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Updated: Mar 1, 2026
11:54
Real-Time Proxy-Control of Re-Parameterized Peripheral Signals using a Close-Loop Interface
Published on: May 8, 2021
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Rapid convergence of optimal control in NMR using numerically-constructed toggling frames
Paul Coote1, Clemens Anklin2, Walter Massefski3
1Department of Biological Chemistry and Molecular Pharmacology, Harvard Medical School, Boston, MA, USA.
Summary
This study introduces a fast numerical method for solving Bloch equations using vectorized computations and a toggling frame. This accelerates nuclear magnetic resonance (NMR) optimal control pulse design, significantly improving efficiency for experiments like 19F fragment screening.
Area of Science:
- Quantum Mechanics
- Nuclear Magnetic Resonance (NMR) Spectroscopy
- Computational Chemistry
Background:
- Solving the Bloch equation is crucial for simulating spin dynamics in NMR.
- Traditional methods involving matrix exponentiation are computationally intensive, especially for time-varying Hamiltonians.
- Efficient NMR optimal control requires rapid simulations of the Bloch equations.
Purpose of the Study:
- To develop a rapid numerical method for solving the Bloch equation for arbitrary time-varying spin-1/2 Hamiltonians.
- To accelerate the design of optimal control pulses in NMR spectroscopy.
- To provide a faster alternative to existing algorithms like GRAPE for pulse generation.
Main Methods:
- Utilized fast, vectorized computations (summation, quaternion multiplication) instead of matrix exponentiation.
- Constructed a toggling frame to render the Hamiltonian time-invariant, allowing for a simple analytical solution.
- Developed a novel algorithm that continuously updates the toggling frame during optimal pulse generation.
Main Results:
- The proposed method significantly reduces computation time compared to traditional approaches.
- Demonstrated the ability to generate optimal control pulses much faster by working in an appropriate toggling frame.
- Successfully applied the rapid optimal pulse generation technique to 19F fragment screening experiments.
Conclusions:
- The new numerical method offers a substantial speed improvement for solving Bloch equations.
- This advancement enables faster and more efficient design of NMR optimal control pulses.
- The method is particularly beneficial for complex NMR experiments requiring extensive simulations, such as fragment screening.
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