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

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.