Researchers have developed a novel method called ELECTRO to create “golden” 3D center-out radial sampling trajectories for magnetic resonance imaging (MRI). These trajectories, where all subsets of consecutive readouts are well spread out on the sphere, offer significant advantages over existing methods like the supergolden and plastic trajectories. The new approach uses repulsive forces to minimize the electric potential energy of the sampling points, resulting in a more consistent and isotropic distribution of readouts. This innovation could lead to improved image quality and flexibility in dynamic 3D MRI applications, such as cardiac and respiratory imaging. The researchers also propose a new metric, the Normalized Mean Nearest neighbor Angular distance (NMNA), to quantify the uniformity of point distributions on the sphere. This work showcases the power of optimization techniques in designing efficient sampling strategies for advanced MRI techniques. Magnetic resonance imaging (MRI) is a widely used medical imaging technique that provides detailed images of the body’s interior structures.
Revolutionizing 3D MRI Sampling with ELECTRO
In MRI, non-Cartesian sampling trajectories based on the golden ratio are commonly used for accelerated dynamic 2D imaging. These golden angle trajectories produce a set of points that sample the unit interval in a well-distributed manner, which translates to uniform sampling of the semi-circle or circle for 2D applications. However, designing a “golden” 3D radial trajectory is considerably more challenging, as the concept of uniformity on a sphere is more complex than on a circle.
The researchers developed a novel method called ELECTRO (ELECTRic potential energy Optimized) to create 3D center-out radial sampling trajectories that maintain the desirable properties of golden angle trajectories. The key idea is to represent the readout directions as point charges on the surface of the unit sphere and then minimize the electric potential energy (EPE) using repulsive forces. This optimization process produces distributions of points that are well spread out on the sphere, ensuring that all subsets of consecutive readouts are also well distributed.
Evaluating Trajectory Performance
To compare the performance of ELECTRO trajectories with other 3D center-out radial trajectories, the researchers introduced a new metric called the Normalized Mean Nearest neighbor Angular distance (NMNA). This measure quantifies the uniformity of point distributions on the sphere, with a value of 1 indicating a random distribution and higher values signifying better-spread-out points.
The analysis revealed that ELECTRO trajectories have a more consistent NMNA across different sphere sizes and regions of the sphere, compared to the supergolden and plastic trajectories. The supergolden and plastic trajectories exhibited significant variations in NMNA, with clustering of readouts in certain areas of the sphere. This clustering can lead to structured aliasing artifacts in the reconstructed images, which is undesirable.
Optimization Strategies for Efficient Computation
The researchers also explored different optimization strategies to efficiently compute the ELECTRO trajectories. They proposed a multi-stage optimization approach, where the EPE of smaller spheres is minimized first, and then larger spheres are gradually added to the objective function. This strategy converged faster and achieved lower energy solutions compared to optimizing the full objective function in a single stage.
Additionally, the researchers used a reduced set of sphere sizes, based on Narayana’s cows sequence, to further improve computational performance. This approach balanced the trade-off between the completeness of the objective function and the computational cost, enabling the pre-calculation of large ELECTRO trajectories suitable for many MRI applications.
Implications and Future Directions
The ELECTRO trajectories developed in this work offer several advantages for dynamic 3D MRI applications, such as cardiac and respiratory imaging. By maintaining a more uniform distribution of readouts on the sphere, ELECTRO trajectories can lead to improved image quality and flexibility in reconstruction algorithms that rely on the golden angle property.
The researchers also demonstrated the resilience of ELECTRO trajectories to realistic experimental factors, such as gradient delays, which can introduce artifacts in the reconstructed images. After retrospective correction of gradient delays, the ELECTRO trajectories were able to maintain their performance, highlighting their practical applicability.
Future work may involve further refinements to the optimization process, exploring alternative objective functions, and investigating the extension of the ELECTRO method to other 3D non-Cartesian sampling trajectories. The development of efficient computational tools and the ability to pre-calculate large ELECTRO trajectories could pave the way for wider adoption of this technique in advanced MRI applications.
Author credit: This article is based on research by Christopher Huynh, Datta Singh Goolaub, Christopher K. Macgowan.
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