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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