Theory of MRI contrast in the annulus fibrosus of the intervertebral disc

Abstract

Objective: Here we develop a three-dimensional analytic model for MR image contrast of collagen lamellae in the annulus fibrosus of the intervertebral disc of the spine, based on the dependence of the MRI signal on collagen fiber orientation.

Materials and methods: High-resolution MRI scans were performed at 1.5 and 7 T on intact whole disc specimens from ovine, bovine, and human spines. An analytic model that approximates the three-dimensional curvature of the disc lamellae was developed to explain inter-lamellar contrast and intensity variations in the annulus. The model is based on the known anisotropic dipolar relaxation of water in tissues with ordered collagen.

Results: Simulated MRI data were generated that reproduced many features of the actual MRI data. The calculated inter-lamellar image contrast demonstrated a strong dependence on the collagen fiber angle and on the circumferential location within the annulus.

Conclusion: This analytic model may be useful for interpreting MR images of the disc and for predicting experimental conditions that will optimize MR image contrast in the annulus fibrosus.

Keywords: Annulus fibrosus; Collagen; Dipolar relaxation; Image contrast; Intervertebral disc.

Fig. 1

Diagram of the vertebrae of the human lumbar spine and an intervertebral disc (L2L3). The local spinal axis is S⃗. The disc consists of nucleus pulposus (NP), annulus fibrosus (AF), and cartilaginous endplates (CEP). Collagen fibers in adjacent lamellae of the AF point in direction Ĉ at angles ±α relative to S⃗

Fig. 2

Tri-axial ellipsoidal coordinate system used to define the disc’s anatomical dimensions (left), and the orientation of its collagen fibers Ĉ relative to the B₀ magnetic field of the MRI scanner (right). In the central xy-plane, the thickness of lamellae and the width of the AF are defined by λ and Δ, respectively. R right, A anterior, and S⃗ points in the superior direction

Fig. 3

Illustration of lamellar shell index n and fiber angle α sign alternation in the AF. Lamellar shells intersect the x-axis in the central xy-plane at the x values indicated

Fig. 4

MRI of lumbar disc specimens: (left) ovine, (right) human L2L3. Discs were oriented with spinal axes ~90° to the magnetic field (B₀ is horizontal in the images). L/R/A/P = left/right/anterior/posterior. Scale bars 1 cm

Fig. 5

A 3D MRI simulation of a disc oriented at (ϕ_B, ψ_B) = (90°, 90°), reproducing the alternating intensity pattern of adjacent lamellae in the AF

Fig. 6

Direct comparison between the simulations and the MRI data: a–c MRI of a bovine tail disc specimen, oriented at (ϕ_B, ψ_B) = (14°, 45°), showing axial, coronal, and sagittal planes of the disc as indicated by reference lines (online version in color), and d–f the corresponding simulated 3D data. g–i MRI of a human lumbar disc specimen (L4L5), oriented at (ϕ_B, ψ_B) = (4°, 27°), and j–l the simulated 3D data. Arrows indicate regions of reduced inter-lamellar contrast in the simulations that appear to match the MRI data. Disc dimensions are given in Table 2

Fig. 7

(Top row) Computed inter-lamellar contrast as a function of azimuthal angle ψ and collagen fiber angle α (Eq. 10), at two orientations of the disc in the magnetic field: (left) (ϕ_B, ψ_B) = (5°, 1°); (right) (ϕ_B, ψ_B) = (60°, 1°). Side bar indicates the normalized linear scale (online version in color). (Bottom row) Single axial slices from simulated 3D MRI data sets of discs oriented in the magnetic field as in the top row, and for α = 60°