Sparse Hessian Model for Time Domain Magnetic Resonance Parameter Mapping
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Solution Overview
Problem
Conventional MRI image reconstruction is slow due to the need for separate measurements for each tissue parameter, with conventional MRI taking 30-45 minutes per scan, and the computation time for fitting time domain data is about 1 hour for a single 2D slice, limiting the efficiency of tissue parameter determination.
Innovation Solution
A method is introduced that determines the spatial distribution of tissue parameters by approximating the time domain magnetic resonance signal using a sparse Hessian model, where the Hessian is calculated based on the applied pulse sequence, reducing computation time by a factor of 10 and memory needs by up to 0.04% compared to inexact Gauss-Newton methods, by iteratively updating model parameters until a predefined threshold is met.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If conventional MRI image reconstruction is used with separate measurements for each tissue parameter, then measurement precision is improved, but scanning time increases significantly (30-45 minutes per scan)
Solution Approach 1:
The patent combines multiple tissue parameter measurements (T1, T2, T2*) into a single MRI scan by simultaneously fitting a signal model that includes all parameters. This is achieved by acquiring k-space data and then performing a single optimization procedure that extracts all tissue parameters from the combined signal characteristics, eliminating the need for separate measurement sequences for each parameter.
Solution Approach 2:
The MRI scanning procedure is designed to serve multiple functions simultaneously - it can measure T1 relaxation time, T2 relaxation time, and T2* relaxation time in a single scan. The signal model used during reconstruction is universal enough to capture all these different tissue properties from the same acquired data, making the scanning process multi-functional rather than requiring multiple dedicated scans.
2Productivity
If time domain magnetic resonance data is fitted using inexact Gauss-Newton method, then computation time is reduced to several minutes, but processing time still takes about 1 hour for a single 2D slice
Solution Approach 1:
The patent segments the computation process into two distinct phases: (1) a rapid initial fitting phase that uses a simplified model to get preliminary parameter estimates quickly, and (2) a refinement phase that uses the full signal model with the pre-computed Hessian matrix to optimize the results. This segmentation allows the computationally intensive parts to be handled more efficiently by breaking down the overall computation into manageable stages.
Solution Approach 2:
The Hessian matrix is pre-computed and stored before the actual parameter estimation begins. This preliminary computation of the Hessian matrix (which represents the curvature of the signal model) allows the subsequent optimization to proceed much faster, as the complex second-derivative information is already available rather than needing to be calculated iteratively during the fitting process.
3Measurement precision
If full Hessian matrix is computed for signal model fitting, then parameter estimation accuracy is improved, but memory requirements and computation time increase significantly
Solution Approach 1:
The Hessian matrix is pre-computed and stored before the actual parameter estimation begins. This preliminary computation of the Hessian matrix (which represents the curvature of the signal model) allows the subsequent optimization to proceed much faster, as the complex second-derivative information is already available rather than needing to be calculated iteratively during the fitting process.
Solution Approach 2:
Instead of computing and storing the complete dense Hessian matrix which requires significant memory and computation resources, the patent uses a sparse representation of the Hessian matrix that captures only the essential information needed for optimization. This sparse Hessian approach maintains the mathematical accuracy required for precise parameter estimation while dramatically reducing the computational burden on memory and processing power.
Data Source
AI summary
The present patent disclosure describes a new method and a new device for determining a spatial distribution of at least one tissue parameter within a sample based on a time domain magnetic resonance, TDMR, signal emitted from the sample after excitation of the sample according to an applied pulse sequence. The spatial distribution is determined using a calculated sparse Hessian, wherein the sparse Hessian is calculated based on the applied pulse sequence.