Mathematical models of cancer (mathematical oncology)
Mathematical oncology writes down how tumours grow, evolve, respond to treatment and interact with the immune system as equations or simulations, then uses them to design doses, schedules and trials. This page gathers every model OnCo covers.
Overview
Mathematical oncology is the use of equations, statistical models and computer simulations to describe cancer and to test treatment ideas before, or alongside, clinical trials. The oldest models describe growth: the Gompertz curve, the log-kill hypothesis and the Norton-Simon hypothesis shaped how chemotherapy is dosed and scheduled. Radiotherapy rests on the linear-quadratic model, fractionation and repopulation models, and tumour control probability. Evolutionary models, adaptive therapy dynamics and clonal evolution describe how resistance emerges and how to delay it.
A second family simulates rather than solves: reaction-diffusion models of glioma spread, agent-based and multicellular simulations, immune-tumour dynamics, tumour mechanics and metastasis seeding models. Pharmacokinetic and pharmacodynamic models link dose to exposure and effect, and minimal residual disease kinetics turn blood tests into forecasts. Digital twin patient models aim to combine all of these for one person.
Each model on this page names its originators, the equation or rule at its core, what it predicted well and where it fails. The models table lists them next to the foundation models and datasets, and the data sources page records the public model repositories, such as BioModels and PhysiCell, that OnCo draws on.
How it works
Describe the tumour, the treatment and the host as variables that change over time; fit the model to data; use it to predict what a different dose, schedule or combination would do.
- Turns scattered observations into testable predictions
- Cheap to run compared with trials
- Explains why regimens work, not only that they do
- Parameters are hard to measure in one patient
- Models can fit the past and still mispredict the future
- Few have been validated prospectively
Latest papers
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