Donald E. Woessner

Numerical solution of the Bloch equations provides insights into the optimum design of PARACEST agents for MRI.

Paramagnetic lanthanide complexes that display unusually slow water exchange between an inner sphere coordination site and bulk water may serve as a new class of MRI contrast agents with the use of chemical exchange saturation transfer (CEST) techniques. To aid in the design of paramagnetic CEST agents for reporting important biological indices in MRI measurements, we formulated a theoretical framework based on the modified Bloch equations that relates the chemical properties of a CEST agent (e.g., water exchange rates and bound water chemical shifts) and various NMR parameters (e.g., relaxation rates and applied B1 field) to the measured CEST effect. Numerical solutions of this formulation for complex exchanging systems were readily obtained without algebraic manipulation or simplification. For paramagnetic CEST agents of the type used here, the CEST effect is relatively insensitive to the bound proton relaxation times, but requires a sufficiently large applied B1 field to highly saturate the Ln3+‐bound water protons. This in turn requires paramagnetic complexes with large Ln3+‐bound water chemical shifts to avoid direct excitation of the exchanging bulk water protons. Although increasing the exchange rate of the bound protons enhances the CEST effect, this also causes exchange broadening and increases the B1 required for saturation. For a given B1, there is an optimal exchange rate that results in a maximal CEST effect. This numerical approach, which was formulated for a three‐pool case, was incorporated into a MATLAB nonlinear least‐square optimization routine, and the results were in excellent agreement with experimental Z‐spectra obtained with an aqueous solution of a paramagnetic CEST agent containing two different types of bound protons (bound water and amide protons). Magn Reson Med 53:790–799, 2005.

Brownian motion and its effects in NMR chemical exchange and relaxation in liquids

At any instant, the magnetic dipolar moments or electric quadrupolar moments of atomic nuclei in a liquid experience interactions that depend on local structural parameters. Because such interactions depend on the distance and orientation of nearby magnetic dipole moments and electric charges, Brownian motions are reflected in the NMR spectra and relaxation times. We can use mathematical models based on our physical and chemical knowledge and intuition to help us interpret NMR data in terms of structure and motions. With proper experiments, we can use this approach to investigate molecular motions, structure, and interactions in liquids; molecular orientations at surfaces; and the range of interfacial order in heterogeneous materials, such as gels and biological tissue.

Investigations into whole water, prototropic and amide proton exchange in lanthanide(III) DOTA-tetraamide chelates

Lanthanide(III) chelates of DOTA-tetraamide ligands have been an area of particular interest since the discovery that water exchange kinetics are dramatically affected by the switch from acetate to amide side-chain donors. More recently these chelates have attracted interest as potential PARACEST agents for use in MRI. In this paper we report the results of studies using chemical exchange saturation transfer (CEST) and some more recently reported chelates to re-examine the exchange processes in this class of chelate. We find that the conclusions of Parker and Aime are, for the most part, solid; water exchange is slow and a substantial amount of prototropic exchange occurs in aqueous solution. The extent of prototropic exchange increases as the pH increases above 8, leading to higher relaxivities at high pH. However, amide protons are found to contribute only a small amount to the relaxivity at high pH.