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We are developing a small bore PET scanner with four-layer depth-of-interaction (DOI) detectors arranged in a hexagonal shape for small animal imaging. In image reconstruction of the small bore DOI-PET, the difficulty is irregular detector sampling caused by inter-detector gaps and the dimension of data increases in proportion to the square of the number of DOI layers. We need to apply an accurate system model based on an on-the-fly calculation because it is difficult to pre-compute and preserve a huge number of lines of response (LORs). In this work, we propose a system model of small bore DOI-PET scanners for fast and accurate 3D image reconstruction. First, we compare two system models which represent the detector response function (DRF) as the combination of several flight paths of gamma-rays and an optimized number of flight paths. Second, we propose anew ray-tracing method based on the Zhao-Reader algorithm. The results show that a high resolution image is reconstructed in 3 hours per OSEM iteration from 1.0times 109 LORs.