Synthesis and Evaluation of GdIII‐Based Magnetic Resonance Contrast Agents for Molecular Imaging of Prostate‐Specific Membrane Antigen

Magnetic resonance (MR) imaging is advantageous because it concurrently provides anatomic, functional, and molecular information. MR molecular imaging can combine the high spatial resolution of this established clinical modality with molecular profiling in vivo. However, as a result of the intrinsically low sensitivity of MR imaging, high local concentrations of biological targets are required to generate discernable MR contrast. We hypothesize that the prostate‐specific membrane antigen (PSMA), an attractive target for imaging and therapy of prostate cancer, could serve as a suitable biomarker for MR‐based molecular imaging. We have synthesized three new high‐affinity, low‐molecular‐weight Gd^III‐based PSMA‐targeted contrast agents containing one to three Gd^III chelates per molecule. We evaluated the relaxometric properties of these agents in solution, in prostate cancer cells, and in an in vivo experimental model to demonstrate the feasibility of PSMA‐based MR molecular imaging.     

Quasi-energy spectral series for a nonlocal Gross-Pitaevskii equation

For a nonlocal Gross-Pitaevskii operator, quasi-energy spectral series have been constructed accurate to O(?^3/2). These series correspond to the closed phase trajectories of the Hamilton-Ehrenfest system, which are stable in a linear approximation. The corresponding monodromy operator has been constructed accurate to Õ(?^3/2) in the class of trajectory-coherent functions.     

The Geometric Phases and Quasienergy Spectral Series of a Hartree-Type Equation with a Quadratic Potential

Based on the ideology of the complex WKB–Maslov method, the general construction of quasiclassically concentrated solutions is given for Hartree-type equations with a quadratic potential and periodic coefficients. Exact expressions are constructed for the quasienergies and associated quasienergy states. In the construction of solutions, an important role is played by the Hamilton–Ehrenfest system of equations obtained in this work. Explicit expressions are found for the geometric phase of Aharonov–Anandan quasienergy states.     

Green's Function of a Hartree-Type Equation with a Quadratic Potential

Using the complex WKB–Maslov method, we consider a solution of the Cauchy problem for a Hartree-type equation with a quadratic potential in the class of semiclassically supported functions. In this class, we obtain the evolution operator explicitly. We find parametric families of symmetry operators of the Hartree-type equation. Using the symmetry operators, we construct a family of exact solutions of this equation.