seattle, Washington, USA Supported in part by PHS grants CA42593.](https://reader035.fdocuments.us/reader035/viewer/2022062714/56649d535503460f94a2fcc2/html5/thumbnails/12.jpg)
Object: voxelized
• Voxelized objects:– Easier to define complex objects.
• Patient scans are voxelized.
– Faster tracking in complex objects.• Obvious which the next voxel is.• However, the time tracking through the object
does increase as the voxelization grows finer.
![Page 13: Simulation of emission tomography Robert L. Harrison University of Washington Medical Center Seattle, Washington, USA Supported in part by PHS grants CA42593.](https://reader035.fdocuments.us/reader035/viewer/2022062714/56649d535503460f94a2fcc2/html5/thumbnails/13.jpg)
Object: processes
• Generate decays.• Decay products.• Tracking particles/photons.
– Compton scatter.– Coherent scatter.– Photoabsorption.– Pair production.– Fluorescence.– Brehmstrahlung.
![Page 14: Simulation of emission tomography Robert L. Harrison University of Washington Medical Center Seattle, Washington, USA Supported in part by PHS grants CA42593.](https://reader035.fdocuments.us/reader035/viewer/2022062714/56649d535503460f94a2fcc2/html5/thumbnails/14.jpg)
Object: generate next decay• Which voxel? Two options:
- Make a list of all the voxels with the sum of activity in them to that point:
voxel1 activity1;
voxel2 activity1 + activity2; ….
voxelN TotalActivity.
- Pick a random number, u, between 0 and TotalActivity.
- Next decay generated in the last voxel with the summed activity < u.
- Generate all the decays in voxel1;
- Generate all the decays in voxel2;
- …
- SimSET uses this method: it is faster.
- The decays are not generated in the correct order timewise.
![Page 15: Simulation of emission tomography Robert L. Harrison University of Washington Medical Center Seattle, Washington, USA Supported in part by PHS grants CA42593.](https://reader035.fdocuments.us/reader035/viewer/2022062714/56649d535503460f94a2fcc2/html5/thumbnails/15.jpg)
Object: generate next decay
- 3 random numbers, one each for x, y, z.
• Choose a random location in the voxel. How?
![Page 16: Simulation of emission tomography Robert L. Harrison University of Washington Medical Center Seattle, Washington, USA Supported in part by PHS grants CA42593.](https://reader035.fdocuments.us/reader035/viewer/2022062714/56649d535503460f94a2fcc2/html5/thumbnails/16.jpg)
Object: generate next decay• When?
– The mean number of decays in a voxel is the product of the scan time and the activity in the voxel.
– The distribution of the actual number of decays is Poisson.
• What distribution do we use to determine the elapsed time to the next decay?- The exponential distribution (1 random number).- Keep generating decays until the sum of the elapsed times is ≥ the scan time.
![Page 17: Simulation of emission tomography Robert L. Harrison University of Washington Medical Center Seattle, Washington, USA Supported in part by PHS grants CA42593.](https://reader035.fdocuments.us/reader035/viewer/2022062714/56649d535503460f94a2fcc2/html5/thumbnails/17.jpg)
Object: generate next decay• What now?• Depends on the isotope: some combination of
– alpha (Helium nuclei)– beta (electrons or positrons)– gamma (photons)
• SimSET only produces one particle per decay:– positron (PET); or– photon (SPECT) < 1000 keV, all photons one energy.– No 124I, a positron emitter that also emits photons:
MeV of photon % of decays
1.37 3
1.51 4
1.69 14
2.09 2
2.26 1.5
![Page 18: Simulation of emission tomography Robert L. Harrison University of Washington Medical Center Seattle, Washington, USA Supported in part by PHS grants CA42593.](https://reader035.fdocuments.us/reader035/viewer/2022062714/56649d535503460f94a2fcc2/html5/thumbnails/18.jpg)
Object: annihilate positron (PET only)
• SimSET does not track positrons.– Too many interactions; too
computationally intensive.– Uses a probabilistic range
model instead.– Positron/electron
annihilation at end of range.– Two (almost) anti-parallel
511 keV photons produced.– Photon polarization not
modeled.
