Mathematical modeling of liver metastases tumour growth and control with radiotherapy
Bibliographic record
Abstract
Generating an optimized radiation treatment plan requires understanding the factors affecting tumour control. Mathematical models of tumour dynamics may help in future studies of factors predicting tumour sensitivity to radiotherapy. In this study, a time-dependent differential model, incorporating biological cancer markers, is presented to describe pre-treatment tumour growth, response to radiation, and recurrence. The model uses Gompertzian-Exponential growth to model pre-treatment tumour growth. The effect of radiotherapy is handled by a realistic cell-kill term that includes a volume-dependent change in tumour sensitivity. Post-treatment, a Gompertzian, accelerated, delayed repopulation is employed. As proof of concept, we examined the fit of the model's prediction using various liver enzyme levels as markers of metastatic liver tumour growth in a liver cancer patient. A tumour clonogen population model was formulated. Each enzyme was coupled to the same tumour population, and served as surrogates of the tumour. This dynamical model was solved numerically and compared to the measured enzyme levels. By minimizing the mean-squared error of the model enzyme predictions, we determined the following tumour model parameters: growth rate prior to treatment was 0.52% per day; the fractional radiation cell kill for the prescribed dose (60 Gy in 15 fractions) was 42% per day, and the tumour repopulation rate was 2.9% per day. These preliminary results provided the basis to test the model in a larger series of patients, to apply biological markers for improving the efficacy of radiotherapy by determining the underlying tumour dynamics.
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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 | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| 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".