Theory of Spin Echo in Restricted Geometries under a Step-wise Gradient Pulse Sequence

摘要: Abstract A closed matrix form solution of the Bloch–Torrey equation is presented for magnetization density spins diffusing in a bounded region under steady gradient field and Stejskal–Tanner pulse sequence, assuming straightforward generalization to any step-wise profile. The expressed terms eigenmodes diffusion propagator given geometry with appropriate boundary conditions (perfectly reflecting or relaxing walls). Applications rectangular, cylindrical, spherical geometries are discussed. relationship multiple approach established an alternative discretization procedure suggested handle arbitrary waveforms.