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Monolithic scintillation detectors are very promising for high resolution and high sensitivity positron emission tomography. These detectors consist of a few cubic centimeters of scintillating material coupled to one or more position-sensitive APD arrays. The entry point of an impinging annihilation photon is estimated from the light distribution on the APD pixels. In this paper, a model will be derived that predicts the line spread function of these detectors. This model includes the influences of the finite width of the measurement beam, scatter of radiation inside the detector, light yield and intrinsic energy resolution of the scintillator, quantum efficiency, gain and excess noise factor of the avalanche photo-diode arrays, and electronic noise. With this model a better understanding of the behavior of the detector is possible, which can make optimization more efficient.