MRI Field Map Estimation via Golden Section Search
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Solution Overview
Problem
Existing multi-point methods for field map estimation in MRI are limited by long echo-spacings, which impair robustness and imaging efficiency, especially at high field strengths, due to increased chemical shift and field inhomogeneities, leading to ambiguity in resolving field inhomogeneities.
Innovation Solution
A method using golden section searches and a multi-resolution pyramidal structure to estimate field maps, which directly locates possible field map values with a smoothness constraint, reducing computational cost and improving robustness by exploiting the smoothly varying nature of field maps.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If multi-point methods are used for field map estimation, then field map accuracy can be improved, but echo-spacing increases which impairs robustness and imaging efficiency
Solution Approach 1:
The patent segments the field map estimation problem into multiple discrete points (grid points) across the imaging domain. By dividing the continuous field map into discrete sampling points, the method can efficiently estimate field values at each point using localized information from multiple echoes, avoiding the need for long echo-spacings while maintaining accuracy. This segmentation enables parallel processing and reduces the temporal constraints on echo-spacing.
Solution Approach 2:
The patent changes the estimation approach from traditional multi-point methods that require long echo-spacings to a method that uses multiple echoes with shorter spacings combined with a cost function minimization approach. By changing the parameter of echo-spacing from long to short durations and combining it with iterative refinement at discrete grid points, the method achieves accurate field map estimation without the temporal penalties of traditional approaches.
2Reliability
If multi-point water-fat separation methods are used, then susceptibility to magnetic field inhomogeneities is reduced, but computational complexity increases
Solution Approach 1:
The patent segments the water-fat separation problem into discrete grid points where field map estimation and species separation are performed independently at each location. This segmentation allows the use of simplified local models at each grid point while combining results across the entire image, reducing overall computational complexity compared to global multi-point methods while maintaining robustness to field inhomogeneities through the use of multiple echoes.
Solution Approach 2:
The patent applies partial action by performing field map estimation and water-fat separation at discrete grid points rather than continuously across the entire image space. By sampling at specific locations and interpolating between them, the method reduces computational burden while still capturing the essential field inhomogeneity effects. The use of a cost function with smoothness constraints provides just enough regularization to ensure reliability without excessive computational overhead.
3Measurement precision
If field map estimation is performed with high precision, then species separation accuracy improves, but computational cost increases
Solution Approach 1:
The patent segments the computational domain into discrete grid points, allowing field map estimation to be performed independently at each point. This segmentation enables the use of efficient local optimization algorithms that converge quickly at each grid point, reducing overall computational cost while maintaining high precision through the accumulation of information from multiple echoes and the application of smoothness constraints across neighboring points.
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
This approach enables efficient and reliable water-fat separation with multi-echo sequences, even with long echo-spacings, by minimizing the least-squares estimation error and maintaining overall smoothness of the field map, resulting in accurate field map estimation and improved imaging efficiency.
Implementation Method 1
nuclear magnetic moments are excited at specific spin precession frequencies which are proportional to the local magnetic field
Implementation Method 2
The radio-frequency signals resulting from the precession of these spins are received using pickup coils
Data Source
AI summary
A method for mapping field inhomogeneity for forming a magnetic resonance image is provided. A magnetic resonance excitation is applied. A plurality of k-space echoes signals is acquired. A periodic cost function is calculated from the acquired plurality of k-space echo signals. A period of the calculated periodic cost function is divided into multiple regions. A search algorithm is used to locate a local minimum in each region. Located local minimums are chosen to provide global smoothness.