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We investigate the physical conditions of the gas, atomic and molecular, in the filaments in the context of Photo-Dissociation Regions (PDRs) using the KOSMA-PDR mode of clumpy clouds. We also compare the [CII] vs. [NII] integrated intensity predictions in Abel et al. 2005 for HII regions and adjacent PDRs in the Galactic disk, and check for their applicability under the extreme physical conditions present in the GC. Our preliminary results show that observed integrated intensities are well reproduced by the PDR model. The gas is exposed to a relatively low Far-UV field between 10^2 - 10^3 Draine fields. The total volume hydrogen density is well constrained between 10^4 - 10^5 cm^-3. The hydrogen ionization rate due to cosmic-rays varies between 10^-15 and 4x10^-15 s^-1, with the highest value ~ 10^-14 s^-1 found towards G0.07+0.04. Our results show that the line-of-sight contribution to the total distance of the filaments to the Arches Cluster is not negligible. The spatial distribution of the [CII]/[NII] ratio shows that the integrated intensity ratios are fairly homogeneously distributed for values below 10 in energy units. Calculations including variation on the [C/N] abundance ratio show that tight constraints on this ratio are needed to reproduce the observations.