Geometrical measurement of cardiac wavelength in reaction-diffusion models
Bibliographic record
Abstract
The dynamics of reentrant arrhythmias often consists in multiple wavelets propagating throughout an excitable medium. An arrhythmia can be sustained only if these reentrant waves have a sufficiently short wavelength defined as the distance traveled by the excitation wave during its refractory period. In a uniform medium, wavelength may be estimated as the product of propagation velocity and refractory period (electrophysiological wavelength). In order to accurately measure wavelength in more general substrates relevant to atrial arrhythmias (heterogeneous and anisotropic), we developed a mathematical framework to define geometrical wavelength at each time instant based on the length of streamlines following the propagation velocity field within refractory regions. Two computational methods were implemented: a Lagrangian approach in which a set of streamlines were integrated, and an Eulerian approach in which wavelength was the solution of a partial differential equation. These methods were compared in 1D/2D tissues and in a model of the left atrium. An advantage of geometrical definition of wavelength is that the wavelength of a wavelet can be tracked over time with high temporal resolution and smaller temporal variability in an anisotropic and heterogeneous medium. The results showed that the average electrophysiological wavelength was consistent with geometrical measurements of wavelength. Wavelets were however often shorter than the electrophysiological wavelength due to interactions with boundaries and other wavelets. These tools may help to assess more accurately the relation between substrate properties and wavelet dynamics in computer models.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 teacher head, 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".