Modeling angiogenesis: A discrete to continuum description
Bibliographic record
Abstract
Angiogenesis is the process by which new blood vessels develop from existing vasculature. During angiogenesis, endothelial tip cells migrate via diffusion and chemotaxis, loops form via tip-to-tip and tip-to-sprout anastomosis, new tip cells are produced via branching, and a vessel network forms as endothelial cells follow the paths of tip cells. The latter process is known as the snail trail. We use a mean-field approximation to systematically derive a continuum model from a two-dimensional lattice-based cellular automaton model of angiogenesis in the corneal assay, based on the snail-trail process. From the two-dimensional continuum model, we derive a one-dimensional model which represents angiogenesis in two dimensions. By comparing the discrete and one-dimensional continuum models, we determine how individual cell behavior manifests at the macroscale. In contrast to the phenomenological continuum models in the literature, we find that endothelial cell creation due to tip cell movement (vessel formation via the snail trail) manifests as a source term of tip cells on the macroscale. Further, we find that phenomenological continuum models, which assume that endothelial cell creation is proportional to the flux of tip cells in the direction of increasing chemoattractant concentration, qualitatively capture vessel formation in two dimensions, but must be modified to accurately represent vessel formation. Additionally, we find that anastomosis imposes restrictions on cell density, which, if violated, leads to ill-posedness in our continuum model. We also deduce that self-loops should be excluded when tip-to-sprout anastomosis is active in the discrete model to ensure propagation of the vascular front.
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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) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.002 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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".