Electric potential energy optimized 3D radial sampling trajectories for MRI
Bibliographic record
Abstract
A novel method for creating “golden” 3D center-out radial MRI sampling trajectories was developed and analyzed. This method, called ELECTRO (ELECTRic potential energy Optimized), uses repulsive forces to minimize electric potential energy. An objective function $$\:G\left(S\right)$$ , the electric potential energies of all subsets of consecutive readouts in a 3D radial trajectory, and its reduced form were minimized using a multi-stage optimization strategy. A metric called normalized mean nearest neighbor angular distance (NMNA) was proposed for describing distributions of points on a sphere. ELECTRO and other relevant golden trajectories were compared in silico using NMNA and point spread function analysis. Consecutive readouts from an ELECTRO trajectory were well spread out, with consistent NMNA values across sphere sizes (σNMNA = 0.005) and between regions on the sphere (NMNA ≈ 1.49). Conversely, the supergolden trajectory had poor consistency in NMNA values (σNMNA = 0.090) and clustering (NMNA = 1.28 at the pole with 40,000 readouts) that lead to artifact in the point spread function. Multi-stage optimization was faster than single-stage and obtained lower values of $$\:G\left(S\right)$$ (e.g., 0.87 vs. 0.91, for a sphere size of 40). In conclusion, ELECTRO trajectories are more golden than other 3D center-out radial trajectories, making them a suitable candidate for dynamic 3D MR imaging.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".