Four-Dimensional Visualization of Topological Fixed Points in Pulsatile Cardiovascular Flows
Bibliographic record
Abstract
Topological features of time-dependent, three-dimensional (3D) vector flow fields, such as wall shear stress (WSS) fixed points, are considered surrogates of pathological blood flow dynamics in cardiovascular diseases. Fixed-point visualizations are typically constrained to two-dimensional (2D) spaces, yet they aim to display complex spatiotemporal (four-dimensional (4D)) dynamics. There is a need for visualization strategies to reduce occlusion and reliance on animations to allow the detection of holistic flow patterns. Using intracranial aneurysms as a use case, we present the fixed-point carousel, a novel approach to visually depicting the "4D" nature of WSS fixed points via (1) topographic mapping of the 3D aneurysm sac to overcome occlusion while preserving fixed-point distances and sac morphological features; and (2) arranging these into a carousel model to present with temporal dimension holistically. Examples are presented for image-based computational fluid dynamic (CFD) models of intracranial aneurysms, illuminating the intricate and distinct fixed-point trajectories and interactions, a necessary step toward understanding the volumetric flow manifolds that drive them for this and other cardiovascular-and potentially nonbiomedical-fluid dynamics applications.
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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 | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.004 | 0.000 |
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".