Theoretical model of the single spin-echo relaxation time for spherical magnetic perturbers

Abstract

Purpose: Magnetically labeled cells and tissue iron deposits provide qualitative means to detect and monitor cardiovascular and cerebrovascular diseases with magnetic resonance imaging. However, to quantitatively examine the extent of pathological micromorphological changes, detailed knowledge about microstructural parameters and relaxation times is required.

Methods: The complex geometrical arrangement of spherical magnetic perturbers is considered in an external magnetic field. They create a magnetic dipole field, whose corresponding spin-echo formation is investigated by analyzing the diffusion process in the dephasing volume. Quantitative predictions of the present analysis are compared with experimental data and empirical models.

Results: Single spin-echo relaxation times can be characterized by morphological parameters such as magnetic particle concentration and size as well as tissue diffusion coefficient and local magnetic susceptibility properties. As expected, no formation of a static dephasing plateau is observed in contrast to the gradient-echo relaxation time. Instead, the relaxation rate drops for large particle sizes and exhibits a prominent maximal value at intermediate sizes. These findings agree well with experimental data and previous theoretical results.

Conclusion: Obtained results for the single spin-echo relaxation time allow to accurately quantify pathological processes in neurodegenerative disease and migration dynamics of magnetically labeled cells with the help of magnetic resonance imaging.

Keywords: relaxation time; spherical magnetic perturber; spin echo.