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Abstract #1546

High Accuracy Numerical Methods for Solving Magnetic Resonance Imaging Equations and Optimizing RF Pulse Sequences

Cem Gultekin1, Jakob Assländer2, and Carlos Fernandez-Granda3
1Mathematics, Courant Institute of Mathematical Science, New York, NY, United States, 2Radiology, New York University Grossman School of Medicine, New York, NY, United States, 3Mathematics and Data Science, Courant Institute of Mathematical Science and Center for Data Science New York University, New York, NY, United States

This work presents a new robust black-box numerical solver that can reliably solve many MRI typical ordinary differential equations. Our adaptive Petrov-Galerkin (PG) method can solve challenging MRI problems with additional complexities such as B0- and B1- inhomogeneities, RF pulses, chemical exchange, and magnetization transfer (MT). We apply the proposed technique to solve an ODE-constrained optimization problem for pulse design via gradient descent. Our method reduces the time required to compute the gradients by three orders of magnitude.

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