Fibonacci Phyllotaxis Radial Spoke Arrangement for MR K-Space Sampling
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Radial three-dimensional data acquisition in k-space faces challenges in achieving uniform spatial sampling density and minimizing eddy current artifacts, often requiring complex compensation of sampling density.
Innovation Solution
The method arranges data points on a spherical surface according to Fibonacci phyllotaxis, using specific equations for polar and azimuthal angles to define spokes, ensuring a uniform distribution and reducing eddy current effects by dividing spokes into sets based on Fibonacci numbers.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Quantity of substance
If points are arranged on a sphere using Archimedean spiral trajectory, then data acquisition covers all spokes, but the separation of adjacent windings is reduced leading to large gradient changes and eddy current artifacts
Solution Approach 1:
The patent divides the set of spokes into multiple subsets, where each subset contains spokes that can be acquired without significant gradient changes. By segmenting the acquisition into separate passes through the center of k-space, each with a limited angular range, the method avoids large gradient transitions while still covering all spokes across multiple repetitions.
Solution Approach 2:
The patent employs periodic repetition of acquisition passes through the center of k-space. Each pass acquires a subset of spokes within a limited angular range, and the process is repeated multiple times to cover all spokes. This periodic action allows the system to return to the center repeatedly, minimizing gradient changes between consecutive acquisitions.
2Productivity
If significant interleaving is used with m>>1, then fewer spokes are acquired per detection step, but the gradient change at transition from one spoke to the next becomes large causing eddy current effects
Solution Approach 1:
The patent segments the spokes into subsets with controlled angular separation, ensuring that consecutive spokes within each subset have small angular differences. This segmentation allows for faster acquisition within each subset while limiting gradient changes, thereby reducing eddy current effects without sacrificing overall productivity.
3Reliability
If radial three-dimensional data acquisition is used, then movement robustness is improved, but uniform distribution of data points in k-space is difficult to achieve
Solution Approach 1:
The patent applies different acquisition strategies to different regions of k-space by organizing spokes into subsets with specific angular ranges. Each subset is optimized for uniform sampling in its local angular region, and the combination of multiple subsets achieves global uniformity while maintaining the movement robustness of radial acquisition.
Data Source
AI summary
For radial data acquisition in three-dimensional k-space in an MR measurement for a magnetic resonance system, data in k-space are acquired along straight-line spokes. Each of the spokes is thereby defined by a point on a sphere and the center point of this sphere, wherein the center point corresponding to the center of k-space. The points are arranged on the sphere such that a distribution of the points obeys the spiral phyllotaxis, in particular the Fibonacci phyllotaxis.