Derivation and validation of a sensitivity formula for knife-edge slit gamma camera: A theoretical and Monte Carlo simulation study

Document Type: Original Article


1 Department of Medical Physics, Faculty of Medical Sciences, Tarbiat Modares University, Tehran, Iran

2 National Institute of Nuclear Physics, Section of Torino, Torino, Italy

3 Clinical Department, Fondazione CNAO, Pavia, Italy

4 Department of Radiation Oncology, University of Arkansas for Medical Sciences, Little Rock, Arkansas, USA


Introduction: Gamma cameras are proposed for online range verification and treatment monitoring in proton therapy.  An Analytical formula was derived and validated for sensitivity of a slit collimator based on the photon fluence concept.
Methods: Fluence formulation was generalized for photons distribution function and solved for high-energy point sources. The effect of the collimator slit size and source off-axis position on the sensitivity of the collimator were included in the formula.
Results: The analytically calculated sensitivities of the slit collimator were in good agreement with Monte Carlo results according to the Bland-Altman agreement test and Pearson correlation (r =0.998) statistical analysis with   . The mean relative error between calculated sensitivities with the derived formula and Monte Carlo was up to 0.8%. Moreover, we found that under certain conditions, the established formula is converted to the Anger equation for the pinhole collimator.
Conclusion: The analytical formula developed in this research can estimate the slit collimator sensitivity with an acceptable accuracy. The derived closed-form sensitivity formula can be applied in KE collimator design and optimization studies.


Main Subjects

  1. Krimmer J, Dauvergne D, Létang J, Testa É. Prompt-gamma monitoring in hadrontherapy: A review. Nucl Instrum Methods Phys Res A: Accel Spectrom Detect Assoc Equip. 2018;878:58-73.
  2. Parodi K. Latest developments in in-vivo imaging for proton therapy. Br J Radiol. 2020 Mar;93(1107):20190787.
  3. Fischetti M, Baroni G, Battistoni G, Bisogni G, Cerello P, Ciocca M. Inter-fractional monitoring of [Formula: see text]C ions treatments: results from a clinical trial at the CNAO facility. Sci Rep. 2020 Nov 26;10(1):20735.
  4. Richter C, Pausch G, Barczyk S, Priegnitz M, Keitz I, Thiele J, Smeets J, Stappen FV, Bombelli L, Fiorini C, Hotoiu L, Perali I, Prieels D, Enghardt W, Baumann M. First clinical application of a prompt gamma based in vivo proton range verification system. Radiother Oncol. 2016 Feb;118(2):232-7.
  5. Xie Y, Bentefour EH, Janssens G, Smeets J, Vander Stappen F, Hotoiu L, Yin L, Dolney D, Avery S, O'Grady F, Prieels D, McDonough J, Solberg TD, Lustig RA, Lin A, Teo BK. Prompt gamma imaging for in vivo range verification of pencil beam scanning proton therapy. Int J Radiat Oncol Biol Phys. 2017 Sep 1;99(1):210-218.
  6. Kalantari F, Rajabi H, Saghari M. Quantification and reduction of the collimator-detector response effect in SPECT by applying a system model during iterative image reconstruction: a simulation study. Nucl Med Commun. 2012 Mar;33(3):228-38.
  7. Mahani H, Raisali G, Kamali-Asl A, Ay MR. Collimator-detector response compensation in molecular SPECT reconstruction using STIR framework. Iran J Nucl Med. 2017;25(Suppl 1):26-34
  8. Metzler SD, Bowsher JE, Smith MF, Jaszczak RJ. Analytic determination of pinhole collimator sensitivity with penetration. IEEE Trans Med Imaging. 2001 Aug;20(8):730-41.
  9. Bom V, Joulaeizadeh L, Beekman F. Real-time prompt gamma monitoring in spot-scanning proton therapy using imaging through a knife-edge-shaped slit. Phys Med Biol. 2012 Jan 21;57(2):297-308
  10. Smeets J, Roellinghoff F, Prieels D, Stichelbaut F, Benilov A, Fiorini C. Prompt gamma imaging with a slit camera for real-time range control in proton therapy. Phys Medicine Biol. 2012 Jun 7;57(11):3371-405.
  11. Lopes PC, Pinto M, Simões H, Biegun A, Dendooven P, Oxley D, Parodi K, Schaart DR, Crespo P. Optimization of collimator designs for real-time proton range verification by measuring prompt gamma rays. 2012 IEEE Nuclear Science Symposium and Medical Imaging Conference Record (NSS/MIC); 2012.
  12. Anger HO. Radioisotope cameras. In: Hine GJ. Instrumentation in Nuclear Medicine.  London: Academic Press; 1974.
  13. Metzler SD, Accorsi R, Novak JR, Ayan AS, Jaszczak RJ. On-axis sensitivity and resolution of a slit-slat collimator. J Nucl Med. 2006 Nov;47(11):1884-90.
  14. Zhang D, Fan P, Lu W, Wang S, Xia Y, Wu Z, et al., editors. Accurate Modeling of Multi Knife-edge Slit Collimator System Response for MeV Prompt Gamma Photons in Proton Therapy Monitoring. 2018 IEEE Nuclear Science Symposium and Medical Imaging Conference Record (NSS/MIC); 2018.
  15. Accorsi R, Novak JR, Ayan AS, Metzler SD. Derivation and validation of a sensitivity formula for slit-slat collimation. IEEE Trans Med Imaging. 2008 May;27(5):709-22.
  16. Deprez K, Pato LR, Vandenberghe S, Van Holen R. Characterization of a SPECT pinhole collimator for optimal detector usage (the lofthole). Phys Med Biol. 2013 Feb 21;58(4):859-85.
  17. Van Der Have F, Vastenhouw B, Ramakers RM, Branderhorst W, Krah JO, Ji C. U-SPECT-II: an ultra-high-resolution device for molecular small-animal imaging. J Nucl Med. 2009 Apr;50(4):599-605.
  18. Hilaire E, Sarrut D, Peyrin F, Maxim V. Proton therapy monitoring by Compton imaging: influence of the large energy spectrum of the prompt-γ radiation. Phys Med Biol. 2016 Apr 21;61(8):3127-46.
  19. Formiconi AR. Geometrical response of multihole collimators. Phys Med Biol. 1998;43(11):3359.
  20. Jan S, Benoit D, Becheva E, Carlier T, Cassol F, Descourt P. GATE V6: a major enhancement of the GATE simulation platform enabling modelling of CT and radiotherapy. Phys Med Biol. 2011;56(4):881.
  21. Strulab D, Santin G, Lazaro D, Breton V, Morel C. GATE (Geant4 Application for Tomographic Emission): a PET/SPECT general-purpose simulation platform. Nucl Phys B-Proc Suppl. 2003;125:75-9.