Microscopic theory of spin–spin and spin–lattice relaxation of bound protons in cellular and myelin membranes—A lateral diffusion model (LDM)
Alexander L. Sukstanskii, Dmitriy A. Yablonskiy
Abstract
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 T 2 (spin–spin) and T 1 (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 T 1 and T 2 relaxation of membrane-bound protons. Moreover, their T 2 relaxation cannot be described in terms of a standard R 2 = 1/T 2 relaxation rate parameter, but rather by a relaxation rate function R 2(t) that depends on time t after RF excitation, having, in the main approximation, a logarithmic behavior: R 2(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 T 1 and T 2 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.