Mathematical modeling reveals how the density of initial tumor and its distance to parent vessels alter the growth trend of vascular tumors
Bibliographic record
Abstract
OBJECTIVES: The aim of this study was to investigate the response of a tumor and parent vessels to stimulating factors in the tumor microenvironment in different configurations. How a tumor grows and induces angiogenesis in different distances of a parent vessel is investigated. Moreover, interstitial fluid pressure and its effects on tumor cell phenotype are considered in the model. METHODS: A multiscale continuum-discrete model of a vascular tumor is utilized to simulate the growth of a cluster of tumor cells positioned in different distances of parent vessels. An agent-based probabilistic angiogenesis model is coupled to a discrete tumor model to simulate branching, anastomosis, blood flow, wall shear stress, and interstitial tumor pressure in which tumor cells are divided to necrotic, hypoxic, and proliferative. RESULTS: Starting the simulations from 9 initial tumor cells, the model proved that tumors grow to a certain size and also reach to a certain distance before being able to induce sprouting. For tumors placed 2 and 2.5 mm away from a parent vessel, initiation of angiogenesis is delayed significantly in comparison with closer distances. For the initial cluster positioned in a distance of 2.5 mm away, first sprout is seen after 47 days. Moreover, dendritic shape of the tumor is seen prior to angiogenesis which is a sign of cells being starved and wandered in the domain to reach the oxygen source. The trend of tumor growth obeys power law function which aligns with the experimental results. DISCUSSION: The mathematical model revealed the importance of geometry and position of an initial tumor cluster in determining the behavior and final architecture of a vascular tumor. As a tumor cell appears in farther distances from a parent vessel, duration of its growth and inducing angiogenesis becomes longer and the chance of suppressing the tumor in the initial days of growth is higher. Also, the importance of angiogenesis in making tumors devastating is again corroborated by mathematical models.
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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 | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.001 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 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".