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Optimal Cancer Therapy TCC 2021/22. Term 2 Jan-Mar 2022.

This course was taught Jan-March 2022.

Welcome to the webpage for the TCC course Optimal Cancer Therapy, a mathematics course looking at cancer modelling and treatment optimisation. For information on signing up etc please visit the TCC webpageLink opens in a new window.

Lecturer: Professor Nigel Burroughs, Warwick.

Timetable: Lectures are 10:00 - 12:00 on Mondays for 8-9 weeks starting Monday 17th January 2022. Lectures are on-line through MSteams.

Assessment: if required will be through an essay/project and needs to be discussed with the lecturer.

Overview. How to model cancer, cancer therapy and the optimisation of a treatment programme will be examined in this course. We will examine stochastic models (branching processes) and deterministic models, predominantly ODEs. Control theory will then be used to optimise timing of drug applications and drug combinations. You should have a basic knowledge of probability theory and ODEs, including phase plane analysis. Topics, such as branching processes and control theory will be covered.

Content. We will start with an overview of cancer biology and mathematical modelling of cancer/tumours. The intent is then to cover these topics (order may vary). Notes are below.

Week 1 (17/1/2022). Introduction.

Cont (17/1/2022). Branching processes.

Week 2 (24/1/2022). Branching process models to model therapy.

Cont. (24/1/2022). Cancer therapy optimisation with ODEs (PMP).

Week 3. (31/1/2022). Models of cancer growth, including cell phase models.

Week 4. (7/2//2022) Alternative cost functions.

Week 5. (14/2/22) Modelling the cell division cycle and coupling to circadian clock. Chronotherapy (time of day drug infusion to optimise outcomes).

Week 6. (21/2/22) Heterogeneous tumours: Adaptive therapy and metronomic therapy. 3 papers are also on MSteams channel under Files (Week6Ppapers). This week covered Carrere et al 2017.

Week 7. (28/2/22). Break no lecture.

Week 8. (7/3/22). Game theory: 3-type tumours, adaptive therapy. Relevant papers are Cunningham et al and Kaznatcheev et al.

Week 9. Dynamic programming control theory (HJB). We apply HJB to optimising the 3-way VEGF-GLY game and an example in stochastic control.

Recommended literature.

Branching process models.

Durrett Richard. Branching process models of cancer. Springer, 2015. Excellent book for course, covering all the branching process material.

Therapy and models. There are no texts that are ideal. These should give you some idea of techniques and models.

Heinz Schättler, Urszula Ledzewicz. Optimal Control for Mathematical Models of Cancer Therapies. Springer 2015.

M. Kuznetsov, J. Clairambault, and V. Volpert. Improving cancer treatments via dynamical biophysical models. {\it Physics of Life Reviews}, 39:1–48, 2021.

General background.

Philipp M. Altrock, Lin L. Liu and Franziska Michor. The mathematics of cancer: integrating quantitative models. Nature Reviews Cancer 15, 730–745 (2015) doi:10.1038/nrc4029.

Helen M. Byrne. Dissecting cancer through mathematics: from the cell to the animal model. Nature Reviews Cancer 10, 221-230 (March 2010) doi:10.1038/nrc2808

Niko Beerenwinkel, Roland F. Schwarz, Moritz Gerstung and Florian Markowetz. Cancer Evolution: Mathematical Models and Computational Inference. Syst Biol (2015). 64 (1): e1-e25.
doi: 10.1093/sysbio/syu081