An Optimal Design Method for MRI Teardrop Gradient Waveforms

Abstract

<p> This thesis presents an optimal design method for MRI (Magnetic Resonance Imaging) teardrop gradient waveforms in two and three dimensions. Teardrop in two dimensions was introduced at ISMRM 2001 by Anand et al. to address the need for a high efficiency balanced k-space trajectory for real-time cardiac SSFP (Steady State Free Precession) imaging.</p> <p> We have modeled 2D and 3D teardrop gradient waveform design as nonlinear convex optimization problems with a variety of constraints including global constraints (e.g., moment nulling for motion insensitivity). Commercial optimization solvers can solve the models efficiently. The implementation of AMPL models and numerical testing results with the solver MOSEK are provided. This optimal design procedure produces physically realizable teardrop waveforms which enable real-time cardiac imaging with equipment otherwise incapable of doing it, and optimally achieves the maximum resolution and motion artifact reduction goals. The research may encompass other waveform design problems in MRI and has built a good foundation for further research in this area.</p>