Simple analytical approximation of the longitudinal electronic relaxation rate of Gd(iii) complexes in solutions

Abstract

More and more sophisticated theoretical models have been developped for a correct description of the relaxation of the electronic spin S ¼ 7/2 of the Gd(III) paramagnetic complexes used as contrast agents in magnetic resonance imaging (MRI). Both the static zero field splitting (ZFS) modulated by the random rotation of the complex and the transient ZFS due to the very fast distortion of this entity must be included in these models. This leads to rather complicated analytical expressions, from which it is difficult to evaluate the respective effects of the physically relevant parameters. However, in the Redfield limit of the theory of electronic spin relaxation, we show that the longitudinal relaxation function G k (t) has a quasi-monoexponential decay characterized by a unique relaxation rate 1/T 1e , which has a simple expression in terms of the applied magnetic field B 0 , of the static and transient ZFS parameters, and of the rotational and vibrational correlation times. For the typical investigated Gd(III) complexes, this expression is shown to have a very satisfactory accuracy for B 0 < 10 T. The various physical parameters as well as the range of validity of the relaxation approximation are discussed in detail. PCCP

Lanthanide Complexes of a Picolinate Ligand Derived from 1,4,7‐Triazacyclononane with Potential Application in Magnetic Resonance Imaging and Time‐Resolved Luminescence Imaging

“…[20][21][22] Rather than using the questionable SBM formalism at low field, Troughton et al [60] contented themselves with interpreting the experimental relaxivity above 0.2 T. Indeed, in this "high"-field region, it depends practically only on the longitudinal electronic relaxation rate 1/T 1e , which is given by general expressions of the McLachlan type. [61][62][63] In this paper, we propose a simple three-step method for interpreting the relaxivity profile of the water protons for all field values. The method avoids both the questionable multiparameter fit of the low-field experimental relaxivity by the SBM expression (see the section Theoretical Basis in the Experimental Section) and/or rather complex simulations with additional adjustable parameters.…”

“…Denote the magnitude of the second-order static ZFS responsible for the low-field electronic relaxation by a 2 . The longitudinal electronic TCF G nor k t) was shown to decrease monoexponentially [22,63] at the rate 1/T analyt 1e…”

“…(t), which will be expressed as sums of decreasing exponentials, even if the Redfield-Abragam validity conditions do not hold, so that such expressions are expected to be only approximate. [22,63,[67][68][69] Let g I and g S be the gyromagnetic ratios of the proton and electron spins, respectively. In an external field B 0 , denote the Larmor angular frequencies of the proton and electron spins by w I = Àg I B 0 and w S = Àg S B 0 .…”

Structure and Dynamics of Lanthanide Complexes of Triethylenetetramine‐N,N,N′,N″,N′′′,N′′′‐hexaacetic Acid (H6ttha) and of Diamides H4ttha(NHR) Derived from H6ttha as Studied by NMR, NMRD, and EPR

“…Here, t v is the correlation time of the modulation of the zero-field splitting, 1/T eSr is a correction for the so-called spin-rotation mechanism, and t R is the rotation correlation time. Although the Solomon ± Bloembergen ± Morgan theory is oversimplified [27] [28], it generally adequately describes NMRD profiles, and it has the advantage of its simplicity. To limit the number of variables in the fitting procedure, diffusion coefficients of the different Ln 3 complexes were estimated by the recently derived semi-empirical Eqn.…”

Relaxation of protons by radicals in rotationally immobilized proteins

“…In most cases, the relaxation efficiency of these compounds is limited by the short electron spin-lattice relaxation times in the range of tens to hundreds of picoseconds, which in turn defines the concentration range where these compounds may be used as practical contrast agents [4][5][6][7][8][9][10][11]. MRI contrast agents currently in use are generally soluble extracellular and blood-pool agents; however, targeting to provide specific anatomical or biochemical information will necessarily involve binding of an agent to a cell surface site or a specific macromolecular matrix [4,12,13].…”