SOLVENT RELAXATION BY UNIFORMLY MAGNETIZED SOLUTE SPHERES - THE CLASSICAL-QUANTAL CONNECTION

RATIONALE AND OBJECTIVES. Large magnetic entities, with diameters in t he range of 4 nm to 4 mu m, are becoming of increasing interest for ma gnetic resonance imaging (MRI). The smaller are iron oxide nanoparticl es, used for the RE system, and the larger are deoxygenated blood cell s, for functional MRI. It can be useful to model such systems as magne tized solute spheres in water. Classical computations of 1/T2 have bee n reported for the larger particles, in the micron range, where the co mputational complexities are simplified by Monte Carlo methods. For sm aller particles, the quantum mechanical (quantal) expressions for oute r sphere relaxation, for both 1/T1 and 1/T2, have been available for s ome time, and are particularly simple to apply at MRI fields. The ques tions that arise, and which the author addresses, are how to interrela te the classical and quantal approaches and when to use which. METHODS . The author compares published results of Monte Carlo calculations of 1/T2 for diamagnetic polystyrene solute spheres of various sizes in w ater, made paramagnetic by addition of dysprosium-(DTPA)(2-), with qua ntum mechanical outer sphere theory applied to the same system. The la tter includes the usual assumption of motional narrowing and yields bo th 1/T1 and 1/T2. RESULTS. For particles with diameters less than abou t 1 mu m, both approaches give identical results for 1/T2. For larger particles, the conditions for motional narrowing breakdown, and quanta l theory overestimates 1/T2. In addition, in the particular system stu died, relaxation becomes so effective near solute that there is insuff icient time for all water molecules to experience their maximal effect . Classical theory handles this well whereas quantal theory does not. CONCLUSIONS. In comparing the classical and quantal approaches, one ba lances computational complexity but broader applicability with more li mited but far simpler mathematics. In addition, because the quantal ap proach shows that 1/T1 and 1/T2 are intimately related, the author sug gests, by analogy, how to extend classical methods to computation of 1 /T1.