K-space View Ordering via Electrostatic Energy Minimization
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Solution Overview
Problem
Current methods for generating uniformly distributed points on a sphere, particularly for medical imaging applications like diffusion-weighted MRI, are computationally inefficient and lack antipodal symmetry, leading to suboptimal image quality and long computation times.
Innovation Solution
A method using a processor to generate a point set with antipodal symmetry by minimizing electrostatic energy potentials, allowing for efficient and uniform distribution of points on a sphere, significantly reducing computation time and improving image quality.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Manufacturing precision
If iterative minimization of electrostatic potential is used to generate uniformly distributed points on a sphere, then uniformity of point distribution is improved, but computation time increases significantly (taking minutes to hours)
Solution Approach 1:
The patent applies preliminary action by pre-calculating and storing optimal point sets on the sphere surface before actual MRI acquisition. The uniformly distributed points are generated in advance using iterative electrostatic potential minimization, then stored in a database for rapid retrieval during clinical scanning, eliminating the need for real-time computation during patient imaging
Solution Approach 2:
The patent uses copying by creating and storing duplicate optimal point sets that can be repeatedly retrieved without recalculation. Once the optimal uniformly distributed points are computed, multiple copies are stored in memory or database, allowing rapid access during different MRI sequences without repeating the computationally intensive generation process
2Manufacturing precision
If existing deterministic schemes are used to generate point sets, then uniform distribution is achieved, but antipodal symmetry is not provided which is required for diffusion-weighting directions
Solution Approach 1:
The patent applies asymmetry in reverse by deliberately imposing symmetry constraints on the point generation process. The iterative electrostatic potential minimization is modified to enforce antipodal symmetry, where for every point at position r, a corresponding point at position -r is also included in the set, ensuring the required symmetry for diffusion-weighting while maintaining uniform distribution
Solution Approach 2:
The patent changes parameters of the point generation algorithm by modifying the electrostatic potential minimization process to include symmetry constraints. The energy function being minimized is adjusted to penalize asymmetric configurations, forcing the generated point sets to exhibit antipodal symmetry while achieving uniform distribution
3Ease of manufacture
If view-ordering strategies are not optimized, then acquisition can proceed without complex planning, but image quality deteriorates due to coherent signal modulations in k-space
Solution Approach 1:
The patent applies preliminary action by pre-determining optimal view-ordering sequences before MRI acquisition. The ordering that minimizes electrostatic potential energy is calculated in advance and stored, then automatically applied during scanning, combining the benefits of optimized image quality with simplified operational workflow
Solution Approach 2:
The patent substitutes mechanical/physical optimization processes with computational algorithms. Instead of relying on trial-and-error or manual optimization of view-ordering, the system uses electrostatic potential energy minimization algorithms to automatically determine optimal sequences, replacing complex manual planning with automated computational design
Applied Scientific Principles
This section explains which scientific principles are used to turn an abstract innovation direction into a practical engineering solution.
Function Achieved in This Case
The method achieves highly uniform and antipodally symmetric point sets, optimizing MRI acquisition parameters, and determining optimal orderings for diffusion-weighting directions, resulting in faster computation times (seven orders of magnitude faster than existing methods) and improved image quality.
Implementation Method 1
determine an order in which points in the generated point set are to be temporally arranged by minimizing electrostatic energy potentials related to the points in the generated point set
Data Source
AI summary
A system and method for determining and ordering magnetic resonance imaging (MRI) acquisition parameters, such as k-space views or diffusion-weighting gradient directions, are provided. The MRI acquisition parameters are defined by generated points that are uniformly distributed on the surface of a sphere. These points may also be antipodally symmetric. The points are ordered by minimizing the electrostatic potential energy of different configurations of the points.