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).