Modeling the Collimator-Detector Scattering Using Stochastic Differential Equations and COMSOL

A. Jeremic[1], T. Farncombe[2], S. Liu[2], and Y. Abdul-Rehman[1]
[1]Department of Electrical and Computer Engineering, McMaster University, Hamilton, Ontario, Canada
[2]Department of Radiology, McMaster University, Hamilton, Ontario, Canada

Single photon emission computed tomography (SPECT) is a nuclear medicine imaging technique that uses gamma rays. It has been especially useful for bone scans, cardiac perfusion imaging, tumor scans and brain imaging. The main advantage of SPECT imaging is that it can target particular tissue receptors allowing one to focus on the imaging of the diseased tissue. In most cases Monte Carlo simulations are employed in order to calculate probability density functions of scattered photons. In this paper we utilize transport equations modeling photon flow based on the definition of Markov processes and present the equivalent set of stochastic differential equation. Then, we solve the corresponding differential equations for an arbitrarily shaper collimator whose geometry is constructed using COMSOL GUI.

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