Time-Optimal MRI Gradient Waveform Design via Arc-Length Parameterization
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Solution Overview
Problem
Designing time-optimal gradient waveforms for arbitrary k-space trajectories in magnetic resonance imaging (MRI) is challenging, particularly for non-trivial cases, as existing methods are limited to specific trajectories and fail to provide efficient solutions for general cases.
Innovation Solution
A method based on optimal control theory that determines gradient amplitude as a function of arc-length along the k-space trajectory, allowing for the calculation of a time-optimal gradient waveform that minimizes traversal time, applicable to arbitrary, random, and non-freely rotatable trajectories.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Loss of time
If gradient amplitude is determined as a function of time for arbitrary k-space trajectories, then the waveform design becomes complex and computationally intensive, but the traversal time cannot be minimized efficiently
Solution Approach 1:
The patent inverts the conventional approach by determining gradient amplitude as a function of arc-length s rather than time t. This inversion transforms the time-optimal control problem into a geometric problem that can be solved more efficiently, directly minimizing traversal time while reducing computational complexity for arbitrary k-space trajectories
Solution Approach 2:
The patent changes the parameterization from time-based to arc-length-based gradient amplitude determination. By expressing gradient amplitude G as a function of arc-length s along the k-space trajectory rather than time t, the method enables direct calculation of time-optimal waveforms with reduced computational burden
2Adaptability or versatility
If existing methods are used for specific k-space trajectories, then the design process is simplified, but the methods fail to provide efficient solutions for general and arbitrary trajectories
Solution Approach 1:
The patent creates a universal method for determining time-optimal gradient waveforms that applies to any arbitrary k-space trajectory. The arc-length parameterization approach provides a single unified framework that handles linear, circular, spiral, and other complex trajectories equally effectively, eliminating the need for trajectory-specific design methods
3Ease of operation
If freely rotatable trajectories are used, then the gradient waveform design is easier, but the scanning efficiency is reduced by up to 5% compared to optimized trajectories
Solution Approach 1:
The patent enables dynamic optimization of gradient waveforms by calculating time-optimal solutions for arbitrary trajectories. The method adapts the gradient amplitude profile to the specific geometric characteristics of each trajectory through arc-length parameterization, achieving up to 5% improvement in scanning efficiency over standardized freely rotatable trajectories
Data Source
AI summary
A method for magnetic resonance imaging (MRI) is provided. A scanning path is specified. Gradient amplitude is determined as a function of arc-length along the scanning path in k-space. A time optimal gradient waveform for scanning the scanning path is calculated from the gradient amplitude. The scanning path is scanned using the time optimal gradient waveform.