The Magic Angle Effect in NMR and MRI of Cartilage

Abstract

This chapter reviews the molecular basis of “magic angle” effect in cartilage beginning from fundamental concepts of physics and physical chemistry. The magic angle effect is due to the unique oriented structure of collagen fibrils that occur in cartilage, tendon, ligaments and other connective tissues. One-dimensional ice-like water bridges bound in a repetitive manner to the backbone of the collagen molecule form a constant time-average proton–proton (P–P) vector coaxial with fibril orientation. Constant P–P induces frequency shifts (Δωmax ∼ 1000 Hz) due to the fixed orientation of an exchangeable proton relative to the fixed magnetic dipole field (ΔBmax ∼ ±10 Gauss) of the neighboring immobilized bridge proton on the same water molecule. The T2* relaxation time caused by rapid dephasing of net magnetization in the x–y plane results from stochastic sampling of solid-like dipole coupling ΔB(θ) by mobile protons. T2*(θ) becomes a function of orientation as the effective local field in the collagen fibril is Be = Bo + ΔB(θ) and ΔB(θ) varies as a function of the angle between the vectors B0 and P–P. The stoichiometric hydration model provides modeling tools to relate changes in T1, T2* and T1ρ with orientation to specific changes in collagen structure. It is anticipated that advanced studies will in future relate measurable molecular shifts to disease progression in osteoarthritis and other injuries to cartilage.