J Nucl Med. 2007; 48 (Supplement 2):93P
Instrumentation & Data Analysis: Instrumentation
Small Animal SPECT |
Analytic expression for the sensitivity of Slit-Slit collimation and verification by Monte Carlo simulation
Ahmet Ayan1,
Scott Metzler1 and
Roberto Accorsi2
1 Radiology, University of Pennsylvania, Philadelphia, Pennsylvania; ;
2 Radiology, Children's Hospital of Philadelphia, Philadelphia, Pennsylvania
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Objectives: An analytic expression for the sensitivity of a Slit-Slit collimator for SPECT imaging is derived and validated by Monte Carlo (MC) simulation. Methods: A Slit-Slit, also known as Skew-Slit, collimator is formed by two orthogonal slits located at different distances from the detector. The geometric sensitivity g is derived with a solid angle calculation. The contribution of photons covering a distance 
L in the collimator are included in the penetrative sensitivity gpen according to the applicable transmission coefficient e-µL; this results in the definition of a sensitivity-effective slit width wse. A MC simulation code with the GEANT4 package was developed to verify both geometrical and penetrative sensitivity. Results: The analytical expression for the geometrical sensitivity is g=w1w2sin3
/{4
h1h2 [1+(h22-h12)cos2 cos2
/h12]3/2} (see Table I for symbols). Penetration is included in gpen by replacing w1 and w2 with sensitivity-effective slit widths: w1,se=w1+(1/µ)[1-[h2/h1]2cot2(
/2)cot2cos2]sin'tan(/2) and w2,se=w2+(1/µ)[1-cot2(/2)cot2sin2]sin'tan(/2) where sin'=sin/[1+(h22-h12) cos2cos2/h12 ]1/2. The sensitivity dependence on , and h was verified with MC simulation. Agreement within statistical uncertainty (<1%) between the derived analytical formulas and simulation validated the formulas. Conclusions: An analytical expression for the sensitivity of a Slit-Slit collimator was derived and validated with MC simulations. This formula along with expressions for field of view and resolution is important for evaluating the cases in which Slit-Slit collimation can outperform other collimation schemes.
Research Support (if any): NIH Grants R01-EB-001910 and R33-EB-001543
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Table I: Definition of the parameters used in the sensitivity formula
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