![Page 19: Simulation of emission tomography Robert L. Harrison University of Washington Medical Center Seattle, Washington, USA Supported in part by PHS grants CA42593.](https://reader035.fdocuments.us/reader035/viewer/2022062714/56649d535503460f94a2fcc2/html5/thumbnails/19.jpg)
Object: pick photon direction
• Generate a random 3D unit vector. How?
• 2 random numbers:– One picks an azimuthal
angle between 0 and .– The other picks the cosine
of the inclination angle between -1 and 1.
– This results in a uniform distribution over the unit sphere.
![Page 20: Simulation of emission tomography Robert L. Harrison University of Washington Medical Center Seattle, Washington, USA Supported in part by PHS grants CA42593.](https://reader035.fdocuments.us/reader035/viewer/2022062714/56649d535503460f94a2fcc2/html5/thumbnails/20.jpg)
Object: track photons
• How far will a photon travel in a uniform medium?
is the material’s attenuation coefficient.
![Page 21: Simulation of emission tomography Robert L. Harrison University of Washington Medical Center Seattle, Washington, USA Supported in part by PHS grants CA42593.](https://reader035.fdocuments.us/reader035/viewer/2022062714/56649d535503460f94a2fcc2/html5/thumbnails/21.jpg)
Object: track photons• How far will a
photon travel in a changing medium?
• Sample a dimensionless distance, free paths, p, from the exponential distribution with = 1.
• Weight the distance traveled by the true ’s.
Travel until
dii = p
![Page 22: Simulation of emission tomography Robert L. Harrison University of Washington Medical Center Seattle, Washington, USA Supported in part by PHS grants CA42593.](https://reader035.fdocuments.us/reader035/viewer/2022062714/56649d535503460f94a2fcc2/html5/thumbnails/22.jpg)
Object: photon interaction• If the photon leaves the object before traveling
the sampled number of free paths, we pass it to the collimator module.
• Otherwise randomly choose an interaction from:– Photoabsorption.– Compton scatter.– Coherent scatter.
• If the photon scatters, continue tracking.• SimSET does not model pair production or
secondary photons.
![Page 23: Simulation of emission tomography Robert L. Harrison University of Washington Medical Center Seattle, Washington, USA Supported in part by PHS grants CA42593.](https://reader035.fdocuments.us/reader035/viewer/2022062714/56649d535503460f94a2fcc2/html5/thumbnails/23.jpg)
Object: choosing interaction type
• If the probability of:– Photoabsorption is p < 1;– Compton scatter is c < 1 - p;– Coherent scatter is 1 - p - c.
• Sample u randomly from (0,1).• If
u < p then photoabsorb;p < u < p + c then Compton scatter;u ≥ p + c then coherent scatter.
Water interaction probabilities
0.0001
0.001
0.01
0.1
1
0 200 400 600 800 1000
Photon energy (keV)
Photoabsorption
Compton
Rayleigh
Lead interaction probabilities
0.0001
0.001
0.01
0.1
1
0 500 1000
Photon energy (keV)
Photoabsorption
Compton
Rayleigh
![Page 24: Simulation of emission tomography Robert L. Harrison University of Washington Medical Center Seattle, Washington, USA Supported in part by PHS grants CA42593.](https://reader035.fdocuments.us/reader035/viewer/2022062714/56649d535503460f94a2fcc2/html5/thumbnails/24.jpg)
Object: simulating interactions
• Photoabsorption:– Discard photon.
• Compton scatter:– Klein-Nishini density function to determine the scatter angle.– Acceptance-rejection method.– Klein-Nishina is a free electron approximation.– Photon loses energy as function of scatter angle.
• Coherent scatter:– Table lookup with linear interpolation to determine scatter angle.– No energy lost.– Generally very small angles (< 5 degrees).
![Page 25: Simulation of emission tomography Robert L. Harrison University of Washington Medical Center Seattle, Washington, USA Supported in part by PHS grants CA42593.](https://reader035.fdocuments.us/reader035/viewer/2022062714/56649d535503460f94a2fcc2/html5/thumbnails/25.jpg)
Collimators
• Tracking is the same as through object.– Fluorescence (ignored in SimSET) is an
issue for Thallium SPECT and deadtime.
• Efficiency is a problem. Of decays in the FOV,– PET: only 1/20 - 1/200 detected.– SPECT: only 1/10000 - 1/1000000 are
detected.
