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Massive collection and explosive growth of biomedical data, demands effective compression for efficient storage, transmission and sharing. Readily available visual data compression techniques have been studied extensively but tailored for natural images/videos, and thus show limited performance on biomedical data which are of different features and larger diversity. Emerging implicit neural representation (INR) is gaining momentum and demonstrates high promise for fitting diverse visual data in target-data-specific manner, but a general compression scheme covering diverse biomedical data is so far absent. To address this issue, we firstly derive a mathematical explanation for INR's spectrum concentration property and an analytical insight on the design of INR based compressor. Further, we propose a Spectrum Concentrated Implicit neural compression (SCI) which adaptively partitions the complex biomedical data into blocks matching INR's concentrated spectrum envelop, and design a funnel shaped neural network capable of representing each block with a small number of parameters. Based on this design, we conduct compression via optimization under given budget and allocate the available parameters with high representation accuracy. The experiments show SCI's superior performance to state-of-the-art methods including commercial compressors, data-driven ones, and INR based counterparts on diverse biomedical data. The source code can be found at https://github.com/RichealYoung/ImplicitNeuralCompression.git.