Real-Time Diffusional Kurtosis Imaging via Constrained Closed-Form Solution
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Solution Overview
Problem
Conventional diffusional kurtosis imaging (DKI) methods require substantial time for post-processing, struggle with noise and motion artifacts, and fail to provide physically plausible tensor estimates, leading to inaccuracies in diffusivity and kurtosis measurements, especially in regions with complex fiber configurations.
Innovation Solution
A method and system for real-time DKI that uses a closed-form solution procedure to determine diffusional kurtosis, incorporating constraints for non-negative diffusivity and kurtosis parameters, allowing for efficient estimation of orientation distribution functions and resolving fiber crossings, using a combination of diffusion and kurtosis tensors with linear least squares formulation and quadratic programming or heuristic algorithms.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If conventional DKI methods are used for post-processing, then diffusional kurtosis imaging can be performed, but substantial time (approximately 1 hour or more) is required for post-processing
Solution Approach 1:
The patent changes the mathematical parameters and computational approach by using a closed-form solution procedure with linear least squares formulation and quadratic programming, replacing the conventional iterative post-processing methods. This parameter change in the computational algorithm reduces post-processing time from approximately 1 hour to a significantly shorter duration while maintaining measurement precision.
Solution Approach 2:
The patent replaces the complex mechanical computation system with a simplified mathematical model using closed-form solutions. By substituting the conventional iterative computational approach with direct mathematical formulas and linear algebra operations, the system achieves faster processing speeds without sacrificing the accuracy of diffusional kurtosis measurements.
2Measurement precision
If conventional DKI methods are used, then diffusional kurtosis can be measured, but the methods struggle with noise and motion artifacts and fail to provide physically plausible tensor estimates
Solution Approach 1:
The patent incorporates constraints in the quadratic programming formulation that provide feedback on the physical plausibility of tensor estimates. The constrained optimization process continuously adjusts the estimation based on physical requirements (non-negative diffusivity and kurtosis parameters), ensuring that only physically plausible tensor estimates are produced while reducing the impact of noise and motion artifacts.
Solution Approach 2:
The patent changes the estimation approach by using constrained quadratic programming with specific physical constraints on diffusivity and kurtosis parameters. This parameter change in the optimization formulation ensures that the resulting tensor estimates are physically plausible, addressing the reliability issue while maintaining measurement precision in the presence of noise and motion artifacts.
3Productivity
If conventional DKI methods are used, then post-processing can be performed, but the methods require substantial time and computational resources
Solution Approach 1:
The patent replaces the computationally intensive iterative post-processing system with a streamlined closed-form mathematical solution. By substituting complex iterative algorithms with direct mathematical formulas and linear algebra operations, the system achieves significantly higher productivity and imaging speed while reducing post-processing time requirements.
Solution Approach 2:
The patent changes the computational parameters and algorithmic approach to use efficient closed-form solutions and constrained quadratic programming. This parameter change in the computational methodology optimizes the balance between processing speed and accuracy, enabling real-time or near-real-time diffusional kurtosis imaging without substantial post-processing time losses.
Data Source
AI summary
Exemplary method, system, and computer-accessible medium can be provided for determining a measure of diffusional kurtosis by receiving data relating to at least one diffusion weighted image, and determining a measure of a diffusional kurtosis as a function of the received data using a closed form solution procedure. In accordance with certain exemplary embodiments of the present disclosure, provided herein are computer-accessible medium, systems and methods for, e.g., imaging in an MRI system, and, more particularly for facilitating estimation of tensors and tensor-derived measures in diffusional kurtosis imaging (DKI). For example, DKI can facilitate a characterization of non-Gaussian diffusion of water molecules in biological tissues. The diffusion and kurtosis tensors parameterizing the DKI model can typically be estimated via unconstrained least squares (LS) methods. In the presence of noise, motion, and imaging artifacts, these methods can be prone to producing physically and/or biologically implausible tensor estimates. The exemplary embodiments of the present disclosure can address at least this deficiency by formulating an exemplary estimation problem, e.g., as linearly constrained linear LS, where the constraints can ensure acceptable tensor estimates.