![Page 26: Simulation of emission tomography Robert L. Harrison University of Washington Medical Center Seattle, Washington, USA Supported in part by PHS grants CA42593.](https://reader035.fdocuments.us/reader035/viewer/2022062714/56649d535503460f94a2fcc2/html5/thumbnails/26.jpg)
Collimators
• SPECT collimators– Hunk of lead with
hexagonal holes.– Collimator and
detector circle patient.– SimSET models
geometric collimator.
• PET collimators– Cylindrical annuli of
lead or tungsten to reduce randoms and scatter.
– Trend towards no collimation in FOV.
![Page 27: Simulation of emission tomography Robert L. Harrison University of Washington Medical Center Seattle, Washington, USA Supported in part by PHS grants CA42593.](https://reader035.fdocuments.us/reader035/viewer/2022062714/56649d535503460f94a2fcc2/html5/thumbnails/27.jpg)
Collimators
• SimSET models only the collimators shown on previous slide.
• Other collimation possibilities (mainly SPECT):– Pinhole.– Rotating slat.– Slit.– Electronic.
• When (if) the photon escapes the collimator, SimSET passes it to the detector module.
![Page 28: Simulation of emission tomography Robert L. Harrison University of Washington Medical Center Seattle, Washington, USA Supported in part by PHS grants CA42593.](https://reader035.fdocuments.us/reader035/viewer/2022062714/56649d535503460f94a2fcc2/html5/thumbnails/28.jpg)
Detectors
• Tracking remains the same, but our interests change.– We are now interested in
where/how much energy is deposited.
![Page 29: Simulation of emission tomography Robert L. Harrison University of Washington Medical Center Seattle, Washington, USA Supported in part by PHS grants CA42593.](https://reader035.fdocuments.us/reader035/viewer/2022062714/56649d535503460f94a2fcc2/html5/thumbnails/29.jpg)
Detectors/electronics
• When a photon interaction deposits energy in the detector crystal, the energy is converted into a shower of scintillation photons.
• The photomultiplier tubes convert (some of) these photons into a electrical signals.
• The electronics convert the signals into a detected position and energy.
• Multiple interactions usually lead to incorrect positioning.
![Page 30: Simulation of emission tomography Robert L. Harrison University of Washington Medical Center Seattle, Washington, USA Supported in part by PHS grants CA42593.](https://reader035.fdocuments.us/reader035/viewer/2022062714/56649d535503460f94a2fcc2/html5/thumbnails/30.jpg)
Detectors/electronics
• SimSET ignores the scintillation photons.– These could be tracked.
• Detected position is computed using the energy-weighted centroid of the interactions in crystal.
• Detected energy is the sum of the energies deposited in crystal. It can be ‘blurred’ with a Gaussian.
• For PET, time-of-flight offset is computed - it can be blurred as well.
![Page 31: Simulation of emission tomography Robert L. Harrison University of Washington Medical Center Seattle, Washington, USA Supported in part by PHS grants CA42593.](https://reader035.fdocuments.us/reader035/viewer/2022062714/56649d535503460f94a2fcc2/html5/thumbnails/31.jpg)
Binning• Line-of-response or crystal pair.• Detected energy.• True, scatter, or random (PET only) state.• Time-of-flight position (PET only).
(Schmitz)
![Page 32: Simulation of emission tomography Robert L. Harrison University of Washington Medical Center Seattle, Washington, USA Supported in part by PHS grants CA42593.](https://reader035.fdocuments.us/reader035/viewer/2022062714/56649d535503460f94a2fcc2/html5/thumbnails/32.jpg)
Take away• For emission tomography, the patient is injected
with (or ingests, etc.) a radio-labeled tracer.• Emission tomography is used to explore
metabolism.• One type of simulation tracks individual photons
through the ‘patient’, collimators and detectors.• Designing such a simulation requires knowledge of
photon interactions with matter.• Some details may be skipped to improve
efficiency, but this will bias the results and should be done with care.
