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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. The models themselves are records, each with what it was fitted to and what it was used to decide.
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.
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.
Query for this technology: (TITLE:"Mathematical models of cancer" OR ABSTRACT:"Mathematical models of cancer" OR TITLE:"mathematical oncology" OR ABSTRACT:"mathematical oncology" OR TITLE:"mathematical models" OR ABSTRACT:"mathematical models" OR TITLE:"mathematical model" OR ABSTRACT:"mathematical model") AND (cancer OR tumor OR tumour OR oncology OR carcinoma OR lymphoma OR leukemia OR leukaemia OR myeloma OR sarcoma OR melanoma OR glioma). Results are unfiltered search hits about Mathematical models of cancer (mathematical oncology), not a curated reading list.
Shares Goldie-Coldman model of resistance, Evolutionary dynamics of drug resistance, Evolutionary game theory in cancer, Clonal evolution and branching models.
Shares Clonal evolution and branching models, Metastatic seeding and dormancy models, Residual disease kinetics (BCR-ABL halving and ctDNA slopes).
Shares Quantitative systems pharmacology (QSP), Pharmacokinetic and pharmacodynamic modelling.
Shares Agent-based and multicellular simulations, Tumour-immune dynamics models.
Shares Clonal evolution and branching models, Clonal evolution and the ecological view of cancer.
Shares Tumour control and normal tissue complication probability (TCP and NTCP), The four Rs and accelerated repopulation.
Shares Adaptive therapy (evolution-based dosing), Clonal evolution and the ecological view of cancer.
Shares Adaptive therapy (evolution-based dosing), Clonal evolution and the ecological view of cancer.
Open-source projects that implement or serve this technology, from OnCo's own catalogue: licence and last activity as the repository reported them on the day of the fetch. Listing is not endorsement; check the licence before reuse and the validation before clinical use.
An agent-based simulator of cells and tissues used to model tumour growth, immune attack and drug response in silico.
Multi-cell modelling with the Cellular Potts approach, used in tumour and angiogenesis simulations.
A Java library from Moffitt's Integrated Mathematical Oncology department for hybrid agent-based and PDE tumour models.