Optimized Diffusion Encoding Gradient Waveforms for MRI
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Solution Overview
Problem
Existing diffusion encoding gradient (DEG) waveforms for diffusion weighted MRI are not optimized for shortest duration and motion compensation, leading to signal losses and inefficiencies in imaging.
Innovation Solution
The Motion Compensated Optimized Diffusion Encoding (MODE) method optimizes parametric waveform models to generate DEG waveforms with the shortest duration possible, using closed-form mathematical expressions for exact b-value representation, allowing for real-time computation and motion compensation without the need for storing precomputed waveforms.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Duration of action of moving object
If CODE method is used to obtain optimized DEG waveforms, then motion compensation is achieved, but waveform duration is not minimized and computational flexibility is limited
Solution Approach 1:
The patent transforms the waveform optimization problem from numerical sample optimization to parametric model optimization. By representing DEG waveforms using parametric models with closed-form expressions, the system changes the parameter space from continuous waveform samples to discrete model parameters, enabling analytical optimization that simultaneously minimizes duration and ensures motion compensation through exact b-value expressions and moment constraints.
Solution Approach 2:
The patent replaces the numerical computation mechanism of CODE with an analytical mathematics mechanism. Instead of using numerical optimization algorithms to compute waveform samples, the invention uses closed-form mathematical expressions and parametric optimization to directly calculate optimal waveform parameters, eliminating the need for iterative numerical methods and precomputation storage.
2Productivity
If numerical optimization is used to compute DEG waveforms, then motion compensation can be achieved, but computational time and storage requirements increase
Solution Approach 1:
The patent extracts the essential characteristics of DEG waveforms into closed-form mathematical expressions and parametric models. By separating the core waveform structure (represented by parametric equations) from specific imaging parameters, the system stores only the compact mathematical formulas rather than precomputed waveform data, dramatically reducing storage requirements while enabling rapid computation for any imaging scenario.
Solution Approach 2:
The patent creates a universal parametric framework that can generate optimal DEG waveforms for any imaging parameters (TE, b-value, motion compensation requirements) using the same closed-form expressions. This universal approach eliminates the need to precompute and store separate waveforms for different scenarios, as the parametric model can adapt to any conditions through parameter adjustment.
3Loss of energy
If DEG waveform duration is minimized, then echo time is reduced and signal loss is decreased, but motion compensation becomes more difficult
Solution Approach 1:
The patent incorporates motion compensation constraints directly into the parametric waveform model definition before optimization. By embedding the moment constraints (M1=0 for velocity compensation, M2=0 for acceleration compensation) as part of the parametric model structure, the system ensures motion compensation is inherently built into the optimized waveforms rather than being applied as a subsequent correction, enabling simultaneous minimization of duration and achievement of motion compensation.
Data Source
AI summary
A method of obtaining analytical expressions for an optimized diffusion encoding gradient (DEG) waveform is disclosed. The method uses a constrained numerical optimization to obtain an optimal configuration of a DEG waveform. The optimization adjusts parameters for a waveform modeled as a finite set of square pulses to maximize an exact b-value equation, while maintaining a waveform shape that also compensates for motion. The optimal configuration is then verified using a waveform model of a set of trapezoidal pulses to obtain an optimal DEG waveform. Generally, the parameters describing the reduced set of trapezoidal pulses are reduced, thereby allowing the optimal DEG waveform to be expressed as closed-form analytical expressions. The analytical expressions simplify the derivation of optimal DEG waveforms for a range of diffusion imaging scanning parameters, thereby improving the quality and versatility of diffusion weighted MRI.