Double-quantum-filtered NMR spectra of 23Na in bovine nasal cartilage tissue and its constituents were measured. The presence of even-rank tensors was detected in the cartilage tissue and in a suspension of collagen fibers, indicating anisotropic motion of the sodium ions. Quantitative analysis of the spectra was performed by calculating the time evolution of the second- and third-rank tensors by solving a modified Redfield equation. Analytical expressions for the spectra were obtained. It is shown that the anisotropy stems from local rather than macroscopic order. A good fit to the observed spectra was obtained for several models that assume isotropic distribution of the directors of the locally ordered sites. The local residual quadrupolar interaction was found to be 550 Hz, demonstrating the sensitivity of double-quantum filtration in the detection of anisotropic motion.