A numerical prediction of spin-lattice relaxation enhancement of water protons by paramagnetic metal ions and free radicals. A contribution to the basic principles of relaxometry in MRI

Abstract

The Solomon-Bloembergen and several simplified equations from literature are criticaUy evaluated with the purpose of selecting an equation for rapid numerical predictions of spin-lattice relaxation data of water protons induced by paramagnetic transition metal and lanthanide ions and organic free radicals. The following equation is proposed for practical applications:where T 1 is the spin-lattice relaxation time, 1/T 1 is the spin-lattice relaxation rate, Yz is the gyromagnetic ratio of the proton of water, 7s is the gyromagnetic ratio of the electron, k is the Boltzman constant, h is the Plank constant, h ~ h/2n, N is the number of paramagnetic species per cubic centimeter, i.e. the Avogadro number/1000, mis the concentration of the paramagnetic species in mM, r/is the viscosity in centipoise at appropriate temperature, T is the appropriate absolute temperature, S is the spin quantum number, and F is a methodical factor which can range between 1-2.7, depending on the magnetic properties of the instrumentation, i.e. -1.07 MHz (0.025 T) --90 MHz (2.1 T), and the relaxation enhancing agent. Ir is proposed to use F = 1 for rapid numerical predictions. This equation is based on models involving translational motions and is suitable for rapid estimates in vitro of spin-latfice relaxation times and rates of protons in water, and water protons in plasma and other biological fluids in the presence of paramagnetic metal ions, their low molecular weight complexes, and free radicals, as exemplified by nitroxyl (aminoxyl) radicals. Although this equation wiU be used for measurements in vitro, the results could also be applied to project the effectiveness of new contrast agents in vivo. It is believed that this equation will be useful in research involving the development of new contrast agents for MRI.

Approximation of weak stability constants of paramagnetic complexes by spin-lattice relaxation measurements of water protons

“…Thus, e.g., metal ion complexes are involved in analyses of metal ions, in removal of toxic cations from the environment of vital biological systems, and in pharmaceutical formulations which are used in human and veterinary medicine. During the past decade, with the advem of magnetic resonance imaging (MRI) asa clinical diagnostic tool, [1][2][3][4] the paramagnetic complexes of transition and lanthanide metal ions have undergone extensive reinvestigations [4][5][6][7][8] in search for new contrast agents. In this connection, the stabilities of these contrast agents attained an important role, whereby two types of stabilities should be distinguished, i.e.…”

“…The relaxation methods also permit the study of very fast reactions [4,7,9,10,15,39,49,50] which occur, e.g., in the exchange of bound water with the bulk water of the inner sphere complexes, and in diffusion processes of outer sphere complexes (~10 lo cm-X). The relaxation methods can be used for the determination of thermodynamic and kinetic stability constants [9,10,16,.…”