Spatial Organization and Correlations of Cell Nuclei in Brain Tumors
Bibliographic record
Abstract
Accepting the hypothesis that cancers are self-organizing, opportunistic systems, it is crucial to understand the collective behavior of cancer cells in their tumorous heterogeneous environment. In the present paper, we ask the following basic question: Is this self-organization of tumor evolution reflected in the manner in which malignant cells are spatially distributed in their heterogeneous environment? We employ a variety of nontrivial statistical microstructural descriptors that arise in the theory of heterogeneous media to characterize the spatial distributions of the nuclei of both benign brain white matter cells and brain glioma cells as obtained from histological images. These descriptors, which include the pair correlation function, structure factor and various nearest neighbor functions, quantify how pairs of cell nuclei are correlated in space in various ways. We map the centroids of the cell nuclei into point distributions to show that while commonly used local spatial statistics (e.g., cell areas and number of neighboring cells) cannot clearly distinguish spatial correlations in distributions of normal and abnormal cell nuclei, their salient structural features are captured very well by the aforementioned microstructural descriptors. We show that the tumorous cells pack more densely than normal cells and exhibit stronger effective repulsions between any pair of cells. Moreover, we demonstrate that brain gliomas are organized in a collective way rather than randomly on intermediate and large length scales. The existence of nontrivial spatial correlations between the abnormal cells strongly supports the view that cancer is not an unorganized collection of malignant cells but rather a complex emergent integrated system.
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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 | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| 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 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".