![Page 33: Simulation of emission tomography Robert L. Harrison University of Washington Medical Center Seattle, Washington, USA Supported in part by PHS grants CA42593.](https://reader035.fdocuments.us/reader035/viewer/2022062714/56649d535503460f94a2fcc2/html5/thumbnails/33.jpg)
![Page 34: Simulation of emission tomography Robert L. Harrison University of Washington Medical Center Seattle, Washington, USA Supported in part by PHS grants CA42593.](https://reader035.fdocuments.us/reader035/viewer/2022062714/56649d535503460f94a2fcc2/html5/thumbnails/34.jpg)
ReferencesJ.T. Bushberg, The essential physics of medical imaging, Lippincott Williams & Wilkins, 2002.
K.P. George et al, Brain Imaging in Neurocommunicative Disorders, in Medical speech-language pathology: a practitioner's guide, ed. A.F. Johnson, Thieme, 1998.
D.E. Heron et al, FDG-PET and PET/CT in Radiation Therapy Simulation and Management of Patients Who Have Primary and Recurrent Breast Cancer, PET Clin, 1:39–49, 2006.
E.G.A. Aird and J. Conway, CT simulation for radiotherapy treatment planning, British J Radiology, 75:937-949, 2002.
R. McGarry and A.T. Turrisi, Lung Cancer, in Handbook of Radiation Oncology: Basic Principles and Clinical Protocols, ed. B.G. Haffty and L.D. Wilson, Jones & Bartlett Publishers, 2008.
R. Schmitz et al, The Physics of PET/CT Scanners, in PET and PET/CT: a clinical guide, ed. E. Lin and A. Alavi, Thieme, 2005.
W.P. Segars and B.M.W. Tsui, Study of the efficacy of respiratory gating in myocardial SPECT using the new 4-D NCAT phantom, IEEE Transactions on Nuclear Science, 49(3):675-679, 2002.
V.W. Stieber et al, Central Nervous System Tumors, in Technical Basis of Radiation Therapy: Practical Clinical Applications, ed. S.H. Levitt et al, Springer, 2008.
P. Suetens, Fundamentals of medical imaging, Cambridge University Press, 2002.
depts.washington.edu/simset/html/simset_main.html
www.wofford.org/ecs/ScientificProgramming/MonteCarlo/index.htm
www.impactscan.org/slides/impactcourse/introduction_to_ct_in_radiotherapy
![Page 35: Simulation of emission tomography Robert L. Harrison University of Washington Medical Center Seattle, Washington, USA Supported in part by PHS grants CA42593.](https://reader035.fdocuments.us/reader035/viewer/2022062714/56649d535503460f94a2fcc2/html5/thumbnails/35.jpg)
What is SimSET used for?
• Optimizing patient studies.• Assessing and improving quantitation.• Prototyping tomographs.
![Page 36: Simulation of emission tomography Robert L. Harrison University of Washington Medical Center Seattle, Washington, USA Supported in part by PHS grants CA42593.](https://reader035.fdocuments.us/reader035/viewer/2022062714/56649d535503460f94a2fcc2/html5/thumbnails/36.jpg)
Variance reduction / importance sampling
![Page 37: Simulation of emission tomography Robert L. Harrison University of Washington Medical Center Seattle, Washington, USA Supported in part by PHS grants CA42593.](https://reader035.fdocuments.us/reader035/viewer/2022062714/56649d535503460f94a2fcc2/html5/thumbnails/37.jpg)
Variance reduction goal
• Increase the precision of the simulation output achieved for a given effort:– Precision of the output is partly dependent
on the number of detections.– Effort is the amount of CPU time we need
for the simulation.
![Page 38: Simulation of emission tomography Robert L. Harrison University of Washington Medical Center Seattle, Washington, USA Supported in part by PHS grants CA42593.](https://reader035.fdocuments.us/reader035/viewer/2022062714/56649d535503460f94a2fcc2/html5/thumbnails/38.jpg)
Variance reduction concepts
• Increasing the efficiency of photon tracking.
• Bias.
• Data correlations.
• Importance sampling.
• Measuring efficiency.
![Page 39: Simulation of emission tomography Robert L. Harrison University of Washington Medical Center Seattle, Washington, USA Supported in part by PHS grants CA42593.](https://reader035.fdocuments.us/reader035/viewer/2022062714/56649d535503460f94a2fcc2/html5/thumbnails/39.jpg)
Variance reduction concepts: photon tracking efficiency.
• Decrease the amount of time we spend per photon
OR
• Increase the likelihood that each photon will be detected.
