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For animal PET systems to achieve high sensitivity without adversely affecting spatial resolution, they must have the ability to measure depth-of-interaction (DOI). In this paper, we propose a novel four-layer PET system, and present the performances of modules built to verify the concept of the system. Each layer in the four-layer PET system has a relative offset of half a crystal pitch from other layers. Performances of the four-layer detector were estimated using a GATE Monte Carlo simulation code. The proposed system consists of six H9500 PMTs, each of which contains 3193 crystals. A sensitivity of 11.8% was obtained at the FOV center position of the proposed system. To verify the concept, we tested a PET module constructed using a H9500 flat panel PMT and LYSO crystals of cross-sectional area 1.5 x 1.5 mm². The PET module was irradiated with a 1.8 MBq 22Na radiation source from the front or side of the crystals to obtain flood images of each crystal. Collimation for side irradiation was achieved using a pair of lead blocks of dimension 50 x 100 x 200 mm³. All crystals in the four layers were clearly identified in flood images, thus verifying the DOI capability of the proposed four-layer PET system. We also investigated the optimal combination of crystal lengths in the four-layer PET system using the GATE Monte Carlo simulation code to generate events from simulated radiation sources, and using the ML-EM algorithm to reconstruct simulated radiation sources. The combination of short crystal lengths near radiation sources and long crystal lengths near the PMT provides better spatial resolution than combinations of same crystal lengths in the four-layer PET system. [ABSTRACT FROM AUTHOR]