Microscopic theory of spin–spin and spin–lattice relaxation of bound protons in cellular and myelin membranes—A lateral diffusion model (LDM)

Purpose: Deciphering salient features of biological tissue cellular microstructure in health and diseases is an ultimate goal of MRI. While most MRI approaches are based on studying MR properties of tissue “free” water indirectly affected by tissue microstructure, other approaches, such as magnetization transfer (MT), directly target signals from tissue-forming macromolecules. However, despite three-decades of successful applications, relationships between MT measurements and tissue microstructure remain elusive, hampering interpretation of experimental results. The goal of this paper is to develop microscopic theory connecting the structure of cellular and myelin membranes to their MR properties. Theory and Methods: Herein we introduce a lateral diffusion model (LDM) that explains the T₂ (spin–spin) and T₁ (spin–lattice) MRI relaxation properties of the macromolecular-bound protons by their dipole–dipole interaction modulated by the lateral diffusion of long lipid molecules forming cellular and myelin membranes. Results: LDM predicts anisotropic T₁ and T₂ relaxation of membrane-bound protons. Moreover, their T₂ relaxation cannot be described in terms of a standard R₂ = 1/T₂ relaxation rate parameter, but rather by a relaxation rate function R₂(t) that depends on time t after RF excitation, having, in the main approximation, a logarithmic behavior: R₂(t) ∼ lnt. This anisotropic non-linear relaxation leads to an absorption lineshape that is different from Super-Lorentzian traditionally used in interpreting MT experiments. Conclusion: LDM-derived analytical equations connect the membrane-bound protons T₁ and T₂ relaxation with dynamic distances between protons in neighboring membrane-forming lipid molecules and their lateral diffusion. This sheds new light on relationships between MT parameters and microstructure of cellular and myelin membranes.