![Page 40: Simulation of emission tomography Robert L. Harrison University of Washington Medical Center Seattle, Washington, USA Supported in part by PHS grants CA42593.](https://reader035.fdocuments.us/reader035/viewer/2022062714/56649d535503460f94a2fcc2/html5/thumbnails/40.jpg)
Variance reduction concepts: photon tracking efficiency.
• In general, decreasing the time spent tracking a photon is considered code optimization (not variance reduction).
• Most variance reduction methods increase the likelihood that photons will be detected.– In emission tomography only 1/20th (3D
PET) to 1/100000th (SPECT) of decays are detected.
![Page 41: Simulation of emission tomography Robert L. Harrison University of Washington Medical Center Seattle, Washington, USA Supported in part by PHS grants CA42593.](https://reader035.fdocuments.us/reader035/viewer/2022062714/56649d535503460f94a2fcc2/html5/thumbnails/41.jpg)
Variance reduction concepts: bias
• Variance reduction methods can be unbiased or biased.– Unbiased methods are safer.– Biased methods can greatly increase
apparent efficiency.
![Page 42: Simulation of emission tomography Robert L. Harrison University of Washington Medical Center Seattle, Washington, USA Supported in part by PHS grants CA42593.](https://reader035.fdocuments.us/reader035/viewer/2022062714/56649d535503460f94a2fcc2/html5/thumbnails/42.jpg)
Variance reduction concepts: bias
![Page 43: Simulation of emission tomography Robert L. Harrison University of Washington Medical Center Seattle, Washington, USA Supported in part by PHS grants CA42593.](https://reader035.fdocuments.us/reader035/viewer/2022062714/56649d535503460f94a2fcc2/html5/thumbnails/43.jpg)
Variance reduction concepts: bias
![Page 44: Simulation of emission tomography Robert L. Harrison University of Washington Medical Center Seattle, Washington, USA Supported in part by PHS grants CA42593.](https://reader035.fdocuments.us/reader035/viewer/2022062714/56649d535503460f94a2fcc2/html5/thumbnails/44.jpg)
Variance reduction concepts: bias
![Page 45: Simulation of emission tomography Robert L. Harrison University of Washington Medical Center Seattle, Washington, USA Supported in part by PHS grants CA42593.](https://reader035.fdocuments.us/reader035/viewer/2022062714/56649d535503460f94a2fcc2/html5/thumbnails/45.jpg)
Variance reduction concepts: data correlations
• In experimental data, different events are uncorrelated.
• Many variance reduction methods add correlations between events.
• In choosing variance reduction methods to use, be clear about how much correlation is acceptable.
![Page 46: Simulation of emission tomography Robert L. Harrison University of Washington Medical Center Seattle, Washington, USA Supported in part by PHS grants CA42593.](https://reader035.fdocuments.us/reader035/viewer/2022062714/56649d535503460f94a2fcc2/html5/thumbnails/46.jpg)
Variance reduction concepts: importance sampling
![Page 47: Simulation of emission tomography Robert L. Harrison University of Washington Medical Center Seattle, Washington, USA Supported in part by PHS grants CA42593.](https://reader035.fdocuments.us/reader035/viewer/2022062714/56649d535503460f94a2fcc2/html5/thumbnails/47.jpg)
Variance reduction concepts: importance sampling
• We can create more decays in cone A than cone B,
• but this would bias our output data.• To avoid bias we give each decay a weight
that tells us how many ‘real world’ decays it represents.
• For our output data we sum weights rather than incrementing counts.
• In all variance reduction techniques, the weight of a decay/photon is adjusted to eliminate bias.
![Page 48: Simulation of emission tomography Robert L. Harrison University of Washington Medical Center Seattle, Washington, USA Supported in part by PHS grants CA42593.](https://reader035.fdocuments.us/reader035/viewer/2022062714/56649d535503460f94a2fcc2/html5/thumbnails/48.jpg)
Variance reduction concepts: measuring efficiency
• If we oversample cone A by a factor of 2, and undersample cone B by a factor of 10, we will collect a lot of events with weight 0.5.
![Page 49: Simulation of emission tomography Robert L. Harrison University of Washington Medical Center Seattle, Washington, USA Supported in part by PHS grants CA42593.](https://reader035.fdocuments.us/reader035/viewer/2022062714/56649d535503460f94a2fcc2/html5/thumbnails/49.jpg)
Variance reduction concepts: measuring efficiency
• But occasionally an event from cone B will scatter and be detected with weight 10.
