On T₂‐shortening by weakly magnetized particles: The chemical exchange model†

Abstract

Chemical exchange (CE) theory is compared with two theories of T 2 -shortening caused by microscopic magnetic centers: inner-and outer-sphere relaxation theory (long-echo limit) and mean gradient diffusion theory (short-echo limit). The CE equation is shown to be identical to these theories in the respective limits and appropriate parameter relationships are derived for spherical particles. The theories are then compared with computer simulations of spherical particles and with a recent general theory, with good agreement in the asymptotic regions. T 2 -shortening by paramagnetic (PM) particles is the basis for many MRI contrast agents and also for functional MRI (in which case the magnetic particles are deoxygenated red blood cells or capillaries). There are also endogenous magnetic materials such as ferritin and hemosiderin that affect MRI image contrast through the same mechanism. In an applied magnetic field these particles become partially aligned with the field; this induced magnetization, in turn, sets up microscopic field gradients that dephase nearby water protons, and hence shorten T 2 and T* 2 .While the complexity of the systems (irregular distributions, unequal magnetizations, varying orientation of capillaries, etc.) makes a general theory of relaxation difficult, there are theories that apply in certain limits, depending on the relative magnitude of three time parameters. In addition, a general theory was recently presented for weakly magnetized particles and applied to randomly distributed spheres (1). One of the time parameters is CP , defined as half the interval between successive 180°pulses in a CPMG sequence, or half the echo time for a single (Hahn) spin-echo sequence ( CP ϭ TE/2). The other two time parameters are inherent in the object or tissue being studied; they are the time to diffuse past a magnetized particle ( D ), and the time for a significant amount of dephasing to occur (i.e., the inverse of the spread in Larmor frequency, 1/⌬ ). These times will be defined more rigorously as specific scenarios are presented.In the "long-echo" limit ( CP ӷ D ), the standard quantum-mechanical theory of relaxation applies, as extended by Gueron and others (2-4) to cover induced magnetization (called the "Curie effect" by Gueron). In the "shortecho" limit ( CP Ӷ D ), the classical theory of diffusion in magnetic gradients, referred to herein as mean gradient diffusion theory (MGDT), may be used under certain conditions (5-7). In addition, a model based on chemical exchange (CE) theory (8 -9) has sometimes been used (10 -13), although this use has not been validated.We will attempt to provide such a validation by comparing CE theory with the two diffusion theories in the appropriate limits and with the more recent theory (1). In the process, we will determine the theoretical relationship between the CE parameters and the diffusion parameters. In some cases this will require new versions of the theoretical equations that are better suited for the comparison. We will also present new computer simula...

Calcium-sensitive MRI contrast agents based on superparamagnetic iron oxide nanoparticles and calmodulin

“…In the presence of stoichiometric quantities of polyvalent biotin-dextran, uncomplexed SA-MACS showed a pronounced increase in hydrodynamic radius and a 2-to 3-fold decrease in T2 relaxivity (data not shown). An inverse relationship between iron oxide cluster size and T2 relaxation rates has been described previously (21) and explained by the extensive theoretical work of Gillis and colleagues (22)(23)(24). For colloidal suspensions of fixed iron oxide volume fraction, the particle size-dependence of T2 relaxivity depends on the quantity ␦ R 2 ͞D, where ␦ is the change in (angular) NMR frequency at the particle equator, R is the radius of the cluster, and D is the self-diffusion coefficient.…”

NMR Transversal Relaxivity of Suspensions of Lanthanide Oxide Nanoparticles

“…33,34 Taking into account that the protons in the layer between the spheres with radii of r p and r diff do not contribute to the relaxivity, we consider the…”

Susceptibility‐induced T2‐shortening and unrestricted diffusion

“…The difference between the two regimes, Eqs. [3] or [6] on one hand and Eq. [4] on the other, is likely to be also due to the unrestricted diffusion assumption.…”

“…[3]. The general theory of Jensen and Chandra (2) has the advantage that it considers the local magnetic field as a sum of contributions from different magnetic centers, while the mean gradient formula with C ϭ 3 was obtained from a single particle calculation.…”

“…This question was briefly addressed in two footnotes in Ref. 3; the present note is aimed at making this point more explicit.…”