Nuclear Spin Relaxation in Paramagnetic Systems:  Electron Spin Relaxation Effects under Near-Redfield Limit Conditions and Beyond

Abstract

The analysis of experimental relaxometric profiles of paramagnetic complexes is usually performed using the Solomon-Bloembergen-Morgan (SBM) theory. The SBM theory is not valid for slowly rotating systems when the electronic levels are split at zero field, in which case a modified theory developed in Florence should be used. However, for many interesting systems, including Gd-based contrast agents for MRI, the electron spin relaxation is rather close to the Redfield limit, where none of these approaches is valid. In the present paper, the SBM theory and modified versions of the Florence model are compared against a general theory valid beyond the Redfield limit (the so-called slow-motion theory). Significant differences are found already for the cases where the electron spin relaxation is in a regime near the Redfield limit, but still within it. Indeed, the values of the parameters describing the electron spin relaxation are underestimated for the SBM theory relative to those used in calculating the slow-motion profiles. The present results are relevant for the interpretation of relaxometric profiles of paramagnetic complexes and proteins, and for the interpretation of the behavior of contrast agents used in MRI, and should be taken into account when planning the improvement of the relaxometric properties for the next generation of contrast agents based on theoretical predictions.

High Relaxivity Gd(III)–DNA Gold Nanostars: Investigation of Shape Effects on Proton Relaxation

“…With the acquired data, proton relaxivity profiles are created and fitted using SBM theory or other more recently developed approaches such as the modified Florence model. 54–56 The analysis of relaxivity profiles provides a means of extracting valuable mechanistic information, including dynamic parameters such as τ r and τ m . 31,57–59 …”

A Modular System for the Synthesis of Multiplexed Magnetic Resonance Probes

“…(Table 3) The change in the values of electron relaxation parameters between 1 to 3 (similar to that observed for other gadolinium complexes when bound to macromolecules) 27,60,61 is likely determined by the simultaneous presence of both static and transient ZFS, which is not fully accounted for in fast rotating systems by available fitting programs. 53, 62 Both profiles of 1 and 3 were fit according to the “modified Florence” approach, and the main features of all profiles could be reproduced as the result of an increase in τ R on passing from 1 to 3 (see Supporting Information, Figure S1). Independent from the electronic parameters, the analysis clearly shows that the NMRD profiles of 3 can only be reproduced for tumbling times that are approximately one order of magnitude larger than those of 1 .…”

Design Principles and Theory of Paramagnetic Fluorine‐Labelled Lanthanide Complexes as Probes for 19F Magnetic Resonance: A Proof‐of‐Concept Study

“…[22][23][24][25][26] Typical imaging fields are around 3.0 T, placing the systems in question firmly in the domain of perturbative spin relaxation theories, [27][28][29][30][31] of which the Bloch-RedfieldWangsness (BRW) theory [28][29][30] is the one most widely used. We shall also reluctantly bow to tradition and use the isotropic tumbling approximation in the treatment below; while the more sophisticated lattice models could be desirable on theoretical grounds, [32][33][34][35][36][37][38][39] the Lorentzian spectral density does appear to work for the small molecules reported here.…”