![Page 50: Simulation of emission tomography Robert L. Harrison University of Washington Medical Center Seattle, Washington, USA Supported in part by PHS grants CA42593.](https://reader035.fdocuments.us/reader035/viewer/2022062714/56649d535503460f94a2fcc2/html5/thumbnails/50.jpg)
Variance reduction concepts: measuring efficiency
• A list of N non-uniformly weighted events is not as valuable as a list of N uniformly weighted events (e.g. counts).
• How valuable are non-uniformly weighted events?
![Page 51: Simulation of emission tomography Robert L. Harrison University of Washington Medical Center Seattle, Washington, USA Supported in part by PHS grants CA42593.](https://reader035.fdocuments.us/reader035/viewer/2022062714/56649d535503460f94a2fcc2/html5/thumbnails/51.jpg)
Variance reduction concepts: measuring efficiency
• We value the data by its signal-to-noise.• We define a ‘quality factor’, 0<Q≤1
which gives the relative value of a list of events as compared to a list of uniformly weighted events.
![Page 52: Simulation of emission tomography Robert L. Harrison University of Washington Medical Center Seattle, Washington, USA Supported in part by PHS grants CA42593.](https://reader035.fdocuments.us/reader035/viewer/2022062714/56649d535503460f94a2fcc2/html5/thumbnails/52.jpg)
Variance reduction concepts: measuring efficiency
• The cost of producing data is the CPU time, T, required to generate it.
• We divide the data’s value by its cost to get a computational figure-of-merit:
![Page 53: Simulation of emission tomography Robert L. Harrison University of Washington Medical Center Seattle, Washington, USA Supported in part by PHS grants CA42593.](https://reader035.fdocuments.us/reader035/viewer/2022062714/56649d535503460f94a2fcc2/html5/thumbnails/53.jpg)
Variance reduction techniques
• Stratification.• Forced detection.• Photon splitting.• Russian roulette.• Fictitious interaction tracking / delta scattering.• Convolution forced detection.• Forced non-absorption.• Forced first interaction in detectors.
![Page 54: Simulation of emission tomography Robert L. Harrison University of Washington Medical Center Seattle, Washington, USA Supported in part by PHS grants CA42593.](https://reader035.fdocuments.us/reader035/viewer/2022062714/56649d535503460f94a2fcc2/html5/thumbnails/54.jpg)
Variance reduction techniques: stratification
• In stratification we sample the starting location/direction of decays/photons based on the probability of detection.
• A decay/photon is weighted to account for any over- or under-sampling.
• Ideally locations/directions are over-/under-sampled in proportion to their probability of detection (productivity).
![Page 55: Simulation of emission tomography Robert L. Harrison University of Washington Medical Center Seattle, Washington, USA Supported in part by PHS grants CA42593.](https://reader035.fdocuments.us/reader035/viewer/2022062714/56649d535503460f94a2fcc2/html5/thumbnails/55.jpg)
Variance reduction techniques: stratification
![Page 56: Simulation of emission tomography Robert L. Harrison University of Washington Medical Center Seattle, Washington, USA Supported in part by PHS grants CA42593.](https://reader035.fdocuments.us/reader035/viewer/2022062714/56649d535503460f94a2fcc2/html5/thumbnails/56.jpg)
Variance reduction techniques: stratification
![Page 57: Simulation of emission tomography Robert L. Harrison University of Washington Medical Center Seattle, Washington, USA Supported in part by PHS grants CA42593.](https://reader035.fdocuments.us/reader035/viewer/2022062714/56649d535503460f94a2fcc2/html5/thumbnails/57.jpg)
Variance reduction techniques: stratification
![Page 58: Simulation of emission tomography Robert L. Harrison University of Washington Medical Center Seattle, Washington, USA Supported in part by PHS grants CA42593.](https://reader035.fdocuments.us/reader035/viewer/2022062714/56649d535503460f94a2fcc2/html5/thumbnails/58.jpg)
Variance reduction techniques: forced detection
• Force a copy of a photon from its current position/direction to the detector.
