Application of optimal control to CPMG refocusing pulse design
Troy W Borneman1, Martin D Hürlimann, David G Cory
1Department of Nuclear Science and Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA. troyb@mit.edu
Journal of Magnetic Resonance (San Diego, Calif. : 1997)
|October 12, 2010
Summary
Optimal control theory designs robust refocusing pulses for Carr-Purcell-Meiboom-Gill (CPMG) sequences, enhancing signal integrity across various magnetic field variations.
Area of Science:
- Magnetic Resonance Imaging
- Quantum Information Processing
Background:
- The Carr-Purcell-Meiboom-Gill (CPMG) sequence is crucial for magnetic resonance measurements.
- Pulse imperfections and magnetic field inhomogeneities limit CPMG sequence performance.
Purpose of the Study:
- To design novel refocusing pulses using optimal control theory (OCT) for CPMG sequences.
- To develop a quantum information processing (QIP)-based model for CPMG dynamics.
- To assess the robustness of designed pulses against B(0) and B(1) offsets.
Main Methods:
- Application of optimal control theory (OCT) to design broadband refocusing pulses.
- Modeling CPMG dynamics as a dephasing Pauli channel using QIP principles.
- Analysis of pulse performance under varying resonance and RF field conditions.
Main Results:
- Designed 10τ(180) pulses achieve over 98% magnetization refocusing.
- Robustness demonstrated for resonance offsets up to 3.2 times the maximum RF amplitude.
- Effective performance maintained despite ±10% RF inhomogeneity.
Conclusions:
- OCT is effective for creating robust CPMG refocusing pulses.
- The QIP-based model provides a quantitative assessment of pulse error effects.
- The developed pulses significantly improve CPMG sequence performance in challenging conditions.
Related Concept Videos
01:28Load-frequency control
Load-frequency control (LFC) is vital for maintaining power system stability, ensuring that frequency and power flows remain within acceptable limits during load changes. Turbine-governor control eliminates rotor accelerations and decelerations following load changes. However, a steady-state frequency error persists when the change in the turbine-governor reference setting is zero. In an interconnected power system, each area agrees to export or import a scheduled amount of power through...
01:27Time and frequency -Domain Interpretation of PI Control
Proportional-Integral (PI) controllers are essential in many control systems to improve stability and performance. They are commonly used in everyday devices like thermostats to enhance system damping and reduce steady-state error. When the zero in the controller's transfer function is optimally placed, the system benefits significantly in terms of stability and accuracy.
Acting as a low-pass filter, the PI controller slows the system's response and extends settling times. This requires careful...
Acting as a low-pass filter, the PI controller slows the system's response and extends settling times. This requires careful...
01:07Time-Domain Interpretation of PD Control
Proportional-Derivative (PD) control is a widely used control method in various engineering systems to enhance stability and performance. In a system with only proportional control, common issues include high maximum overshoot and oscillation, observed in both the error signal and its rate of change. This behavior can be divided into three distinct phases: initial overshoot, subsequent undershoot, and gradual stabilization.
Consider the example of control of motor torque. Initially, a positive...
Consider the example of control of motor torque. Initially, a positive...
01:24Time and frequency -Domain Interpretation of Phase-lead Control
Phase-lead controllers are commonly used in various control systems to enhance response speed and stability. Adjusting the brightness on a television screen offers a practical example of phase-lead control. When contrast is enhanced, a phase-lead controller is employed. Mathematically, phase-lead control is identified when the first parameter is smaller than the second.
The design of phase-lead control involves the strategic placement of poles and zeros to balance steady-state error and system...
The design of phase-lead control involves the strategic placement of poles and zeros to balance steady-state error and system...
01:24PI Controller: Design
Proportional Integral (PI) controllers are a fundamental component in modern control systems, widely used to enhance performance and mitigate steady-state errors. They are particularly effective in applications such as automatic brightness adjustment on smartphones, where they excel at mitigating steady-state errors for step-function inputs. Unlike PD controllers, which require time-varying errors to function optimally, PI controllers leverage their integral component to address residual...
01:10Control Systems
Control systems are everywhere in contemporary society, influencing diverse applications from aerospace to automated manufacturing. These systems can be found naturally within biological processes, such as blood sugar regulation and heart rate adjustment in response to stress, as well as in man-made systems like elevators and automated vehicles. A control system is essentially a network of subsystems and processes that collaboratively convert specific inputs into desired outputs.
At the heart...
At the heart...