Multidimensional B-spline parameterization of the detection probability of the PET scanner Biograph 16 using GATE

GATE (Geant4 Application for Emission Tomography) is a widespread, well validated and very versatile application for Monte Carlo simulations in emission tomography. It allows very detailed simulations of positron emission tomography (PET) or single photon emission computed tomography (SPECT) scanners using the general purpose Monte Carlo code Geant4. We present a method to accelerate GATE simulations when on the one hand the detection probability in the different crystals needs to be computed accurately taking into account the complex geometry of the detection system and on the other hand information on photon statistics is not required. The simulation is split into two parts. Inside the scanner (phantom or voxelized patient) the particles are tracked conventionally. When a particle leaves the phantom, the particle is transported to a virtual boundary that replaces the detection system in the simulation and the detection probability is calculated analytically by evaluating a multi-dimensional B-spline function taking into account the state of the photon on this virual border (position, incident angles, energy). The B-spline function itself is calculated by performing a conventional Monte Carlo simulation. This ¿pre¿-simulation needs to be performed only once for each scanner type. The presented method was tested by simulating the PET scanner Biograph HiREZ and using a realistic voxelized attenuation phantom. The results show good agreement between conventional GATE simulations and simulations using the B-spline. The simulations could be accelerated by a factor of around 23 yielding the same statistical accuracy.