![Page 59: Simulation of emission tomography Robert L. Harrison University of Washington Medical Center Seattle, Washington, USA Supported in part by PHS grants CA42593.](https://reader035.fdocuments.us/reader035/viewer/2022062714/56649d535503460f94a2fcc2/html5/thumbnails/59.jpg)
Variance reduction techniques: forced detection
• At photon creation and after each scatter:– Create a copy of the photon.– Force an interaction in the field-of-view.– Force the interaction to be a scatter.– Force the scatter to be in a detectable direction.– Force the photon through the attenuating material to the
detector.
• Continue tracking original photon.
![Page 60: Simulation of emission tomography Robert L. Harrison University of Washington Medical Center Seattle, Washington, USA Supported in part by PHS grants CA42593.](https://reader035.fdocuments.us/reader035/viewer/2022062714/56649d535503460f94a2fcc2/html5/thumbnails/60.jpg)
Variance reduction techniques: forced detection
– Create a copy of the photon.– Force an interaction in the field-of-view (FOV).
![Page 61: Simulation of emission tomography Robert L. Harrison University of Washington Medical Center Seattle, Washington, USA Supported in part by PHS grants CA42593.](https://reader035.fdocuments.us/reader035/viewer/2022062714/56649d535503460f94a2fcc2/html5/thumbnails/61.jpg)
Variance reduction techniques: forced detection
– Force the interaction to be a scatter.– Force the scatter to be in a detectable direction.
![Page 62: Simulation of emission tomography Robert L. Harrison University of Washington Medical Center Seattle, Washington, USA Supported in part by PHS grants CA42593.](https://reader035.fdocuments.us/reader035/viewer/2022062714/56649d535503460f94a2fcc2/html5/thumbnails/62.jpg)
Variance reduction techniques: forced detection
– Force the photon through the attenuating material to the detector.
– (This step is also done for true photons before any other tracking is done.)
![Page 63: Simulation of emission tomography Robert L. Harrison University of Washington Medical Center Seattle, Washington, USA Supported in part by PHS grants CA42593.](https://reader035.fdocuments.us/reader035/viewer/2022062714/56649d535503460f94a2fcc2/html5/thumbnails/63.jpg)
Variance reduction techniques: forced detection
• Continue tracking original photon normally:– If it exits the object, discard it.
– If it is absorbed, discard it.
– If it scatters, repeat forced detection steps.
![Page 64: Simulation of emission tomography Robert L. Harrison University of Washington Medical Center Seattle, Washington, USA Supported in part by PHS grants CA42593.](https://reader035.fdocuments.us/reader035/viewer/2022062714/56649d535503460f94a2fcc2/html5/thumbnails/64.jpg)
Variance reduction techniques: stratification and forced detection
• Stratification and forced detection are complimentary techniques.– The weight
differences introduced by stratification tend to be reduced by forced detection.
![Page 65: Simulation of emission tomography Robert L. Harrison University of Washington Medical Center Seattle, Washington, USA Supported in part by PHS grants CA42593.](https://reader035.fdocuments.us/reader035/viewer/2022062714/56649d535503460f94a2fcc2/html5/thumbnails/65.jpg)
Variance reduction techniques: photon splitting
aa
5 11111⇒
![Page 66: Simulation of emission tomography Robert L. Harrison University of Washington Medical Center Seattle, Washington, USA Supported in part by PHS grants CA42593.](https://reader035.fdocuments.us/reader035/viewer/2022062714/56649d535503460f94a2fcc2/html5/thumbnails/66.jpg)
Variance reduction techniques: Russian roulette
aa
0.21⇒or( )nothing20%80%
![Page 67: Simulation of emission tomography Robert L. Harrison University of Washington Medical Center Seattle, Washington, USA Supported in part by PHS grants CA42593.](https://reader035.fdocuments.us/reader035/viewer/2022062714/56649d535503460f94a2fcc2/html5/thumbnails/67.jpg)
Variance reduction techniques: splitting and roulette
a
Start trackinga photonFinish trackinga photonCPU timeSplitting doesn’tmake senseRoulette doesn’tmake senseSplitting may bedangerous
![Page 68: Simulation of emission tomography Robert L. Harrison University of Washington Medical Center Seattle, Washington, USA Supported in part by PHS grants CA42593.](https://reader035.fdocuments.us/reader035/viewer/2022062714/56649d535503460f94a2fcc2/html5/thumbnails/68.jpg)
Variance reduction techniques: fictitious interaction tracking (delta scattering)
• Tracking through a voxelized phantom takes time.
