Variance reduction

A collimated SPECT camera detects only about 1 in 5000 emitted photons, so brute-force Monte Carlo is slow, both for characterizing the collimator-detector response (CDR) and for imaging patient phantoms. This package gives you two ways to speed it up, and they suit different needs.

Strategy	Bias	Speed	Use
Forced detection (TsForcedDetectionProjection)	approximate model, needs calibration	very fast	fast projections, patient sims
Native OpenTOPAS VR (Vr/…)	unbiased, preserves the answer	faster	speeding up full-MC while keeping absolute accuracy

Forced detection: fast projections

Forced detection replaces the physical collimator and crystal with a thin forced-detection surface and the ForcedDetectionProjection scorer, so it does not transport every photon through them. Every forward gamma that crosses the surface is projected analytically through the collimator (the Metz-Frey transmission) onto a weighted detector pixel. Because no collimator or crystal transport happens, this runs orders of magnitude faster. See examples/vr/forced_detection.txt.

The scorer parameters are HoleDiameter, SeptalThickness, and CollimatorLength (the collimator model); PixelSizeX/Y and NPixelsX/Y (the detector); and EnergyWindowLow/High (or ListMode to record every photon for post-hoc windowing). IncludeSeptalPenetration and SeptalMuPerMM add penetration. The surface component's local +z must point toward the detector. Sum the Weight column per pixel to form the projection.

Calibrate the absolute scale

The built-in transmission is uncalibrated: it is geometric only, with penetration off, and it uses the physical hole length L in place of the effective length L_eff. The absolute sensitivity therefore differs from full-MC (about 1.3e-5 against the full-MC and measured 9.1e-5 for Symbia LEHR). The projection shape and the relative contrast are correct, so calibrate the absolute scale against a full-MC or measured reference before you trust absolute counts. Producing calibrated fast models is the job of a separate model-building pipeline; this package ships the scorer.

Native OpenTOPAS variance reduction

OpenTOPAS ships its own biasing techniques, turned on with b:Vr/UseVarianceReduction = "True" and defined as s:Vr/<name>/Type = "<type>". A complete, runnable example is examples/vr/native_vr.txt, which also shows the validation workflow below.

• Directional splitting (UniformSplitting with UseDirectionalSplitting) splits secondaries in a region and aims them at a target point (TransX/Y/Z) within a radius (RMax), applied through Geant4's setSecBiasing and setDirectionalSplitting.
• Forced interaction (ForcedInteraction) forces gammas to interact in a region (ForcedDistances, processesNamed, CorrectByWeight).
• Particle splitting (GeometricalParticleSplit) splits tracks entering a component, with an optional Russian-roulette ROI (SplitNumber, RussianRoulette/ROIRadius, RussianRoulette/ROITrans).
• Also available: ImportanceSampling, WeightWindow, CrossSectionEnhancement, RangeRejection.

Validate every biased run, and sum weights

Native VR changes particle weights. Always run the biased setup against a short unbiased baseline (Vr/UseVarianceReduction = "False") and confirm the scored quantity agrees within statistics, and only score with a weight-aware scorer. OpenTOPAS's EnergyDeposit applies the weight, and this package's EDepSpectrum writes a Weight column, so histogram Edep weighted by Weight (sum weights per bin), not raw row counts. Without VR every weight is 1, so summing weights equals counting rows. Verified: with bremsstrahlung split ×10, EDepSpectrum records the split photons at weight 0.1.

Geant4 directional splitting biases secondary photon production (for example bremsstrahlung); it does not split the Compton-scattered gamma that continues as the primary track. On its own it therefore gives little gain for the core SPECT problem, getting scattered and primary gammas through a collimator to a small detector (run native_vr.txt with VR on and off: the deposited energy is essentially identical). For SPECT the effective variance reduction is forced detection above. Reach for native VR when a technique matches your problem (for example importance sampling through thick shielding), and always validate it.

Variance reduction for multi-view acquisitions

Forced detection extends to a full tomographic study: build one deck per view with the ForcedDetectionProjection surface held fixed and the phantom rotated about its long axis to the view angle, applying each view's activity decay. Rotating the phantom rather than the detector sidesteps two OpenTOPAS 4.2.p2 quirks: the forced-detection scorer's transform is wrong for a component inside a Group, and the surface then needs only one static RotX=90 instead of a compound rotation. Each view projects in seconds.

Forced detection replaces only the collimator and crystal transport, not the photon transport through the patient. At high history counts, where the phantom's self-attenuation dominates the run time, the wall-clock is therefore close to full-MC. Its real gain is detection efficiency: every forward photon contributes its weighted collimator transmission instead of surviving a roughly 1-in-5000 lottery, which yields clean projection statistics from far fewer histories. That gain is largest for high-resolution collimators such as LEHR and for count-starved views (low activity, late decay). The absolute scale is model-based, so calibrate it against full-MC or measurement as above.

Which to use

• For SPECT, use forced detection: CDR characterization, fast projections, multi-view acquisitions, and large patient sweeps. Calibrate the absolute scale once against full-MC. This is the recommended path.
• Reach for native OpenTOPAS VR only when a specific technique fits your problem (for example importance sampling through thick shielding, or particle splitting into a hard-to-reach region), and always validate the biased run against an unbiased baseline while summing weights.