Spin locking in liquid entrapped in nanocavities: Application to study connective tissues

Abstract

Study of the spin-lattice relaxation in the spin-locking state offers important information about atomic and molecular motions, which cannot be obtained by spin lattice relaxation in strong external magnetic fields. The application of this technique for the investigation of the spin-lattice relaxation in biological samples with fibril structures reveals an anisotropy effect for the relaxation time under spin locking, T_1ρ. To explain the anisotropy of the spin-lattice relaxation under spin-locking in connective tissue a model which represents a tissue by a set of nanocavities containing water is used. The developed model allows us to estimate the correlation time for water molecular motion in articular cartilage, τ_c=30μs and the averaged nanocavity volume, V≃5400nm³. Based on the developed model which represents a connective tissue by a set of nanocavities containing water, a good agreement with the experimental data from an articular cartilage and a tendon was demonstrated. The fitting parameters were obtained for each layer in each region of the articular cartilage. These parameters vary with the known anatomic microstructures of the tissue. Through Gaussian distributions to nanocavity directions, we have calculated the anisotropy of the relaxation time under spin locking T_1ρ for a human Achilles tendon specimen and an articular cartilage. The value of the fitting parameters obtained at matching of calculation to experimental results can be used in future investigations for characterizing the fine fibril structure of biological samples.

Keywords: Anisotropy; Cartilage; Nanocavity; Spin lattice relaxation time T(1)(ρ); Spin locking.

Fig. 1

Relaxation time under spin locking T_1ρ as a function of the correlation time, τ_c: solid blue - ${\omega }_1=2\pi \times 2000\frac{1}{s}$, dashed red - ${\omega }_1=2\pi \times 500\frac{1}{s}$. V=5400 nm³, $n=33\frac{\mathit{\text{molecules}}}{n{m}^3}$, and F = 2π. The inset shows the minimum of the T_1ρ at ${\omega }_1=2\pi \times 500\frac{1}{s}$.

Fig. 2

Angular dependence of the normalized spin locking relaxation rates 〈R_1ρ (θ)〉 for human Achilles tendon specimens. The blue solid line is calculated according to Eq. (24). The red circles are the experimental data from [20]. The fitting parameters are given in Table 1.

Fig. 3

Normalized angular dependence of the relaxation rate 〈R_1ρ (θ)〉 for the lateral region: the deep (a), middle (b), and superficial (c) layers. Blue solid line - calculations according Eq. (24), red circles - experimental data from [21]. The fitting parameters are given in Table 1.

Fig. 4

Normalized angular dependence of relaxation rate 〈R_1ρ (θ)〉 for the apex region: the deep (a), middle (b), and superficial (c) layers. Blue solid line - calculations according Eq. (24), red circles - experimental data from [21]. The fitting parameters are given in Table 1.

Fig. 5

Normalized angular dependence of relaxation rate 〈R_1ρ (θ)〉 for the medial region: the deep (a), middle (b), and superficial (c) layers. Blue solid line - calculations according Eq. (24), red circles - experimental data from [21]. The fitting parameters are given in Table 1.