RF Pulse Design for Non-Constant Gradient MRI Trajectories
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Solution Overview
Problem
The Shinnar-Le Roux (SLR) RF pulse design algorithm is limited to designing one-dimensional pulses for constant gradient trajectories and cannot handle multidimensional or non-constant gradient waveforms, making it inadequate for modern MRI systems that require more complex pulse sequences.
Innovation Solution
A method is developed to parameterize spin-domain rotation parameters, reducing the complexity of designing RF pulses on non-constant gradient trajectories by introducing new variables, allowing for the generation of both multidimensional and one-dimensional RF pulses on non-constant gradients without requiring multidimensional minimum-phase filter design.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of manufacture
If the Shinnar-Le Roux (SLR) algorithm is used to design RF pulses, then the design process is simplified into a linear problem with easy inversion, but the algorithm is limited to one-dimensional pulses for constant gradient trajectories only
Solution Approach 1:
The patent extends the SLR algorithm from one-dimensional to multidimensional pulse design by introducing additional spatial dimensions and time-varying gradient components. The method formulates a multidimensional optimization problem that simultaneously designs RF pulses for multiple spatial dimensions and non-constant gradient waveforms, thereby resolving the limitation of the original SLR algorithm while maintaining its linear problem structure.
Solution Approach 2:
The patent incorporates time-varying gradient waveforms into the pulse design framework, transitioning from static constant gradient trajectories to dynamic non-constant gradients. This allows the system to handle time-dependent gradient patterns while maintaining the linear invertibility characteristic of the SLR algorithm, thus expanding adaptability without sacrificing ease of design.
2Adaptability or versatility
If non-constant gradient waveforms are used in MRI, then imaging capabilities are enhanced, but the computational complexity increases to prohibitively 2Nt−1 nonuniformly-spaced taps
Solution Approach 1:
The patent reformulates the optimization problem by changing the parameterization of the pulse design. Instead of directly solving for 2Nt−1 nonuniformly-spaced taps, the method uses a reduced set of Nt+1 parameters that capture the essential characteristics of non-constant gradient waveforms. This parameter transformation maintains the ability to handle complex gradients while reducing computational complexity from exponential to linear scale.
3Measurement precision
If multidimensional RF pulses on non-constant gradients are designed, then imaging precision is improved, but the degrees of freedom are insufficient with only Nt samples in the RF pulse
Solution Approach 1:
The patent adds an additional dimension to the parameter space by introducing Nt+1 parameters instead of the traditional Nt samples. This extra degree of freedom enables the system to simultaneously design multidimensional pulses on non-constant gradients while maintaining sufficient constraints for precise imaging. The additional parameter provides the necessary flexibility to handle the increased complexity of multidimensional pulse design.
Data Source
AI summary
Methods and systems for designing excitation pulses for magnetic resonance imaging are provided. One method includes parameterizing spin-domain rotation parameters to define parameterized variables and defining a constrained optimization problem based on the parameterized variables. The method also includes solving the constrained optimization problem and generating parameters for the RF pulses based on the solved problem, wherein the RF pulses are one of multidimensional RF pulses on non-constant gradient trajectories or one dimensional RF pulses on non-constant gradient trajectories.