Spectral Circle Analysis for MRS Metabolite Separation
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Solution Overview
Problem
Current magnetic resonance spectroscopy (MRS) technologies face challenges in consistency and accuracy, particularly in separating closely spaced spectral profiles and correcting baseline shifts, limiting their clinical utility and reproducibility.
Innovation Solution
The method employs spectral circles computed using linear fractional transformations (LFTs) applied to MRI data, shifting and rotating these circles to eliminate baseline offsets and separate overlapping spectral profiles, allowing for accurate metabolite concentration estimation by determining the area under dephased real parts of vectors.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If traditional MRS spectral analysis methods are used, then the analysis process is simple, but the accuracy and consistency of metabolite concentration measurement deteriorates due to inability to separate closely spaced spectral profiles and correct baseline shifts
Solution Approach 1:
The patent segments the complex spectral analysis problem into distinct geometric operations: (1) representing spectral profiles as circles in the complex plane, (2) separating overlapping spectral circles through geometric transformation, (3) correcting baseline shifts by translating circles to standardized positions, and (4) integrating areas to determine metabolite concentrations. This segmentation transforms an intractable spectral deconvolution problem into a series of manageable geometric operations.
Solution Approach 2:
The patent changes the parameter representation from traditional frequency-domain spectral amplitudes to geometric parameters (circle center coordinates, radii, and positions in the complex plane). This parameter transformation enables the use of geometric operations to separate and analyze overlapping spectral profiles, fundamentally improving measurement accuracy while providing a systematic framework for baseline correction.
2Reliability
If spectral profiles are not separated, then the analysis method remains straightforward, but the reliability of MRS results deteriorates due to overlapping spectral profiles and baseline offsets
Solution Approach 1:
The patent introduces the complex plane as an intermediary representation space where spectral profiles are transformed from their original frequency-domain form into circular geometric representations. This intermediary transformation enables reliable separation of overlapping profiles through geometric operations, and provides a natural framework for baseline correction by translating circles to standardized positions, thereby ensuring consistent and reliable MRS results.
Solution Approach 2:
The patent moves the spectral analysis from the one-dimensional frequency axis to the two-dimensional complex plane, adding a geometric dimension to the analysis. This dimensional expansion allows overlapping spectral profiles to be separated by their spatial positions and orientations in the complex plane, enabling reliable decomposition and analysis that is not possible in the original one-dimensional frequency domain.
3Measurement precision
If baseline offsets are not corrected, then the processing steps remain minimal, but the measurement precision deteriorates due to inaccurate area calculations under spectral peaks
Solution Approach 1:
The patent performs baseline correction as a preliminary step before area calculation by translating spectral circles to standardized positions in the complex plane. This preliminary geometric transformation eliminates baseline offsets, ensuring that subsequent area integrations accurately reflect the true spectral peak areas and thereby improving measurement precision without requiring complex iterative baseline correction procedures.
Data Source
AI summary
A method comprising collecting magnetic resonance imaging (MRI) scanner data corresponding to a region of interest, establishing a spectral peak profile associated with at least one metabolite in the region of interest, wherein the spectral peak profile comprises a term in the FID vector signal included in the collected MRI scanner data, selecting at least three counter indices and corresponding points on the spectral peak profile to compute a linear fractional transformation (LFT), computing an N-dimensional vector outlining a spectral circle in a complex plane by applying the LFT to each counter index included in a set of equally-spaced counter indices associated with a three-dimensional spectrum representation of the collected MRI scanner data, shifting the spectral circle to eliminate a baseline offset for a magnitude spectrum associated with the complex plane, rotating the shifted spectral circle to produce a rotated spectral circle.