From cell population models to tumor control probability: Including cell cycle effects
Bibliographic record
Abstract
BACKGROUND: Classical expressions for the tumor control probability (TCP) are based on models for the survival fraction of cancer cells after radiation treatment. We focus on the derivation of expressions for TCP from dynamic cell population models. In particular, we derive a TCP formula for a generalized cell population model that includes the cell cycle by considering a compartment of actively proliferating cells and a compartment of quiescent cells, with the quiescent cells being less sensitive to radiation than the actively proliferating cells. METHODS: We generalize previously derived TCP formulas of Zaider and Minerbo and of Dawson and Hillen to derive a TCP formula from our cell population model. We then use six prostate cancer treatment protocols as a case study to show how our TCP formula works and how the cell cycle affects the tumor treatment. RESULTS: The TCP formulas of Zaider-Minerbo and of Dawson-Hillen are special cases of the TCP formula presented here. The former one represents the case with no quiescent cells while the latter one assumes that all newly born cells enter a quiescent cell phase before becoming active. From our case study, we observe that inclusion of the cell cycle lowers the TCP. CONCLUSION: The cell cycle can be understood as the sequestration of cells in the quiescent compartment, where they are less sensitive to radiation. We suggest that our model can be used in combination with synchronization methods to optimize treatment timing.
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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 | 0.002 | 0.010 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.003 | 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".