![Page 69: Simulation of emission tomography Robert L. Harrison University of Washington Medical Center Seattle, Washington, USA Supported in part by PHS grants CA42593.](https://reader035.fdocuments.us/reader035/viewer/2022062714/56649d535503460f94a2fcc2/html5/thumbnails/69.jpg)
Variance reduction techniques: fictitious interaction tracking (delta scattering)
• Fictitious interaction tracking pretends that the everything has the same attenuation coefficient as bone.
• A new interaction possibility is added for each tissue, the fictitious interaction.
• The distance to travel can then be computed directly.
• If a fictitious interaction is selected, the photon continues in the same direction, unchanged.
![Page 70: Simulation of emission tomography Robert L. Harrison University of Washington Medical Center Seattle, Washington, USA Supported in part by PHS grants CA42593.](https://reader035.fdocuments.us/reader035/viewer/2022062714/56649d535503460f94a2fcc2/html5/thumbnails/70.jpg)
Variance reduction techniques: convolution forced detection
• Convolution forced detection is mainly used for SPECT.
• Tracking is similar to regular forced detection until the forced scatter direction is chosen.
![Page 71: Simulation of emission tomography Robert L. Harrison University of Washington Medical Center Seattle, Washington, USA Supported in part by PHS grants CA42593.](https://reader035.fdocuments.us/reader035/viewer/2022062714/56649d535503460f94a2fcc2/html5/thumbnails/71.jpg)
Variance reduction techniques: convolution forced detection
• The direction is chosen perpendicular to the current collimator position.
• The photon’s weight is distributed over the detector by convolving with a depth dependent point-spread function.
![Page 72: Simulation of emission tomography Robert L. Harrison University of Washington Medical Center Seattle, Washington, USA Supported in part by PHS grants CA42593.](https://reader035.fdocuments.us/reader035/viewer/2022062714/56649d535503460f94a2fcc2/html5/thumbnails/72.jpg)
Variance reduction techniques: forced non-absorption
• At interactions in the object and collimator, do not allow the photon to be absorbed.
![Page 73: Simulation of emission tomography Robert L. Harrison University of Washington Medical Center Seattle, Washington, USA Supported in part by PHS grants CA42593.](https://reader035.fdocuments.us/reader035/viewer/2022062714/56649d535503460f94a2fcc2/html5/thumbnails/73.jpg)
Variance reduction techniques: forced first interaction
• In the detector, force at least one interaction to occur.
![Page 74: Simulation of emission tomography Robert L. Harrison University of Washington Medical Center Seattle, Washington, USA Supported in part by PHS grants CA42593.](https://reader035.fdocuments.us/reader035/viewer/2022062714/56649d535503460f94a2fcc2/html5/thumbnails/74.jpg)
Variance reduction techniques: bias and correlation
• With the exception of convolution forced detection, all the techniques discussed are unbiased.
• Forced detection adds minimal correlations to the output data.
• Photon splitting can add noticeable correlations to the output data if done too late in the photon tracking.
• Convolution forced detection adds noticeable correlations between neighboring bins in the output data.
![Page 75: Simulation of emission tomography Robert L. Harrison University of Washington Medical Center Seattle, Washington, USA Supported in part by PHS grants CA42593.](https://reader035.fdocuments.us/reader035/viewer/2022062714/56649d535503460f94a2fcc2/html5/thumbnails/75.jpg)
Variance reduction: closing thoughts
• Variance reduction methods can improve the efficiency of emission tomography simulations.
• They require substantially more effort to implement than normal Monte Carlo.
• Efficiency gains using variance reduction are very problem dependent.– As little as 1.5 - 2 for some 3D PET simulations.– 1000+ for some SPECT simulations.
• Events with extremely high weights can be a problem.
![Page 76: Simulation of emission tomography Robert L. Harrison University of Washington Medical Center Seattle, Washington, USA Supported in part by PHS grants CA42593.](https://reader035.fdocuments.us/reader035/viewer/2022062714/56649d535503460f94a2fcc2/html5/thumbnails/76.jpg)