Rotational Invariants of Cumulant Expansion for dMRI Tissue Characterization
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Solution Overview
Problem
Current diffusion magnetic resonance imaging (dMRI) techniques struggle to efficiently classify symmetries and define tensor invariants that are independent of the choice of basis, limiting their ability to generate basis-independent scalar maps for tissue characterization, particularly in the context of brain pathology, development, and aging.
Innovation Solution
The development of Rotational Invariants of Cumulant Expansion (RICE) techniques, which provide a full classification of rotational invariants of diffusion and covariance tensors, allowing for the generation of hardware-independent 'fingerprint' maps that can be used in machine learning classifiers for brain pathology and aging, utilizing minimal acquisition protocols such as icosahedral directions to determine tensor elements within 1-2 minutes on a clinical scanner.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If conventional dMRI techniques are used to probe diffusion motion, then tissue microstructure information can be obtained, but the ability to efficiently classify symmetries and define basis-independent tensor invariants is limited
Solution Approach 1:
The patent segments the complex task of tensor invariant classification by decomposing the diffusion signal into distinct tensor components (diffusion tensor D and covariance tensor C) and systematically identifying rotational invariants for each component. This segmentation allows systematic classification of symmetries without overwhelming complexity.
Solution Approach 2:
The patent introduces rotational invariants as intermediary quantities that bridge the raw dMRI signal and tissue property characterization. These invariants serve as basis-independent fingerprints that mediate between the complex tensor mathematics and practical tissue characterization applications.
2Measurement precision
If full tensor component estimation is performed, then comprehensive tissue characterization is achieved, but the number of required measurements and scan time increase
Solution Approach 1:
The patent applies partial action by identifying and measuring only the minimal set of tensor components and rotational invariants necessary for meaningful tissue characterization. Rather than measuring all possible tensor components, the method selectively acquires data in specific directions (e.g., 6 directions for diffusion tensor, additional directions for covariance tensor) that suffice to compute the essential rotational invariants.
Solution Approach 2:
The patent changes the parameter space by transforming from measuring all tensor components to measuring rotational invariants. This parameter transformation allows comprehensive tissue characterization through fewer measurements, as rotational invariants are basis-independent and capture the essential physical properties without redundant information.
3Loss of information
If basis-dependent tensor components are used, then detailed information is captured, but hardware independence and reproducibility are compromised
Solution Approach 1:
The patent creates hardware-independent copies of tissue properties through rotational invariants. These invariants are constructed from tensor components in a way that eliminates dependence on the specific basis or coordinate system used during acquisition, producing reproducible fingerprints that can be compared across different scanners and protocols.
Solution Approach 2:
The patent transforms basis-dependent tensor components into basis-independent rotational invariants through specific mathematical operations (contraction with rotation matrices, formation of scalar products). This parameter transformation preserves information completeness while achieving hardware independence, as the invariants remain unchanged under rotation of the coordinate system.
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
RICE techniques enable fast and robust estimation of tensor invariants, providing a hardware-independent 'fingerprint' of dMRI signals that improve machine learning classifiers for brain pathology and aging, while reducing the number of required measurements and scan time.
Implementation Method 1
Diffusion magnetic resonance imaging (dMRI), based on diffusion nuclear magnetic resonance (NMR), is a non-invasive imaging modality that provides information about the architecture of any physical structure, in which the spin-carrying atoms or molecules can diffuse over a certain time set by the NMR measurement.
Implementation Method 2
diffusion nuclear magnetic resonance (NMR), is a non-invasive imaging modality that provides information about the architecture of any physical structure, in which the spin-carrying atoms or molecules can diffuse over a certain time set by the NMR measurement.
Implementation Method 3
Typical experimental settings probe such motion at a scale of micrometers or tens of micrometers, orders of magnitude below MRI imaging resolution. Hence, tissue microstructure imaging with dMRI can become sensitive, and possibly specific, to developmental, aging and disease processes that originate at this scale
Data Source
AI summary
Exemplary system, method and computer arrangement for determining invariants associated with at least one physical structure are described, which can include a receipt of at least one particular component which is a component of a diffusion tensor and/or a component of a covariance tensor, whereas the at least particular component is associated with the at least one physical structure. Then, it is possible to generate the invariants of the diffusion tensor and/or the covariance tensor based on the particular component. The physical structure can be (i) a biological tissue, (ii) a composite material, (iii) a continuous medium, and/or (iv) a random medium. For the biological tissue, the particular component can be based on diffusion magnetic resonance (dMR) image of the tissue.