The multicomponent relaxation observed in nuclear magnetic resonance experiments in biological tissues makes it difficult to establish a correlation between specific relaxation times and tissue structural parameters. The analysis of a nanostructure (the characteristic size of 10-1000 nm) is usually based on formulas for relaxation times which depend on structural parameters at the atomic or molecular levels in the size range of 0.1-5 nm. We have recently developed an analysis method in which relaxation times' anisotropy in a sample is explicitly related to its structure of nanocavities containing a liquid or gas. However, the method is based on the analysis of experimental data on the anisotropy of relaxation times obtained by using the standard NMR technique and rotating the sample relative to a magnetic field and requires a series of experiments. In the present study, to address this challenge, we develop a new method of analysis of a multi-exponential magnetic resonance signal that does not require determining relaxation times and eliminates the sample rotation and the necessity of a series of experiments. Using the magnetic resonance imaging (MRI) technique, the total signal from the whole sample was obtained as a sum of the signals (echo decays) from all voxels. In contrast to previous research, the volumes of nanocavities and their angular distribution can be obtained by analyzing a single total signal for the entire cartilage. In addition, within the framework of this approach, it is possible to identify the reason for the multicomponent nature of relaxation. The proposed method for analyzing a single multi-exponential signal (transverse relaxation) was implemented on cartilage. Using the signal, three anatomical zones of cartilage were studied, revealing significant structural differences between them. The proposed method not only avoids the need for sample rotation but also enables repeated application of layer-by-layer magnetic resonance imaging with micron resolution. The study results allow us to suggest that water molecules contributing to the echo decay are more likely located in nanocavities formed by the fibrillar structure rather than inside the fibrils.